ConnectPP---0.7.2.THM-Prf.s

%------------------------------------------------------------------------------
% File     : ConnectPP---0.7.2
% Problem  : SWW225+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n020.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 09:04:54 AM UTC 2026

% Result   : Theorem 39.62s 49.90s
% Output   : Proof 39.64s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
fof(fact_ext,axiom,
    ! [V_ga_2,V_fa_2] :
      ( ! [B_x] : hAPP(V_fa_2,B_x) = hAPP(V_ga_2,B_x)
     => V_fa_2 = V_ga_2 ),
    file('theBenchmark.p',fact_ext) ).

fof(fact_fz_I1_J,axiom,
    c_SEQ_Osubseq(v_f____),
    file('theBenchmark.p',fact_fz_I1_J) ).

fof(fact__096N1_A_L_AN2_A_060_061_Af_A_IN1_A_L_AN2_J_096,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),
    file('theBenchmark.p',fact__096N1_A_L_AN2_A_060_061_Af_A_IN1_A_L_AN2_J_096) ).

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_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_add__le__cancel__right,axiom,
    ! [V_b_2,V_c_2,V_a_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_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
      <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ),
    file('theBenchmark.p',fact_add__le__cancel__right) ).

fof(fact_add__le__cancel__left,axiom,
    ! [V_b_2,V_a_2,V_c_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_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))
      <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_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_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_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_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_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_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_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_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_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_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__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__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_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_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_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_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_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_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__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_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_ga_2,V_fa_2,T_a,T_b] :
      ( class_Orderings_Oord(T_b)
     => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2,V_ga_2)
       => c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,V_x_2),hAPP(V_ga_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_ga_2,V_fa_2,T_a,T_b] :
      ( class_Orderings_Oord(T_b)
     => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2,V_ga_2)
       => c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,V_x_2),hAPP(V_ga_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_ga_2,V_fa_2,T_a,T_b] :
      ( class_Orderings_Oord(T_b)
     => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2,V_ga_2)
      <=> ! [B_x] : c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,B_x),hAPP(V_ga_2,B_x)) ) ),
    file('theBenchmark.p',fact_le__fun__def) ).

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_c_2,V_a_2,V_b_2,T_a] :
      ( class_Groups_Ocancel__semigroup__add(T_a)
     => ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2) = c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2)
      <=> V_b_2 = V_c_2 ) ),
    file('theBenchmark.p',fact_add__right__cancel) ).

fof(fact_add__left__cancel,axiom,
    ! [V_c_2,V_b_2,V_a_2,T_a] :
      ( class_Groups_Ocancel__semigroup__add(T_a)
     => ( c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2)
      <=> V_b_2 = V_c_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_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_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__n__not__n,axiom,
    ! [V_n] : c_Nat_OSuc(V_n) != V_n,
    file('theBenchmark.p',fact_Suc__n__not__n) ).

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_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_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__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_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_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_real__of__nat__le__iff,axiom,
    ! [V_m_2,V_n_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(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_seq__suble,axiom,
    ! [V_n_2,V_fa_2] :
      ( c_SEQ_Osubseq(V_fa_2)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,hAPP(V_fa_2,V_n_2)) ),
    file('theBenchmark.p',fact_seq__suble) ).

fof(fact_real__of__nat__add,axiom,
    ! [V_n,V_m] : hAPP(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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)),
    file('theBenchmark.p',fact_real__of__nat__add) ).

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_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_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_lift__Suc__mono__le,axiom,
    ! [V_n_H_2,V_n_2,V_fa_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( ! [B_n] : c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_fa_2,B_n),hAPP(V_fa_2,c_Nat_OSuc(B_n)))
       => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_n_H_2)
         => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_fa_2,V_n_2),hAPP(V_fa_2,V_n_H_2)) ) ) ),
    file('theBenchmark.p',fact_lift__Suc__mono__le) ).

fof(fact_real__of__nat__inject,axiom,
    ! [V_m_2,V_n_2] :
      ( hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2) = hAPP(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__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_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_decseq__def,axiom,
    ! [V_X_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( c_SEQ_Odecseq(T_a,V_X_2)
      <=> ! [B_m,B_n] :
            ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n)
           => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m)) ) ) ),
    file('theBenchmark.p',fact_decseq__def) ).

fof(fact_incseq__def,axiom,
    ! [V_X_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( c_SEQ_Oincseq(T_a,V_X_2)
      <=> ! [B_m,B_n] :
            ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n)
           => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n)) ) ) ),
    file('theBenchmark.p',fact_incseq__def) ).

fof(fact_monoseq__def,axiom,
    ! [V_X_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( c_SEQ_Omonoseq(T_a,V_X_2)
      <=> ( ! [B_m,B_n] :
              ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n)
             => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m)) )
          | ! [B_m,B_n] :
              ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n)
             => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n)) ) ) ) ),
    file('theBenchmark.p',fact_monoseq__def) ).

fof(fact_monoseq__Suc,axiom,
    ! [V_X_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( c_SEQ_Omonoseq(T_a,V_X_2)
      <=> ( ! [B_n] : c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,c_Nat_OSuc(B_n)),hAPP(V_X_2,B_n))
          | ! [B_n] : c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,c_Nat_OSuc(B_n))) ) ) ),
    file('theBenchmark.p',fact_monoseq__Suc) ).

fof(fact_real__of__nat__Suc,axiom,
    ! [V_n] : hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(V_n)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(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_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_incseq__imp__monoseq,axiom,
    ! [V_X_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( c_SEQ_Oincseq(T_a,V_X_2)
       => c_SEQ_Omonoseq(T_a,V_X_2) ) ),
    file('theBenchmark.p',fact_incseq__imp__monoseq) ).

fof(fact_decseq__imp__monoseq,axiom,
    ! [V_X_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( c_SEQ_Odecseq(T_a,V_X_2)
       => c_SEQ_Omonoseq(T_a,V_X_2) ) ),
    file('theBenchmark.p',fact_decseq__imp__monoseq) ).

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_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_incseq__SucI,axiom,
    ! [V_X_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( ! [B_n] : c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,c_Nat_OSuc(B_n)))
       => c_SEQ_Oincseq(T_a,V_X_2) ) ),
    file('theBenchmark.p',fact_incseq__SucI) ).

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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(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_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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2)) ),
    file('theBenchmark.p',fact_nat__less__real__le) ).

fof(fact_monoI2,axiom,
    ! [V_X_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( ! [B_m,B_n] :
            ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n)
           => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m)) )
       => c_SEQ_Omonoseq(T_a,V_X_2) ) ),
    file('theBenchmark.p',fact_monoI2) ).

fof(fact_monoI1,axiom,
    ! [V_X_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( ! [B_m,B_n] :
            ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n)
           => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n)) )
       => c_SEQ_Omonoseq(T_a,V_X_2) ) ),
    file('theBenchmark.p',fact_monoI1) ).

fof(fact_mono__SucI2,axiom,
    ! [V_X_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( ! [B_n] : c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,c_Nat_OSuc(B_n)),hAPP(V_X_2,B_n))
       => c_SEQ_Omonoseq(T_a,V_X_2) ) ),
    file('theBenchmark.p',fact_mono__SucI2) ).

fof(fact_mono__SucI1,axiom,
    ! [V_X_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( ! [B_n] : c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,c_Nat_OSuc(B_n)))
       => c_SEQ_Omonoseq(T_a,V_X_2) ) ),
    file('theBenchmark.p',fact_mono__SucI1) ).

fof(fact_real__of__nat__one,axiom,
    hAPP(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_of__nat__aux_Osimps_I2_J,axiom,
    ! [V_i_2,V_n_2,V_inc_2,T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,c_Nat_OSuc(V_n_2),V_i_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,V_n_2,hAPP(V_inc_2,V_i_2)) ),
    file('theBenchmark.p',fact_of__nat__aux_Osimps_I2_J) ).

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_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_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_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_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_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_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_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__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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_eq__iff__diff__eq__0,axiom,
    ! [V_b_2,V_a_2,T_a] :
      ( class_Groups_Oab__group__add(T_a)
     => ( V_a_2 = V_b_2
      <=> c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('theBenchmark.p',fact_eq__iff__diff__eq__0) ).

fof(fact_less__iff__diff__less__0,axiom,
    ! [V_b_2,V_a_2,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
      <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) ),
    file('theBenchmark.p',fact_less__iff__diff__less__0) ).

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_right__minus__eq,axiom,
    ! [V_b_2,V_a_2,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
      <=> V_a_2 = V_b_2 ) ),
    file('theBenchmark.p',fact_right__minus__eq) ).

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_of__nat__aux_Osimps_I1_J,axiom,
    ! [V_i_2,V_inc_2,T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2) = V_i_2 ),
    file('theBenchmark.p',fact_of__nat__aux_Osimps_I1_J) ).

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__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__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_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_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_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_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__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__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__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_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_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__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__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_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_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_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_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_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__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_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_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_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_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_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_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__eq__diff__eq,axiom,
    ! [V_da_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( class_Groups_Oab__group__add(T_a)
     => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_da_2)
       => ( V_a_2 = V_b_2
        <=> V_c_2 = V_da_2 ) ) ),
    file('theBenchmark.p',fact_diff__eq__diff__eq) ).

fof(fact_diff__eq__diff__less,axiom,
    ! [V_da_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_da_2)
       => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
        <=> c_Orderings_Oord__class_Oless(T_a,V_c_2,V_da_2) ) ) ),
    file('theBenchmark.p',fact_diff__eq__diff__less) ).

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_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_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_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_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_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_zero__less__double__add__iff__zero__less__single__add,axiom,
    ! [V_a_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_a_2,V_a_2))
      <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_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_a_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_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
      <=> c_Orderings_Oord__class_Oless(T_a,V_a_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_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_le__iff__diff__le__0,axiom,
    ! [V_b_2,V_a_2,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
      <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) ),
    file('theBenchmark.p',fact_le__iff__diff__le__0) ).

fof(fact_nat__diff__split,axiom,
    ! [V_b_2,V_a_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))
    <=> ( ! [B_d] :
            ( V_a_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_a_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_nat__diff__split__asm,axiom,
    ! [V_b_2,V_a_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))
    <=> ~ ( ? [B_d] :
              ( ~ hBOOL(hAPP(V_P_2,B_d))
              & V_a_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_a_2,V_b_2) ) ) ),
    file('theBenchmark.p',fact_nat__diff__split__asm) ).

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_real__of__nat__less__iff,axiom,
    ! [V_m_2,V_n_2] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(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_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_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_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_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__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__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__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__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_diff__eq__diff__less__eq,axiom,
    ! [V_da_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_da_2)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
        <=> c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,V_da_2) ) ) ),
    file('theBenchmark.p',fact_diff__eq__diff__less__eq) ).

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_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_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_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__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_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_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__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_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_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_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_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_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_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_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_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__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_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_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__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_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__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_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_add__less__cancel__right,axiom,
    ! [V_b_2,V_c_2,V_a_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_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
      <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ),
    file('theBenchmark.p',fact_add__less__cancel__right) ).

fof(fact_add__less__cancel__left,axiom,
    ! [V_b_2,V_a_2,V_c_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_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))
      <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ),
    file('theBenchmark.p',fact_add__less__cancel__left) ).

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__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__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__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__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_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_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_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_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_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_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_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_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_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__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__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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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__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__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_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_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_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_double__zero__sym,axiom,
    ! [V_a_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_a_2,V_a_2)
      <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('theBenchmark.p',fact_double__zero__sym) ).

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_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_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_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_add__0__iff,axiom,
    ! [V_a_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_a_2)
      <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('theBenchmark.p',fact_add__0__iff) ).

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_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_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_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_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_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_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_subseq__def,axiom,
    ! [V_fa_2] :
      ( c_SEQ_Osubseq(V_fa_2)
    <=> ! [B_m,B_n] :
          ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n)
         => c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_m),hAPP(V_fa_2,B_n)) ) ),
    file('theBenchmark.p',fact_subseq__def) ).

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_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_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_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_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__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_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_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__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_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__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_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_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_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_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__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__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_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_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__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__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__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_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_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_zero__le__double__add__iff__zero__le__single__add,axiom,
    ! [V_a_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_a_2,V_a_2))
      <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ),
    file('theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).

fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
    ! [V_a_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_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
      <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
    file('theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).

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_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__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__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__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_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_real__of__nat__1,axiom,
    hAPP(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_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_subseq__Suc__iff,axiom,
    ! [V_fa_2] :
      ( c_SEQ_Osubseq(V_fa_2)
    <=> ! [B_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_n),hAPP(V_fa_2,c_Nat_OSuc(B_n))) ),
    file('theBenchmark.p',fact_subseq__Suc__iff) ).

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_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_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__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_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_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_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_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_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_even__less__0__iff,axiom,
    ! [V_a_2,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
      <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
    file('theBenchmark.p',fact_even__less__0__iff) ).

fof(fact_d_I1_J,axiom,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____),
    file('theBenchmark.p',fact_d_I1_J) ).

fof(fact_rp,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r),
    file('theBenchmark.p',fact_rp) ).

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),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)),
    file('theBenchmark.p',fact_real__of__nat__ge__zero) ).

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_less__fun__def,axiom,
    ! [V_ga_2,V_fa_2,T_a,T_b] :
      ( class_Orderings_Oord(T_b)
     => ( c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_fa_2,V_ga_2)
      <=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_ga_2,V_fa_2)
          & c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2,V_ga_2) ) ) ),
    file('theBenchmark.p',fact_less__fun__def) ).

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__of__nat__zero,axiom,
    hAPP(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] :
      ( hAPP(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,hAPP(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_real__of__nat__diff,axiom,
    ! [V_m,V_n] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
     => hAPP(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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)) ),
    file('theBenchmark.p',fact_real__of__nat__diff) ).

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_real__of__nat__le__zero__cancel__iff,axiom,
    ! [V_n_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(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),hAPP(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__gt__zero__cancel__iff,axiom,
    ! [V_n_2] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(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_double__eq__0__iff,axiom,
    ! [V_a_2,T_a] :
      ( class_Groups_Olinordered__ab__group__add(T_a)
     => ( c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
      <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('theBenchmark.p',fact_double__eq__0__iff) ).

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_ath,axiom,
    ! [V_e,V_x,V_m] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_m,V_x)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_m,V_e))
       => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_m)),V_e) ) ),
    file('theBenchmark.p',fact_ath) ).

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_natceiling__eq,axiom,
    ! [V_x,V_n] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(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,hAPP(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_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_expand__Suc,axiom,
    ! [V_v] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v))
     => c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    file('theBenchmark.p',fact_expand__Suc) ).

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_abs__one,axiom,
    ! [T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_abs__one) ).

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_number__of__reorient,axiom,
    ! [V_x_2,V_wa_2,T_a] :
      ( class_Int_Onumber(T_a)
     => ( c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = V_x_2
      <=> V_x_2 = c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) ) ),
    file('theBenchmark.p',fact_number__of__reorient) ).

fof(fact_eq__number__of,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( ( class_Int_Oring__char__0(T_a)
        & class_Int_Onumber__ring(T_a) )
     => ( c_Int_Onumber__class_Onumber__of(T_a,V_x_2) = c_Int_Onumber__class_Onumber__of(T_a,V_y_2)
      <=> V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_eq__number__of) ).

fof(fact_natceiling__real__of__nat,axiom,
    ! [V_n] : c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)) = V_n,
    file('theBenchmark.p',fact_natceiling__real__of__nat) ).

fof(fact_abs__eq__0,axiom,
    ! [V_a_2,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => ( c_Groups_Oabs__class_Oabs(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
      <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('theBenchmark.p',fact_abs__eq__0) ).

fof(fact_abs__zero,axiom,
    ! [T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_abs__zero) ).

fof(fact_abs__le__D1,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)
       => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ),
    file('theBenchmark.p',fact_abs__le__D1) ).

fof(fact_abs__ge__self,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) ),
    file('theBenchmark.p',fact_abs__ge__self) ).

fof(fact_abs__add__abs,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)) ),
    file('theBenchmark.p',fact_abs__add__abs) ).

fof(fact_abs__minus__commute,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)) ),
    file('theBenchmark.p',fact_abs__minus__commute) ).

fof(fact_abs__idempotent,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) = c_Groups_Oabs__class_Oabs(T_a,V_a) ),
    file('theBenchmark.p',fact_abs__idempotent) ).

fof(fact_le__number__of,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( ( class_Rings_Olinordered__idom(T_a)
        & class_Int_Onumber__ring(T_a) )
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,V_y_2) ) ),
    file('theBenchmark.p',fact_le__number__of) ).

fof(fact_less__number__of,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( ( class_Rings_Olinordered__idom(T_a)
        & class_Int_Onumber__ring(T_a) )
     => ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
      <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,V_y_2) ) ),
    file('theBenchmark.p',fact_less__number__of) ).

fof(fact_add__number__of__left,axiom,
    ! [V_z,V_w,V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_z)) = c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)),V_z) ),
    file('theBenchmark.p',fact_add__number__of__left) ).

fof(fact_add__number__of__eq,axiom,
    ! [V_w,V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)) ),
    file('theBenchmark.p',fact_add__number__of__eq) ).

fof(fact_number__of__add,axiom,
    ! [V_w,V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)) = c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)) ),
    file('theBenchmark.p',fact_number__of__add) ).

fof(fact_number__of__diff,axiom,
    ! [V_w,V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_v,V_w)) = c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)) ),
    file('theBenchmark.p',fact_number__of__diff) ).

fof(fact_abs__real__of__nat__cancel,axiom,
    ! [V_x] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_x)) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_x),
    file('theBenchmark.p',fact_abs__real__of__nat__cancel) ).

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_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_real__natceiling__ge,axiom,
    ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatceiling(V_x))),
    file('theBenchmark.p',fact_real__natceiling__ge) ).

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_abs__ge__zero,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) ),
    file('theBenchmark.p',fact_abs__ge__zero) ).

fof(fact_abs__le__zero__iff,axiom,
    ! [V_a_2,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
      <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('theBenchmark.p',fact_abs__le__zero__iff) ).

fof(fact_abs__of__nonneg,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
       => c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ),
    file('theBenchmark.p',fact_abs__of__nonneg) ).

fof(fact_abs__not__less__zero,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)) ),
    file('theBenchmark.p',fact_abs__not__less__zero) ).

fof(fact_zero__less__abs__iff,axiom,
    ! [V_a_2,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a_2))
      <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('theBenchmark.p',fact_zero__less__abs__iff) ).

fof(fact_abs__of__pos,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
       => c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ),
    file('theBenchmark.p',fact_abs__of__pos) ).

fof(fact_abs__triangle__ineq,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))) ),
    file('theBenchmark.p',fact_abs__triangle__ineq) ).

fof(fact_abs__triangle__ineq3,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))) ),
    file('theBenchmark.p',fact_abs__triangle__ineq3) ).

fof(fact_abs__triangle__ineq2,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))) ),
    file('theBenchmark.p',fact_abs__triangle__ineq2) ).

fof(fact_abs__triangle__ineq2__sym,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a))) ),
    file('theBenchmark.p',fact_abs__triangle__ineq2__sym) ).

fof(fact_abs__diff__less__iff,axiom,
    ! [V_ra_2,V_a_2,V_x_2,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x_2,V_a_2)),V_ra_2)
      <=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ra_2))
          & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ra_2),V_x_2) ) ) ),
    file('theBenchmark.p',fact_abs__diff__less__iff) ).

fof(fact_le__number__of__eq__not__less,axiom,
    ! [V_wa_2,V_v_2,T_a] :
      ( ( class_Orderings_Olinorder(T_a)
        & class_Int_Onumber(T_a) )
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
      <=> ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Int_Onumber__class_Onumber__of(T_a,V_v_2)) ) ),
    file('theBenchmark.p',fact_le__number__of__eq__not__less) ).

fof(fact_add__number__of__diff1,axiom,
    ! [V_c,V_w,V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_c)) = c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)),V_c) ),
    file('theBenchmark.p',fact_add__number__of__diff1) ).

fof(fact_natceiling__le,axiom,
    ! [V_a,V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,hAPP(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_natceiling__le__eq,axiom,
    ! [V_a_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_a_2)
      <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a_2)) ) ),
    file('theBenchmark.p',fact_natceiling__le__eq) ).

fof(fact_natceiling__subtract,axiom,
    ! [V_x,V_a] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a),V_x)
     => c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,hAPP(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_abs__triangle__ineq4,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))) ),
    file('theBenchmark.p',fact_abs__triangle__ineq4) ).

fof(fact_abs__diff__triangle__ineq,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(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(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d)))) ),
    file('theBenchmark.p',fact_abs__diff__triangle__ineq) ).

fof(fact_abs__add__one__not__less__self,axiom,
    ! [V_x] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x),
    file('theBenchmark.p',fact_abs__add__one__not__less__self) ).

fof(fact_abs__add__one__gt__zero,axiom,
    ! [V_x] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x))),
    file('theBenchmark.p',fact_abs__add__one__gt__zero) ).

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_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,hAPP(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_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_wr,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),v_r),
    file('theBenchmark.p',fact_wr) ).

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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),B_n))
          & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(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_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_lemma__interval,axiom,
    ! [V_b,V_x,V_a] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,V_x)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_b)
       => ? [B_d] :
            ( ! [B_y] :
                ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,B_y)),B_d)
               => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B_y,V_b)
                  & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_a,B_y) ) )
            & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d) ) ) ),
    file('theBenchmark.p',fact_lemma__interval) ).

fof(fact_reals__Archimedean6a,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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(B_n)))
          & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),B_n),V_r) ) ),
    file('theBenchmark.p',fact_reals__Archimedean6a) ).

fof(fact_g_I1_J,axiom,
    ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_g____(B_n)),v_r),
    file('theBenchmark.p',fact_g_I1_J) ).

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_int__one__le__iff__zero__less,axiom,
    ! [V_za_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_za_2)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_za_2) ),
    file('theBenchmark.p',fact_int__one__le__iff__zero__less) ).

fof(fact_zle__add1__eq__le,axiom,
    ! [V_za_2,V_wa_2] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_wa_2,V_za_2) ),
    file('theBenchmark.p',fact_zle__add1__eq__le) ).

fof(fact_zle__diff1__eq,axiom,
    ! [V_za_2,V_wa_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_wa_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2) ),
    file('theBenchmark.p',fact_zle__diff1__eq) ).

fof(fact_zless__add1__eq,axiom,
    ! [V_za_2,V_wa_2] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    <=> ( V_wa_2 = V_za_2
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2) ) ),
    file('theBenchmark.p',fact_zless__add1__eq) ).

fof(fact_add1__zle__eq,axiom,
    ! [V_za_2,V_wa_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_wa_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_za_2)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2) ),
    file('theBenchmark.p',fact_add1__zle__eq) ).

fof(fact_odd__less__0,axiom,
    ! [V_za_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_za_2),V_za_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    file('theBenchmark.p',fact_odd__less__0) ).

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_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_zabs__less__one__iff,axiom,
    ! [V_za_2] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_za_2),c_Groups_Oone__class_Oone(tc_Int_Oint))
    <=> V_za_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    file('theBenchmark.p',fact_zabs__less__one__iff) ).

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

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_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_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_zless__le,axiom,
    ! [V_wa_2,V_za_2] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,V_wa_2)
    <=> ( V_za_2 != V_wa_2
        & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_za_2,V_wa_2) ) ),
    file('theBenchmark.p',fact_zless__le) ).

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__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_plus__numeral__code_I9_J,axiom,
    ! [V_w,V_v] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)),
    file('theBenchmark.p',fact_plus__numeral__code_I9_J) ).

fof(fact_less__eq__number__of__int__code,axiom,
    ! [V_l_2,V_k_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ),
    file('theBenchmark.p',fact_less__eq__number__of__int__code) ).

fof(fact_natfloor__number__of__eq,axiom,
    ! [V_n] : c_RComplete_Onatfloor(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_n)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_n),
    file('theBenchmark.p',fact_natfloor__number__of__eq) ).

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_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_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__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_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_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_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_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_natfloor__real__of__nat,axiom,
    ! [V_n] : c_RComplete_Onatfloor(hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)) = V_n,
    file('theBenchmark.p',fact_natfloor__real__of__nat) ).

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_natceiling__number__of__eq,axiom,
    ! [V_n] : c_RComplete_Onatceiling(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_n)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_n),
    file('theBenchmark.p',fact_natceiling__number__of__eq) ).

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_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_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_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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_x) ),
    file('theBenchmark.p',fact_real__natfloor__le) ).

fof(fact_le__natfloor,axiom,
    ! [V_a,V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(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_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)),hAPP(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)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(B_N))) ) ),
    file('theBenchmark.p',fact_lemma__NBseq__def2) ).

fof(fact_le__natfloor__eq,axiom,
    ! [V_a_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_a_2,c_RComplete_Onatfloor(V_x_2))
      <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a_2),V_x_2) ) ),
    file('theBenchmark.p',fact_le__natfloor__eq) ).

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_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,hAPP(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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a),V_x)
     => c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,hAPP(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)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(V_x))),
    file('theBenchmark.p',fact_real__natfloor__gt__diff__one) ).

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,hAPP(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_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,hAPP(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,hAPP(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,hAPP(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,hAPP(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_norm__triangle__ineq3,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_Oabs__class_Oabs(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__ineq3) ).

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_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__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_N1,axiom,
    ! [B_n] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_N1____,B_n)
     => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,B_n)),v_z____)),v_d____) ),
    file('theBenchmark.p',fact_N1) ).

fof(fact_number__of__is__id,axiom,
    ! [V_k] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k) = V_k,
    file('theBenchmark.p',fact_number__of__is__id) ).

fof(fact_real__norm__def,axiom,
    ! [V_r] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r),
    file('theBenchmark.p',fact_real__norm__def) ).

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_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_abs__norm__cancel,axiom,
    ! [V_a,T_a] :
      ( class_RealVector_Oreal__normed__vector(T_a)
     => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a)) = c_RealVector_Onorm__class_Onorm(T_a,V_a) ),
    file('theBenchmark.p',fact_abs__norm__cancel) ).

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_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_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_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_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_norm__number__of,axiom,
    ! [V_w,T_a] :
      ( ( class_RealVector_Oreal__normed__algebra__1(T_a)
        & class_Int_Onumber__ring(T_a) )
     => c_RealVector_Onorm__class_Onorm(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_w)) ),
    file('theBenchmark.p',fact_norm__number__of) ).

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_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_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_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_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_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_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_fz_I2_J,axiom,
    ! [B_e] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_e)
     => ? [B_N] :
        ! [B_n] :
          ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_N,B_n)
         => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,B_n)),v_z____)),B_e) ) ),
    file('theBenchmark.p',fact_fz_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__096EX_AN_O_AALL_An_062_061N_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ad_096,axiom,
    ? [B_N] :
    ! [B_n] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_N,B_n)
     => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,B_n)),v_z____)),v_d____) ),
    file('theBenchmark.p',fact__096EX_AN_O_AALL_An_062_061N_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ad_096) ).

fof(fact__096_B_Bthesis_O_A_I_B_BN1_O_AALL_An_062_061N1_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ad_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
    ~ ! [B_N1] :
        ~ ! [B_n] :
            ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_N1,B_n)
           => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,B_n)),v_z____)),v_d____) ),
    file('theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_BN1_O_AALL_An_062_061N1_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ad_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).

fof(fact_natceiling__add__number__of,axiom,
    ! [V_x,V_n] :
      ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_n))
     => ( 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_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_n))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_n)) ) ),
    file('theBenchmark.p',fact_natceiling__add__number__of) ).

fof(fact_natfloor__add__number__of,axiom,
    ! [V_x,V_n] :
      ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_n))
     => ( 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_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_n))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_n)) ) ),
    file('theBenchmark.p',fact_natfloor__add__number__of) ).

fof(fact_not__neg__0,axiom,
    ~ c_Nat__Numeral_Oneg(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    file('theBenchmark.p',fact_not__neg__0) ).

fof(fact_not__neg__1,axiom,
    ~ c_Nat__Numeral_Oneg(c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('theBenchmark.p',fact_not__neg__1) ).

fof(fact_not__neg__eq__ge__0,axiom,
    ! [V_x_2] :
      ( ~ c_Nat__Numeral_Oneg(V_x_2)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x_2) ),
    file('theBenchmark.p',fact_not__neg__eq__ge__0) ).

fof(fact_neg__def,axiom,
    ! [V_Z_2] :
      ( c_Nat__Numeral_Oneg(V_Z_2)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_Z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    file('theBenchmark.p',fact_neg__def) ).

fof(fact_neg__imp__number__of__eq__0,axiom,
    ! [V_v] :
      ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))
     => c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_neg__imp__number__of__eq__0) ).

fof(fact_eq__nat__number__of,axiom,
    ! [V_v_H_2,V_v_2] :
      ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2)
    <=> ( ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_2))
         => ( ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H_2))
             => V_v_2 = V_v_H_2 )
            & ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H_2))
             => c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
        & ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_2))
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ),
    file('theBenchmark.p',fact_eq__nat__number__of) ).

fof(fact_nat__number__of__add__left,axiom,
    ! [V_k,V_v_H,V_v] :
      ( ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))
       => ( ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H))
           => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H),V_k)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_v_H)),V_k) )
          & ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H))
           => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H),V_k)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),V_k) ) ) )
      & ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))
       => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H),V_k)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H),V_k) ) ),
    file('theBenchmark.p',fact_nat__number__of__add__left) ).

fof(fact_real__of__nat__number__of,axiom,
    ! [V_v] :
      ( ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))
       => hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_v) )
      & ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))
       => hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    file('theBenchmark.p',fact_real__of__nat__number__of) ).

fof(fact_le__natfloor__eq__number__of,axiom,
    ! [V_x_2,V_n_2] :
      ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_n_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_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_n_2),c_RComplete_Onatfloor(V_x_2))
        <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_n_2),V_x_2) ) ) ),
    file('theBenchmark.p',fact_le__natfloor__eq__number__of) ).

fof(fact_natceiling__le__eq__number__of,axiom,
    ! [V_x_2,V_n_2] :
      ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_n_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),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_n_2))
        <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_n_2)) ) ) ),
    file('theBenchmark.p',fact_natceiling__le__eq__number__of) ).

fof(fact_Suc__nat__number__of__add,axiom,
    ! [V_n,V_v] :
      ( ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))
       => c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),V_n)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(V_v)),V_n) )
      & ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))
       => c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),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__nat__number__of__add) ).

fof(fact_Suc__nat__number__of,axiom,
    ! [V_v] :
      ( ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))
       => c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(V_v)) )
      & ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))
       => c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_Suc__nat__number__of) ).

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_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_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_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_complex__i__not__number__of,axiom,
    ! [V_w] : c_Complex_Oii != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,V_w),
    file('theBenchmark.p',fact_complex__i__not__number__of) ).

fof(fact_succ__def,axiom,
    ! [V_k] : c_Int_Osucc(V_k) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('theBenchmark.p',fact_succ__def) ).

fof(fact_number__of__succ,axiom,
    ! [V_k,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => c_Int_Onumber__class_Onumber__of(T_a,c_Int_Osucc(V_k)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_k)) ),
    file('theBenchmark.p',fact_number__of__succ) ).

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_Bseq__iff1a,axiom,
    ! [V_X_2,T_a] :
      ( class_RealVector_Oreal__normed__vector(T_a)
     => ( c_SEQ_OBseq(T_a,V_X_2)
      <=> ? [B_N] :
          ! [B_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(B_N))) ) ),
    file('theBenchmark.p',fact_Bseq__iff1a) ).

fof(fact_Bseq__iff,axiom,
    ! [V_X_2,T_a] :
      ( class_RealVector_Oreal__normed__vector(T_a)
     => ( c_SEQ_OBseq(T_a,V_X_2)
      <=> ? [B_N] :
          ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(B_N))) ) ),
    file('theBenchmark.p',fact_Bseq__iff) ).

fof(fact_Bseq__def,axiom,
    ! [V_X_2,T_a] :
      ( class_RealVector_Oreal__normed__vector(T_a)
     => ( c_SEQ_OBseq(T_a,V_X_2)
      <=> ? [B_K] :
            ( ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,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) ) ) ),
    file('theBenchmark.p',fact_Bseq__def) ).

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_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_BseqD,axiom,
    ! [V_X_2,T_a] :
      ( class_RealVector_Oreal__normed__vector(T_a)
     => ( c_SEQ_OBseq(T_a,V_X_2)
       => ? [B_K] :
            ( ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,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) ) ) ),
    file('theBenchmark.p',fact_BseqD) ).

fof(fact_BseqI,axiom,
    ! [V_X_2,V_K_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),V_K_2)
       => ( ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),V_K_2)
         => c_SEQ_OBseq(T_a,V_X_2) ) ) ),
    file('theBenchmark.p',fact_BseqI) ).

fof(fact_nat__1__add__number__of,axiom,
    ! [V_v] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
       => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(V_v)) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
       => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__1__add__number__of) ).

fof(fact_nat__number__of__add__1,axiom,
    ! [V_v] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
       => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(V_v)) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
       => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__number__of__add__1) ).

fof(fact_Pls__def,axiom,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('theBenchmark.p',fact_Pls__def) ).

fof(fact_add__Pls,axiom,
    ! [V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,V_k) = V_k,
    file('theBenchmark.p',fact_add__Pls) ).

fof(fact_add__Pls__right,axiom,
    ! [V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,c_Int_OPls) = V_k,
    file('theBenchmark.p',fact_add__Pls__right) ).

fof(fact_rel__simps_I19_J,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
    file('theBenchmark.p',fact_rel__simps_I19_J) ).

fof(fact_rel__simps_I2_J,axiom,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
    file('theBenchmark.p',fact_rel__simps_I2_J) ).

fof(fact_diff__bin__simps_I1_J,axiom,
    ! [V_k] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,c_Int_OPls) = V_k,
    file('theBenchmark.p',fact_diff__bin__simps_I1_J) ).

fof(fact_number__of__Pls,axiom,
    ! [T_a] :
      ( class_Int_Onumber__ring(T_a)
     => c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_number__of__Pls) ).

fof(fact_semiring__norm_I112_J,axiom,
    ! [T_a] :
      ( class_Int_Onumber__ring(T_a)
     => c_Groups_Ozero__class_Ozero(T_a) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls) ),
    file('theBenchmark.p',fact_semiring__norm_I112_J) ).

fof(fact_add__numeral__0,axiom,
    ! [V_a,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls),V_a) = V_a ),
    file('theBenchmark.p',fact_add__numeral__0) ).

fof(fact_add__numeral__0__right,axiom,
    ! [V_a,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls)) = V_a ),
    file('theBenchmark.p',fact_add__numeral__0__right) ).

fof(fact_nat__number__of__Pls,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_nat__number__of__Pls) ).

fof(fact_semiring__norm_I113_J,axiom,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),
    file('theBenchmark.p',fact_semiring__norm_I113_J) ).

fof(fact_bin__less__0__simps_I1_J,axiom,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    file('theBenchmark.p',fact_bin__less__0__simps_I1_J) ).

fof(fact_zero__is__num__zero,axiom,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls),
    file('theBenchmark.p',fact_zero__is__num__zero) ).

fof(fact_not__neg__number__of__Pls,axiom,
    ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)),
    file('theBenchmark.p',fact_not__neg__number__of__Pls) ).

fof(fact_eq__0__number__of,axiom,
    ! [V_v_2] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls) ),
    file('theBenchmark.p',fact_eq__0__number__of) ).

fof(fact_eq__number__of__0,axiom,
    ! [V_v_2] :
      ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls) ),
    file('theBenchmark.p',fact_eq__number__of__0) ).

fof(fact_less__nat__number__of,axiom,
    ! [V_v_H_2,V_v_2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2))
    <=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2)
        & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2)
         => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_H_2) ) ) ),
    file('theBenchmark.p',fact_less__nat__number__of) ).

fof(fact_le__nat__number__of,axiom,
    ! [V_v_H_2,V_v_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2))
    <=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,V_v_H_2)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls) ) ),
    file('theBenchmark.p',fact_le__nat__number__of) ).

fof(fact_le__special_I3_J,axiom,
    ! [V_x_2,T_a] :
      ( ( class_Rings_Olinordered__idom(T_a)
        & class_Int_Onumber__ring(T_a) )
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Ozero__class_Ozero(T_a))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,c_Int_OPls) ) ),
    file('theBenchmark.p',fact_le__special_I3_J) ).

fof(fact_le__special_I1_J,axiom,
    ! [V_y_2,T_a] :
      ( ( class_Rings_Olinordered__idom(T_a)
        & class_Int_Onumber__ring(T_a) )
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_y_2) ) ),
    file('theBenchmark.p',fact_le__special_I1_J) ).

fof(fact_less__special_I3_J,axiom,
    ! [V_x_2,T_a] :
      ( ( class_Rings_Olinordered__idom(T_a)
        & class_Int_Onumber__ring(T_a) )
     => ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Ozero__class_Ozero(T_a))
      <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,c_Int_OPls) ) ),
    file('theBenchmark.p',fact_less__special_I3_J) ).

fof(fact_less__special_I1_J,axiom,
    ! [V_y_2,T_a] :
      ( ( class_Rings_Olinordered__idom(T_a)
        & class_Int_Onumber__ring(T_a) )
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
      <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_y_2) ) ),
    file('theBenchmark.p',fact_less__special_I1_J) ).

fof(fact_less__0__number__of,axiom,
    ! [V_v_2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_2) ),
    file('theBenchmark.p',fact_less__0__number__of) ).

fof(fact_add__nat__number__of,axiom,
    ! [V_v_H,V_v] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
       => ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_H,c_Int_OPls)
           => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_v_H)) )
          & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_H,c_Int_OPls)
           => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v) ) ) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
       => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H) ) ),
    file('theBenchmark.p',fact_add__nat__number__of) ).

fof(fact_number__of2,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)),
    file('theBenchmark.p',fact_number__of2) ).

fof(fact_nat__number__of__diff__1,axiom,
    ! [V_v] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v,c_Int_OPls)
       => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Opred(V_v)) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v,c_Int_OPls)
       => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__number__of__diff__1) ).

fof(fact_Suc__diff__number__of,axiom,
    ! [V_m,V_v] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Opred(V_v))) ),
    file('theBenchmark.p',fact_Suc__diff__number__of) ).

fof(fact_expi__zero,axiom,
    c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
    file('theBenchmark.p',fact_expi__zero) ).

fof(fact_succ__pred,axiom,
    ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x,
    file('theBenchmark.p',fact_succ__pred) ).

fof(fact_le__iff__pred__less,axiom,
    ! [V_l_2,V_k_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(V_k_2),V_l_2) ),
    file('theBenchmark.p',fact_le__iff__pred__less) ).

fof(fact_pred__def,axiom,
    ! [V_k] : c_Int_Opred(V_k) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('theBenchmark.p',fact_pred__def) ).

fof(fact_neg__number__of__pred__iff__0,axiom,
    ! [V_v_2] :
      ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_Opred(V_v_2)))
    <=> c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_neg__number__of__pred__iff__0) ).

fof(fact_decr__lemma,axiom,
    ! [V_z,V_x,V_d] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d)
     => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z)),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)),V_z) ),
    file('theBenchmark.p',fact_decr__lemma) ).

fof(fact_incr__lemma,axiom,
    ! [V_x,V_z,V_d] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d)
     => c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z)),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d))) ),
    file('theBenchmark.p',fact_incr__lemma) ).

fof(fact_of__nat__number__of__lemma,axiom,
    ! [V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Groups_Ozero__class_Ozero(T_a) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Int_Onumber__class_Onumber__of(T_a,V_v) ) ) ),
    file('theBenchmark.p',fact_of__nat__number__of__lemma) ).

fof(fact_zmult__zless__mono2__lemma,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_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
       => c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_j)) ) ),
    file('theBenchmark.p',fact_zmult__zless__mono2__lemma) ).

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_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__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__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_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_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_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__eq__0__iff,axiom,
    ! [V_b_2,V_a_2,T_a] :
      ( class_Rings_Oring__no__zero__divisors(T_a)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
      <=> ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a)
          | V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('theBenchmark.p',fact_mult__eq__0__iff) ).

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_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_mult__number__of__left,axiom,
    ! [V_z,V_w,V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w))),V_z) ),
    file('theBenchmark.p',fact_mult__number__of__left) ).

fof(fact_times__numeral__code_I5_J,axiom,
    ! [V_w,V_v] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)),
    file('theBenchmark.p',fact_times__numeral__code_I5_J) ).

fof(fact_arith__simps_I32_J,axiom,
    ! [V_w,V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_v)),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) ),
    file('theBenchmark.p',fact_arith__simps_I32_J) ).

fof(fact_number__of__mult,axiom,
    ! [V_w,V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => c_Int_Onumber__class_Onumber__of(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_v)),c_Int_Onumber__class_Onumber__of(T_a,V_w)) ),
    file('theBenchmark.p',fact_number__of__mult) ).

fof(fact_not__neg__int,axiom,
    ! [V_n] : ~ c_Nat__Numeral_Oneg(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),
    file('theBenchmark.p',fact_not__neg__int) ).

fof(fact_abs__int__eq,axiom,
    ! [V_m] : c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m),
    file('theBenchmark.p',fact_abs__int__eq) ).

fof(fact_abs__of__nat,axiom,
    ! [V_n,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => c_Groups_Oabs__class_Oabs(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n) ),
    file('theBenchmark.p',fact_abs__of__nat) ).

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_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__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__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_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_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_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_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_crossproduct__eq,axiom,
    ! [V_za_2,V_x_2,V_y_2,V_wa_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_wa_2),V_y_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_za_2)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_wa_2),V_za_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2))
      <=> ( V_y_2 = V_za_2
          | V_wa_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_da_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
     => ( ( V_c_2 != V_da_2
          & V_a_2 != V_b_2 )
      <=> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_da_2)) != c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_da_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_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_abs__mult__self,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ),
    file('theBenchmark.p',fact_abs__mult__self) ).

fof(fact_abs__mult,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => c_Groups_Oabs__class_Oabs(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_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)) ),
    file('theBenchmark.p',fact_abs__mult) ).

fof(fact_real__eq__of__nat,axiom,
    c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),
    file('theBenchmark.p',fact_real__eq__of__nat) ).

fof(fact_real__of__nat__def,axiom,
    c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),
    file('theBenchmark.p',fact_real__of__nat__def) ).

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_of__nat__eq__iff,axiom,
    ! [V_n_2,V_m_2,T_a] :
      ( class_Nat_Osemiring__char__0(T_a)
     => ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)
      <=> V_m_2 = V_n_2 ) ),
    file('theBenchmark.p',fact_of__nat__eq__iff) ).

fof(fact_of__nat__mult,axiom,
    ! [V_n,V_m,T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ),
    file('theBenchmark.p',fact_of__nat__mult) ).

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_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_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_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_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_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_norm__of__nat,axiom,
    ! [V_n,T_a] :
      ( class_RealVector_Oreal__normed__algebra__1(T_a)
     => c_RealVector_Onorm__class_Onorm(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),V_n) ),
    file('theBenchmark.p',fact_norm__of__nat) ).

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_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_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_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_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_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_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__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_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_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__Pls,axiom,
    ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls,
    file('theBenchmark.p',fact_mult__Pls) ).

fof(fact_of__nat__0__le__iff,axiom,
    ! [V_n,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ),
    file('theBenchmark.p',fact_of__nat__0__le__iff) ).

fof(fact_zero__le__imp__of__nat,axiom,
    ! [V_m,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)) ),
    file('theBenchmark.p',fact_zero__le__imp__of__nat) ).

fof(fact_of__nat__less__0__iff,axiom,
    ! [V_m,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ~ c_Orderings_Oord__class_Oless(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m),c_Groups_Ozero__class_Ozero(T_a)) ),
    file('theBenchmark.p',fact_of__nat__less__0__iff) ).

fof(fact_of__nat__0,axiom,
    ! [T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_of__nat__0) ).

fof(fact_of__nat__less__imp__less,axiom,
    ! [V_n,V_m,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ),
    file('theBenchmark.p',fact_of__nat__less__imp__less) ).

fof(fact_less__imp__of__nat__less,axiom,
    ! [V_n,V_m,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
       => c_Orderings_Oord__class_Oless(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ),
    file('theBenchmark.p',fact_less__imp__of__nat__less) ).

fof(fact_of__nat__less__iff,axiom,
    ! [V_n_2,V_m_2,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2))
      <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ),
    file('theBenchmark.p',fact_of__nat__less__iff) ).

fof(fact_of__nat__le__iff,axiom,
    ! [V_n_2,V_m_2,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ),
    file('theBenchmark.p',fact_of__nat__le__iff) ).

fof(fact_of__nat__add,axiom,
    ! [V_n,V_m,T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ),
    file('theBenchmark.p',fact_of__nat__add) ).

fof(fact_of__nat__1,axiom,
    ! [T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_of__nat__1) ).

fof(fact_transfer__int__nat__numerals_I1_J,axiom,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('theBenchmark.p',fact_transfer__int__nat__numerals_I1_J) ).

fof(fact_int__0,axiom,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('theBenchmark.p',fact_int__0) ).

fof(fact_int__eq__0__conv,axiom,
    ! [V_n_2] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_int__eq__0__conv) ).

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_zero__le__mult__iff,axiom,
    ! [V_b_2,V_a_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_a_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_a_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_a_2) ) ) ) ),
    file('theBenchmark.p',fact_zero__le__mult__iff) ).

fof(fact_mult__le__0__iff,axiom,
    ! [V_b_2,V_a_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_a_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_a_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_a_2) ) ) ) ),
    file('theBenchmark.p',fact_mult__le__0__iff) ).

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__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__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__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__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__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__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_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__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_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__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__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_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_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_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_c_2,V_a_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_a_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2))
      <=> ( ( c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)
            & c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) )
          | ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
            & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) ) ) ) ),
    file('theBenchmark.p',fact_mult__less__cancel__right__disj) ).

fof(fact_mult__less__cancel__left__disj,axiom,
    ! [V_b_2,V_a_2,V_c_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_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
      <=> ( ( c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)
            & c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) )
          | ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
            & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) ) ) ) ),
    file('theBenchmark.p',fact_mult__less__cancel__left__disj) ).

fof(fact_mult__less__cancel__left__pos,axiom,
    ! [V_b_2,V_a_2,V_c_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_c_2)
       => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
        <=> c_Orderings_Oord__class_Oless(T_a,V_a_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_a_2,V_c_2,T_a] :
      ( class_Rings_Olinordered__ring__strict(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_c_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_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
        <=> c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_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_transfer__int__nat__quantifiers_I1_J,axiom,
    ! [V_P_2] :
      ( ! [B_x] :
          ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B_x)
         => hBOOL(hAPP(V_P_2,B_x)) )
    <=> ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ),
    file('theBenchmark.p',fact_transfer__int__nat__quantifiers_I1_J) ).

fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
    ! [V_P_2] :
      ( ? [B_x] :
          ( hBOOL(hAPP(V_P_2,B_x))
          & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B_x) )
    <=> ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ),
    file('theBenchmark.p',fact_transfer__int__nat__quantifiers_I2_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
    ! [V_z] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).

fof(fact_zero__zle__int,axiom,
    ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),
    file('theBenchmark.p',fact_zero__zle__int) ).

fof(fact_int__less__0__conv,axiom,
    ! [V_k] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    file('theBenchmark.p',fact_int__less__0__conv) ).

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_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_Nat__Transfer_Otransfer__int__nat__relations_I2_J,axiom,
    ! [V_y_2,V_x_2] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__relations_I2_J) ).

fof(fact_zless__int,axiom,
    ! [V_n_2,V_m_2] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ),
    file('theBenchmark.p',fact_zless__int) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__relations_I3_J,axiom,
    ! [V_y_2,V_x_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2,V_y_2) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__relations_I3_J) ).

fof(fact_zle__int,axiom,
    ! [V_n_2,V_m_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ),
    file('theBenchmark.p',fact_zle__int) ).

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_left__distrib__number__of,axiom,
    ! [V_v,V_b,V_a,T_b] :
      ( ( class_Rings_Osemiring(T_b)
        & class_Int_Onumber(T_b) )
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Groups_Oplus__class_Oplus(T_b,V_a,V_b)),c_Int_Onumber__class_Onumber__of(T_b,V_v)) = c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),c_Int_Onumber__class_Onumber__of(T_b,V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),c_Int_Onumber__class_Onumber__of(T_b,V_v))) ),
    file('theBenchmark.p',fact_left__distrib__number__of) ).

fof(fact_right__distrib__number__of,axiom,
    ! [V_c,V_b,V_v,T_b] :
      ( ( class_Rings_Osemiring(T_b)
        & class_Int_Onumber(T_b) )
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)),c_Groups_Oplus__class_Oplus(T_b,V_b,V_c)) = c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)),V_c)) ),
    file('theBenchmark.p',fact_right__distrib__number__of) ).

fof(fact_zle__iff__zadd,axiom,
    ! [V_za_2,V_wa_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_wa_2,V_za_2)
    <=> ? [B_n] : V_za_2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_wa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)) ),
    file('theBenchmark.p',fact_zle__iff__zadd) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
    ! [V_y,V_x] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_y)),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J) ).

fof(fact_zadd__int,axiom,
    ! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),
    file('theBenchmark.p',fact_zadd__int) ).

fof(fact_zadd__int__left,axiom,
    ! [V_z,V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n),V_z)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),V_z),
    file('theBenchmark.p',fact_zadd__int__left) ).

fof(fact_eq__add__iff2,axiom,
    ! [V_da_2,V_b_2,V_c_2,V_e_2,V_a_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_a_2),V_e_2),V_c_2) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_da_2)
      <=> V_c_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_a_2)),V_e_2),V_da_2) ) ),
    file('theBenchmark.p',fact_eq__add__iff2) ).

fof(fact_eq__add__iff1,axiom,
    ! [V_da_2,V_b_2,V_c_2,V_e_2,V_a_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_a_2),V_e_2),V_c_2) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_da_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_a_2,V_b_2)),V_e_2),V_c_2) = V_da_2 ) ),
    file('theBenchmark.p',fact_eq__add__iff1) ).

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_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_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_right__diff__distrib__number__of,axiom,
    ! [V_c,V_b,V_v,T_b] :
      ( ( class_Rings_Oring(T_b)
        & class_Int_Onumber(T_b) )
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)),c_Groups_Ominus__class_Ominus(T_b,V_b,V_c)) = c_Groups_Ominus__class_Ominus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)),V_c)) ),
    file('theBenchmark.p',fact_right__diff__distrib__number__of) ).

fof(fact_left__diff__distrib__number__of,axiom,
    ! [V_v,V_b,V_a,T_b] :
      ( ( class_Rings_Oring(T_b)
        & class_Int_Onumber(T_b) )
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Groups_Ominus__class_Ominus(T_b,V_a,V_b)),c_Int_Onumber__class_Onumber__of(T_b,V_v)) = c_Groups_Ominus__class_Ominus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),c_Int_Onumber__class_Onumber__of(T_b,V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),c_Int_Onumber__class_Onumber__of(T_b,V_v))) ),
    file('theBenchmark.p',fact_left__diff__distrib__number__of) ).

fof(fact_transfer__int__nat__numerals_I2_J,axiom,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('theBenchmark.p',fact_transfer__int__nat__numerals_I2_J) ).

fof(fact_int__1,axiom,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint),
    file('theBenchmark.p',fact_int__1) ).

fof(fact_abs__mult__less,axiom,
    ! [V_d,V_b,V_c,V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_c)
       => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_b),V_d)
         => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d)) ) ) ),
    file('theBenchmark.p',fact_abs__mult__less) ).

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_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_abs__zmult__eq__1,axiom,
    ! [V_n,V_m] :
      ( c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n)) = c_Groups_Oone__class_Oone(tc_Int_Oint)
     => c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    file('theBenchmark.p',fact_abs__zmult__eq__1) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
    ! [V_y,V_x] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_x,V_y)),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J) ).

fof(fact_of__nat__Suc,axiom,
    ! [V_m,T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Nat_OSuc(V_m)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)) ),
    file('theBenchmark.p',fact_of__nat__Suc) ).

fof(fact_of__nat__diff,axiom,
    ! [V_m,V_n,T_a] :
      ( class_Rings_Oring__1(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Ominus__class_Ominus(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ),
    file('theBenchmark.p',fact_of__nat__diff) ).

fof(fact_mult__le__cancel__left__pos,axiom,
    ! [V_b_2,V_a_2,V_c_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_c_2)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
        <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_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_a_2,V_c_2,T_a] :
      ( class_Rings_Olinordered__ring__strict(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_c_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_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
        <=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_a_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_int__le__0__conv,axiom,
    ! [V_n_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_int__le__0__conv) ).

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_int__Suc0__eq__1,axiom,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Int_Oint),
    file('theBenchmark.p',fact_int__Suc0__eq__1) ).

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_le__add__iff1,axiom,
    ! [V_da_2,V_b_2,V_c_2,V_e_2,V_a_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_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_da_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_a_2,V_b_2)),V_e_2),V_c_2),V_da_2) ) ),
    file('theBenchmark.p',fact_le__add__iff1) ).

fof(fact_le__add__iff2,axiom,
    ! [V_da_2,V_b_2,V_c_2,V_e_2,V_a_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_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_da_2))
      <=> c_Orderings_Oord__class_Oless__eq(T_a,V_c_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_a_2)),V_e_2),V_da_2)) ) ),
    file('theBenchmark.p',fact_le__add__iff2) ).

fof(fact_less__add__iff2,axiom,
    ! [V_da_2,V_b_2,V_c_2,V_e_2,V_a_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_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_da_2))
      <=> c_Orderings_Oord__class_Oless(T_a,V_c_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_a_2)),V_e_2),V_da_2)) ) ),
    file('theBenchmark.p',fact_less__add__iff2) ).

fof(fact_less__add__iff1,axiom,
    ! [V_da_2,V_b_2,V_c_2,V_e_2,V_a_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_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_da_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_a_2,V_b_2)),V_e_2),V_c_2),V_da_2) ) ),
    file('theBenchmark.p',fact_less__add__iff1) ).

fof(fact_zless__iff__Suc__zadd,axiom,
    ! [V_za_2,V_wa_2] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2)
    <=> ? [B_n] : V_za_2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_wa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(B_n))) ),
    file('theBenchmark.p',fact_zless__iff__Suc__zadd) ).

fof(fact_int__Suc,axiom,
    ! [V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(V_m)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),
    file('theBenchmark.p',fact_int__Suc) ).

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_abs__eq__mult,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oordered__ring__abs(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_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,c_Groups_Ozero__class_Ozero(T_a),V_a) ) )
       => c_Groups_Oabs__class_Oabs(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_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)) ) ),
    file('theBenchmark.p',fact_abs__eq__mult) ).

fof(fact_abs__mult__pos,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)
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_y)),V_x) = c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)) ) ),
    file('theBenchmark.p',fact_abs__mult__pos) ).

fof(fact_zdiff__int,axiom,
    ! [V_m,V_n] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
     => c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) ),
    file('theBenchmark.p',fact_zdiff__int) ).

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_of__nat__0__less__iff,axiom,
    ! [V_n_2,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),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_of__nat__0__less__iff) ).

fof(fact_zero__less__int__conv,axiom,
    ! [V_n_2] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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_zero__less__int__conv) ).

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_int__nat__number__of,axiom,
    ! [V_v] :
      ( ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v) )
      & ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_int__nat__number__of) ).

fof(fact_of__nat__number__of__eq,axiom,
    ! [V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => ( ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Int_Onumber__class_Onumber__of(T_a,V_v) )
        & ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('theBenchmark.p',fact_of__nat__number__of__eq) ).

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_zdiff__int__split,axiom,
    ! [V_y_2,V_x_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_x_2,V_y_2))))
    <=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2)
         => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_y_2,V_x_2)
         => hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))) ) ) ),
    file('theBenchmark.p',fact_zdiff__int__split) ).

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_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_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_real__mult__right__cancel,axiom,
    ! [V_b_2,V_a_2,V_c_2] :
      ( V_c_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a_2),V_c_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_c_2)
      <=> V_a_2 = V_b_2 ) ),
    file('theBenchmark.p',fact_real__mult__right__cancel) ).

fof(fact_real__mult__left__cancel,axiom,
    ! [V_b_2,V_a_2,V_c_2] :
      ( V_c_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_b_2)
      <=> V_a_2 = V_b_2 ) ),
    file('theBenchmark.p',fact_real__mult__left__cancel) ).

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_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__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__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__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_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_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_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_real__of__nat__mult,axiom,
    ! [V_n,V_m] : hAPP(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),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)),
    file('theBenchmark.p',fact_real__of__nat__mult) ).

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_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_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_int__int__eq,axiom,
    ! [V_n_2,V_m_2] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)
    <=> V_m_2 = V_n_2 ),
    file('theBenchmark.p',fact_int__int__eq) ).

fof(fact_zmult__int,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),
    file('theBenchmark.p',fact_zmult__int) ).

fof(fact_int__mult,axiom,
    ! [V_n,V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),
    file('theBenchmark.p',fact_int__mult) ).

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_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_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_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_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_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_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_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__Transfer_Otransfer__int__nat__relations_I1_J,axiom,
    ! [V_y_2,V_x_2] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)
    <=> V_x_2 = V_y_2 ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__relations_I1_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
    ! [V_y,V_x] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y)),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J) ).

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_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_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__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__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_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_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_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_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_za_2] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_za_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_za_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_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_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_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_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_expi__add,axiom,
    ! [V_b,V_a] : c_Complex_Oexpi(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(V_a)),c_Complex_Oexpi(V_b)),
    file('theBenchmark.p',fact_expi__add) ).

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_real__mult__le__cancel__iff2,axiom,
    ! [V_y_2,V_x_2,V_za_2] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_za_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_za_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_real__mult__le__cancel__iff1,axiom,
    ! [V_y_2,V_x_2,V_za_2] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_za_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_za_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_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_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_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_rabs__ratiotest__lemma,axiom,
    ! [V_y,V_x,V_c] :
      ( 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_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y)))
       => V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    file('theBenchmark.p',fact_rabs__ratiotest__lemma) ).

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_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_mult__nat__number__of,axiom,
    ! [V_v_H,V_v] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H)) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_mult__nat__number__of) ).

fof(fact_nat__number__of__mult__left,axiom,
    ! [V_k,V_v_H,V_v] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H))),V_k) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)),V_k)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__number__of__mult__left) ).

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_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_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__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_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__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__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_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_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__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__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__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__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_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_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_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_decr__mult__lemma,axiom,
    ! [V_k_2,V_P_2,V_da_2] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_da_2)
     => ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
           => hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B_x,V_da_2))) )
       => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
         => ! [B_x] :
              ( hBOOL(hAPP(V_P_2,B_x))
             => hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_da_2)))) ) ) ) ),
    file('theBenchmark.p',fact_decr__mult__lemma) ).

fof(fact_incr__mult__lemma,axiom,
    ! [V_k_2,V_P_2,V_da_2] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_da_2)
     => ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
           => hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B_x,V_da_2))) )
       => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
         => ! [B_x] :
              ( hBOOL(hAPP(V_P_2,B_x))
             => hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_da_2)))) ) ) ) ),
    file('theBenchmark.p',fact_incr__mult__lemma) ).

fof(fact_zero__less__imp__eq__int,axiom,
    ! [V_k] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)
     => ? [B_n] :
          ( V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B_n) ) ),
    file('theBenchmark.p',fact_zero__less__imp__eq__int) ).

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__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__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_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),hAPP(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_cis__real__of__nat__Suc__mult,axiom,
    ! [V_a,V_n] : c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(V_n))),V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)),V_a))),
    file('theBenchmark.p',fact_cis__real__of__nat__Suc__mult) ).

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_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_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_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_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_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_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_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_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_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_power__eq__0__iff__number__of,axiom,
    ! [V_wa_2,V_a_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_a_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2)) = c_Groups_Ozero__class_Ozero(T_a)
      <=> ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('theBenchmark.p',fact_power__eq__0__iff__number__of) ).

fof(fact_cis__mult,axiom,
    ! [V_b,V_a] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),c_Complex_Ocis(V_b)) = c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a,V_b)),
    file('theBenchmark.p',fact_cis__mult) ).

fof(fact_cis__zero,axiom,
    c_Complex_Ocis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
    file('theBenchmark.p',fact_cis__zero) ).

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_power__0__left__number__of,axiom,
    ! [V_w,T_a] :
      ( ( class_Rings_Osemiring__0(T_a)
        & class_Power_Opower(T_a) )
     => ( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w)) = c_Groups_Ozero__class_Ozero(T_a) )
        & ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w)) = c_Groups_Oone__class_Oone(T_a) ) ) ),
    file('theBenchmark.p',fact_power__0__left__number__of) ).

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_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_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_zpower__int,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)),
    file('theBenchmark.p',fact_zpower__int) ).

fof(fact_int__power,axiom,
    ! [V_n,V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n),
    file('theBenchmark.p',fact_int__power) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
    ! [V_n,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x),V_n)),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J) ).

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_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_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__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__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_power__real__of__nat,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m)),V_n) = hAPP(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__power,axiom,
    ! [V_n,V_m] : hAPP(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),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m)),V_n),
    file('theBenchmark.p',fact_real__of__nat__power) ).

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_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_zero__less__power__nat__eq__number__of,axiom,
    ! [V_wa_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),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2)))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
        | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_zero__less__power__nat__eq__number__of) ).

fof(fact_zero__le__zpower__abs,axiom,
    ! [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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x)),V_n)),
    file('theBenchmark.p',fact_zero__le__zpower__abs) ).

fof(fact_natfloor__power,axiom,
    ! [V_n,V_x] :
      ( V_x = hAPP(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_DeMoivre,axiom,
    ! [V_n,V_a] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),V_n) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)),V_a)),
    file('theBenchmark.p',fact_DeMoivre) ).

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

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__abs,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n) ),
    file('theBenchmark.p',fact_power__abs) ).

fof(fact_of__nat__power,axiom,
    ! [V_n,V_m,T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),V_n) ),
    file('theBenchmark.p',fact_of__nat__power) ).

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__inject__exp,axiom,
    ! [V_n_2,V_m_2,V_a_2,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a_2)
       => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)
        <=> V_m_2 = V_n_2 ) ) ),
    file('theBenchmark.p',fact_power__inject__exp) ).

fof(fact_power__eq__0__iff,axiom,
    ! [V_n_2,V_a_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_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a)
      <=> ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('theBenchmark.p',fact_power__eq__0__iff) ).

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_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__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__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__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_zero__le__power__abs,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__idom(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),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n)) ),
    file('theBenchmark.p',fact_zero__le__power__abs) ).

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__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__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__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__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_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_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_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_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_power_Opower_Opower__0,axiom,
    ! [V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_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_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Nat_OSuc(V_n_2)) = hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),V_n_2)),
    file('theBenchmark.p',fact_power_Opower_Opower__Suc) ).

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),hAPP(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),hAPP(c_RealDef_Oreal(tc_Nat_Onat),B_n)),V_y),V_x) ) ) ),
    file('theBenchmark.p',fact_reals__Archimedean4) ).

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_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_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_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__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__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_neg__imp__zdiv__nonneg__iff,axiom,
    ! [V_a_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_a_2,V_b_2))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    file('theBenchmark.p',fact_neg__imp__zdiv__nonneg__iff) ).

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_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_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_nonneg1__imp__zdiv__pos__iff,axiom,
    ! [V_b_2,V_a_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_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_a_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_a_2) ) ) ),
    file('theBenchmark.p',fact_nonneg1__imp__zdiv__pos__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_pos__imp__zdiv__nonneg__iff,axiom,
    ! [V_a_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_a_2,V_b_2))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2) ) ),
    file('theBenchmark.p',fact_pos__imp__zdiv__nonneg__iff) ).

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_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(fact_zdiv__zmult2__eq,axiom,
    ! [V_b,V_a,V_c] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c)
     => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),V_c) ),
    file('theBenchmark.p',fact_zdiv__zmult2__eq) ).

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_div__mult__mult1,axiom,
    ! [V_b,V_a,V_c,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
       => c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(T_a,V_a,V_b) ) ),
    file('theBenchmark.p',fact_div__mult__mult1) ).

fof(fact_div__mult__mult2,axiom,
    ! [V_b,V_a,V_c,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
       => c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(T_a,V_a,V_b) ) ),
    file('theBenchmark.p',fact_div__mult__mult2) ).

fof(fact_div__mult__self1__is__id,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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b) = V_a ) ),
    file('theBenchmark.p',fact_div__mult__self1__is__id) ).

fof(fact_div__mult__self2__is__id,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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b) = V_a ) ),
    file('theBenchmark.p',fact_div__mult__self2__is__id) ).

fof(fact_div__mult__mult1__if,axiom,
    ! [V_b,V_a,V_c,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( ( V_c != c_Groups_Ozero__class_Ozero(T_a)
         => c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(T_a,V_a,V_b) )
        & ( V_c = c_Groups_Ozero__class_Ozero(T_a)
         => c_Divides_Odiv__class_Odiv(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_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('theBenchmark.p',fact_div__mult__mult1__if) ).

fof(fact_zdiv__self,axiom,
    ! [V_a] :
      ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    file('theBenchmark.p',fact_zdiv__self) ).

fof(fact_div__self,axiom,
    ! [V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
       => c_Divides_Odiv__class_Odiv(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ),
    file('theBenchmark.p',fact_div__self) ).

fof(fact_zdiv__zero,axiom,
    ! [V_b] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('theBenchmark.p',fact_zdiv__zero) ).

fof(fact_div__0,axiom,
    ! [V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Odiv(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_div__0) ).

fof(fact_div__by__0,axiom,
    ! [V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_div__by__0) ).

fof(fact_Divides_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_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_y)) ) ),
    file('theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I1_J) ).

fof(fact_pos__imp__zdiv__neg__iff,axiom,
    ! [V_a_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(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    file('theBenchmark.p',fact_pos__imp__zdiv__neg__iff) ).

fof(fact_neg__imp__zdiv__neg__iff,axiom,
    ! [V_a_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(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),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_a_2) ) ),
    file('theBenchmark.p',fact_neg__imp__zdiv__neg__iff) ).

fof(fact_div__neg__pos__less0,axiom,
    ! [V_b,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)
       => c_Orderings_Oord__class_Oless(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__neg__pos__less0) ).

fof(fact_div__by__1,axiom,
    ! [V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a ),
    file('theBenchmark.p',fact_div__by__1) ).

fof(fact_divmod__int__rel__div__eq,axiom,
    ! [V_r_1,V_y,V_b_1,V_a_1] :
      ( V_a_1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y),V_r_1)
     => ( ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1)
           => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r_1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
              & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_1,V_r_1) ) )
          & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1)
           => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_1,V_b_1)
              & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_1) ) ) )
       => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ),
    file('theBenchmark.p',fact_divmod__int__rel__div__eq) ).

fof(fact_split__zdiv,axiom,
    ! [V_k_2,V_n_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))
    <=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
         => ! [B_i] :
              ( ? [B_j] :
                  ( V_n_2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i),B_j)
                  & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B_j,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
                  & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,B_j) )
             => hBOOL(hAPP(V_P_2,B_i)) ) )
        & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
         => ! [B_i] :
              ( ? [B_j] :
                  ( V_n_2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i),B_j)
                  & c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j,V_k_2)
                  & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B_j) )
             => hBOOL(hAPP(V_P_2,B_i)) ) )
        & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
    file('theBenchmark.p',fact_split__zdiv) ).

fof(fact_DeMoivre2,axiom,
    ! [V_n,V_a,V_r] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Orcis(V_r,V_a)),V_n) = c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_r),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)),V_a)),
    file('theBenchmark.p',fact_DeMoivre2) ).

fof(fact_realpow__pos__nth__unique,axiom,
    ! [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(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
       => ? [B_x] :
            ( ! [B_y] :
                ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_y),V_n) = V_a
                  & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_y) )
               => B_y = B_x )
            & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_x),V_n) = V_a
            & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_x) ) ) ),
    file('theBenchmark.p',fact_realpow__pos__nth__unique) ).

fof(fact_nat__mult__div__cancel__disj,axiom,
    ! [V_n,V_m,V_k] :
      ( ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) )
      & ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Divides_Odiv__class_Odiv(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_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__mult__div__cancel__disj) ).

fof(fact_div__mult2__eq,axiom,
    ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,V_b),V_c),
    file('theBenchmark.p',fact_div__mult2__eq) ).

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

fof(fact_div__1,axiom,
    ! [V_m] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = V_m,
    file('theBenchmark.p',fact_div__1) ).

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

fof(fact_div__le__mono,axiom,
    ! [V_k,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_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_k),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_k)) ),
    file('theBenchmark.p',fact_div__le__mono) ).

fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
    ! [V_y,V_x] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_x,V_y)),
    file('theBenchmark.p',fact_Divides_Otransfer__int__nat__functions_I1_J) ).

fof(fact_zdiv__int,axiom,
    ! [V_b,V_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,V_b)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b)),
    file('theBenchmark.p',fact_zdiv__int) ).

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

fof(fact_nat__mult__div__cancel1,axiom,
    ! [V_n,V_m,V_k] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
     => c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) ),
    file('theBenchmark.p',fact_nat__mult__div__cancel1) ).

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

fof(fact_div__mult__self1__is__m,axiom,
    ! [V_m,V_n] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
     => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m),V_n) = V_m ),
    file('theBenchmark.p',fact_div__mult__self1__is__m) ).

fof(fact_div__le__mono2,axiom,
    ! [V_k,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__eq(tc_Nat_Onat,V_m,V_n)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_n),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_m)) ) ),
    file('theBenchmark.p',fact_div__le__mono2) ).

fof(fact_complex__mod__rcis,axiom,
    ! [V_a,V_r] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(V_r,V_a)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r),
    file('theBenchmark.p',fact_complex__mod__rcis) ).

fof(fact_rcis__zero__mod,axiom,
    ! [V_a] : c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    file('theBenchmark.p',fact_rcis__zero__mod) ).

fof(fact_cis__rcis__eq,axiom,
    ! [V_a] : c_Complex_Ocis(V_a) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_a),
    file('theBenchmark.p',fact_cis__rcis__eq) ).

fof(fact_div__if,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,V_m,V_n)
         => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)) )
        & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
         => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    file('theBenchmark.p',fact_div__if) ).

fof(fact_div__geq,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,V_m,V_n)
       => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)) ) ),
    file('theBenchmark.p',fact_div__geq) ).

fof(fact_split__div,axiom,
    ! [V_k_2,V_n_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n_2,V_k_2)))
    <=> ( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => ! [B_i,B_j] :
              ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_k_2)
             => ( V_n_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i),B_j)
               => hBOOL(hAPP(V_P_2,B_i)) ) ) )
        & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
    file('theBenchmark.p',fact_split__div) ).

fof(fact_split__div__lemma,axiom,
    ! [V_m_2,V_q_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,V_m_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),c_Nat_OSuc(V_q_2)))
          & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_q_2),V_m_2) )
      <=> V_q_2 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2) ) ),
    file('theBenchmark.p',fact_split__div__lemma) ).

fof(fact_split__div_H,axiom,
    ! [V_n_2,V_m_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2)))
    <=> ( ? [B_q] :
            ( hBOOL(hAPP(V_P_2,B_q))
            & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),c_Nat_OSuc(B_q)))
            & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q),V_m_2) )
        | ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    file('theBenchmark.p',fact_split__div_H) ).

fof(fact_le__div__geq,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__eq(tc_Nat_Onat,V_n,V_m)
       => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)) ) ),
    file('theBenchmark.p',fact_le__div__geq) ).

fof(fact_rcis__mult,axiom,
    ! [V_b,V_r2,V_a,V_r1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Orcis(V_r1,V_a)),c_Complex_Orcis(V_r2,V_b)) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r1),V_r2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a,V_b)),
    file('theBenchmark.p',fact_rcis__mult) ).

fof(fact_realpow__pos__nth,axiom,
    ! [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(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
       => ? [B_r] :
            ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_r),V_n) = V_a
            & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_r) ) ) ),
    file('theBenchmark.p',fact_realpow__pos__nth) ).

fof(fact_natfloor__div__nat,axiom,
    ! [V_y,V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_y)
       => c_RComplete_Onatfloor(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_y))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_y) ) ),
    file('theBenchmark.p',fact_natfloor__div__nat) ).

fof(fact_real__of__nat__div4,axiom,
    ! [V_x,V_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_x)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_x))),
    file('theBenchmark.p',fact_real__of__nat__div4) ).

fof(fact_nonzero__power__divide,axiom,
    ! [V_n,V_a,V_b,T_a] :
      ( class_Fields_Ofield(T_a)
     => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)),V_n) = c_Rings_Oinverse__class_Odivide(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_nonzero__power__divide) ).

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_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_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__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_Complex__Ocomplex__Rings_Oidom,axiom,
    class_Rings_Oidom(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).

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_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__ring,axiom,
    class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring) ).

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_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_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__ring,axiom,
    class_Rings_Ocomm__ring(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring) ).

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_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_Int__Oint__Rings_Oidom,axiom,
    class_Rings_Oidom(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).

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_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__Rings_Ocomm__ring,axiom,
    class_Rings_Ocomm__ring(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).

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__ab__group__add__abs,axiom,
    class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add__abs) ).

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_Oordered__ring__abs,axiom,
    class_Rings_Oordered__ring__abs(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring__abs) ).

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__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__Nat_Osemiring__char__0,axiom,
    class_Nat_Osemiring__char__0(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Nat_Osemiring__char__0) ).

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__1,axiom,
    class_Rings_Osemiring__1(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Osemiring__1) ).

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__Rings_Omult__zero,axiom,
    class_Rings_Omult__zero(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).

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__Int_Onumber__ring,axiom,
    class_Int_Onumber__ring(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Int_Onumber__ring) ).

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__Int_Onumber,axiom,
    class_Int_Onumber(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Int_Onumber) ).

fof(arity_Int__Oint__Groups_Oone,axiom,
    class_Groups_Oone(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Oone) ).

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__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__Nat_Osemiring__char__0,axiom,
    class_Nat_Osemiring__char__0(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Nat_Osemiring__char__0) ).

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__1,axiom,
    class_Rings_Osemiring__1(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__1) ).

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__Int_Onumber,axiom,
    class_Int_Onumber(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Int_Onumber) ).

fof(arity_Nat__Onat__Groups_Oone,axiom,
    class_Groups_Oone(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).

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__Groups_Oordered__ab__group__add__abs,axiom,
    class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).

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_Oordered__ring__abs,axiom,
    class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring__abs) ).

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,axiom,
    class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring) ).

fof(arity_RealDef__Oreal__Nat_Osemiring__char__0,axiom,
    class_Nat_Osemiring__char__0(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Nat_Osemiring__char__0) ).

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__1,axiom,
    class_Rings_Osemiring__1(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__1) ).

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__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__Int_Onumber__ring,axiom,
    class_Int_Onumber__ring(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Int_Onumber__ring) ).

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__Int_Onumber,axiom,
    class_Int_Onumber(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Int_Onumber) ).

fof(arity_RealDef__Oreal__Groups_Oone,axiom,
    class_Groups_Oone(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oone) ).

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,axiom,
    class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring) ).

fof(arity_Complex__Ocomplex__Nat_Osemiring__char__0,axiom,
    class_Nat_Osemiring__char__0(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Nat_Osemiring__char__0) ).

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__1,axiom,
    class_Rings_Osemiring__1(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring__1) ).

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__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__Int_Onumber__ring,axiom,
    class_Int_Onumber__ring(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Int_Onumber__ring) ).

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__Int_Onumber,axiom,
    class_Int_Onumber(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Int_Onumber) ).

fof(arity_Complex__Ocomplex__Groups_Oone,axiom,
    class_Groups_Oone(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Oone) ).

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__ab__group__add__abs,axiom,
    ! [T_1] :
      ( class_Rings_Olinordered__idom(T_1)
     => class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs) ).

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_Oordered__ring__abs,axiom,
    ! [T_1] :
      ( class_Rings_Olinordered__idom(T_1)
     => class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring__abs) ).

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__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__Nat_Osemiring__char__0,axiom,
    ! [T_1] :
      ( class_Rings_Olinordered__idom(T_1)
     => class_Nat_Osemiring__char__0(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Nat_Osemiring__char__0) ).

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__1,axiom,
    ! [T_1] :
      ( class_Rings_Ocomm__semiring__1(T_1)
     => class_Rings_Osemiring__1(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring__1) ).

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__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__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__Int_Onumber__ring,axiom,
    ! [T_1] :
      ( class_Rings_Ocomm__ring__1(T_1)
     => class_Int_Onumber__ring(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Int_Onumber__ring) ).

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__Int_Onumber,axiom,
    ! [T_1] :
      ( class_Rings_Ocomm__ring__1(T_1)
     => class_Int_Onumber(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Int_Onumber) ).

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(conj_0,conjecture,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
    file('theBenchmark.p',conj_0) ).

fof(f_1_1,plain,
    ! [V_ga_2,V_fa_2] :
      ( V_fa_2 = V_ga_2
      | ? [B_x] : hAPP(V_fa_2,B_x) != hAPP(V_ga_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_2,U_1] :
      ( 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,
    c_SEQ_Osubseq(v_f____),
    inference(fof_nnf,[status(thm)],[fact_fz_I1_J]) ).

fof(f_2_2,plain,
    c_SEQ_Osubseq(v_f____),
    inference(definitional_conversion,[status(esa)],[f_2_1]) ).

cnf(f_2_3,plain,
    c_SEQ_Osubseq(v_f____),
    inference(clausify,[status(thm)],[f_2_2]) ).

fof(f_3_1,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),
    inference(fof_nnf,[status(thm)],[fact__096N1_A_L_AN2_A_060_061_Af_A_IN1_A_L_AN2_J_096]) ).

fof(f_3_2,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),
    inference(definitional_conversion,[status(esa)],[f_3_1]) ).

cnf(f_3_3,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),
    inference(clausify,[status(thm)],[f_3_2]) ).

fof(f_4_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_4_2,plain,
    ! [U_4,U_3] :
      ( c_Orderings_Oord__class_Oless__eq(U_3,U_4,U_4)
      | ~ class_Orderings_Opreorder(U_3) ),
    inference(variable_rename,[status(thm)],[f_4_1]) ).

fof(f_4_3,plain,
    ! [U_3,U_4] :
      ( c_Orderings_Oord__class_Oless__eq(U_3,U_4,U_4)
      | ~ class_Orderings_Opreorder(U_3) ),
    inference(definitional_conversion,[status(esa)],[f_4_2]) ).

cnf(f_4_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_3,U_4,U_4)
    | ~ class_Orderings_Opreorder(U_3) ),
    inference(clausify,[status(thm)],[f_4_3]) ).

fof(f_5_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_5_2,plain,
    ! [U_6,U_5] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_5,c_Nat_OSuc(U_6)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_5,U_6)),
    inference(variable_rename,[status(thm)],[f_5_1]) ).

fof(f_5_3,plain,
    ! [U_5,U_6] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_5,c_Nat_OSuc(U_6)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_5,U_6)),
    inference(definitional_conversion,[status(esa)],[f_5_2]) ).

cnf(f_5_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_5,c_Nat_OSuc(U_6)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_5,U_6)),
    inference(clausify,[status(thm)],[f_5_3]) ).

fof(f_6_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_6_2,plain,
    ! [U_8,U_7] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_7),U_8) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_7,U_8)),
    inference(variable_rename,[status(thm)],[f_6_1]) ).

fof(f_6_3,plain,
    ! [U_7,U_8] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_7),U_8) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_7,U_8)),
    inference(definitional_conversion,[status(esa)],[f_6_2]) ).

cnf(f_6_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_7),U_8) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_7,U_8)),
    inference(clausify,[status(thm)],[f_6_3]) ).

fof(f_7_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_7_2,plain,
    ! [U_10,U_9] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_9),U_10) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_9,c_Nat_OSuc(U_10)),
    inference(variable_rename,[status(thm)],[f_7_1]) ).

fof(f_7_3,plain,
    ! [U_9,U_10] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_9),U_10) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_9,c_Nat_OSuc(U_10)),
    inference(definitional_conversion,[status(esa)],[f_7_2]) ).

cnf(f_7_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_9),U_10) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_9,c_Nat_OSuc(U_10)),
    inference(clausify,[status(thm)],[f_7_3]) ).

fof(f_8_1,plain,
    ! [V_b_2,V_c_2,V_a_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) )
        & ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2)) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right]) ).

fof(f_8_2,plain,
    ! [U_14,U_13,U_12,U_11] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_11,c_Groups_Oplus__class_Oplus(U_11,U_12,U_13),c_Groups_Oplus__class_Oplus(U_11,U_14,U_13))
          | ~ c_Orderings_Oord__class_Oless__eq(U_11,U_12,U_14) )
        & ( c_Orderings_Oord__class_Oless__eq(U_11,U_12,U_14)
          | ~ c_Orderings_Oord__class_Oless__eq(U_11,c_Groups_Oplus__class_Oplus(U_11,U_12,U_13),c_Groups_Oplus__class_Oplus(U_11,U_14,U_13)) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_11) ),
    inference(variable_rename,[status(thm)],[f_8_1]) ).

fof(f_8_3,plain,
    ( ! [U_11,U_12,U_13,U_14] :
        ( c_Orderings_Oord__class_Oless__eq(U_11,c_Groups_Oplus__class_Oplus(U_11,U_12,U_13),c_Groups_Oplus__class_Oplus(U_11,U_14,U_13))
        | ~ c_Orderings_Oord__class_Oless__eq(U_11,U_12,U_14)
        | ~ sP0(U_11,U_12,U_13,U_14) )
    & ! [U_11,U_12,U_13,U_14] :
        ( c_Orderings_Oord__class_Oless__eq(U_11,U_12,U_14)
        | ~ c_Orderings_Oord__class_Oless__eq(U_11,c_Groups_Oplus__class_Oplus(U_11,U_12,U_13),c_Groups_Oplus__class_Oplus(U_11,U_14,U_13))
        | ~ sP0(U_11,U_12,U_13,U_14) )
    & ! [U_11,U_12,U_13,U_14] :
        ( sP0(U_11,U_12,U_13,U_14)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_11) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_8_2]) ).

cnf(f_8_4,plain,
    ( sP0(U_11,U_12,U_13,U_14)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_11) ),
    inference(clausify,[status(thm)],[f_8_3]) ).

cnf(f_8_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_11,U_12,U_14)
    | ~ c_Orderings_Oord__class_Oless__eq(U_11,c_Groups_Oplus__class_Oplus(U_11,U_12,U_13),c_Groups_Oplus__class_Oplus(U_11,U_14,U_13))
    | ~ sP0(U_11,U_12,U_13,U_14) ),
    inference(clausify,[status(thm)],[f_8_3]) ).

cnf(f_8_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_11,c_Groups_Oplus__class_Oplus(U_11,U_12,U_13),c_Groups_Oplus__class_Oplus(U_11,U_14,U_13))
    | ~ c_Orderings_Oord__class_Oless__eq(U_11,U_12,U_14)
    | ~ sP0(U_11,U_12,U_13,U_14) ),
    inference(clausify,[status(thm)],[f_8_3]) ).

fof(f_9_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) )
        & ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_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_9_2,plain,
    ! [U_18,U_17,U_16,U_15] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_15,c_Groups_Oplus__class_Oplus(U_15,U_16,U_17),c_Groups_Oplus__class_Oplus(U_15,U_16,U_18))
          | ~ c_Orderings_Oord__class_Oless__eq(U_15,U_17,U_18) )
        & ( c_Orderings_Oord__class_Oless__eq(U_15,U_17,U_18)
          | ~ c_Orderings_Oord__class_Oless__eq(U_15,c_Groups_Oplus__class_Oplus(U_15,U_16,U_17),c_Groups_Oplus__class_Oplus(U_15,U_16,U_18)) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_15) ),
    inference(variable_rename,[status(thm)],[f_9_1]) ).

fof(f_9_3,plain,
    ( ! [U_18,U_15,U_17,U_16] :
        ( c_Orderings_Oord__class_Oless__eq(U_15,c_Groups_Oplus__class_Oplus(U_15,U_16,U_17),c_Groups_Oplus__class_Oplus(U_15,U_16,U_18))
        | ~ c_Orderings_Oord__class_Oless__eq(U_15,U_17,U_18)
        | ~ sP1(U_18,U_15,U_17,U_16) )
    & ! [U_18,U_15,U_17,U_16] :
        ( c_Orderings_Oord__class_Oless__eq(U_15,U_17,U_18)
        | ~ c_Orderings_Oord__class_Oless__eq(U_15,c_Groups_Oplus__class_Oplus(U_15,U_16,U_17),c_Groups_Oplus__class_Oplus(U_15,U_16,U_18))
        | ~ sP1(U_18,U_15,U_17,U_16) )
    & ! [U_18,U_15,U_17,U_16] :
        ( sP1(U_18,U_15,U_17,U_16)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_15) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_9_2]) ).

cnf(f_9_4,plain,
    ( sP1(U_18,U_15,U_17,U_16)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_15) ),
    inference(clausify,[status(thm)],[f_9_3]) ).

cnf(f_9_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_15,U_17,U_18)
    | ~ c_Orderings_Oord__class_Oless__eq(U_15,c_Groups_Oplus__class_Oplus(U_15,U_16,U_17),c_Groups_Oplus__class_Oplus(U_15,U_16,U_18))
    | ~ sP1(U_18,U_15,U_17,U_16) ),
    inference(clausify,[status(thm)],[f_9_3]) ).

cnf(f_9_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_15,c_Groups_Oplus__class_Oplus(U_15,U_16,U_17),c_Groups_Oplus__class_Oplus(U_15,U_16,U_18))
    | ~ c_Orderings_Oord__class_Oless__eq(U_15,U_17,U_18)
    | ~ sP1(U_18,U_15,U_17,U_16) ),
    inference(clausify,[status(thm)],[f_9_3]) ).

fof(f_10_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_10_2,plain,
    ! [U_22,U_21,U_20,U_19] :
      ( c_Orderings_Oord__class_Oless__eq(U_19,c_Groups_Oplus__class_Oplus(U_19,U_20,U_22),c_Groups_Oplus__class_Oplus(U_19,U_21,U_22))
      | ~ c_Orderings_Oord__class_Oless__eq(U_19,U_20,U_21)
      | ~ class_Groups_Oordered__ab__semigroup__add(U_19) ),
    inference(variable_rename,[status(thm)],[f_10_1]) ).

fof(f_10_3,plain,
    ! [U_20,U_19,U_21,U_22] :
      ( c_Orderings_Oord__class_Oless__eq(U_19,c_Groups_Oplus__class_Oplus(U_19,U_20,U_22),c_Groups_Oplus__class_Oplus(U_19,U_21,U_22))
      | ~ c_Orderings_Oord__class_Oless__eq(U_19,U_20,U_21)
      | ~ class_Groups_Oordered__ab__semigroup__add(U_19) ),
    inference(definitional_conversion,[status(esa)],[f_10_2]) ).

cnf(f_10_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_19,c_Groups_Oplus__class_Oplus(U_19,U_20,U_22),c_Groups_Oplus__class_Oplus(U_19,U_21,U_22))
    | ~ c_Orderings_Oord__class_Oless__eq(U_19,U_20,U_21)
    | ~ class_Groups_Oordered__ab__semigroup__add(U_19) ),
    inference(clausify,[status(thm)],[f_10_3]) ).

fof(f_11_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_11_2,plain,
    ! [U_26,U_25,U_24,U_23] :
      ( c_Orderings_Oord__class_Oless__eq(U_23,c_Groups_Oplus__class_Oplus(U_23,U_26,U_24),c_Groups_Oplus__class_Oplus(U_23,U_26,U_25))
      | ~ c_Orderings_Oord__class_Oless__eq(U_23,U_24,U_25)
      | ~ class_Groups_Oordered__ab__semigroup__add(U_23) ),
    inference(variable_rename,[status(thm)],[f_11_1]) ).

fof(f_11_3,plain,
    ! [U_24,U_25,U_26,U_23] :
      ( c_Orderings_Oord__class_Oless__eq(U_23,c_Groups_Oplus__class_Oplus(U_23,U_26,U_24),c_Groups_Oplus__class_Oplus(U_23,U_26,U_25))
      | ~ c_Orderings_Oord__class_Oless__eq(U_23,U_24,U_25)
      | ~ class_Groups_Oordered__ab__semigroup__add(U_23) ),
    inference(definitional_conversion,[status(esa)],[f_11_2]) ).

cnf(f_11_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_23,c_Groups_Oplus__class_Oplus(U_23,U_26,U_24),c_Groups_Oplus__class_Oplus(U_23,U_26,U_25))
    | ~ c_Orderings_Oord__class_Oless__eq(U_23,U_24,U_25)
    | ~ class_Groups_Oordered__ab__semigroup__add(U_23) ),
    inference(clausify,[status(thm)],[f_11_3]) ).

fof(f_12_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_12_2,plain,
    ! [U_31,U_30,U_29,U_28,U_27] :
      ( c_Orderings_Oord__class_Oless__eq(U_27,c_Groups_Oplus__class_Oplus(U_27,U_28,U_30),c_Groups_Oplus__class_Oplus(U_27,U_29,U_31))
      | ~ c_Orderings_Oord__class_Oless__eq(U_27,U_30,U_31)
      | ~ c_Orderings_Oord__class_Oless__eq(U_27,U_28,U_29)
      | ~ class_Groups_Oordered__ab__semigroup__add(U_27) ),
    inference(variable_rename,[status(thm)],[f_12_1]) ).

fof(f_12_3,plain,
    ! [U_31,U_28,U_29,U_30,U_27] :
      ( c_Orderings_Oord__class_Oless__eq(U_27,c_Groups_Oplus__class_Oplus(U_27,U_28,U_30),c_Groups_Oplus__class_Oplus(U_27,U_29,U_31))
      | ~ c_Orderings_Oord__class_Oless__eq(U_27,U_30,U_31)
      | ~ c_Orderings_Oord__class_Oless__eq(U_27,U_28,U_29)
      | ~ class_Groups_Oordered__ab__semigroup__add(U_27) ),
    inference(definitional_conversion,[status(esa)],[f_12_2]) ).

cnf(f_12_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_27,c_Groups_Oplus__class_Oplus(U_27,U_28,U_30),c_Groups_Oplus__class_Oplus(U_27,U_29,U_31))
    | ~ c_Orderings_Oord__class_Oless__eq(U_27,U_30,U_31)
    | ~ c_Orderings_Oord__class_Oless__eq(U_27,U_28,U_29)
    | ~ class_Groups_Oordered__ab__semigroup__add(U_27) ),
    inference(clausify,[status(thm)],[f_12_3]) ).

fof(f_13_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_13_2,plain,
    ! [U_35,U_34,U_33,U_32] :
      ( c_Orderings_Oord__class_Oless__eq(U_32,U_33,U_35)
      | ~ c_Orderings_Oord__class_Oless__eq(U_32,c_Groups_Oplus__class_Oplus(U_32,U_33,U_34),c_Groups_Oplus__class_Oplus(U_32,U_35,U_34))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_32) ),
    inference(variable_rename,[status(thm)],[f_13_1]) ).

fof(f_13_3,plain,
    ! [U_34,U_35,U_33,U_32] :
      ( c_Orderings_Oord__class_Oless__eq(U_32,U_33,U_35)
      | ~ c_Orderings_Oord__class_Oless__eq(U_32,c_Groups_Oplus__class_Oplus(U_32,U_33,U_34),c_Groups_Oplus__class_Oplus(U_32,U_35,U_34))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_32) ),
    inference(definitional_conversion,[status(esa)],[f_13_2]) ).

cnf(f_13_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_32,U_33,U_35)
    | ~ c_Orderings_Oord__class_Oless__eq(U_32,c_Groups_Oplus__class_Oplus(U_32,U_33,U_34),c_Groups_Oplus__class_Oplus(U_32,U_35,U_34))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_32) ),
    inference(clausify,[status(thm)],[f_13_3]) ).

fof(f_14_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_14_2,plain,
    ! [U_39,U_38,U_37,U_36] :
      ( c_Orderings_Oord__class_Oless__eq(U_36,U_38,U_39)
      | ~ c_Orderings_Oord__class_Oless__eq(U_36,c_Groups_Oplus__class_Oplus(U_36,U_37,U_38),c_Groups_Oplus__class_Oplus(U_36,U_37,U_39))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_36) ),
    inference(variable_rename,[status(thm)],[f_14_1]) ).

fof(f_14_3,plain,
    ! [U_36,U_37,U_38,U_39] :
      ( c_Orderings_Oord__class_Oless__eq(U_36,U_38,U_39)
      | ~ c_Orderings_Oord__class_Oless__eq(U_36,c_Groups_Oplus__class_Oplus(U_36,U_37,U_38),c_Groups_Oplus__class_Oplus(U_36,U_37,U_39))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_36) ),
    inference(definitional_conversion,[status(esa)],[f_14_2]) ).

cnf(f_14_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_36,U_38,U_39)
    | ~ c_Orderings_Oord__class_Oless__eq(U_36,c_Groups_Oplus__class_Oplus(U_36,U_37,U_38),c_Groups_Oplus__class_Oplus(U_36,U_37,U_39))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_36) ),
    inference(clausify,[status(thm)],[f_14_3]) ).

fof(f_15_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_15_2,plain,
    ! [U_40] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_40,U_40),
    inference(variable_rename,[status(thm)],[f_15_1]) ).

fof(f_15_3,plain,
    ! [U_40] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_40,U_40),
    inference(definitional_conversion,[status(esa)],[f_15_2]) ).

cnf(f_15_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_40,U_40),
    inference(clausify,[status(thm)],[f_15_3]) ).

fof(f_16_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_16_2,plain,
    ! [U_42,U_41] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_42,U_41)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_41,U_42) ),
    inference(variable_rename,[status(thm)],[f_16_1]) ).

fof(f_16_3,plain,
    ! [U_42,U_41] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_42,U_41)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_41,U_42) ),
    inference(definitional_conversion,[status(esa)],[f_16_2]) ).

cnf(f_16_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_42,U_41)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_41,U_42) ),
    inference(clausify,[status(thm)],[f_16_3]) ).

fof(f_17_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_17_2,plain,
    ! [U_44,U_43] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_43,U_44)
      | U_43 != U_44 ),
    inference(variable_rename,[status(thm)],[f_17_1]) ).

fof(f_17_3,plain,
    ! [U_44,U_43] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_43,U_44)
      | U_43 != U_44 ),
    inference(definitional_conversion,[status(esa)],[f_17_2]) ).

cnf(f_17_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_43,U_44)
    | U_43 != U_44 ),
    inference(clausify,[status(thm)],[f_17_3]) ).

fof(f_18_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_18_2,plain,
    ! [U_47,U_46,U_45] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_45,U_47)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_46,U_47)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_45,U_46) ),
    inference(variable_rename,[status(thm)],[f_18_1]) ).

fof(f_18_3,plain,
    ! [U_46,U_45,U_47] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_45,U_47)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_46,U_47)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_45,U_46) ),
    inference(definitional_conversion,[status(esa)],[f_18_2]) ).

cnf(f_18_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_45,U_47)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_46,U_47)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_45,U_46) ),
    inference(clausify,[status(thm)],[f_18_3]) ).

fof(f_19_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_19_2,plain,
    ! [U_49,U_48] :
      ( U_48 = U_49
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_49,U_48)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_48,U_49) ),
    inference(variable_rename,[status(thm)],[f_19_1]) ).

fof(f_19_3,plain,
    ! [U_49,U_48] :
      ( U_48 = U_49
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_49,U_48)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_48,U_49) ),
    inference(definitional_conversion,[status(esa)],[f_19_2]) ).

cnf(f_19_4,plain,
    ( U_48 = U_49
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_49,U_48)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_48,U_49) ),
    inference(clausify,[status(thm)],[f_19_3]) ).

fof(f_20_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_20_2,plain,
    ! [U_51,U_50] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_50,U_51)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_50),U_51) ),
    inference(variable_rename,[status(thm)],[f_20_1]) ).

fof(f_20_3,plain,
    ! [U_51,U_50] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_50,U_51)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_50),U_51) ),
    inference(definitional_conversion,[status(esa)],[f_20_2]) ).

cnf(f_20_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_50,U_51)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_50),U_51) ),
    inference(clausify,[status(thm)],[f_20_3]) ).

fof(f_21_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_21_2,plain,
    ! [U_53,U_52] :
      ( U_52 = c_Nat_OSuc(U_53)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_52,U_53)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_52,c_Nat_OSuc(U_53)) ),
    inference(variable_rename,[status(thm)],[f_21_1]) ).

fof(f_21_3,plain,
    ! [U_53,U_52] :
      ( U_52 = c_Nat_OSuc(U_53)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_52,U_53)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_52,c_Nat_OSuc(U_53)) ),
    inference(definitional_conversion,[status(esa)],[f_21_2]) ).

cnf(f_21_4,plain,
    ( U_52 = c_Nat_OSuc(U_53)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_52,U_53)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_52,c_Nat_OSuc(U_53)) ),
    inference(clausify,[status(thm)],[f_21_3]) ).

fof(f_22_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_22_2,plain,
    ! [U_55,U_54] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_54,c_Nat_OSuc(U_55))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_54,U_55) ),
    inference(variable_rename,[status(thm)],[f_22_1]) ).

fof(f_22_3,plain,
    ! [U_55,U_54] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_54,c_Nat_OSuc(U_55))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_54,U_55) ),
    inference(definitional_conversion,[status(esa)],[f_22_2]) ).

cnf(f_22_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_54,c_Nat_OSuc(U_55))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_54,U_55) ),
    inference(clausify,[status(thm)],[f_22_3]) ).

fof(f_23_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_23_2,plain,
    ! [U_57,U_56] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_56),c_Nat_OSuc(U_57))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_56,U_57) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_56,U_57)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_56),c_Nat_OSuc(U_57)) ) ),
    inference(variable_rename,[status(thm)],[f_23_1]) ).

fof(f_23_3,plain,
    ( ! [U_61,U_59] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_59),c_Nat_OSuc(U_61))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_59,U_61) )
    & ! [U_60,U_58] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_58,U_60)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_58),c_Nat_OSuc(U_60)) ) ),
    inference(miniscope,[status(thm)],[f_23_2]) ).

fof(f_23_4,plain,
    ( ! [U_59,U_61] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_59),c_Nat_OSuc(U_61))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_59,U_61) )
    & ! [U_60,U_58] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_58,U_60)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_58),c_Nat_OSuc(U_60)) ) ),
    inference(definitional_conversion,[status(esa)],[f_23_3]) ).

cnf(f_23_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_58,U_60)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_58),c_Nat_OSuc(U_60)) ),
    inference(clausify,[status(thm)],[f_23_4]) ).

cnf(f_23_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_59),c_Nat_OSuc(U_61))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_59,U_61) ),
    inference(clausify,[status(thm)],[f_23_4]) ).

fof(f_24_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_24_2,plain,
    ! [U_63,U_62] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_62,c_Nat_OSuc(U_63))
        | ( U_62 != c_Nat_OSuc(U_63)
          & ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_62,U_63) ) )
      & ( U_62 = c_Nat_OSuc(U_63)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_62,U_63)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_62,c_Nat_OSuc(U_63)) ) ),
    inference(variable_rename,[status(thm)],[f_24_1]) ).

fof(f_24_3,plain,
    ( ! [U_67,U_65] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_65,c_Nat_OSuc(U_67))
        | ( U_65 != c_Nat_OSuc(U_67)
          & ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_65,U_67) ) )
    & ! [U_66,U_64] :
        ( U_64 = c_Nat_OSuc(U_66)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_64,U_66)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_64,c_Nat_OSuc(U_66)) ) ),
    inference(miniscope,[status(thm)],[f_24_2]) ).

fof(f_24_4,plain,
    ( ! [U_65,U_67] :
        ( U_65 != c_Nat_OSuc(U_67)
        | ~ sP2(U_65,U_67) )
    & ! [U_65,U_67] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_65,U_67)
        | ~ sP2(U_65,U_67) )
    & ! [U_65,U_67] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_65,c_Nat_OSuc(U_67))
        | sP2(U_65,U_67) )
    & ! [U_66,U_64] :
        ( U_64 = c_Nat_OSuc(U_66)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_64,U_66)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_64,c_Nat_OSuc(U_66)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_24_3]) ).

cnf(f_24_5,plain,
    ( U_64 = c_Nat_OSuc(U_66)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_64,U_66)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_64,c_Nat_OSuc(U_66)) ),
    inference(clausify,[status(thm)],[f_24_4]) ).

cnf(f_24_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_65,c_Nat_OSuc(U_67))
    | sP2(U_65,U_67) ),
    inference(clausify,[status(thm)],[f_24_4]) ).

cnf(f_24_7,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_65,U_67)
    | ~ sP2(U_65,U_67) ),
    inference(clausify,[status(thm)],[f_24_4]) ).

cnf(f_24_8,plain,
    ( U_65 != c_Nat_OSuc(U_67)
    | ~ sP2(U_65,U_67) ),
    inference(clausify,[status(thm)],[f_24_4]) ).

fof(f_25_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_25_2,plain,
    ! [U_69,U_68] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_68,U_69)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_69),U_68) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_69),U_68)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_68,U_69) ) ),
    inference(variable_rename,[status(thm)],[f_25_1]) ).

fof(f_25_3,plain,
    ( ! [U_73,U_71] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_71,U_73)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_73),U_71) )
    & ! [U_72,U_70] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_72),U_70)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_70,U_72) ) ),
    inference(miniscope,[status(thm)],[f_25_2]) ).

fof(f_25_4,plain,
    ( ! [U_71,U_73] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_71,U_73)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_73),U_71) )
    & ! [U_70,U_72] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_72),U_70)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_70,U_72) ) ),
    inference(definitional_conversion,[status(esa)],[f_25_3]) ).

cnf(f_25_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_72),U_70)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_70,U_72) ),
    inference(clausify,[status(thm)],[f_25_4]) ).

cnf(f_25_6,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_71,U_73)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_73),U_71) ),
    inference(clausify,[status(thm)],[f_25_4]) ).

fof(f_26_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_26_2,plain,
    ! [U_74] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_74),U_74),
    inference(variable_rename,[status(thm)],[f_26_1]) ).

fof(f_26_3,plain,
    ! [U_74] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_74),U_74),
    inference(definitional_conversion,[status(esa)],[f_26_2]) ).

cnf(f_26_4,plain,
    ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_74),U_74),
    inference(clausify,[status(thm)],[f_26_3]) ).

fof(f_27_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_27_2,plain,
    ! [U_77,U_76,U_75] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_76,U_77)
        & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_75,U_77) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_75,U_76),U_77) ),
    inference(variable_rename,[status(thm)],[f_27_1]) ).

fof(f_27_3,plain,
    ( ! [U_75,U_76,U_77] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_76,U_77)
        | ~ sP3(U_75,U_76,U_77) )
    & ! [U_75,U_76,U_77] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_75,U_77)
        | ~ sP3(U_75,U_76,U_77) )
    & ! [U_75,U_76,U_77] :
        ( sP3(U_75,U_76,U_77)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_75,U_76),U_77) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_27_2]) ).

cnf(f_27_4,plain,
    ( sP3(U_75,U_76,U_77)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_75,U_76),U_77) ),
    inference(clausify,[status(thm)],[f_27_3]) ).

cnf(f_27_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_75,U_77)
    | ~ sP3(U_75,U_76,U_77) ),
    inference(clausify,[status(thm)],[f_27_3]) ).

cnf(f_27_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_76,U_77)
    | ~ sP3(U_75,U_76,U_77) ),
    inference(clausify,[status(thm)],[f_27_3]) ).

fof(f_28_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_28_2,plain,
    ! [U_80,U_79,U_78] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_78,U_80)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_78,U_79),U_80) ),
    inference(variable_rename,[status(thm)],[f_28_1]) ).

fof(f_28_3,plain,
    ! [U_80,U_79,U_78] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_78,U_80)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_78,U_79),U_80) ),
    inference(definitional_conversion,[status(esa)],[f_28_2]) ).

cnf(f_28_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_78,U_80)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_78,U_79),U_80) ),
    inference(clausify,[status(thm)],[f_28_3]) ).

fof(f_29_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_29_2,plain,
    ! [U_83,U_82,U_81] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_82,U_83)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_81,U_82),U_83) ),
    inference(variable_rename,[status(thm)],[f_29_1]) ).

fof(f_29_3,plain,
    ! [U_83,U_82] :
      ( ! [U_81] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_81,U_82),U_83)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_82,U_83) ),
    inference(miniscope,[status(thm)],[f_29_2]) ).

fof(f_29_4,plain,
    ! [U_82,U_81,U_83] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_81,U_82),U_83)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_82,U_83) ),
    inference(definitional_conversion,[status(esa)],[f_29_3]) ).

cnf(f_29_5,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_81,U_82),U_83)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_82,U_83) ),
    inference(clausify,[status(thm)],[f_29_4]) ).

fof(f_30_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_30_2,plain,
    ! [U_87,U_86,U_85,U_84] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_84,U_86),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_85,U_87))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_86,U_87)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_84,U_85) ),
    inference(variable_rename,[status(thm)],[f_30_1]) ).

fof(f_30_3,plain,
    ! [U_85,U_84,U_86,U_87] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_84,U_86),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_85,U_87))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_86,U_87)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_84,U_85) ),
    inference(definitional_conversion,[status(esa)],[f_30_2]) ).

cnf(f_30_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_84,U_86),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_85,U_87))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_86,U_87)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_84,U_85) ),
    inference(clausify,[status(thm)],[f_30_3]) ).

fof(f_31_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_31_2,plain,
    ! [U_90,U_89,U_88] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_88,U_90),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_89,U_90))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_88,U_89) ),
    inference(variable_rename,[status(thm)],[f_31_1]) ).

fof(f_31_3,plain,
    ! [U_88,U_89,U_90] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_88,U_90),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_89,U_90))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_88,U_89) ),
    inference(definitional_conversion,[status(esa)],[f_31_2]) ).

cnf(f_31_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_88,U_90),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_89,U_90))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_88,U_89) ),
    inference(clausify,[status(thm)],[f_31_3]) ).

fof(f_32_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_32_2,plain,
    ! [U_93,U_92,U_91] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_91,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_93,U_92))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_91,U_92) ),
    inference(variable_rename,[status(thm)],[f_32_1]) ).

fof(f_32_3,plain,
    ! [U_92,U_91,U_93] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_91,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_93,U_92))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_91,U_92) ),
    inference(definitional_conversion,[status(esa)],[f_32_2]) ).

cnf(f_32_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_91,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_93,U_92))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_91,U_92) ),
    inference(clausify,[status(thm)],[f_32_3]) ).

fof(f_33_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_33_2,plain,
    ! [U_96,U_95,U_94] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_94,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_95,U_96))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_94,U_95) ),
    inference(variable_rename,[status(thm)],[f_33_1]) ).

fof(f_33_3,plain,
    ! [U_95,U_94,U_96] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_94,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_95,U_96))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_94,U_95) ),
    inference(definitional_conversion,[status(esa)],[f_33_2]) ).

cnf(f_33_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_94,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_95,U_96))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_94,U_95) ),
    inference(clausify,[status(thm)],[f_33_3]) ).

fof(f_34_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_34_2,plain,
    ! [U_99,U_98,U_97] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_97,U_98),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_97,U_99))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_98,U_99) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_98,U_99)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_97,U_98),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_97,U_99)) ) ),
    inference(variable_rename,[status(thm)],[f_34_1]) ).

fof(f_34_3,plain,
    ( ! [U_105,U_103] :
        ( ! [U_101] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_101,U_103),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_101,U_105))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_103,U_105) )
    & ! [U_104,U_102] :
        ( ! [U_100] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_100,U_102),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_100,U_104))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_102,U_104) ) ),
    inference(miniscope,[status(thm)],[f_34_2]) ).

fof(f_34_4,plain,
    ( ! [U_105,U_103,U_101] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_101,U_103),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_101,U_105))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_103,U_105) )
    & ! [U_100,U_102,U_104] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_100,U_102),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_100,U_104))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_102,U_104) ) ),
    inference(definitional_conversion,[status(esa)],[f_34_3]) ).

cnf(f_34_5,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_100,U_102),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_100,U_104))
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_102,U_104) ),
    inference(clausify,[status(thm)],[f_34_4]) ).

cnf(f_34_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_101,U_103),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_101,U_105))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_103,U_105) ),
    inference(clausify,[status(thm)],[f_34_4]) ).

fof(f_35_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_35_2,plain,
    ! [U_109,U_108] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_108,U_109)
        | ! [U_107] : U_109 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_108,U_107) )
      & ( ? [U_106] : U_109 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_108,U_106)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_108,U_109) ) ),
    inference(variable_rename,[status(thm)],[f_35_1]) ).

fof(f_35_3,plain,
    ( ! [U_113,U_111] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_111,U_113)
        | ! [U_107] : U_113 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_111,U_107) )
    & ! [U_112,U_110] :
        ( ? [U_106] : U_112 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_110,U_106)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_110,U_112) ) ),
    inference(miniscope,[status(thm)],[f_35_2]) ).

fof(f_35_4,plain,
    ( ! [U_113,U_111] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_111,U_113)
        | ! [U_107] : U_113 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_111,U_107) )
    & ! [U_112,U_110] :
        ( U_112 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_110,sK2(U_112,U_110))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_110,U_112) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_106,sK2(U_112,U_110))],[f_35_3]) ).

fof(f_35_5,plain,
    ( ! [U_107,U_113,U_111] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_111,U_113)
        | U_113 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_111,U_107) )
    & ! [U_110,U_112] :
        ( U_112 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_110,sK2(U_112,U_110))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_110,U_112) ) ),
    inference(definitional_conversion,[status(esa)],[f_35_4]) ).

cnf(f_35_6,plain,
    ( U_112 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_110,sK2(U_112,U_110))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_110,U_112) ),
    inference(clausify,[status(thm)],[f_35_5]) ).

cnf(f_35_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_111,U_113)
    | U_113 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_111,U_107) ),
    inference(clausify,[status(thm)],[f_35_5]) ).

fof(f_36_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_36_2,plain,
    ! [U_115,U_114] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_114,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_114,U_115)),
    inference(variable_rename,[status(thm)],[f_36_1]) ).

fof(f_36_3,plain,
    ! [U_115,U_114] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_114,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_114,U_115)),
    inference(definitional_conversion,[status(esa)],[f_36_2]) ).

cnf(f_36_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_114,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_114,U_115)),
    inference(clausify,[status(thm)],[f_36_3]) ).

fof(f_37_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_37_2,plain,
    ! [U_117,U_116] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_116,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_117,U_116)),
    inference(variable_rename,[status(thm)],[f_37_1]) ).

fof(f_37_3,plain,
    ! [U_117,U_116] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_116,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_117,U_116)),
    inference(definitional_conversion,[status(esa)],[f_37_2]) ).

cnf(f_37_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_116,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_117,U_116)),
    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_120,U_119,U_118] :
      ( c_Orderings_Oord__class_Oless__eq(U_118,U_120,U_119)
      | c_Orderings_Oord__class_Oless__eq(U_118,U_119,U_120)
      | ~ class_Orderings_Olinorder(U_118) ),
    inference(variable_rename,[status(thm)],[f_38_1]) ).

fof(f_38_3,plain,
    ! [U_120,U_118,U_119] :
      ( c_Orderings_Oord__class_Oless__eq(U_118,U_120,U_119)
      | c_Orderings_Oord__class_Oless__eq(U_118,U_119,U_120)
      | ~ class_Orderings_Olinorder(U_118) ),
    inference(definitional_conversion,[status(esa)],[f_38_2]) ).

cnf(f_38_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_118,U_120,U_119)
    | c_Orderings_Oord__class_Oless__eq(U_118,U_119,U_120)
    | ~ class_Orderings_Olinorder(U_118) ),
    inference(clausify,[status(thm)],[f_38_3]) ).

fof(f_39_1,plain,
    ! [V_x_2,V_ga_2,V_fa_2,T_a,T_b] :
      ( c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,V_x_2),hAPP(V_ga_2,V_x_2))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2,V_ga_2)
      | ~ class_Orderings_Oord(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__funE]) ).

fof(f_39_2,plain,
    ! [U_125,U_124,U_123,U_122,U_121] :
      ( c_Orderings_Oord__class_Oless__eq(U_121,hAPP(U_123,U_125),hAPP(U_124,U_125))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_122,U_121),U_123,U_124)
      | ~ class_Orderings_Oord(U_121) ),
    inference(variable_rename,[status(thm)],[f_39_1]) ).

fof(f_39_3,plain,
    ! [U_121,U_122,U_123,U_124,U_125] :
      ( c_Orderings_Oord__class_Oless__eq(U_121,hAPP(U_123,U_125),hAPP(U_124,U_125))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_122,U_121),U_123,U_124)
      | ~ class_Orderings_Oord(U_121) ),
    inference(definitional_conversion,[status(esa)],[f_39_2]) ).

cnf(f_39_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_121,hAPP(U_123,U_125),hAPP(U_124,U_125))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_122,U_121),U_123,U_124)
    | ~ class_Orderings_Oord(U_121) ),
    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_129,U_128,U_127,U_126] :
      ( c_Orderings_Oord__class_Oless__eq(U_126,U_129,U_128)
      | ~ c_Orderings_Oord__class_Oless__eq(U_126,U_129,U_127)
      | ~ c_Orderings_Oord__class_Oless__eq(U_126,U_127,U_128)
      | ~ class_Orderings_Oorder(U_126) ),
    inference(variable_rename,[status(thm)],[f_40_1]) ).

fof(f_40_3,plain,
    ! [U_129,U_126,U_128,U_127] :
      ( c_Orderings_Oord__class_Oless__eq(U_126,U_129,U_128)
      | ~ c_Orderings_Oord__class_Oless__eq(U_126,U_129,U_127)
      | ~ c_Orderings_Oord__class_Oless__eq(U_126,U_127,U_128)
      | ~ class_Orderings_Oorder(U_126) ),
    inference(definitional_conversion,[status(esa)],[f_40_2]) ).

cnf(f_40_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_126,U_129,U_128)
    | ~ c_Orderings_Oord__class_Oless__eq(U_126,U_129,U_127)
    | ~ c_Orderings_Oord__class_Oless__eq(U_126,U_127,U_128)
    | ~ class_Orderings_Oorder(U_126) ),
    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_132,U_131,U_130] :
      ( U_132 = U_131
      | ~ c_Orderings_Oord__class_Oless__eq(U_130,U_132,U_131)
      | ~ c_Orderings_Oord__class_Oless__eq(U_130,U_131,U_132)
      | ~ class_Orderings_Oorder(U_130) ),
    inference(variable_rename,[status(thm)],[f_41_1]) ).

fof(f_41_3,plain,
    ! [U_130,U_131,U_132] :
      ( U_132 = U_131
      | ~ c_Orderings_Oord__class_Oless__eq(U_130,U_132,U_131)
      | ~ c_Orderings_Oord__class_Oless__eq(U_130,U_131,U_132)
      | ~ class_Orderings_Oorder(U_130) ),
    inference(definitional_conversion,[status(esa)],[f_41_2]) ).

cnf(f_41_4,plain,
    ( U_132 = U_131
    | ~ c_Orderings_Oord__class_Oless__eq(U_130,U_132,U_131)
    | ~ c_Orderings_Oord__class_Oless__eq(U_130,U_131,U_132)
    | ~ class_Orderings_Oorder(U_130) ),
    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_136,U_135,U_134,U_133] :
      ( c_Orderings_Oord__class_Oless__eq(U_133,U_134,U_136)
      | ~ c_Orderings_Oord__class_Oless__eq(U_133,U_135,U_136)
      | ~ c_Orderings_Oord__class_Oless__eq(U_133,U_134,U_135)
      | ~ class_Orderings_Opreorder(U_133) ),
    inference(variable_rename,[status(thm)],[f_42_1]) ).

fof(f_42_3,plain,
    ! [U_133,U_134,U_135,U_136] :
      ( c_Orderings_Oord__class_Oless__eq(U_133,U_134,U_136)
      | ~ c_Orderings_Oord__class_Oless__eq(U_133,U_135,U_136)
      | ~ c_Orderings_Oord__class_Oless__eq(U_133,U_134,U_135)
      | ~ class_Orderings_Opreorder(U_133) ),
    inference(definitional_conversion,[status(esa)],[f_42_2]) ).

cnf(f_42_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_133,U_134,U_136)
    | ~ c_Orderings_Oord__class_Oless__eq(U_133,U_135,U_136)
    | ~ c_Orderings_Oord__class_Oless__eq(U_133,U_134,U_135)
    | ~ class_Orderings_Opreorder(U_133) ),
    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_139,U_138,U_137] :
      ( U_138 = U_139
      | ~ c_Orderings_Oord__class_Oless__eq(U_137,U_139,U_138)
      | ~ c_Orderings_Oord__class_Oless__eq(U_137,U_138,U_139)
      | ~ class_Orderings_Oorder(U_137) ),
    inference(variable_rename,[status(thm)],[f_43_1]) ).

fof(f_43_3,plain,
    ! [U_139,U_138,U_137] :
      ( U_138 = U_139
      | ~ c_Orderings_Oord__class_Oless__eq(U_137,U_139,U_138)
      | ~ c_Orderings_Oord__class_Oless__eq(U_137,U_138,U_139)
      | ~ class_Orderings_Oorder(U_137) ),
    inference(definitional_conversion,[status(esa)],[f_43_2]) ).

cnf(f_43_4,plain,
    ( U_138 = U_139
    | ~ c_Orderings_Oord__class_Oless__eq(U_137,U_139,U_138)
    | ~ c_Orderings_Oord__class_Oless__eq(U_137,U_138,U_139)
    | ~ class_Orderings_Oorder(U_137) ),
    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_143,U_142,U_141,U_140] :
      ( c_Orderings_Oord__class_Oless__eq(U_140,U_143,U_142)
      | U_141 != U_143
      | ~ c_Orderings_Oord__class_Oless__eq(U_140,U_141,U_142)
      | ~ class_Orderings_Oorder(U_140) ),
    inference(variable_rename,[status(thm)],[f_44_1]) ).

fof(f_44_3,plain,
    ! [U_140,U_143,U_142,U_141] :
      ( c_Orderings_Oord__class_Oless__eq(U_140,U_143,U_142)
      | U_141 != U_143
      | ~ c_Orderings_Oord__class_Oless__eq(U_140,U_141,U_142)
      | ~ class_Orderings_Oorder(U_140) ),
    inference(definitional_conversion,[status(esa)],[f_44_2]) ).

cnf(f_44_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_140,U_143,U_142)
    | U_141 != U_143
    | ~ c_Orderings_Oord__class_Oless__eq(U_140,U_141,U_142)
    | ~ class_Orderings_Oorder(U_140) ),
    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_147,U_146,U_145,U_144] :
      ( c_Orderings_Oord__class_Oless__eq(U_144,U_145,U_147)
      | U_146 != U_147
      | ~ c_Orderings_Oord__class_Oless__eq(U_144,U_145,U_146)
      | ~ class_Orderings_Oord(U_144) ),
    inference(variable_rename,[status(thm)],[f_45_1]) ).

fof(f_45_3,plain,
    ! [U_145,U_146,U_147,U_144] :
      ( c_Orderings_Oord__class_Oless__eq(U_144,U_145,U_147)
      | U_146 != U_147
      | ~ c_Orderings_Oord__class_Oless__eq(U_144,U_145,U_146)
      | ~ class_Orderings_Oord(U_144) ),
    inference(definitional_conversion,[status(esa)],[f_45_2]) ).

cnf(f_45_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_144,U_145,U_147)
    | U_146 != U_147
    | ~ c_Orderings_Oord__class_Oless__eq(U_144,U_145,U_146)
    | ~ class_Orderings_Oord(U_144) ),
    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_151,U_150,U_149,U_148] :
      ( c_Orderings_Oord__class_Oless__eq(U_148,U_151,U_149)
      | ~ c_Orderings_Oord__class_Oless__eq(U_148,U_151,U_150)
      | U_149 != U_150
      | ~ class_Orderings_Oorder(U_148) ),
    inference(variable_rename,[status(thm)],[f_46_1]) ).

fof(f_46_3,plain,
    ! [U_150,U_151,U_148,U_149] :
      ( c_Orderings_Oord__class_Oless__eq(U_148,U_151,U_149)
      | ~ c_Orderings_Oord__class_Oless__eq(U_148,U_151,U_150)
      | U_149 != U_150
      | ~ class_Orderings_Oorder(U_148) ),
    inference(definitional_conversion,[status(esa)],[f_46_2]) ).

cnf(f_46_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_148,U_151,U_149)
    | ~ c_Orderings_Oord__class_Oless__eq(U_148,U_151,U_150)
    | U_149 != U_150
    | ~ class_Orderings_Oorder(U_148) ),
    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_155,U_154,U_153,U_152] :
      ( c_Orderings_Oord__class_Oless__eq(U_152,U_153,U_155)
      | ~ c_Orderings_Oord__class_Oless__eq(U_152,U_154,U_155)
      | U_153 != U_154
      | ~ class_Orderings_Oord(U_152) ),
    inference(variable_rename,[status(thm)],[f_47_1]) ).

fof(f_47_3,plain,
    ! [U_153,U_154,U_155,U_152] :
      ( c_Orderings_Oord__class_Oless__eq(U_152,U_153,U_155)
      | ~ c_Orderings_Oord__class_Oless__eq(U_152,U_154,U_155)
      | U_153 != U_154
      | ~ class_Orderings_Oord(U_152) ),
    inference(definitional_conversion,[status(esa)],[f_47_2]) ).

cnf(f_47_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_152,U_153,U_155)
    | ~ c_Orderings_Oord__class_Oless__eq(U_152,U_154,U_155)
    | U_153 != U_154
    | ~ class_Orderings_Oord(U_152) ),
    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_158,U_157,U_156] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_156,U_158,U_157)
          | U_158 != U_157 )
        & ( U_158 = U_157
          | ~ c_Orderings_Oord__class_Oless__eq(U_156,U_158,U_157) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(U_156,U_157,U_158)
      | ~ class_Orderings_Oorder(U_156) ),
    inference(variable_rename,[status(thm)],[f_48_1]) ).

fof(f_48_3,plain,
    ( ! [U_158,U_156,U_157] :
        ( c_Orderings_Oord__class_Oless__eq(U_156,U_158,U_157)
        | U_158 != U_157
        | ~ sP4(U_158,U_156,U_157) )
    & ! [U_158,U_156,U_157] :
        ( U_158 = U_157
        | ~ c_Orderings_Oord__class_Oless__eq(U_156,U_158,U_157)
        | ~ sP4(U_158,U_156,U_157) )
    & ! [U_158,U_156,U_157] :
        ( sP4(U_158,U_156,U_157)
        | ~ c_Orderings_Oord__class_Oless__eq(U_156,U_157,U_158)
        | ~ class_Orderings_Oorder(U_156) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4])],[f_48_2]) ).

cnf(f_48_4,plain,
    ( sP4(U_158,U_156,U_157)
    | ~ c_Orderings_Oord__class_Oless__eq(U_156,U_157,U_158)
    | ~ class_Orderings_Oorder(U_156) ),
    inference(clausify,[status(thm)],[f_48_3]) ).

cnf(f_48_5,plain,
    ( U_158 = U_157
    | ~ c_Orderings_Oord__class_Oless__eq(U_156,U_158,U_157)
    | ~ sP4(U_158,U_156,U_157) ),
    inference(clausify,[status(thm)],[f_48_3]) ).

cnf(f_48_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_156,U_158,U_157)
    | U_158 != U_157
    | ~ sP4(U_158,U_156,U_157) ),
    inference(clausify,[status(thm)],[f_48_3]) ).

fof(f_49_1,plain,
    ! [V_x_2,V_ga_2,V_fa_2,T_a,T_b] :
      ( c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,V_x_2),hAPP(V_ga_2,V_x_2))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2,V_ga_2)
      | ~ class_Orderings_Oord(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__funD]) ).

fof(f_49_2,plain,
    ! [U_163,U_162,U_161,U_160,U_159] :
      ( c_Orderings_Oord__class_Oless__eq(U_159,hAPP(U_161,U_163),hAPP(U_162,U_163))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_160,U_159),U_161,U_162)
      | ~ class_Orderings_Oord(U_159) ),
    inference(variable_rename,[status(thm)],[f_49_1]) ).

fof(f_49_3,plain,
    ! [U_162,U_160,U_159,U_163,U_161] :
      ( c_Orderings_Oord__class_Oless__eq(U_159,hAPP(U_161,U_163),hAPP(U_162,U_163))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_160,U_159),U_161,U_162)
      | ~ class_Orderings_Oord(U_159) ),
    inference(definitional_conversion,[status(esa)],[f_49_2]) ).

cnf(f_49_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_159,hAPP(U_161,U_163),hAPP(U_162,U_163))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_160,U_159),U_161,U_162)
    | ~ class_Orderings_Oord(U_159) ),
    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_166,U_165,U_164] :
      ( c_Orderings_Oord__class_Oless__eq(U_164,U_165,U_166)
      | U_165 != U_166
      | ~ class_Orderings_Opreorder(U_164) ),
    inference(variable_rename,[status(thm)],[f_50_1]) ).

fof(f_50_3,plain,
    ! [U_165,U_166,U_164] :
      ( c_Orderings_Oord__class_Oless__eq(U_164,U_165,U_166)
      | U_165 != U_166
      | ~ class_Orderings_Opreorder(U_164) ),
    inference(definitional_conversion,[status(esa)],[f_50_2]) ).

cnf(f_50_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_164,U_165,U_166)
    | U_165 != U_166
    | ~ class_Orderings_Opreorder(U_164) ),
    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_169,U_168,U_167] :
      ( ( ( U_168 = U_169
          | ~ c_Orderings_Oord__class_Oless__eq(U_167,U_169,U_168)
          | ~ c_Orderings_Oord__class_Oless__eq(U_167,U_168,U_169) )
        & ( ( c_Orderings_Oord__class_Oless__eq(U_167,U_169,U_168)
            & c_Orderings_Oord__class_Oless__eq(U_167,U_168,U_169) )
          | U_168 != U_169 ) )
      | ~ class_Orderings_Oorder(U_167) ),
    inference(variable_rename,[status(thm)],[f_51_1]) ).

fof(f_51_3,plain,
    ( ! [U_168,U_167,U_169] :
        ( c_Orderings_Oord__class_Oless__eq(U_167,U_169,U_168)
        | ~ sP5(U_168,U_167,U_169) )
    & ! [U_168,U_167,U_169] :
        ( c_Orderings_Oord__class_Oless__eq(U_167,U_168,U_169)
        | ~ sP5(U_168,U_167,U_169) )
    & ! [U_168,U_167,U_169] :
        ( U_168 = U_169
        | ~ c_Orderings_Oord__class_Oless__eq(U_167,U_169,U_168)
        | ~ c_Orderings_Oord__class_Oless__eq(U_167,U_168,U_169)
        | ~ sP6(U_168,U_167,U_169) )
    & ! [U_168,U_167,U_169] :
        ( sP5(U_168,U_167,U_169)
        | U_168 != U_169
        | ~ sP6(U_168,U_167,U_169) )
    & ! [U_168,U_167,U_169] :
        ( sP6(U_168,U_167,U_169)
        | ~ class_Orderings_Oorder(U_167) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5,sP6])],[f_51_2]) ).

cnf(f_51_4,plain,
    ( sP6(U_168,U_167,U_169)
    | ~ class_Orderings_Oorder(U_167) ),
    inference(clausify,[status(thm)],[f_51_3]) ).

cnf(f_51_5,plain,
    ( sP5(U_168,U_167,U_169)
    | U_168 != U_169
    | ~ sP6(U_168,U_167,U_169) ),
    inference(clausify,[status(thm)],[f_51_3]) ).

cnf(f_51_6,plain,
    ( U_168 = U_169
    | ~ c_Orderings_Oord__class_Oless__eq(U_167,U_169,U_168)
    | ~ c_Orderings_Oord__class_Oless__eq(U_167,U_168,U_169)
    | ~ sP6(U_168,U_167,U_169) ),
    inference(clausify,[status(thm)],[f_51_3]) ).

cnf(f_51_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_167,U_168,U_169)
    | ~ sP5(U_168,U_167,U_169) ),
    inference(clausify,[status(thm)],[f_51_3]) ).

cnf(f_51_8,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_167,U_169,U_168)
    | ~ sP5(U_168,U_167,U_169) ),
    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_172,U_171,U_170] :
      ( c_Orderings_Oord__class_Oless__eq(U_170,U_172,U_171)
      | c_Orderings_Oord__class_Oless__eq(U_170,U_171,U_172)
      | ~ class_Orderings_Olinorder(U_170) ),
    inference(variable_rename,[status(thm)],[f_52_1]) ).

fof(f_52_3,plain,
    ! [U_171,U_170,U_172] :
      ( c_Orderings_Oord__class_Oless__eq(U_170,U_172,U_171)
      | c_Orderings_Oord__class_Oless__eq(U_170,U_171,U_172)
      | ~ class_Orderings_Olinorder(U_170) ),
    inference(definitional_conversion,[status(esa)],[f_52_2]) ).

cnf(f_52_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_170,U_172,U_171)
    | c_Orderings_Oord__class_Oless__eq(U_170,U_171,U_172)
    | ~ class_Orderings_Olinorder(U_170) ),
    inference(clausify,[status(thm)],[f_52_3]) ).

fof(f_53_1,plain,
    ! [V_ga_2,V_fa_2,T_a,T_b] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2,V_ga_2)
          | ? [B_x] : ~ c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,B_x),hAPP(V_ga_2,B_x)) )
        & ( ! [B_x] : c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,B_x),hAPP(V_ga_2,B_x))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2,V_ga_2) ) )
      | ~ class_Orderings_Oord(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__fun__def]) ).

fof(f_53_2,plain,
    ! [U_178,U_177,U_176,U_175] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_176,U_175),U_177,U_178)
          | ? [U_174] : ~ c_Orderings_Oord__class_Oless__eq(U_175,hAPP(U_177,U_174),hAPP(U_178,U_174)) )
        & ( ! [U_173] : c_Orderings_Oord__class_Oless__eq(U_175,hAPP(U_177,U_173),hAPP(U_178,U_173))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_176,U_175),U_177,U_178) ) )
      | ~ class_Orderings_Oord(U_175) ),
    inference(variable_rename,[status(thm)],[f_53_1]) ).

fof(f_53_3,plain,
    ! [U_178,U_177,U_176,U_175] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_176,U_175),U_177,U_178)
          | ~ c_Orderings_Oord__class_Oless__eq(U_175,hAPP(U_177,sK3(U_178,U_177,U_176,U_175)),hAPP(U_178,sK3(U_178,U_177,U_176,U_175))) )
        & ( ! [U_173] : c_Orderings_Oord__class_Oless__eq(U_175,hAPP(U_177,U_173),hAPP(U_178,U_173))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_176,U_175),U_177,U_178) ) )
      | ~ class_Orderings_Oord(U_175) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_174,sK3(U_178,U_177,U_176,U_175))],[f_53_2]) ).

fof(f_53_4,plain,
    ( ! [U_177,U_178,U_173,U_176,U_175] :
        ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_176,U_175),U_177,U_178)
        | ~ c_Orderings_Oord__class_Oless__eq(U_175,hAPP(U_177,sK3(U_178,U_177,U_176,U_175)),hAPP(U_178,sK3(U_178,U_177,U_176,U_175)))
        | ~ sP7(U_177,U_178,U_173,U_176,U_175) )
    & ! [U_177,U_178,U_173,U_176,U_175] :
        ( c_Orderings_Oord__class_Oless__eq(U_175,hAPP(U_177,U_173),hAPP(U_178,U_173))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_176,U_175),U_177,U_178)
        | ~ sP7(U_177,U_178,U_173,U_176,U_175) )
    & ! [U_177,U_178,U_173,U_176,U_175] :
        ( sP7(U_177,U_178,U_173,U_176,U_175)
        | ~ class_Orderings_Oord(U_175) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_53_3]) ).

cnf(f_53_5,plain,
    ( sP7(U_177,U_178,U_173,U_176,U_175)
    | ~ class_Orderings_Oord(U_175) ),
    inference(clausify,[status(thm)],[f_53_4]) ).

cnf(f_53_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_175,hAPP(U_177,U_173),hAPP(U_178,U_173))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_176,U_175),U_177,U_178)
    | ~ sP7(U_177,U_178,U_173,U_176,U_175) ),
    inference(clausify,[status(thm)],[f_53_4]) ).

cnf(f_53_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_176,U_175),U_177,U_178)
    | ~ c_Orderings_Oord__class_Oless__eq(U_175,hAPP(U_177,sK3(U_178,U_177,U_176,U_175)),hAPP(U_178,sK3(U_178,U_177,U_176,U_175)))
    | ~ sP7(U_177,U_178,U_173,U_176,U_175) ),
    inference(clausify,[status(thm)],[f_53_4]) ).

fof(f_54_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_54_2,plain,
    ! [U_182,U_181,U_180,U_179] :
      ( U_180 = U_182
      | c_Groups_Oplus__class_Oplus(U_179,U_180,U_181) != c_Groups_Oplus__class_Oplus(U_179,U_182,U_181)
      | ~ class_Groups_Ocancel__semigroup__add(U_179) ),
    inference(variable_rename,[status(thm)],[f_54_1]) ).

fof(f_54_3,plain,
    ! [U_181,U_179,U_180,U_182] :
      ( U_180 = U_182
      | c_Groups_Oplus__class_Oplus(U_179,U_180,U_181) != c_Groups_Oplus__class_Oplus(U_179,U_182,U_181)
      | ~ class_Groups_Ocancel__semigroup__add(U_179) ),
    inference(definitional_conversion,[status(esa)],[f_54_2]) ).

cnf(f_54_4,plain,
    ( U_180 = U_182
    | c_Groups_Oplus__class_Oplus(U_179,U_180,U_181) != c_Groups_Oplus__class_Oplus(U_179,U_182,U_181)
    | ~ class_Groups_Ocancel__semigroup__add(U_179) ),
    inference(clausify,[status(thm)],[f_54_3]) ).

fof(f_55_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_55_2,plain,
    ! [U_186,U_185,U_184,U_183] :
      ( U_185 = U_186
      | c_Groups_Oplus__class_Oplus(U_183,U_184,U_185) != c_Groups_Oplus__class_Oplus(U_183,U_184,U_186)
      | ~ class_Groups_Ocancel__ab__semigroup__add(U_183) ),
    inference(variable_rename,[status(thm)],[f_55_1]) ).

fof(f_55_3,plain,
    ! [U_183,U_184,U_185,U_186] :
      ( U_185 = U_186
      | c_Groups_Oplus__class_Oplus(U_183,U_184,U_185) != c_Groups_Oplus__class_Oplus(U_183,U_184,U_186)
      | ~ class_Groups_Ocancel__ab__semigroup__add(U_183) ),
    inference(definitional_conversion,[status(esa)],[f_55_2]) ).

cnf(f_55_4,plain,
    ( U_185 = U_186
    | c_Groups_Oplus__class_Oplus(U_183,U_184,U_185) != c_Groups_Oplus__class_Oplus(U_183,U_184,U_186)
    | ~ class_Groups_Ocancel__ab__semigroup__add(U_183) ),
    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__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq]) ).

fof(f_56_2,plain,
    ! [U_190,U_189,U_188,U_187] :
      ( U_189 = U_190
      | c_Groups_Oplus__class_Oplus(U_187,U_188,U_189) != c_Groups_Oplus__class_Oplus(U_187,U_188,U_190)
      | ~ class_Groups_Ocancel__semigroup__add(U_187) ),
    inference(variable_rename,[status(thm)],[f_56_1]) ).

fof(f_56_3,plain,
    ! [U_189,U_188,U_187,U_190] :
      ( U_189 = U_190
      | c_Groups_Oplus__class_Oplus(U_187,U_188,U_189) != c_Groups_Oplus__class_Oplus(U_187,U_188,U_190)
      | ~ class_Groups_Ocancel__semigroup__add(U_187) ),
    inference(definitional_conversion,[status(esa)],[f_56_2]) ).

cnf(f_56_4,plain,
    ( U_189 = U_190
    | c_Groups_Oplus__class_Oplus(U_187,U_188,U_189) != c_Groups_Oplus__class_Oplus(U_187,U_188,U_190)
    | ~ class_Groups_Ocancel__semigroup__add(U_187) ),
    inference(clausify,[status(thm)],[f_56_3]) ).

fof(f_57_1,plain,
    ! [V_c_2,V_a_2,V_b_2,T_a] :
      ( ( ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2) = c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2)
          | V_b_2 != V_c_2 )
        & ( V_b_2 = V_c_2
          | c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2) != c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2) ) )
      | ~ class_Groups_Ocancel__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__right__cancel]) ).

fof(f_57_2,plain,
    ! [U_194,U_193,U_192,U_191] :
      ( ( ( c_Groups_Oplus__class_Oplus(U_191,U_192,U_193) = c_Groups_Oplus__class_Oplus(U_191,U_194,U_193)
          | U_192 != U_194 )
        & ( U_192 = U_194
          | c_Groups_Oplus__class_Oplus(U_191,U_192,U_193) != c_Groups_Oplus__class_Oplus(U_191,U_194,U_193) ) )
      | ~ class_Groups_Ocancel__semigroup__add(U_191) ),
    inference(variable_rename,[status(thm)],[f_57_1]) ).

fof(f_57_3,plain,
    ( ! [U_193,U_192,U_191,U_194] :
        ( c_Groups_Oplus__class_Oplus(U_191,U_192,U_193) = c_Groups_Oplus__class_Oplus(U_191,U_194,U_193)
        | U_192 != U_194
        | ~ sP8(U_193,U_192,U_191,U_194) )
    & ! [U_193,U_192,U_191,U_194] :
        ( U_192 = U_194
        | c_Groups_Oplus__class_Oplus(U_191,U_192,U_193) != c_Groups_Oplus__class_Oplus(U_191,U_194,U_193)
        | ~ sP8(U_193,U_192,U_191,U_194) )
    & ! [U_193,U_192,U_191,U_194] :
        ( sP8(U_193,U_192,U_191,U_194)
        | ~ class_Groups_Ocancel__semigroup__add(U_191) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8])],[f_57_2]) ).

cnf(f_57_4,plain,
    ( sP8(U_193,U_192,U_191,U_194)
    | ~ class_Groups_Ocancel__semigroup__add(U_191) ),
    inference(clausify,[status(thm)],[f_57_3]) ).

cnf(f_57_5,plain,
    ( U_192 = U_194
    | c_Groups_Oplus__class_Oplus(U_191,U_192,U_193) != c_Groups_Oplus__class_Oplus(U_191,U_194,U_193)
    | ~ sP8(U_193,U_192,U_191,U_194) ),
    inference(clausify,[status(thm)],[f_57_3]) ).

cnf(f_57_6,plain,
    ( c_Groups_Oplus__class_Oplus(U_191,U_192,U_193) = c_Groups_Oplus__class_Oplus(U_191,U_194,U_193)
    | U_192 != U_194
    | ~ sP8(U_193,U_192,U_191,U_194) ),
    inference(clausify,[status(thm)],[f_57_3]) ).

fof(f_58_1,plain,
    ! [V_c_2,V_b_2,V_a_2,T_a] :
      ( ( ( c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2)
          | V_b_2 != V_c_2 )
        & ( V_b_2 = V_c_2
          | c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2) != c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2) ) )
      | ~ class_Groups_Ocancel__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__left__cancel]) ).

fof(f_58_2,plain,
    ! [U_198,U_197,U_196,U_195] :
      ( ( ( c_Groups_Oplus__class_Oplus(U_195,U_196,U_197) = c_Groups_Oplus__class_Oplus(U_195,U_196,U_198)
          | U_197 != U_198 )
        & ( U_197 = U_198
          | c_Groups_Oplus__class_Oplus(U_195,U_196,U_197) != c_Groups_Oplus__class_Oplus(U_195,U_196,U_198) ) )
      | ~ class_Groups_Ocancel__semigroup__add(U_195) ),
    inference(variable_rename,[status(thm)],[f_58_1]) ).

fof(f_58_3,plain,
    ( ! [U_195,U_198,U_196,U_197] :
        ( c_Groups_Oplus__class_Oplus(U_195,U_196,U_197) = c_Groups_Oplus__class_Oplus(U_195,U_196,U_198)
        | U_197 != U_198
        | ~ sP9(U_195,U_198,U_196,U_197) )
    & ! [U_195,U_198,U_196,U_197] :
        ( U_197 = U_198
        | c_Groups_Oplus__class_Oplus(U_195,U_196,U_197) != c_Groups_Oplus__class_Oplus(U_195,U_196,U_198)
        | ~ sP9(U_195,U_198,U_196,U_197) )
    & ! [U_195,U_198,U_196,U_197] :
        ( sP9(U_195,U_198,U_196,U_197)
        | ~ class_Groups_Ocancel__semigroup__add(U_195) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP9])],[f_58_2]) ).

cnf(f_58_4,plain,
    ( sP9(U_195,U_198,U_196,U_197)
    | ~ class_Groups_Ocancel__semigroup__add(U_195) ),
    inference(clausify,[status(thm)],[f_58_3]) ).

cnf(f_58_5,plain,
    ( U_197 = U_198
    | c_Groups_Oplus__class_Oplus(U_195,U_196,U_197) != c_Groups_Oplus__class_Oplus(U_195,U_196,U_198)
    | ~ sP9(U_195,U_198,U_196,U_197) ),
    inference(clausify,[status(thm)],[f_58_3]) ).

cnf(f_58_6,plain,
    ( c_Groups_Oplus__class_Oplus(U_195,U_196,U_197) = c_Groups_Oplus__class_Oplus(U_195,U_196,U_198)
    | U_197 != U_198
    | ~ sP9(U_195,U_198,U_196,U_197) ),
    inference(clausify,[status(thm)],[f_58_3]) ).

fof(f_59_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_59_2,plain,
    ! [U_202,U_201,U_200,U_199] :
      ( c_Groups_Oplus__class_Oplus(U_199,c_Groups_Oplus__class_Oplus(U_199,U_200,U_201),U_202) = c_Groups_Oplus__class_Oplus(U_199,U_200,c_Groups_Oplus__class_Oplus(U_199,U_201,U_202))
      | ~ class_Groups_Oab__semigroup__add(U_199) ),
    inference(variable_rename,[status(thm)],[f_59_1]) ).

fof(f_59_3,plain,
    ! [U_202,U_200,U_199,U_201] :
      ( c_Groups_Oplus__class_Oplus(U_199,c_Groups_Oplus__class_Oplus(U_199,U_200,U_201),U_202) = c_Groups_Oplus__class_Oplus(U_199,U_200,c_Groups_Oplus__class_Oplus(U_199,U_201,U_202))
      | ~ class_Groups_Oab__semigroup__add(U_199) ),
    inference(definitional_conversion,[status(esa)],[f_59_2]) ).

cnf(f_59_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_199,c_Groups_Oplus__class_Oplus(U_199,U_200,U_201),U_202) = c_Groups_Oplus__class_Oplus(U_199,U_200,c_Groups_Oplus__class_Oplus(U_199,U_201,U_202))
    | ~ class_Groups_Oab__semigroup__add(U_199) ),
    inference(clausify,[status(thm)],[f_59_3]) ).

fof(f_60_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_60_2,plain,
    ! [U_204,U_203] :
      ( U_203 = U_204
      | c_Nat_OSuc(U_203) != c_Nat_OSuc(U_204) ),
    inference(variable_rename,[status(thm)],[f_60_1]) ).

fof(f_60_3,plain,
    ! [U_204,U_203] :
      ( U_203 = U_204
      | c_Nat_OSuc(U_203) != c_Nat_OSuc(U_204) ),
    inference(definitional_conversion,[status(esa)],[f_60_2]) ).

cnf(f_60_4,plain,
    ( U_203 = U_204
    | c_Nat_OSuc(U_203) != c_Nat_OSuc(U_204) ),
    inference(clausify,[status(thm)],[f_60_3]) ).

fof(f_61_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_61_2,plain,
    ! [U_206,U_205] :
      ( ( c_Nat_OSuc(U_205) = c_Nat_OSuc(U_206)
        | U_205 != U_206 )
      & ( U_205 = U_206
        | c_Nat_OSuc(U_205) != c_Nat_OSuc(U_206) ) ),
    inference(variable_rename,[status(thm)],[f_61_1]) ).

fof(f_61_3,plain,
    ( ! [U_210,U_208] :
        ( c_Nat_OSuc(U_208) = c_Nat_OSuc(U_210)
        | U_208 != U_210 )
    & ! [U_209,U_207] :
        ( U_207 = U_209
        | c_Nat_OSuc(U_207) != c_Nat_OSuc(U_209) ) ),
    inference(miniscope,[status(thm)],[f_61_2]) ).

fof(f_61_4,plain,
    ( ! [U_210,U_208] :
        ( c_Nat_OSuc(U_208) = c_Nat_OSuc(U_210)
        | U_208 != U_210 )
    & ! [U_209,U_207] :
        ( U_207 = U_209
        | c_Nat_OSuc(U_207) != c_Nat_OSuc(U_209) ) ),
    inference(definitional_conversion,[status(esa)],[f_61_3]) ).

cnf(f_61_5,plain,
    ( U_207 = U_209
    | c_Nat_OSuc(U_207) != c_Nat_OSuc(U_209) ),
    inference(clausify,[status(thm)],[f_61_4]) ).

cnf(f_61_6,plain,
    ( c_Nat_OSuc(U_208) = c_Nat_OSuc(U_210)
    | U_208 != U_210 ),
    inference(clausify,[status(thm)],[f_61_4]) ).

fof(f_62_1,plain,
    ! [V_n] : c_Nat_OSuc(V_n) != V_n,
    inference(fof_nnf,[status(thm)],[fact_Suc__n__not__n]) ).

fof(f_62_2,plain,
    ! [U_211] : c_Nat_OSuc(U_211) != U_211,
    inference(variable_rename,[status(thm)],[f_62_1]) ).

fof(f_62_3,plain,
    ! [U_211] : c_Nat_OSuc(U_211) != U_211,
    inference(definitional_conversion,[status(esa)],[f_62_2]) ).

cnf(f_62_4,plain,
    c_Nat_OSuc(U_211) != U_211,
    inference(clausify,[status(thm)],[f_62_3]) ).

fof(f_63_1,plain,
    ! [V_n] : V_n != c_Nat_OSuc(V_n),
    inference(fof_nnf,[status(thm)],[fact_n__not__Suc__n]) ).

fof(f_63_2,plain,
    ! [U_212] : U_212 != c_Nat_OSuc(U_212),
    inference(variable_rename,[status(thm)],[f_63_1]) ).

fof(f_63_3,plain,
    ! [U_212] : U_212 != c_Nat_OSuc(U_212),
    inference(definitional_conversion,[status(esa)],[f_63_2]) ).

cnf(f_63_4,plain,
    U_212 != c_Nat_OSuc(U_212),
    inference(clausify,[status(thm)],[f_63_3]) ).

fof(f_64_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_64_2,plain,
    ! [U_215,U_214,U_213] :
      ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_213,U_214) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_215,U_214)
        | U_213 != U_215 )
      & ( U_213 = U_215
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_213,U_214) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_215,U_214) ) ),
    inference(variable_rename,[status(thm)],[f_64_1]) ).

fof(f_64_3,plain,
    ( ! [U_221,U_219,U_217] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_217,U_219) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_221,U_219)
        | U_217 != U_221 )
    & ! [U_220,U_218,U_216] :
        ( U_216 = U_220
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_216,U_218) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_220,U_218) ) ),
    inference(miniscope,[status(thm)],[f_64_2]) ).

fof(f_64_4,plain,
    ( ! [U_219,U_221,U_217] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_217,U_219) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_221,U_219)
        | U_217 != U_221 )
    & ! [U_216,U_218,U_220] :
        ( U_216 = U_220
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_216,U_218) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_220,U_218) ) ),
    inference(definitional_conversion,[status(esa)],[f_64_3]) ).

cnf(f_64_5,plain,
    ( U_216 = U_220
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_216,U_218) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_220,U_218) ),
    inference(clausify,[status(thm)],[f_64_4]) ).

cnf(f_64_6,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_217,U_219) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_221,U_219)
    | U_217 != U_221 ),
    inference(clausify,[status(thm)],[f_64_4]) ).

fof(f_65_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_65_2,plain,
    ! [U_224,U_223,U_222] :
      ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_222,U_223) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_222,U_224)
        | U_223 != U_224 )
      & ( U_223 = U_224
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_222,U_223) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_222,U_224) ) ),
    inference(variable_rename,[status(thm)],[f_65_1]) ).

fof(f_65_3,plain,
    ( ! [U_230,U_228] :
        ( ! [U_226] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_226,U_228) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_226,U_230)
        | U_228 != U_230 )
    & ! [U_229,U_227] :
        ( ! [U_225] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_225,U_227) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_225,U_229)
        | U_227 = U_229 ) ),
    inference(miniscope,[status(thm)],[f_65_2]) ).

fof(f_65_4,plain,
    ( ! [U_228,U_226,U_230] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_226,U_228) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_226,U_230)
        | U_228 != U_230 )
    & ! [U_225,U_227,U_229] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_225,U_227) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_225,U_229)
        | U_227 = U_229 ) ),
    inference(definitional_conversion,[status(esa)],[f_65_3]) ).

cnf(f_65_5,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_225,U_227) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_225,U_229)
    | U_227 = U_229 ),
    inference(clausify,[status(thm)],[f_65_4]) ).

cnf(f_65_6,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_226,U_228) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_226,U_230)
    | U_228 != U_230 ),
    inference(clausify,[status(thm)],[f_65_4]) ).

fof(f_66_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_66_2,plain,
    ! [U_233,U_232,U_231] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_231,U_232),U_233) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_231,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_232,U_233)),
    inference(variable_rename,[status(thm)],[f_66_1]) ).

fof(f_66_3,plain,
    ! [U_233,U_232,U_231] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_231,U_232),U_233) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_231,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_232,U_233)),
    inference(definitional_conversion,[status(esa)],[f_66_2]) ).

cnf(f_66_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_231,U_232),U_233) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_231,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_232,U_233)),
    inference(clausify,[status(thm)],[f_66_3]) ).

fof(f_67_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_67_2,plain,
    ! [U_236,U_235,U_234] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_234,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_235,U_236)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_235,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_234,U_236)),
    inference(variable_rename,[status(thm)],[f_67_1]) ).

fof(f_67_3,plain,
    ! [U_235,U_234,U_236] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_234,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_235,U_236)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_235,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_234,U_236)),
    inference(definitional_conversion,[status(esa)],[f_67_2]) ).

cnf(f_67_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_234,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_235,U_236)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_235,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_234,U_236)),
    inference(clausify,[status(thm)],[f_67_3]) ).

fof(f_68_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_68_2,plain,
    ! [U_238,U_237] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_237,U_238) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_238,U_237),
    inference(variable_rename,[status(thm)],[f_68_1]) ).

fof(f_68_3,plain,
    ! [U_238,U_237] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_237,U_238) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_238,U_237),
    inference(definitional_conversion,[status(esa)],[f_68_2]) ).

cnf(f_68_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_237,U_238) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_238,U_237),
    inference(clausify,[status(thm)],[f_68_3]) ).

fof(f_69_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_real__of__nat__le__iff]) ).

fof(f_69_2,plain,
    ! [U_240,U_239] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_239),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_240))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_239,U_240) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_239,U_240)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_239),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_240)) ) ),
    inference(variable_rename,[status(thm)],[f_69_1]) ).

fof(f_69_3,plain,
    ( ! [U_244,U_242] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_242),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_244))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_242,U_244) )
    & ! [U_243,U_241] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_241,U_243)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_241),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_243)) ) ),
    inference(miniscope,[status(thm)],[f_69_2]) ).

fof(f_69_4,plain,
    ( ! [U_244,U_242] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_242),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_244))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_242,U_244) )
    & ! [U_243,U_241] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_241,U_243)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_241),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_243)) ) ),
    inference(definitional_conversion,[status(esa)],[f_69_3]) ).

cnf(f_69_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_241,U_243)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_241),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_243)) ),
    inference(clausify,[status(thm)],[f_69_4]) ).

cnf(f_69_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_242),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_244))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_242,U_244) ),
    inference(clausify,[status(thm)],[f_69_4]) ).

fof(f_70_1,plain,
    ! [V_n_2,V_fa_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,hAPP(V_fa_2,V_n_2))
      | ~ c_SEQ_Osubseq(V_fa_2) ),
    inference(fof_nnf,[status(thm)],[fact_seq__suble]) ).

fof(f_70_2,plain,
    ! [U_246,U_245] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_246,hAPP(U_245,U_246))
      | ~ c_SEQ_Osubseq(U_245) ),
    inference(variable_rename,[status(thm)],[f_70_1]) ).

fof(f_70_3,plain,
    ! [U_246,U_245] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_246,hAPP(U_245,U_246))
      | ~ c_SEQ_Osubseq(U_245) ),
    inference(definitional_conversion,[status(esa)],[f_70_2]) ).

cnf(f_70_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_246,hAPP(U_245,U_246))
    | ~ c_SEQ_Osubseq(U_245) ),
    inference(clausify,[status(thm)],[f_70_3]) ).

fof(f_71_1,plain,
    ! [V_n,V_m] : hAPP(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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)),
    inference(fof_nnf,[status(thm)],[fact_real__of__nat__add]) ).

fof(f_71_2,plain,
    ! [U_248,U_247] : hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_247,U_248)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_247),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_248)),
    inference(variable_rename,[status(thm)],[f_71_1]) ).

fof(f_71_3,plain,
    ! [U_247,U_248] : hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_247,U_248)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_247),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_248)),
    inference(definitional_conversion,[status(esa)],[f_71_2]) ).

cnf(f_71_4,plain,
    hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_247,U_248)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_247),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_248)),
    inference(clausify,[status(thm)],[f_71_3]) ).

fof(f_72_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_72_2,plain,
    ! [U_251,U_250,U_249] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_249,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_251,U_250))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_249,U_250) ),
    inference(variable_rename,[status(thm)],[f_72_1]) ).

fof(f_72_3,plain,
    ! [U_251,U_250,U_249] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_249,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_251,U_250))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_249,U_250) ),
    inference(definitional_conversion,[status(esa)],[f_72_2]) ).

cnf(f_72_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_249,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_251,U_250))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_249,U_250) ),
    inference(clausify,[status(thm)],[f_72_3]) ).

fof(f_73_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_73_2,plain,
    ! [U_254,U_253,U_252] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_252,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_253,U_254))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_252,U_253) ),
    inference(variable_rename,[status(thm)],[f_73_1]) ).

fof(f_73_3,plain,
    ! [U_254,U_253,U_252] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_252,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_253,U_254))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_252,U_253) ),
    inference(definitional_conversion,[status(esa)],[f_73_2]) ).

cnf(f_73_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_252,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_253,U_254))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_252,U_253) ),
    inference(clausify,[status(thm)],[f_73_3]) ).

fof(f_74_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_74_2,plain,
    ! [U_258,U_257] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_257,U_258)
        | ! [U_256] : U_258 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_257,U_256) )
      & ( ? [U_255] : U_258 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_257,U_255)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_257,U_258) ) ),
    inference(variable_rename,[status(thm)],[f_74_1]) ).

fof(f_74_3,plain,
    ( ! [U_262,U_260] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_260,U_262)
        | ! [U_256] : U_262 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_260,U_256) )
    & ! [U_261,U_259] :
        ( ? [U_255] : U_261 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_259,U_255)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_259,U_261) ) ),
    inference(miniscope,[status(thm)],[f_74_2]) ).

fof(f_74_4,plain,
    ( ! [U_262,U_260] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_260,U_262)
        | ! [U_256] : U_262 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_260,U_256) )
    & ! [U_261,U_259] :
        ( U_261 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_259,sK4(U_261,U_259))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_259,U_261) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_255,sK4(U_261,U_259))],[f_74_3]) ).

fof(f_74_5,plain,
    ( ! [U_262,U_256,U_260] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_260,U_262)
        | U_262 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_260,U_256) )
    & ! [U_259,U_261] :
        ( U_261 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_259,sK4(U_261,U_259))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_259,U_261) ) ),
    inference(definitional_conversion,[status(esa)],[f_74_4]) ).

cnf(f_74_6,plain,
    ( U_261 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_259,sK4(U_261,U_259))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_259,U_261) ),
    inference(clausify,[status(thm)],[f_74_5]) ).

cnf(f_74_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_260,U_262)
    | U_262 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_260,U_256) ),
    inference(clausify,[status(thm)],[f_74_5]) ).

fof(f_75_1,plain,
    ! [V_n_H_2,V_n_2,V_fa_2,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_fa_2,V_n_2),hAPP(V_fa_2,V_n_H_2))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_n_H_2)
      | ? [B_n] : ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_fa_2,B_n),hAPP(V_fa_2,c_Nat_OSuc(B_n)))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_lift__Suc__mono__le]) ).

fof(f_75_2,plain,
    ! [U_267,U_266,U_265,U_264] :
      ( c_Orderings_Oord__class_Oless__eq(U_264,hAPP(U_265,U_266),hAPP(U_265,U_267))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_266,U_267)
      | ? [U_263] : ~ c_Orderings_Oord__class_Oless__eq(U_264,hAPP(U_265,U_263),hAPP(U_265,c_Nat_OSuc(U_263)))
      | ~ class_Orderings_Oorder(U_264) ),
    inference(variable_rename,[status(thm)],[f_75_1]) ).

fof(f_75_3,plain,
    ! [U_267,U_266,U_265,U_264] :
      ( c_Orderings_Oord__class_Oless__eq(U_264,hAPP(U_265,U_266),hAPP(U_265,U_267))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_266,U_267)
      | ~ c_Orderings_Oord__class_Oless__eq(U_264,hAPP(U_265,sK5(U_267,U_266,U_265,U_264)),hAPP(U_265,c_Nat_OSuc(sK5(U_267,U_266,U_265,U_264))))
      | ~ class_Orderings_Oorder(U_264) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_263,sK5(U_267,U_266,U_265,U_264))],[f_75_2]) ).

fof(f_75_4,plain,
    ! [U_264,U_265,U_266,U_267] :
      ( c_Orderings_Oord__class_Oless__eq(U_264,hAPP(U_265,U_266),hAPP(U_265,U_267))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_266,U_267)
      | ~ c_Orderings_Oord__class_Oless__eq(U_264,hAPP(U_265,sK5(U_267,U_266,U_265,U_264)),hAPP(U_265,c_Nat_OSuc(sK5(U_267,U_266,U_265,U_264))))
      | ~ class_Orderings_Oorder(U_264) ),
    inference(definitional_conversion,[status(esa)],[f_75_3]) ).

cnf(f_75_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_264,hAPP(U_265,U_266),hAPP(U_265,U_267))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_266,U_267)
    | ~ c_Orderings_Oord__class_Oless__eq(U_264,hAPP(U_265,sK5(U_267,U_266,U_265,U_264)),hAPP(U_265,c_Nat_OSuc(sK5(U_267,U_266,U_265,U_264))))
    | ~ class_Orderings_Oorder(U_264) ),
    inference(clausify,[status(thm)],[f_75_4]) ).

fof(f_76_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2)
        | V_n_2 != V_m_2 )
      & ( V_n_2 = V_m_2
        | hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2) != hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_real__of__nat__inject]) ).

fof(f_76_2,plain,
    ! [U_269,U_268] :
      ( ( hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_268) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_269)
        | U_268 != U_269 )
      & ( U_268 = U_269
        | hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_268) != hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_269) ) ),
    inference(variable_rename,[status(thm)],[f_76_1]) ).

fof(f_76_3,plain,
    ( ! [U_273,U_271] :
        ( hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_271) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_273)
        | U_271 != U_273 )
    & ! [U_272,U_270] :
        ( U_270 = U_272
        | hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_270) != hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_272) ) ),
    inference(miniscope,[status(thm)],[f_76_2]) ).

fof(f_76_4,plain,
    ( ! [U_271,U_273] :
        ( hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_271) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_273)
        | U_271 != U_273 )
    & ! [U_272,U_270] :
        ( U_270 = U_272
        | hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_270) != hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_272) ) ),
    inference(definitional_conversion,[status(esa)],[f_76_3]) ).

cnf(f_76_5,plain,
    ( U_270 = U_272
    | hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_270) != hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_272) ),
    inference(clausify,[status(thm)],[f_76_4]) ).

cnf(f_76_6,plain,
    ( hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_271) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_273)
    | U_271 != U_273 ),
    inference(clausify,[status(thm)],[f_76_4]) ).

fof(f_77_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_77_2,plain,
    ! [U_276,U_275,U_274] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_276,U_274),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_276,U_275))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_274,U_275) ),
    inference(variable_rename,[status(thm)],[f_77_1]) ).

fof(f_77_3,plain,
    ! [U_275,U_274,U_276] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_276,U_274),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_276,U_275))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_274,U_275) ),
    inference(definitional_conversion,[status(esa)],[f_77_2]) ).

cnf(f_77_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_276,U_274),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_276,U_275))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_274,U_275) ),
    inference(clausify,[status(thm)],[f_77_3]) ).

fof(f_78_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_78_2,plain,
    ! [U_278,U_277] :
      ( U_277 = U_278
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_278,U_277)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_277,U_278) ),
    inference(variable_rename,[status(thm)],[f_78_1]) ).

fof(f_78_3,plain,
    ! [U_277,U_278] :
      ( U_277 = U_278
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_278,U_277)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_277,U_278) ),
    inference(definitional_conversion,[status(esa)],[f_78_2]) ).

cnf(f_78_4,plain,
    ( U_277 = U_278
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_278,U_277)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_277,U_278) ),
    inference(clausify,[status(thm)],[f_78_3]) ).

fof(f_79_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_79_2,plain,
    ! [U_281,U_280,U_279] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_279,U_281)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_280,U_281)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_279,U_280) ),
    inference(variable_rename,[status(thm)],[f_79_1]) ).

fof(f_79_3,plain,
    ! [U_281,U_279,U_280] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_279,U_281)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_280,U_281)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_279,U_280) ),
    inference(definitional_conversion,[status(esa)],[f_79_2]) ).

cnf(f_79_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_279,U_281)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_280,U_281)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_279,U_280) ),
    inference(clausify,[status(thm)],[f_79_3]) ).

fof(f_80_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_80_2,plain,
    ! [U_283,U_282] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_283,U_282)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_282,U_283) ),
    inference(variable_rename,[status(thm)],[f_80_1]) ).

fof(f_80_3,plain,
    ! [U_283,U_282] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_283,U_282)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_282,U_283) ),
    inference(definitional_conversion,[status(esa)],[f_80_2]) ).

cnf(f_80_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_283,U_282)
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_282,U_283) ),
    inference(clausify,[status(thm)],[f_80_3]) ).

fof(f_81_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_81_2,plain,
    ! [U_284] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_284,U_284),
    inference(variable_rename,[status(thm)],[f_81_1]) ).

fof(f_81_3,plain,
    ! [U_284] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_284,U_284),
    inference(definitional_conversion,[status(esa)],[f_81_2]) ).

cnf(f_81_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_284,U_284),
    inference(clausify,[status(thm)],[f_81_3]) ).

fof(f_82_1,plain,
    ! [V_X_2,T_a] :
      ( ( ( c_SEQ_Odecseq(T_a,V_X_2)
          | ? [B_m,B_n] :
              ( ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m))
              & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n) ) )
        & ( ! [B_m,B_n] :
              ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m))
              | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n) )
          | ~ c_SEQ_Odecseq(T_a,V_X_2) ) )
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_decseq__def]) ).

fof(f_82_2,plain,
    ! [U_290,U_289] :
      ( ( ( c_SEQ_Odecseq(U_289,U_290)
          | ? [U_288,U_287] :
              ( ~ c_Orderings_Oord__class_Oless__eq(U_289,hAPP(U_290,U_287),hAPP(U_290,U_288))
              & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_288,U_287) ) )
        & ( ! [U_286,U_285] :
              ( c_Orderings_Oord__class_Oless__eq(U_289,hAPP(U_290,U_285),hAPP(U_290,U_286))
              | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_286,U_285) )
          | ~ c_SEQ_Odecseq(U_289,U_290) ) )
      | ~ class_Orderings_Oorder(U_289) ),
    inference(variable_rename,[status(thm)],[f_82_1]) ).

fof(f_82_3,plain,
    ! [U_290,U_289] :
      ( ( ( c_SEQ_Odecseq(U_289,U_290)
          | ? [U_287] :
              ( ~ c_Orderings_Oord__class_Oless__eq(U_289,hAPP(U_290,U_287),hAPP(U_290,sK6(U_290,U_289)))
              & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK6(U_290,U_289),U_287) ) )
        & ( ! [U_286,U_285] :
              ( c_Orderings_Oord__class_Oless__eq(U_289,hAPP(U_290,U_285),hAPP(U_290,U_286))
              | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_286,U_285) )
          | ~ c_SEQ_Odecseq(U_289,U_290) ) )
      | ~ class_Orderings_Oorder(U_289) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_288,sK6(U_290,U_289))],[f_82_2]) ).

fof(f_82_4,plain,
    ! [U_290,U_289] :
      ( ( ( c_SEQ_Odecseq(U_289,U_290)
          | ( ~ c_Orderings_Oord__class_Oless__eq(U_289,hAPP(U_290,sK7(U_290,U_289)),hAPP(U_290,sK6(U_290,U_289)))
            & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK6(U_290,U_289),sK7(U_290,U_289)) ) )
        & ( ! [U_286,U_285] :
              ( c_Orderings_Oord__class_Oless__eq(U_289,hAPP(U_290,U_285),hAPP(U_290,U_286))
              | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_286,U_285) )
          | ~ c_SEQ_Odecseq(U_289,U_290) ) )
      | ~ class_Orderings_Oorder(U_289) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_287,sK7(U_290,U_289))],[f_82_3]) ).

fof(f_82_5,plain,
    ( ! [U_289,U_290] :
        ( ~ c_Orderings_Oord__class_Oless__eq(U_289,hAPP(U_290,sK7(U_290,U_289)),hAPP(U_290,sK6(U_290,U_289)))
        | ~ sP10(U_289,U_290) )
    & ! [U_289,U_290] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK6(U_290,U_289),sK7(U_290,U_289))
        | ~ sP10(U_289,U_290) )
    & ! [U_285,U_286,U_289,U_290] :
        ( c_SEQ_Odecseq(U_289,U_290)
        | sP10(U_289,U_290)
        | ~ sP11(U_285,U_286,U_289,U_290) )
    & ! [U_285,U_286,U_289,U_290] :
        ( c_Orderings_Oord__class_Oless__eq(U_289,hAPP(U_290,U_285),hAPP(U_290,U_286))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_286,U_285)
        | ~ c_SEQ_Odecseq(U_289,U_290)
        | ~ sP11(U_285,U_286,U_289,U_290) )
    & ! [U_285,U_286,U_289,U_290] :
        ( sP11(U_285,U_286,U_289,U_290)
        | ~ class_Orderings_Oorder(U_289) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP10,sP11])],[f_82_4]) ).

cnf(f_82_6,plain,
    ( sP11(U_285,U_286,U_289,U_290)
    | ~ class_Orderings_Oorder(U_289) ),
    inference(clausify,[status(thm)],[f_82_5]) ).

cnf(f_82_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_289,hAPP(U_290,U_285),hAPP(U_290,U_286))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_286,U_285)
    | ~ c_SEQ_Odecseq(U_289,U_290)
    | ~ sP11(U_285,U_286,U_289,U_290) ),
    inference(clausify,[status(thm)],[f_82_5]) ).

cnf(f_82_8,plain,
    ( c_SEQ_Odecseq(U_289,U_290)
    | sP10(U_289,U_290)
    | ~ sP11(U_285,U_286,U_289,U_290) ),
    inference(clausify,[status(thm)],[f_82_5]) ).

cnf(f_82_9,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK6(U_290,U_289),sK7(U_290,U_289))
    | ~ sP10(U_289,U_290) ),
    inference(clausify,[status(thm)],[f_82_5]) ).

cnf(f_82_10,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(U_289,hAPP(U_290,sK7(U_290,U_289)),hAPP(U_290,sK6(U_290,U_289)))
    | ~ sP10(U_289,U_290) ),
    inference(clausify,[status(thm)],[f_82_5]) ).

fof(f_83_1,plain,
    ! [V_X_2,T_a] :
      ( ( ( c_SEQ_Oincseq(T_a,V_X_2)
          | ? [B_m,B_n] :
              ( ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n))
              & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n) ) )
        & ( ! [B_m,B_n] :
              ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n))
              | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n) )
          | ~ c_SEQ_Oincseq(T_a,V_X_2) ) )
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_incseq__def]) ).

fof(f_83_2,plain,
    ! [U_296,U_295] :
      ( ( ( c_SEQ_Oincseq(U_295,U_296)
          | ? [U_294,U_293] :
              ( ~ c_Orderings_Oord__class_Oless__eq(U_295,hAPP(U_296,U_294),hAPP(U_296,U_293))
              & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_294,U_293) ) )
        & ( ! [U_292,U_291] :
              ( c_Orderings_Oord__class_Oless__eq(U_295,hAPP(U_296,U_292),hAPP(U_296,U_291))
              | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_292,U_291) )
          | ~ c_SEQ_Oincseq(U_295,U_296) ) )
      | ~ class_Orderings_Oorder(U_295) ),
    inference(variable_rename,[status(thm)],[f_83_1]) ).

fof(f_83_3,plain,
    ! [U_296,U_295] :
      ( ( ( c_SEQ_Oincseq(U_295,U_296)
          | ? [U_293] :
              ( ~ c_Orderings_Oord__class_Oless__eq(U_295,hAPP(U_296,sK8(U_296,U_295)),hAPP(U_296,U_293))
              & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK8(U_296,U_295),U_293) ) )
        & ( ! [U_292,U_291] :
              ( c_Orderings_Oord__class_Oless__eq(U_295,hAPP(U_296,U_292),hAPP(U_296,U_291))
              | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_292,U_291) )
          | ~ c_SEQ_Oincseq(U_295,U_296) ) )
      | ~ class_Orderings_Oorder(U_295) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_294,sK8(U_296,U_295))],[f_83_2]) ).

fof(f_83_4,plain,
    ! [U_296,U_295] :
      ( ( ( c_SEQ_Oincseq(U_295,U_296)
          | ( ~ c_Orderings_Oord__class_Oless__eq(U_295,hAPP(U_296,sK8(U_296,U_295)),hAPP(U_296,sK9(U_296,U_295)))
            & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK8(U_296,U_295),sK9(U_296,U_295)) ) )
        & ( ! [U_292,U_291] :
              ( c_Orderings_Oord__class_Oless__eq(U_295,hAPP(U_296,U_292),hAPP(U_296,U_291))
              | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_292,U_291) )
          | ~ c_SEQ_Oincseq(U_295,U_296) ) )
      | ~ class_Orderings_Oorder(U_295) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_293,sK9(U_296,U_295))],[f_83_3]) ).

fof(f_83_5,plain,
    ( ! [U_295,U_296] :
        ( ~ c_Orderings_Oord__class_Oless__eq(U_295,hAPP(U_296,sK8(U_296,U_295)),hAPP(U_296,sK9(U_296,U_295)))
        | ~ sP12(U_295,U_296) )
    & ! [U_295,U_296] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK8(U_296,U_295),sK9(U_296,U_295))
        | ~ sP12(U_295,U_296) )
    & ! [U_291,U_292,U_295,U_296] :
        ( c_SEQ_Oincseq(U_295,U_296)
        | sP12(U_295,U_296)
        | ~ sP13(U_291,U_292,U_295,U_296) )
    & ! [U_291,U_292,U_295,U_296] :
        ( c_Orderings_Oord__class_Oless__eq(U_295,hAPP(U_296,U_292),hAPP(U_296,U_291))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_292,U_291)
        | ~ c_SEQ_Oincseq(U_295,U_296)
        | ~ sP13(U_291,U_292,U_295,U_296) )
    & ! [U_291,U_292,U_295,U_296] :
        ( sP13(U_291,U_292,U_295,U_296)
        | ~ class_Orderings_Oorder(U_295) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP12,sP13])],[f_83_4]) ).

cnf(f_83_6,plain,
    ( sP13(U_291,U_292,U_295,U_296)
    | ~ class_Orderings_Oorder(U_295) ),
    inference(clausify,[status(thm)],[f_83_5]) ).

cnf(f_83_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_295,hAPP(U_296,U_292),hAPP(U_296,U_291))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_292,U_291)
    | ~ c_SEQ_Oincseq(U_295,U_296)
    | ~ sP13(U_291,U_292,U_295,U_296) ),
    inference(clausify,[status(thm)],[f_83_5]) ).

cnf(f_83_8,plain,
    ( c_SEQ_Oincseq(U_295,U_296)
    | sP12(U_295,U_296)
    | ~ sP13(U_291,U_292,U_295,U_296) ),
    inference(clausify,[status(thm)],[f_83_5]) ).

cnf(f_83_9,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK8(U_296,U_295),sK9(U_296,U_295))
    | ~ sP12(U_295,U_296) ),
    inference(clausify,[status(thm)],[f_83_5]) ).

cnf(f_83_10,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(U_295,hAPP(U_296,sK8(U_296,U_295)),hAPP(U_296,sK9(U_296,U_295)))
    | ~ sP12(U_295,U_296) ),
    inference(clausify,[status(thm)],[f_83_5]) ).

fof(f_84_1,plain,
    ! [V_X_2,T_a] :
      ( ( ( c_SEQ_Omonoseq(T_a,V_X_2)
          | ( ? [B_m,B_n] :
                ( ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m))
                & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n) )
            & ? [B_m,B_n] :
                ( ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n))
                & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n) ) ) )
        & ( ! [B_m,B_n] :
              ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m))
              | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n) )
          | ! [B_m,B_n] :
              ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n))
              | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n) )
          | ~ c_SEQ_Omonoseq(T_a,V_X_2) ) )
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_monoseq__def]) ).

fof(f_84_2,plain,
    ! [U_306,U_305] :
      ( ( ( c_SEQ_Omonoseq(U_305,U_306)
          | ( ? [U_304,U_303] :
                ( ~ c_Orderings_Oord__class_Oless__eq(U_305,hAPP(U_306,U_303),hAPP(U_306,U_304))
                & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_304,U_303) )
            & ? [U_302,U_301] :
                ( ~ c_Orderings_Oord__class_Oless__eq(U_305,hAPP(U_306,U_302),hAPP(U_306,U_301))
                & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_302,U_301) ) ) )
        & ( ! [U_300,U_299] :
              ( c_Orderings_Oord__class_Oless__eq(U_305,hAPP(U_306,U_299),hAPP(U_306,U_300))
              | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_300,U_299) )
          | ! [U_298,U_297] :
              ( c_Orderings_Oord__class_Oless__eq(U_305,hAPP(U_306,U_298),hAPP(U_306,U_297))
              | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_298,U_297) )
          | ~ c_SEQ_Omonoseq(U_305,U_306) ) )
      | ~ class_Orderings_Oorder(U_305) ),
    inference(variable_rename,[status(thm)],[f_84_1]) ).

fof(f_84_3,plain,
    ! [U_306,U_305] :
      ( ( ( c_SEQ_Omonoseq(U_305,U_306)
          | ( ? [U_304,U_303] :
                ( ~ c_Orderings_Oord__class_Oless__eq(U_305,hAPP(U_306,U_303),hAPP(U_306,U_304))
                & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_304,U_303) )
            & ? [U_301] :
                ( ~ c_Orderings_Oord__class_Oless__eq(U_305,hAPP(U_306,sK10(U_306,U_305)),hAPP(U_306,U_301))
                & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK10(U_306,U_305),U_301) ) ) )
        & ( ! [U_300,U_299] :
              ( c_Orderings_Oord__class_Oless__eq(U_305,hAPP(U_306,U_299),hAPP(U_306,U_300))
              | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_300,U_299) )
          | ! [U_298,U_297] :
              ( c_Orderings_Oord__class_Oless__eq(U_305,hAPP(U_306,U_298),hAPP(U_306,U_297))
              | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_298,U_297) )
          | ~ c_SEQ_Omonoseq(U_305,U_306) ) )
      | ~ class_Orderings_Oorder(U_305) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_302,sK10(U_306,U_305))],[f_84_2]) ).

fof(f_84_4,plain,
    ! [U_306,U_305] :
      ( ( ( c_SEQ_Omonoseq(U_305,U_306)
          | ( ? [U_304,U_303] :
                ( ~ c_Orderings_Oord__class_Oless__eq(U_305,hAPP(U_306,U_303),hAPP(U_306,U_304))
                & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_304,U_303) )
            & ~ c_Orderings_Oord__class_Oless__eq(U_305,hAPP(U_306,sK10(U_306,U_305)),hAPP(U_306,sK11(U_306,U_305)))
            & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK10(U_306,U_305),sK11(U_306,U_305)) ) )
        & ( ! [U_300,U_299] :
              ( c_Orderings_Oord__class_Oless__eq(U_305,hAPP(U_306,U_299),hAPP(U_306,U_300))
              | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_300,U_299) )
          | ! [U_298,U_297] :
              ( c_Orderings_Oord__class_Oless__eq(U_305,hAPP(U_306,U_298),hAPP(U_306,U_297))
              | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_298,U_297) )
          | ~ c_SEQ_Omonoseq(U_305,U_306) ) )
      | ~ class_Orderings_Oorder(U_305) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_301,sK11(U_306,U_305))],[f_84_3]) ).

fof(f_84_5,plain,
    ! [U_306,U_305] :
      ( ( ( c_SEQ_Omonoseq(U_305,U_306)
          | ( ? [U_303] :
                ( ~ c_Orderings_Oord__class_Oless__eq(U_305,hAPP(U_306,U_303),hAPP(U_306,sK12(U_306,U_305)))
                & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK12(U_306,U_305),U_303) )
            & ~ c_Orderings_Oord__class_Oless__eq(U_305,hAPP(U_306,sK10(U_306,U_305)),hAPP(U_306,sK11(U_306,U_305)))
            & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK10(U_306,U_305),sK11(U_306,U_305)) ) )
        & ( ! [U_300,U_299] :
              ( c_Orderings_Oord__class_Oless__eq(U_305,hAPP(U_306,U_299),hAPP(U_306,U_300))
              | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_300,U_299) )
          | ! [U_298,U_297] :
              ( c_Orderings_Oord__class_Oless__eq(U_305,hAPP(U_306,U_298),hAPP(U_306,U_297))
              | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_298,U_297) )
          | ~ c_SEQ_Omonoseq(U_305,U_306) ) )
      | ~ class_Orderings_Oorder(U_305) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_304,sK12(U_306,U_305))],[f_84_4]) ).

fof(f_84_6,plain,
    ! [U_306,U_305] :
      ( ( ( c_SEQ_Omonoseq(U_305,U_306)
          | ( ~ c_Orderings_Oord__class_Oless__eq(U_305,hAPP(U_306,sK13(U_306,U_305)),hAPP(U_306,sK12(U_306,U_305)))
            & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK12(U_306,U_305),sK13(U_306,U_305))
            & ~ c_Orderings_Oord__class_Oless__eq(U_305,hAPP(U_306,sK10(U_306,U_305)),hAPP(U_306,sK11(U_306,U_305)))
            & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK10(U_306,U_305),sK11(U_306,U_305)) ) )
        & ( ! [U_300,U_299] :
              ( c_Orderings_Oord__class_Oless__eq(U_305,hAPP(U_306,U_299),hAPP(U_306,U_300))
              | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_300,U_299) )
          | ! [U_298,U_297] :
              ( c_Orderings_Oord__class_Oless__eq(U_305,hAPP(U_306,U_298),hAPP(U_306,U_297))
              | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_298,U_297) )
          | ~ c_SEQ_Omonoseq(U_305,U_306) ) )
      | ~ class_Orderings_Oorder(U_305) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_303,sK13(U_306,U_305))],[f_84_5]) ).

fof(f_84_7,plain,
    ( ! [U_305,U_306] :
        ( ~ c_Orderings_Oord__class_Oless__eq(U_305,hAPP(U_306,sK13(U_306,U_305)),hAPP(U_306,sK12(U_306,U_305)))
        | ~ sP14(U_305,U_306) )
    & ! [U_305,U_306] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK12(U_306,U_305),sK13(U_306,U_305))
        | ~ sP14(U_305,U_306) )
    & ! [U_305,U_306] :
        ( ~ c_Orderings_Oord__class_Oless__eq(U_305,hAPP(U_306,sK10(U_306,U_305)),hAPP(U_306,sK11(U_306,U_305)))
        | ~ sP14(U_305,U_306) )
    & ! [U_305,U_306] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK10(U_306,U_305),sK11(U_306,U_305))
        | ~ sP14(U_305,U_306) )
    & ! [U_298,U_300,U_305,U_306,U_297,U_299] :
        ( c_SEQ_Omonoseq(U_305,U_306)
        | sP14(U_305,U_306)
        | ~ sP15(U_298,U_300,U_305,U_306,U_297,U_299) )
    & ! [U_298,U_300,U_305,U_306,U_297,U_299] :
        ( c_Orderings_Oord__class_Oless__eq(U_305,hAPP(U_306,U_299),hAPP(U_306,U_300))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_300,U_299)
        | c_Orderings_Oord__class_Oless__eq(U_305,hAPP(U_306,U_298),hAPP(U_306,U_297))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_298,U_297)
        | ~ c_SEQ_Omonoseq(U_305,U_306)
        | ~ sP15(U_298,U_300,U_305,U_306,U_297,U_299) )
    & ! [U_298,U_300,U_305,U_306,U_297,U_299] :
        ( sP15(U_298,U_300,U_305,U_306,U_297,U_299)
        | ~ class_Orderings_Oorder(U_305) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP14,sP15])],[f_84_6]) ).

cnf(f_84_8,plain,
    ( sP15(U_298,U_300,U_305,U_306,U_297,U_299)
    | ~ class_Orderings_Oorder(U_305) ),
    inference(clausify,[status(thm)],[f_84_7]) ).

cnf(f_84_9,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_305,hAPP(U_306,U_299),hAPP(U_306,U_300))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_300,U_299)
    | c_Orderings_Oord__class_Oless__eq(U_305,hAPP(U_306,U_298),hAPP(U_306,U_297))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_298,U_297)
    | ~ c_SEQ_Omonoseq(U_305,U_306)
    | ~ sP15(U_298,U_300,U_305,U_306,U_297,U_299) ),
    inference(clausify,[status(thm)],[f_84_7]) ).

cnf(f_84_10,plain,
    ( c_SEQ_Omonoseq(U_305,U_306)
    | sP14(U_305,U_306)
    | ~ sP15(U_298,U_300,U_305,U_306,U_297,U_299) ),
    inference(clausify,[status(thm)],[f_84_7]) ).

cnf(f_84_11,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK10(U_306,U_305),sK11(U_306,U_305))
    | ~ sP14(U_305,U_306) ),
    inference(clausify,[status(thm)],[f_84_7]) ).

cnf(f_84_12,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(U_305,hAPP(U_306,sK10(U_306,U_305)),hAPP(U_306,sK11(U_306,U_305)))
    | ~ sP14(U_305,U_306) ),
    inference(clausify,[status(thm)],[f_84_7]) ).

cnf(f_84_13,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK12(U_306,U_305),sK13(U_306,U_305))
    | ~ sP14(U_305,U_306) ),
    inference(clausify,[status(thm)],[f_84_7]) ).

cnf(f_84_14,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(U_305,hAPP(U_306,sK13(U_306,U_305)),hAPP(U_306,sK12(U_306,U_305)))
    | ~ sP14(U_305,U_306) ),
    inference(clausify,[status(thm)],[f_84_7]) ).

fof(f_85_1,plain,
    ! [V_X_2,T_a] :
      ( ( ( c_SEQ_Omonoseq(T_a,V_X_2)
          | ( ? [B_n] : ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,c_Nat_OSuc(B_n)),hAPP(V_X_2,B_n))
            & ? [B_n] : ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,c_Nat_OSuc(B_n))) ) )
        & ( ! [B_n] : c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,c_Nat_OSuc(B_n)),hAPP(V_X_2,B_n))
          | ! [B_n] : c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,c_Nat_OSuc(B_n)))
          | ~ c_SEQ_Omonoseq(T_a,V_X_2) ) )
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_monoseq__Suc]) ).

fof(f_85_2,plain,
    ! [U_312,U_311] :
      ( ( ( c_SEQ_Omonoseq(U_311,U_312)
          | ( ? [U_310] : ~ c_Orderings_Oord__class_Oless__eq(U_311,hAPP(U_312,c_Nat_OSuc(U_310)),hAPP(U_312,U_310))
            & ? [U_309] : ~ c_Orderings_Oord__class_Oless__eq(U_311,hAPP(U_312,U_309),hAPP(U_312,c_Nat_OSuc(U_309))) ) )
        & ( ! [U_308] : c_Orderings_Oord__class_Oless__eq(U_311,hAPP(U_312,c_Nat_OSuc(U_308)),hAPP(U_312,U_308))
          | ! [U_307] : c_Orderings_Oord__class_Oless__eq(U_311,hAPP(U_312,U_307),hAPP(U_312,c_Nat_OSuc(U_307)))
          | ~ c_SEQ_Omonoseq(U_311,U_312) ) )
      | ~ class_Orderings_Oorder(U_311) ),
    inference(variable_rename,[status(thm)],[f_85_1]) ).

fof(f_85_3,plain,
    ! [U_312,U_311] :
      ( ( ( c_SEQ_Omonoseq(U_311,U_312)
          | ( ? [U_310] : ~ c_Orderings_Oord__class_Oless__eq(U_311,hAPP(U_312,c_Nat_OSuc(U_310)),hAPP(U_312,U_310))
            & ~ c_Orderings_Oord__class_Oless__eq(U_311,hAPP(U_312,sK14(U_312,U_311)),hAPP(U_312,c_Nat_OSuc(sK14(U_312,U_311)))) ) )
        & ( ! [U_308] : c_Orderings_Oord__class_Oless__eq(U_311,hAPP(U_312,c_Nat_OSuc(U_308)),hAPP(U_312,U_308))
          | ! [U_307] : c_Orderings_Oord__class_Oless__eq(U_311,hAPP(U_312,U_307),hAPP(U_312,c_Nat_OSuc(U_307)))
          | ~ c_SEQ_Omonoseq(U_311,U_312) ) )
      | ~ class_Orderings_Oorder(U_311) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_309,sK14(U_312,U_311))],[f_85_2]) ).

fof(f_85_4,plain,
    ! [U_312,U_311] :
      ( ( ( c_SEQ_Omonoseq(U_311,U_312)
          | ( ~ c_Orderings_Oord__class_Oless__eq(U_311,hAPP(U_312,c_Nat_OSuc(sK15(U_312,U_311))),hAPP(U_312,sK15(U_312,U_311)))
            & ~ c_Orderings_Oord__class_Oless__eq(U_311,hAPP(U_312,sK14(U_312,U_311)),hAPP(U_312,c_Nat_OSuc(sK14(U_312,U_311)))) ) )
        & ( ! [U_308] : c_Orderings_Oord__class_Oless__eq(U_311,hAPP(U_312,c_Nat_OSuc(U_308)),hAPP(U_312,U_308))
          | ! [U_307] : c_Orderings_Oord__class_Oless__eq(U_311,hAPP(U_312,U_307),hAPP(U_312,c_Nat_OSuc(U_307)))
          | ~ c_SEQ_Omonoseq(U_311,U_312) ) )
      | ~ class_Orderings_Oorder(U_311) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_310,sK15(U_312,U_311))],[f_85_3]) ).

fof(f_85_5,plain,
    ( ! [U_312,U_311] :
        ( ~ c_Orderings_Oord__class_Oless__eq(U_311,hAPP(U_312,c_Nat_OSuc(sK15(U_312,U_311))),hAPP(U_312,sK15(U_312,U_311)))
        | ~ sP16(U_312,U_311) )
    & ! [U_312,U_311] :
        ( ~ c_Orderings_Oord__class_Oless__eq(U_311,hAPP(U_312,sK14(U_312,U_311)),hAPP(U_312,c_Nat_OSuc(sK14(U_312,U_311))))
        | ~ sP16(U_312,U_311) )
    & ! [U_312,U_311,U_308,U_307] :
        ( c_SEQ_Omonoseq(U_311,U_312)
        | sP16(U_312,U_311)
        | ~ sP17(U_312,U_311,U_308,U_307) )
    & ! [U_312,U_311,U_308,U_307] :
        ( c_Orderings_Oord__class_Oless__eq(U_311,hAPP(U_312,c_Nat_OSuc(U_308)),hAPP(U_312,U_308))
        | c_Orderings_Oord__class_Oless__eq(U_311,hAPP(U_312,U_307),hAPP(U_312,c_Nat_OSuc(U_307)))
        | ~ c_SEQ_Omonoseq(U_311,U_312)
        | ~ sP17(U_312,U_311,U_308,U_307) )
    & ! [U_312,U_311,U_308,U_307] :
        ( sP17(U_312,U_311,U_308,U_307)
        | ~ class_Orderings_Oorder(U_311) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP16,sP17])],[f_85_4]) ).

cnf(f_85_6,plain,
    ( sP17(U_312,U_311,U_308,U_307)
    | ~ class_Orderings_Oorder(U_311) ),
    inference(clausify,[status(thm)],[f_85_5]) ).

cnf(f_85_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_311,hAPP(U_312,c_Nat_OSuc(U_308)),hAPP(U_312,U_308))
    | c_Orderings_Oord__class_Oless__eq(U_311,hAPP(U_312,U_307),hAPP(U_312,c_Nat_OSuc(U_307)))
    | ~ c_SEQ_Omonoseq(U_311,U_312)
    | ~ sP17(U_312,U_311,U_308,U_307) ),
    inference(clausify,[status(thm)],[f_85_5]) ).

cnf(f_85_8,plain,
    ( c_SEQ_Omonoseq(U_311,U_312)
    | sP16(U_312,U_311)
    | ~ sP17(U_312,U_311,U_308,U_307) ),
    inference(clausify,[status(thm)],[f_85_5]) ).

cnf(f_85_9,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(U_311,hAPP(U_312,sK14(U_312,U_311)),hAPP(U_312,c_Nat_OSuc(sK14(U_312,U_311))))
    | ~ sP16(U_312,U_311) ),
    inference(clausify,[status(thm)],[f_85_5]) ).

cnf(f_85_10,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(U_311,hAPP(U_312,c_Nat_OSuc(sK15(U_312,U_311))),hAPP(U_312,sK15(U_312,U_311)))
    | ~ sP16(U_312,U_311) ),
    inference(clausify,[status(thm)],[f_85_5]) ).

fof(f_86_1,plain,
    ! [V_n] : hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(V_n)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(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_86_2,plain,
    ! [U_313] : hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_313)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_313),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(variable_rename,[status(thm)],[f_86_1]) ).

fof(f_86_3,plain,
    ! [U_313] : hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_313)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_313),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(definitional_conversion,[status(esa)],[f_86_2]) ).

cnf(f_86_4,plain,
    hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_313)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_313),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(clausify,[status(thm)],[f_86_3]) ).

fof(f_87_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_87_2,plain,
    ! [U_316,U_315,U_314] :
      ( c_Groups_Oplus__class_Oplus(U_314,U_315,U_316) = c_Groups_Oplus__class_Oplus(U_314,U_316,U_315)
      | ~ class_Rings_Ocomm__semiring__1(U_314) ),
    inference(variable_rename,[status(thm)],[f_87_1]) ).

fof(f_87_3,plain,
    ! [U_314,U_316,U_315] :
      ( c_Groups_Oplus__class_Oplus(U_314,U_315,U_316) = c_Groups_Oplus__class_Oplus(U_314,U_316,U_315)
      | ~ class_Rings_Ocomm__semiring__1(U_314) ),
    inference(definitional_conversion,[status(esa)],[f_87_2]) ).

cnf(f_87_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_314,U_315,U_316) = c_Groups_Oplus__class_Oplus(U_314,U_316,U_315)
    | ~ class_Rings_Ocomm__semiring__1(U_314) ),
    inference(clausify,[status(thm)],[f_87_3]) ).

fof(f_88_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_88_2,plain,
    ! [U_320,U_319,U_318,U_317] :
      ( c_Groups_Oplus__class_Oplus(U_317,U_318,c_Groups_Oplus__class_Oplus(U_317,U_319,U_320)) = c_Groups_Oplus__class_Oplus(U_317,U_319,c_Groups_Oplus__class_Oplus(U_317,U_318,U_320))
      | ~ class_Rings_Ocomm__semiring__1(U_317) ),
    inference(variable_rename,[status(thm)],[f_88_1]) ).

fof(f_88_3,plain,
    ! [U_318,U_317,U_319,U_320] :
      ( c_Groups_Oplus__class_Oplus(U_317,U_318,c_Groups_Oplus__class_Oplus(U_317,U_319,U_320)) = c_Groups_Oplus__class_Oplus(U_317,U_319,c_Groups_Oplus__class_Oplus(U_317,U_318,U_320))
      | ~ class_Rings_Ocomm__semiring__1(U_317) ),
    inference(definitional_conversion,[status(esa)],[f_88_2]) ).

cnf(f_88_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_317,U_318,c_Groups_Oplus__class_Oplus(U_317,U_319,U_320)) = c_Groups_Oplus__class_Oplus(U_317,U_319,c_Groups_Oplus__class_Oplus(U_317,U_318,U_320))
    | ~ class_Rings_Ocomm__semiring__1(U_317) ),
    inference(clausify,[status(thm)],[f_88_3]) ).

fof(f_89_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_89_2,plain,
    ! [U_324,U_323,U_322,U_321] :
      ( c_Groups_Oplus__class_Oplus(U_321,U_322,c_Groups_Oplus__class_Oplus(U_321,U_323,U_324)) = c_Groups_Oplus__class_Oplus(U_321,c_Groups_Oplus__class_Oplus(U_321,U_322,U_323),U_324)
      | ~ class_Rings_Ocomm__semiring__1(U_321) ),
    inference(variable_rename,[status(thm)],[f_89_1]) ).

fof(f_89_3,plain,
    ! [U_322,U_321,U_323,U_324] :
      ( c_Groups_Oplus__class_Oplus(U_321,U_322,c_Groups_Oplus__class_Oplus(U_321,U_323,U_324)) = c_Groups_Oplus__class_Oplus(U_321,c_Groups_Oplus__class_Oplus(U_321,U_322,U_323),U_324)
      | ~ class_Rings_Ocomm__semiring__1(U_321) ),
    inference(definitional_conversion,[status(esa)],[f_89_2]) ).

cnf(f_89_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_321,U_322,c_Groups_Oplus__class_Oplus(U_321,U_323,U_324)) = c_Groups_Oplus__class_Oplus(U_321,c_Groups_Oplus__class_Oplus(U_321,U_322,U_323),U_324)
    | ~ class_Rings_Ocomm__semiring__1(U_321) ),
    inference(clausify,[status(thm)],[f_89_3]) ).

fof(f_90_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_90_2,plain,
    ! [U_328,U_327,U_326,U_325] :
      ( c_Groups_Oplus__class_Oplus(U_325,c_Groups_Oplus__class_Oplus(U_325,U_326,U_327),U_328) = c_Groups_Oplus__class_Oplus(U_325,U_326,c_Groups_Oplus__class_Oplus(U_325,U_327,U_328))
      | ~ class_Rings_Ocomm__semiring__1(U_325) ),
    inference(variable_rename,[status(thm)],[f_90_1]) ).

fof(f_90_3,plain,
    ! [U_326,U_325,U_327,U_328] :
      ( c_Groups_Oplus__class_Oplus(U_325,c_Groups_Oplus__class_Oplus(U_325,U_326,U_327),U_328) = c_Groups_Oplus__class_Oplus(U_325,U_326,c_Groups_Oplus__class_Oplus(U_325,U_327,U_328))
      | ~ class_Rings_Ocomm__semiring__1(U_325) ),
    inference(definitional_conversion,[status(esa)],[f_90_2]) ).

cnf(f_90_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_325,c_Groups_Oplus__class_Oplus(U_325,U_326,U_327),U_328) = c_Groups_Oplus__class_Oplus(U_325,U_326,c_Groups_Oplus__class_Oplus(U_325,U_327,U_328))
    | ~ class_Rings_Ocomm__semiring__1(U_325) ),
    inference(clausify,[status(thm)],[f_90_3]) ).

fof(f_91_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_91_2,plain,
    ! [U_332,U_331,U_330,U_329] :
      ( c_Groups_Oplus__class_Oplus(U_329,c_Groups_Oplus__class_Oplus(U_329,U_330,U_331),U_332) = c_Groups_Oplus__class_Oplus(U_329,c_Groups_Oplus__class_Oplus(U_329,U_330,U_332),U_331)
      | ~ class_Rings_Ocomm__semiring__1(U_329) ),
    inference(variable_rename,[status(thm)],[f_91_1]) ).

fof(f_91_3,plain,
    ! [U_330,U_329,U_331,U_332] :
      ( c_Groups_Oplus__class_Oplus(U_329,c_Groups_Oplus__class_Oplus(U_329,U_330,U_331),U_332) = c_Groups_Oplus__class_Oplus(U_329,c_Groups_Oplus__class_Oplus(U_329,U_330,U_332),U_331)
      | ~ class_Rings_Ocomm__semiring__1(U_329) ),
    inference(definitional_conversion,[status(esa)],[f_91_2]) ).

cnf(f_91_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_329,c_Groups_Oplus__class_Oplus(U_329,U_330,U_331),U_332) = c_Groups_Oplus__class_Oplus(U_329,c_Groups_Oplus__class_Oplus(U_329,U_330,U_332),U_331)
    | ~ class_Rings_Ocomm__semiring__1(U_329) ),
    inference(clausify,[status(thm)],[f_91_3]) ).

fof(f_92_1,plain,
    ! [V_X_2,T_a] :
      ( c_SEQ_Omonoseq(T_a,V_X_2)
      | ~ c_SEQ_Oincseq(T_a,V_X_2)
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_incseq__imp__monoseq]) ).

fof(f_92_2,plain,
    ! [U_334,U_333] :
      ( c_SEQ_Omonoseq(U_333,U_334)
      | ~ c_SEQ_Oincseq(U_333,U_334)
      | ~ class_Orderings_Oorder(U_333) ),
    inference(variable_rename,[status(thm)],[f_92_1]) ).

fof(f_92_3,plain,
    ! [U_333,U_334] :
      ( c_SEQ_Omonoseq(U_333,U_334)
      | ~ c_SEQ_Oincseq(U_333,U_334)
      | ~ class_Orderings_Oorder(U_333) ),
    inference(definitional_conversion,[status(esa)],[f_92_2]) ).

cnf(f_92_4,plain,
    ( c_SEQ_Omonoseq(U_333,U_334)
    | ~ c_SEQ_Oincseq(U_333,U_334)
    | ~ class_Orderings_Oorder(U_333) ),
    inference(clausify,[status(thm)],[f_92_3]) ).

fof(f_93_1,plain,
    ! [V_X_2,T_a] :
      ( c_SEQ_Omonoseq(T_a,V_X_2)
      | ~ c_SEQ_Odecseq(T_a,V_X_2)
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_decseq__imp__monoseq]) ).

fof(f_93_2,plain,
    ! [U_336,U_335] :
      ( c_SEQ_Omonoseq(U_335,U_336)
      | ~ c_SEQ_Odecseq(U_335,U_336)
      | ~ class_Orderings_Oorder(U_335) ),
    inference(variable_rename,[status(thm)],[f_93_1]) ).

fof(f_93_3,plain,
    ! [U_336,U_335] :
      ( c_SEQ_Omonoseq(U_335,U_336)
      | ~ c_SEQ_Odecseq(U_335,U_336)
      | ~ class_Orderings_Oorder(U_335) ),
    inference(definitional_conversion,[status(esa)],[f_93_2]) ).

cnf(f_93_4,plain,
    ( c_SEQ_Omonoseq(U_335,U_336)
    | ~ c_SEQ_Odecseq(U_335,U_336)
    | ~ class_Orderings_Oorder(U_335) ),
    inference(clausify,[status(thm)],[f_93_3]) ).

fof(f_94_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_94_2,plain,
    ! [U_338,U_337] :
      ( ( ( c_Groups_Oone__class_Oone(U_337) = U_338
          | U_338 != c_Groups_Oone__class_Oone(U_337) )
        & ( U_338 = c_Groups_Oone__class_Oone(U_337)
          | c_Groups_Oone__class_Oone(U_337) != U_338 ) )
      | ~ class_Groups_Oone(U_337) ),
    inference(variable_rename,[status(thm)],[f_94_1]) ).

fof(f_94_3,plain,
    ( ! [U_338,U_337] :
        ( c_Groups_Oone__class_Oone(U_337) = U_338
        | U_338 != c_Groups_Oone__class_Oone(U_337)
        | ~ sP18(U_338,U_337) )
    & ! [U_338,U_337] :
        ( U_338 = c_Groups_Oone__class_Oone(U_337)
        | c_Groups_Oone__class_Oone(U_337) != U_338
        | ~ sP18(U_338,U_337) )
    & ! [U_338,U_337] :
        ( sP18(U_338,U_337)
        | ~ class_Groups_Oone(U_337) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP18])],[f_94_2]) ).

cnf(f_94_4,plain,
    ( sP18(U_338,U_337)
    | ~ class_Groups_Oone(U_337) ),
    inference(clausify,[status(thm)],[f_94_3]) ).

cnf(f_94_5,plain,
    ( U_338 = c_Groups_Oone__class_Oone(U_337)
    | c_Groups_Oone__class_Oone(U_337) != U_338
    | ~ sP18(U_338,U_337) ),
    inference(clausify,[status(thm)],[f_94_3]) ).

cnf(f_94_6,plain,
    ( c_Groups_Oone__class_Oone(U_337) = U_338
    | U_338 != c_Groups_Oone__class_Oone(U_337)
    | ~ sP18(U_338,U_337) ),
    inference(clausify,[status(thm)],[f_94_3]) ).

fof(f_95_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_95_2,plain,
    ! [U_343,U_342,U_341,U_340,U_339] :
      ( c_Groups_Oplus__class_Oplus(U_339,c_Groups_Oplus__class_Oplus(U_339,U_340,U_341),c_Groups_Oplus__class_Oplus(U_339,U_342,U_343)) = c_Groups_Oplus__class_Oplus(U_339,c_Groups_Oplus__class_Oplus(U_339,U_340,U_342),c_Groups_Oplus__class_Oplus(U_339,U_341,U_343))
      | ~ class_Rings_Ocomm__semiring__1(U_339) ),
    inference(variable_rename,[status(thm)],[f_95_1]) ).

fof(f_95_3,plain,
    ! [U_341,U_340,U_339,U_342,U_343] :
      ( c_Groups_Oplus__class_Oplus(U_339,c_Groups_Oplus__class_Oplus(U_339,U_340,U_341),c_Groups_Oplus__class_Oplus(U_339,U_342,U_343)) = c_Groups_Oplus__class_Oplus(U_339,c_Groups_Oplus__class_Oplus(U_339,U_340,U_342),c_Groups_Oplus__class_Oplus(U_339,U_341,U_343))
      | ~ class_Rings_Ocomm__semiring__1(U_339) ),
    inference(definitional_conversion,[status(esa)],[f_95_2]) ).

cnf(f_95_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_339,c_Groups_Oplus__class_Oplus(U_339,U_340,U_341),c_Groups_Oplus__class_Oplus(U_339,U_342,U_343)) = c_Groups_Oplus__class_Oplus(U_339,c_Groups_Oplus__class_Oplus(U_339,U_340,U_342),c_Groups_Oplus__class_Oplus(U_339,U_341,U_343))
    | ~ class_Rings_Ocomm__semiring__1(U_339) ),
    inference(clausify,[status(thm)],[f_95_3]) ).

fof(f_96_1,plain,
    ! [V_X_2,T_a] :
      ( c_SEQ_Oincseq(T_a,V_X_2)
      | ? [B_n] : ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,c_Nat_OSuc(B_n)))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_incseq__SucI]) ).

fof(f_96_2,plain,
    ! [U_346,U_345] :
      ( c_SEQ_Oincseq(U_345,U_346)
      | ? [U_344] : ~ c_Orderings_Oord__class_Oless__eq(U_345,hAPP(U_346,U_344),hAPP(U_346,c_Nat_OSuc(U_344)))
      | ~ class_Orderings_Oorder(U_345) ),
    inference(variable_rename,[status(thm)],[f_96_1]) ).

fof(f_96_3,plain,
    ! [U_346,U_345] :
      ( c_SEQ_Oincseq(U_345,U_346)
      | ~ c_Orderings_Oord__class_Oless__eq(U_345,hAPP(U_346,sK16(U_346,U_345)),hAPP(U_346,c_Nat_OSuc(sK16(U_346,U_345))))
      | ~ class_Orderings_Oorder(U_345) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_344,sK16(U_346,U_345))],[f_96_2]) ).

fof(f_96_4,plain,
    ! [U_346,U_345] :
      ( c_SEQ_Oincseq(U_345,U_346)
      | ~ c_Orderings_Oord__class_Oless__eq(U_345,hAPP(U_346,sK16(U_346,U_345)),hAPP(U_346,c_Nat_OSuc(sK16(U_346,U_345))))
      | ~ class_Orderings_Oorder(U_345) ),
    inference(definitional_conversion,[status(esa)],[f_96_3]) ).

cnf(f_96_5,plain,
    ( c_SEQ_Oincseq(U_345,U_346)
    | ~ c_Orderings_Oord__class_Oless__eq(U_345,hAPP(U_346,sK16(U_346,U_345)),hAPP(U_346,c_Nat_OSuc(sK16(U_346,U_345))))
    | ~ class_Orderings_Oorder(U_345) ),
    inference(clausify,[status(thm)],[f_96_4]) ).

fof(f_97_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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(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_97_2,plain,
    ! [U_348,U_347] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_347,U_348)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_347),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_348),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
      & ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_347),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_348),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_347,U_348) ) ),
    inference(variable_rename,[status(thm)],[f_97_1]) ).

fof(f_97_3,plain,
    ( ! [U_352,U_350] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_350,U_352)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_350),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_352),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
    & ! [U_351,U_349] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_349),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_351),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_349,U_351) ) ),
    inference(miniscope,[status(thm)],[f_97_2]) ).

fof(f_97_4,plain,
    ( ! [U_350,U_352] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_350,U_352)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_350),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_352),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
    & ! [U_349,U_351] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_349),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_351),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_349,U_351) ) ),
    inference(definitional_conversion,[status(esa)],[f_97_3]) ).

cnf(f_97_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_349),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_351),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_349,U_351) ),
    inference(clausify,[status(thm)],[f_97_4]) ).

cnf(f_97_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_350,U_352)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_350),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_352),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
    inference(clausify,[status(thm)],[f_97_4]) ).

fof(f_98_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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(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_98_2,plain,
    ! [U_354,U_353] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_353,U_354)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_353),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_354)) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_353),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_354))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_353,U_354) ) ),
    inference(variable_rename,[status(thm)],[f_98_1]) ).

fof(f_98_3,plain,
    ( ! [U_358,U_356] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_356,U_358)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_356),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_358)) )
    & ! [U_357,U_355] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_355),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_357))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_355,U_357) ) ),
    inference(miniscope,[status(thm)],[f_98_2]) ).

fof(f_98_4,plain,
    ( ! [U_358,U_356] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_356,U_358)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_356),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_358)) )
    & ! [U_357,U_355] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_355),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_357))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_355,U_357) ) ),
    inference(definitional_conversion,[status(esa)],[f_98_3]) ).

cnf(f_98_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_355),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_357))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_355,U_357) ),
    inference(clausify,[status(thm)],[f_98_4]) ).

cnf(f_98_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_356,U_358)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_356),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_358)) ),
    inference(clausify,[status(thm)],[f_98_4]) ).

fof(f_99_1,plain,
    ! [V_X_2,T_a] :
      ( c_SEQ_Omonoseq(T_a,V_X_2)
      | ? [B_m,B_n] :
          ( ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m))
          & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n) )
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_monoI2]) ).

fof(f_99_2,plain,
    ! [U_362,U_361] :
      ( c_SEQ_Omonoseq(U_361,U_362)
      | ? [U_360,U_359] :
          ( ~ c_Orderings_Oord__class_Oless__eq(U_361,hAPP(U_362,U_359),hAPP(U_362,U_360))
          & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_360,U_359) )
      | ~ class_Orderings_Oorder(U_361) ),
    inference(variable_rename,[status(thm)],[f_99_1]) ).

fof(f_99_3,plain,
    ! [U_362,U_361] :
      ( c_SEQ_Omonoseq(U_361,U_362)
      | ? [U_359] :
          ( ~ c_Orderings_Oord__class_Oless__eq(U_361,hAPP(U_362,U_359),hAPP(U_362,sK17(U_362,U_361)))
          & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK17(U_362,U_361),U_359) )
      | ~ class_Orderings_Oorder(U_361) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_360,sK17(U_362,U_361))],[f_99_2]) ).

fof(f_99_4,plain,
    ! [U_362,U_361] :
      ( c_SEQ_Omonoseq(U_361,U_362)
      | ( ~ c_Orderings_Oord__class_Oless__eq(U_361,hAPP(U_362,sK18(U_362,U_361)),hAPP(U_362,sK17(U_362,U_361)))
        & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK17(U_362,U_361),sK18(U_362,U_361)) )
      | ~ class_Orderings_Oorder(U_361) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_359,sK18(U_362,U_361))],[f_99_3]) ).

fof(f_99_5,plain,
    ( ! [U_361,U_362] :
        ( ~ c_Orderings_Oord__class_Oless__eq(U_361,hAPP(U_362,sK18(U_362,U_361)),hAPP(U_362,sK17(U_362,U_361)))
        | ~ sP19(U_361,U_362) )
    & ! [U_361,U_362] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK17(U_362,U_361),sK18(U_362,U_361))
        | ~ sP19(U_361,U_362) )
    & ! [U_361,U_362] :
        ( c_SEQ_Omonoseq(U_361,U_362)
        | sP19(U_361,U_362)
        | ~ class_Orderings_Oorder(U_361) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP19])],[f_99_4]) ).

cnf(f_99_6,plain,
    ( c_SEQ_Omonoseq(U_361,U_362)
    | sP19(U_361,U_362)
    | ~ class_Orderings_Oorder(U_361) ),
    inference(clausify,[status(thm)],[f_99_5]) ).

cnf(f_99_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK17(U_362,U_361),sK18(U_362,U_361))
    | ~ sP19(U_361,U_362) ),
    inference(clausify,[status(thm)],[f_99_5]) ).

cnf(f_99_8,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(U_361,hAPP(U_362,sK18(U_362,U_361)),hAPP(U_362,sK17(U_362,U_361)))
    | ~ sP19(U_361,U_362) ),
    inference(clausify,[status(thm)],[f_99_5]) ).

fof(f_100_1,plain,
    ! [V_X_2,T_a] :
      ( c_SEQ_Omonoseq(T_a,V_X_2)
      | ? [B_m,B_n] :
          ( ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n))
          & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n) )
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_monoI1]) ).

fof(f_100_2,plain,
    ! [U_366,U_365] :
      ( c_SEQ_Omonoseq(U_365,U_366)
      | ? [U_364,U_363] :
          ( ~ c_Orderings_Oord__class_Oless__eq(U_365,hAPP(U_366,U_364),hAPP(U_366,U_363))
          & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_364,U_363) )
      | ~ class_Orderings_Oorder(U_365) ),
    inference(variable_rename,[status(thm)],[f_100_1]) ).

fof(f_100_3,plain,
    ! [U_366,U_365] :
      ( c_SEQ_Omonoseq(U_365,U_366)
      | ? [U_363] :
          ( ~ c_Orderings_Oord__class_Oless__eq(U_365,hAPP(U_366,sK19(U_366,U_365)),hAPP(U_366,U_363))
          & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK19(U_366,U_365),U_363) )
      | ~ class_Orderings_Oorder(U_365) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_364,sK19(U_366,U_365))],[f_100_2]) ).

fof(f_100_4,plain,
    ! [U_366,U_365] :
      ( c_SEQ_Omonoseq(U_365,U_366)
      | ( ~ c_Orderings_Oord__class_Oless__eq(U_365,hAPP(U_366,sK19(U_366,U_365)),hAPP(U_366,sK20(U_366,U_365)))
        & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK19(U_366,U_365),sK20(U_366,U_365)) )
      | ~ class_Orderings_Oorder(U_365) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_363,sK20(U_366,U_365))],[f_100_3]) ).

fof(f_100_5,plain,
    ( ! [U_365,U_366] :
        ( ~ c_Orderings_Oord__class_Oless__eq(U_365,hAPP(U_366,sK19(U_366,U_365)),hAPP(U_366,sK20(U_366,U_365)))
        | ~ sP20(U_365,U_366) )
    & ! [U_365,U_366] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK19(U_366,U_365),sK20(U_366,U_365))
        | ~ sP20(U_365,U_366) )
    & ! [U_365,U_366] :
        ( c_SEQ_Omonoseq(U_365,U_366)
        | sP20(U_365,U_366)
        | ~ class_Orderings_Oorder(U_365) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP20])],[f_100_4]) ).

cnf(f_100_6,plain,
    ( c_SEQ_Omonoseq(U_365,U_366)
    | sP20(U_365,U_366)
    | ~ class_Orderings_Oorder(U_365) ),
    inference(clausify,[status(thm)],[f_100_5]) ).

cnf(f_100_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK19(U_366,U_365),sK20(U_366,U_365))
    | ~ sP20(U_365,U_366) ),
    inference(clausify,[status(thm)],[f_100_5]) ).

cnf(f_100_8,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(U_365,hAPP(U_366,sK19(U_366,U_365)),hAPP(U_366,sK20(U_366,U_365)))
    | ~ sP20(U_365,U_366) ),
    inference(clausify,[status(thm)],[f_100_5]) ).

fof(f_101_1,plain,
    ! [V_X_2,T_a] :
      ( c_SEQ_Omonoseq(T_a,V_X_2)
      | ? [B_n] : ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,c_Nat_OSuc(B_n)),hAPP(V_X_2,B_n))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mono__SucI2]) ).

fof(f_101_2,plain,
    ! [U_369,U_368] :
      ( c_SEQ_Omonoseq(U_368,U_369)
      | ? [U_367] : ~ c_Orderings_Oord__class_Oless__eq(U_368,hAPP(U_369,c_Nat_OSuc(U_367)),hAPP(U_369,U_367))
      | ~ class_Orderings_Oorder(U_368) ),
    inference(variable_rename,[status(thm)],[f_101_1]) ).

fof(f_101_3,plain,
    ! [U_369,U_368] :
      ( c_SEQ_Omonoseq(U_368,U_369)
      | ~ c_Orderings_Oord__class_Oless__eq(U_368,hAPP(U_369,c_Nat_OSuc(sK21(U_369,U_368))),hAPP(U_369,sK21(U_369,U_368)))
      | ~ class_Orderings_Oorder(U_368) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_367,sK21(U_369,U_368))],[f_101_2]) ).

fof(f_101_4,plain,
    ! [U_368,U_369] :
      ( c_SEQ_Omonoseq(U_368,U_369)
      | ~ c_Orderings_Oord__class_Oless__eq(U_368,hAPP(U_369,c_Nat_OSuc(sK21(U_369,U_368))),hAPP(U_369,sK21(U_369,U_368)))
      | ~ class_Orderings_Oorder(U_368) ),
    inference(definitional_conversion,[status(esa)],[f_101_3]) ).

cnf(f_101_5,plain,
    ( c_SEQ_Omonoseq(U_368,U_369)
    | ~ c_Orderings_Oord__class_Oless__eq(U_368,hAPP(U_369,c_Nat_OSuc(sK21(U_369,U_368))),hAPP(U_369,sK21(U_369,U_368)))
    | ~ class_Orderings_Oorder(U_368) ),
    inference(clausify,[status(thm)],[f_101_4]) ).

fof(f_102_1,plain,
    ! [V_X_2,T_a] :
      ( c_SEQ_Omonoseq(T_a,V_X_2)
      | ? [B_n] : ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,c_Nat_OSuc(B_n)))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mono__SucI1]) ).

fof(f_102_2,plain,
    ! [U_372,U_371] :
      ( c_SEQ_Omonoseq(U_371,U_372)
      | ? [U_370] : ~ c_Orderings_Oord__class_Oless__eq(U_371,hAPP(U_372,U_370),hAPP(U_372,c_Nat_OSuc(U_370)))
      | ~ class_Orderings_Oorder(U_371) ),
    inference(variable_rename,[status(thm)],[f_102_1]) ).

fof(f_102_3,plain,
    ! [U_372,U_371] :
      ( c_SEQ_Omonoseq(U_371,U_372)
      | ~ c_Orderings_Oord__class_Oless__eq(U_371,hAPP(U_372,sK22(U_372,U_371)),hAPP(U_372,c_Nat_OSuc(sK22(U_372,U_371))))
      | ~ class_Orderings_Oorder(U_371) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_370,sK22(U_372,U_371))],[f_102_2]) ).

fof(f_102_4,plain,
    ! [U_371,U_372] :
      ( c_SEQ_Omonoseq(U_371,U_372)
      | ~ c_Orderings_Oord__class_Oless__eq(U_371,hAPP(U_372,sK22(U_372,U_371)),hAPP(U_372,c_Nat_OSuc(sK22(U_372,U_371))))
      | ~ class_Orderings_Oorder(U_371) ),
    inference(definitional_conversion,[status(esa)],[f_102_3]) ).

cnf(f_102_5,plain,
    ( c_SEQ_Omonoseq(U_371,U_372)
    | ~ c_Orderings_Oord__class_Oless__eq(U_371,hAPP(U_372,sK22(U_372,U_371)),hAPP(U_372,c_Nat_OSuc(sK22(U_372,U_371))))
    | ~ class_Orderings_Oorder(U_371) ),
    inference(clausify,[status(thm)],[f_102_4]) ).

fof(f_103_1,plain,
    hAPP(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_103_2,plain,
    hAPP(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_103_1]) ).

cnf(f_103_3,plain,
    hAPP(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_103_2]) ).

fof(f_104_1,plain,
    ! [V_i_2,V_n_2,V_inc_2,T_a] :
      ( c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,c_Nat_OSuc(V_n_2),V_i_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,V_n_2,hAPP(V_inc_2,V_i_2))
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__aux_Osimps_I2_J]) ).

fof(f_104_2,plain,
    ! [U_376,U_375,U_374,U_373] :
      ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_373,U_374,c_Nat_OSuc(U_375),U_376) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_373,U_374,U_375,hAPP(U_374,U_376))
      | ~ class_Rings_Osemiring__1(U_373) ),
    inference(variable_rename,[status(thm)],[f_104_1]) ).

fof(f_104_3,plain,
    ! [U_374,U_373,U_375,U_376] :
      ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_373,U_374,c_Nat_OSuc(U_375),U_376) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_373,U_374,U_375,hAPP(U_374,U_376))
      | ~ class_Rings_Osemiring__1(U_373) ),
    inference(definitional_conversion,[status(esa)],[f_104_2]) ).

cnf(f_104_4,plain,
    ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_373,U_374,c_Nat_OSuc(U_375),U_376) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_373,U_374,U_375,hAPP(U_374,U_376))
    | ~ class_Rings_Osemiring__1(U_373) ),
    inference(clausify,[status(thm)],[f_104_3]) ).

fof(f_105_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_105_2,plain,
    ! [U_379,U_378,U_377] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_378,U_377)),U_379) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_378),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_377,U_379))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_377,U_378) ),
    inference(variable_rename,[status(thm)],[f_105_1]) ).

fof(f_105_3,plain,
    ! [U_377,U_379,U_378] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_378,U_377)),U_379) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_378),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_377,U_379))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_377,U_378) ),
    inference(definitional_conversion,[status(esa)],[f_105_2]) ).

cnf(f_105_4,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_378,U_377)),U_379) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_378),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_377,U_379))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_377,U_378) ),
    inference(clausify,[status(thm)],[f_105_3]) ).

fof(f_106_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_106_2,plain,
    ! [U_380] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_380,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_106_1]) ).

fof(f_106_3,plain,
    ! [U_380] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_380,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_106_2]) ).

cnf(f_106_4,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_380,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_106_3]) ).

fof(f_107_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_107_2,plain,
    ! [U_381] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_381,c_Nat_OSuc(U_381)),
    inference(variable_rename,[status(thm)],[f_107_1]) ).

fof(f_107_3,plain,
    ! [U_381] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_381,c_Nat_OSuc(U_381)),
    inference(definitional_conversion,[status(esa)],[f_107_2]) ).

cnf(f_107_4,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_381,c_Nat_OSuc(U_381)),
    inference(clausify,[status(thm)],[f_107_3]) ).

fof(f_108_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_108_2,plain,
    ! [U_383,U_382] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_382),c_Nat_OSuc(U_383))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_382,U_383) ),
    inference(variable_rename,[status(thm)],[f_108_1]) ).

fof(f_108_3,plain,
    ! [U_382,U_383] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_382),c_Nat_OSuc(U_383))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_382,U_383) ),
    inference(definitional_conversion,[status(esa)],[f_108_2]) ).

cnf(f_108_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_382),c_Nat_OSuc(U_383))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_382,U_383) ),
    inference(clausify,[status(thm)],[f_108_3]) ).

fof(f_109_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_109_2,plain,
    ! [U_384] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_384),
    inference(variable_rename,[status(thm)],[f_109_1]) ).

fof(f_109_3,plain,
    ! [U_384] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_384),
    inference(definitional_conversion,[status(esa)],[f_109_2]) ).

cnf(f_109_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_384),
    inference(clausify,[status(thm)],[f_109_3]) ).

fof(f_110_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_110_2,plain,
    ! [U_385] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(U_385)),
    inference(variable_rename,[status(thm)],[f_110_1]) ).

fof(f_110_3,plain,
    ! [U_385] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(U_385)),
    inference(definitional_conversion,[status(esa)],[f_110_2]) ).

cnf(f_110_4,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(U_385)),
    inference(clausify,[status(thm)],[f_110_3]) ).

fof(f_111_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_111_2,plain,
    ! [U_386] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_386),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_386,
    inference(variable_rename,[status(thm)],[f_111_1]) ).

fof(f_111_3,plain,
    ! [U_386] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_386),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_386,
    inference(definitional_conversion,[status(esa)],[f_111_2]) ).

cnf(f_111_4,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_386),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_386,
    inference(clausify,[status(thm)],[f_111_3]) ).

fof(f_112_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_112_2,plain,
    ! [U_388,U_387] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_387,c_Nat_OSuc(U_388)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_387,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_388),
    inference(variable_rename,[status(thm)],[f_112_1]) ).

fof(f_112_3,plain,
    ! [U_387,U_388] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_387,c_Nat_OSuc(U_388)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_387,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_388),
    inference(definitional_conversion,[status(esa)],[f_112_2]) ).

cnf(f_112_4,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_387,c_Nat_OSuc(U_388)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_387,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_388),
    inference(clausify,[status(thm)],[f_112_3]) ).

fof(f_113_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_113_2,plain,
    ! [U_389] :
      ( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_389,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_389
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_389) ),
    inference(variable_rename,[status(thm)],[f_113_1]) ).

fof(f_113_3,plain,
    ! [U_389] :
      ( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_389,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_389
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_389) ),
    inference(definitional_conversion,[status(esa)],[f_113_2]) ).

cnf(f_113_4,plain,
    ( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_389,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_389
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_389) ),
    inference(clausify,[status(thm)],[f_113_3]) ).

fof(f_114_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_114_2,plain,
    ! [U_390] :
      ( U_390 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_390,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_390) ),
    inference(variable_rename,[status(thm)],[f_114_1]) ).

fof(f_114_3,plain,
    ! [U_390] :
      ( U_390 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_390,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_390) ),
    inference(definitional_conversion,[status(esa)],[f_114_2]) ).

cnf(f_114_4,plain,
    ( U_390 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_390,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_390) ),
    inference(clausify,[status(thm)],[f_114_3]) ).

fof(f_115_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_115_2,plain,
    ! [U_392,U_391] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_391,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_391,U_392)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_115_1]) ).

fof(f_115_3,plain,
    ! [U_391,U_392] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_391,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_391,U_392)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_115_2]) ).

cnf(f_115_4,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_391,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_391,U_392)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_115_3]) ).

fof(f_116_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_116_2,plain,
    ! [U_394,U_393] :
      ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_393,U_394) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_393,U_394) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_393,U_394)
        | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_393,U_394) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_116_1]) ).

fof(f_116_3,plain,
    ( ! [U_398,U_396] :
        ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_396,U_398) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_396,U_398) )
    & ! [U_397,U_395] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_395,U_397)
        | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_395,U_397) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_116_2]) ).

fof(f_116_4,plain,
    ( ! [U_398,U_396] :
        ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_396,U_398) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_396,U_398) )
    & ! [U_395,U_397] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_395,U_397)
        | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_395,U_397) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_116_3]) ).

cnf(f_116_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_395,U_397)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_395,U_397) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_116_4]) ).

cnf(f_116_6,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_396,U_398) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_396,U_398) ),
    inference(clausify,[status(thm)],[f_116_4]) ).

fof(f_117_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_117_2,plain,
    ! [U_400,U_399] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_399,U_400) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_399,U_400) ),
    inference(variable_rename,[status(thm)],[f_117_1]) ).

fof(f_117_3,plain,
    ! [U_400,U_399] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_399,U_400) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_399,U_400) ),
    inference(definitional_conversion,[status(esa)],[f_117_2]) ).

cnf(f_117_4,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_399,U_400) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_399,U_400) ),
    inference(clausify,[status(thm)],[f_117_3]) ).

fof(f_118_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_118_2,plain,
    ! [U_403] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_403)
        | ! [U_402] : U_403 != c_Nat_OSuc(U_402) )
      & ( ? [U_401] : U_403 = c_Nat_OSuc(U_401)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_403) ) ),
    inference(variable_rename,[status(thm)],[f_118_1]) ).

fof(f_118_3,plain,
    ( ! [U_405] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_405)
        | ! [U_402] : U_405 != c_Nat_OSuc(U_402) )
    & ! [U_404] :
        ( ? [U_401] : U_404 = c_Nat_OSuc(U_401)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_404) ) ),
    inference(miniscope,[status(thm)],[f_118_2]) ).

fof(f_118_4,plain,
    ( ! [U_405] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_405)
        | ! [U_402] : U_405 != c_Nat_OSuc(U_402) )
    & ! [U_404] :
        ( U_404 = c_Nat_OSuc(sK23(U_404))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_404) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_401,sK23(U_404))],[f_118_3]) ).

fof(f_118_5,plain,
    ( ! [U_402,U_405] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_405)
        | U_405 != c_Nat_OSuc(U_402) )
    & ! [U_404] :
        ( U_404 = c_Nat_OSuc(sK23(U_404))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_404) ) ),
    inference(definitional_conversion,[status(esa)],[f_118_4]) ).

cnf(f_118_6,plain,
    ( U_404 = c_Nat_OSuc(sK23(U_404))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_404) ),
    inference(clausify,[status(thm)],[f_118_5]) ).

cnf(f_118_7,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_405)
    | U_405 != c_Nat_OSuc(U_402) ),
    inference(clausify,[status(thm)],[f_118_5]) ).

fof(f_119_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_119_2,plain,
    ! [U_406] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_406,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | U_406 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_406 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_406,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(variable_rename,[status(thm)],[f_119_1]) ).

fof(f_119_3,plain,
    ( ! [U_408] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_408,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | U_408 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_407] :
        ( U_407 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_407,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(miniscope,[status(thm)],[f_119_2]) ).

fof(f_119_4,plain,
    ( ! [U_408] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_408,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | U_408 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_407] :
        ( U_407 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_407,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(definitional_conversion,[status(esa)],[f_119_3]) ).

cnf(f_119_5,plain,
    ( U_407 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_407,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_119_4]) ).

cnf(f_119_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_408,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | U_408 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_119_4]) ).

fof(f_120_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_120_2,plain,
    ! [U_412,U_411] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_411,c_Nat_OSuc(U_412))
        | ( ! [U_410] :
              ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_410,U_412)
              | U_411 != c_Nat_OSuc(U_410) )
          & U_411 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( ? [U_409] :
            ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_409,U_412)
            & U_411 = c_Nat_OSuc(U_409) )
        | U_411 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_411,c_Nat_OSuc(U_412)) ) ),
    inference(variable_rename,[status(thm)],[f_120_1]) ).

fof(f_120_3,plain,
    ( ! [U_416,U_414] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_414,c_Nat_OSuc(U_416))
        | ( ! [U_410] :
              ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_410,U_416)
              | U_414 != c_Nat_OSuc(U_410) )
          & U_414 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_415,U_413] :
        ( ? [U_409] :
            ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_409,U_415)
            & U_413 = c_Nat_OSuc(U_409) )
        | U_413 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_413,c_Nat_OSuc(U_415)) ) ),
    inference(miniscope,[status(thm)],[f_120_2]) ).

fof(f_120_4,plain,
    ( ! [U_416,U_414] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_414,c_Nat_OSuc(U_416))
        | ( ! [U_410] :
              ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_410,U_416)
              | U_414 != c_Nat_OSuc(U_410) )
          & U_414 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_415,U_413] :
        ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK24(U_415,U_413),U_415)
          & U_413 = c_Nat_OSuc(sK24(U_415,U_413)) )
        | U_413 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_413,c_Nat_OSuc(U_415)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_409,sK24(U_415,U_413))],[f_120_3]) ).

fof(f_120_5,plain,
    ( ! [U_416,U_414,U_410] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_410,U_416)
        | U_414 != c_Nat_OSuc(U_410)
        | ~ sP22(U_416,U_414,U_410) )
    & ! [U_416,U_414,U_410] :
        ( U_414 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP22(U_416,U_414,U_410) )
    & ! [U_415,U_413] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK24(U_415,U_413),U_415)
        | ~ sP21(U_415,U_413) )
    & ! [U_415,U_413] :
        ( U_413 = c_Nat_OSuc(sK24(U_415,U_413))
        | ~ sP21(U_415,U_413) )
    & ! [U_416,U_414,U_410] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_414,c_Nat_OSuc(U_416))
        | sP22(U_416,U_414,U_410) )
    & ! [U_415,U_413] :
        ( sP21(U_415,U_413)
        | U_413 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_413,c_Nat_OSuc(U_415)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP21,sP22])],[f_120_4]) ).

cnf(f_120_6,plain,
    ( sP21(U_415,U_413)
    | U_413 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_413,c_Nat_OSuc(U_415)) ),
    inference(clausify,[status(thm)],[f_120_5]) ).

cnf(f_120_7,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_414,c_Nat_OSuc(U_416))
    | sP22(U_416,U_414,U_410) ),
    inference(clausify,[status(thm)],[f_120_5]) ).

cnf(f_120_8,plain,
    ( U_413 = c_Nat_OSuc(sK24(U_415,U_413))
    | ~ sP21(U_415,U_413) ),
    inference(clausify,[status(thm)],[f_120_5]) ).

cnf(f_120_9,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK24(U_415,U_413),U_415)
    | ~ sP21(U_415,U_413) ),
    inference(clausify,[status(thm)],[f_120_5]) ).

cnf(f_120_10,plain,
    ( U_414 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP22(U_416,U_414,U_410) ),
    inference(clausify,[status(thm)],[f_120_5]) ).

cnf(f_120_11,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_410,U_416)
    | U_414 != c_Nat_OSuc(U_410)
    | ~ sP22(U_416,U_414,U_410) ),
    inference(clausify,[status(thm)],[f_120_5]) ).

fof(f_121_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_121_2,plain,
    ! [U_417] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_417,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_121_1]) ).

fof(f_121_3,plain,
    ! [U_417] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_417,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_121_2]) ).

cnf(f_121_4,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_417,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_121_3]) ).

fof(f_122_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_122_2,plain,
    ! [U_418] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_418,U_418),
    inference(variable_rename,[status(thm)],[f_122_1]) ).

fof(f_122_3,plain,
    ! [U_418] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_418,U_418),
    inference(definitional_conversion,[status(esa)],[f_122_2]) ).

cnf(f_122_4,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_418,U_418),
    inference(clausify,[status(thm)],[f_122_3]) ).

fof(f_123_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_123_2,plain,
    ! [U_420,U_419] :
      ( ~ c_Orderings_Oord__class_Oless(U_419,U_420,U_420)
      | ~ class_Orderings_Opreorder(U_419) ),
    inference(variable_rename,[status(thm)],[f_123_1]) ).

fof(f_123_3,plain,
    ! [U_419,U_420] :
      ( ~ c_Orderings_Oord__class_Oless(U_419,U_420,U_420)
      | ~ class_Orderings_Opreorder(U_419) ),
    inference(definitional_conversion,[status(esa)],[f_123_2]) ).

cnf(f_123_4,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_419,U_420,U_420)
    | ~ class_Orderings_Opreorder(U_419) ),
    inference(clausify,[status(thm)],[f_123_3]) ).

fof(f_124_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_124_2,plain,
    ! [U_421] :
      ( ( U_421 != 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_421) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_421)
        | U_421 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_124_1]) ).

fof(f_124_3,plain,
    ( ! [U_423] :
        ( U_423 != 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_423) )
    & ! [U_422] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_422)
        | U_422 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_124_2]) ).

fof(f_124_4,plain,
    ( ! [U_423] :
        ( U_423 != 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_423) )
    & ! [U_422] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_422)
        | U_422 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_124_3]) ).

cnf(f_124_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_422)
    | U_422 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_124_4]) ).

cnf(f_124_6,plain,
    ( U_423 != 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_423) ),
    inference(clausify,[status(thm)],[f_124_4]) ).

fof(f_125_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_125_2,plain,
    ! [U_425,U_424] :
      ( ( U_424 != U_425
        | ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_425,U_424)
          & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_424,U_425) ) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_425,U_424)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_424,U_425)
        | U_424 = U_425 ) ),
    inference(variable_rename,[status(thm)],[f_125_1]) ).

fof(f_125_3,plain,
    ( ! [U_429,U_427] :
        ( U_427 != U_429
        | ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_429,U_427)
          & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_427,U_429) ) )
    & ! [U_428,U_426] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_428,U_426)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_426,U_428)
        | U_426 = U_428 ) ),
    inference(miniscope,[status(thm)],[f_125_2]) ).

fof(f_125_4,plain,
    ( ! [U_427,U_429] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_429,U_427)
        | ~ sP23(U_427,U_429) )
    & ! [U_427,U_429] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_427,U_429)
        | ~ sP23(U_427,U_429) )
    & ! [U_427,U_429] :
        ( U_427 != U_429
        | sP23(U_427,U_429) )
    & ! [U_426,U_428] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_428,U_426)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_426,U_428)
        | U_426 = U_428 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP23])],[f_125_3]) ).

cnf(f_125_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_428,U_426)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_426,U_428)
    | U_426 = U_428 ),
    inference(clausify,[status(thm)],[f_125_4]) ).

cnf(f_125_6,plain,
    ( U_427 != U_429
    | sP23(U_427,U_429) ),
    inference(clausify,[status(thm)],[f_125_4]) ).

cnf(f_125_7,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_427,U_429)
    | ~ sP23(U_427,U_429) ),
    inference(clausify,[status(thm)],[f_125_4]) ).

cnf(f_125_8,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_429,U_427)
    | ~ sP23(U_427,U_429) ),
    inference(clausify,[status(thm)],[f_125_4]) ).

fof(f_126_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_126_2,plain,
    ! [U_432,U_431,U_430] :
      ( ( ( U_431 != U_432
          | ( ~ c_Orderings_Oord__class_Oless(U_430,U_432,U_431)
            & ~ c_Orderings_Oord__class_Oless(U_430,U_431,U_432) ) )
        & ( c_Orderings_Oord__class_Oless(U_430,U_432,U_431)
          | c_Orderings_Oord__class_Oless(U_430,U_431,U_432)
          | U_431 = U_432 ) )
      | ~ class_Orderings_Olinorder(U_430) ),
    inference(variable_rename,[status(thm)],[f_126_1]) ).

fof(f_126_3,plain,
    ( ! [U_432,U_430,U_431] :
        ( ~ c_Orderings_Oord__class_Oless(U_430,U_432,U_431)
        | ~ sP24(U_432,U_430,U_431) )
    & ! [U_432,U_430,U_431] :
        ( ~ c_Orderings_Oord__class_Oless(U_430,U_431,U_432)
        | ~ sP24(U_432,U_430,U_431) )
    & ! [U_432,U_430,U_431] :
        ( U_431 != U_432
        | sP24(U_432,U_430,U_431)
        | ~ sP25(U_432,U_430,U_431) )
    & ! [U_432,U_430,U_431] :
        ( c_Orderings_Oord__class_Oless(U_430,U_432,U_431)
        | c_Orderings_Oord__class_Oless(U_430,U_431,U_432)
        | U_431 = U_432
        | ~ sP25(U_432,U_430,U_431) )
    & ! [U_432,U_430,U_431] :
        ( sP25(U_432,U_430,U_431)
        | ~ class_Orderings_Olinorder(U_430) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP24,sP25])],[f_126_2]) ).

cnf(f_126_4,plain,
    ( sP25(U_432,U_430,U_431)
    | ~ class_Orderings_Olinorder(U_430) ),
    inference(clausify,[status(thm)],[f_126_3]) ).

cnf(f_126_5,plain,
    ( c_Orderings_Oord__class_Oless(U_430,U_432,U_431)
    | c_Orderings_Oord__class_Oless(U_430,U_431,U_432)
    | U_431 = U_432
    | ~ sP25(U_432,U_430,U_431) ),
    inference(clausify,[status(thm)],[f_126_3]) ).

cnf(f_126_6,plain,
    ( U_431 != U_432
    | sP24(U_432,U_430,U_431)
    | ~ sP25(U_432,U_430,U_431) ),
    inference(clausify,[status(thm)],[f_126_3]) ).

cnf(f_126_7,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_430,U_431,U_432)
    | ~ sP24(U_432,U_430,U_431) ),
    inference(clausify,[status(thm)],[f_126_3]) ).

cnf(f_126_8,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_430,U_432,U_431)
    | ~ sP24(U_432,U_430,U_431) ),
    inference(clausify,[status(thm)],[f_126_3]) ).

fof(f_127_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_127_2,plain,
    ! [U_435,U_434,U_433] :
      ( ( ( ~ c_Orderings_Oord__class_Oless(U_433,U_434,U_435)
          | ( U_434 != U_435
            & ~ c_Orderings_Oord__class_Oless(U_433,U_435,U_434) ) )
        & ( U_434 = U_435
          | c_Orderings_Oord__class_Oless(U_433,U_435,U_434)
          | c_Orderings_Oord__class_Oless(U_433,U_434,U_435) ) )
      | ~ class_Orderings_Olinorder(U_433) ),
    inference(variable_rename,[status(thm)],[f_127_1]) ).

fof(f_127_3,plain,
    ( ! [U_434,U_435,U_433] :
        ( U_434 != U_435
        | ~ sP26(U_434,U_435,U_433) )
    & ! [U_434,U_435,U_433] :
        ( ~ c_Orderings_Oord__class_Oless(U_433,U_435,U_434)
        | ~ sP26(U_434,U_435,U_433) )
    & ! [U_434,U_435,U_433] :
        ( ~ c_Orderings_Oord__class_Oless(U_433,U_434,U_435)
        | sP26(U_434,U_435,U_433)
        | ~ sP27(U_434,U_435,U_433) )
    & ! [U_434,U_435,U_433] :
        ( U_434 = U_435
        | c_Orderings_Oord__class_Oless(U_433,U_435,U_434)
        | c_Orderings_Oord__class_Oless(U_433,U_434,U_435)
        | ~ sP27(U_434,U_435,U_433) )
    & ! [U_434,U_435,U_433] :
        ( sP27(U_434,U_435,U_433)
        | ~ class_Orderings_Olinorder(U_433) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP26,sP27])],[f_127_2]) ).

cnf(f_127_4,plain,
    ( sP27(U_434,U_435,U_433)
    | ~ class_Orderings_Olinorder(U_433) ),
    inference(clausify,[status(thm)],[f_127_3]) ).

cnf(f_127_5,plain,
    ( U_434 = U_435
    | c_Orderings_Oord__class_Oless(U_433,U_435,U_434)
    | c_Orderings_Oord__class_Oless(U_433,U_434,U_435)
    | ~ sP27(U_434,U_435,U_433) ),
    inference(clausify,[status(thm)],[f_127_3]) ).

cnf(f_127_6,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_433,U_434,U_435)
    | sP26(U_434,U_435,U_433)
    | ~ sP27(U_434,U_435,U_433) ),
    inference(clausify,[status(thm)],[f_127_3]) ).

cnf(f_127_7,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_433,U_435,U_434)
    | ~ sP26(U_434,U_435,U_433) ),
    inference(clausify,[status(thm)],[f_127_3]) ).

cnf(f_127_8,plain,
    ( U_434 != U_435
    | ~ sP26(U_434,U_435,U_433) ),
    inference(clausify,[status(thm)],[f_127_3]) ).

fof(f_128_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_128_2,plain,
    ! [U_436] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_436) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_128_1]) ).

fof(f_128_3,plain,
    ! [U_436] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_436) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_128_2]) ).

cnf(f_128_4,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_436) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_128_3]) ).

fof(f_129_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_129_2,plain,
    ! [U_438,U_437] :
      ( ( ( c_Groups_Ozero__class_Ozero(U_437) = U_438
          | U_438 != c_Groups_Ozero__class_Ozero(U_437) )
        & ( U_438 = c_Groups_Ozero__class_Ozero(U_437)
          | c_Groups_Ozero__class_Ozero(U_437) != U_438 ) )
      | ~ class_Groups_Ozero(U_437) ),
    inference(variable_rename,[status(thm)],[f_129_1]) ).

fof(f_129_3,plain,
    ( ! [U_437,U_438] :
        ( c_Groups_Ozero__class_Ozero(U_437) = U_438
        | U_438 != c_Groups_Ozero__class_Ozero(U_437)
        | ~ sP28(U_437,U_438) )
    & ! [U_437,U_438] :
        ( U_438 = c_Groups_Ozero__class_Ozero(U_437)
        | c_Groups_Ozero__class_Ozero(U_437) != U_438
        | ~ sP28(U_437,U_438) )
    & ! [U_437,U_438] :
        ( sP28(U_437,U_438)
        | ~ class_Groups_Ozero(U_437) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP28])],[f_129_2]) ).

cnf(f_129_4,plain,
    ( sP28(U_437,U_438)
    | ~ class_Groups_Ozero(U_437) ),
    inference(clausify,[status(thm)],[f_129_3]) ).

cnf(f_129_5,plain,
    ( U_438 = c_Groups_Ozero__class_Ozero(U_437)
    | c_Groups_Ozero__class_Ozero(U_437) != U_438
    | ~ sP28(U_437,U_438) ),
    inference(clausify,[status(thm)],[f_129_3]) ).

cnf(f_129_6,plain,
    ( c_Groups_Ozero__class_Ozero(U_437) = U_438
    | U_438 != c_Groups_Ozero__class_Ozero(U_437)
    | ~ sP28(U_437,U_438) ),
    inference(clausify,[status(thm)],[f_129_3]) ).

fof(f_130_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_130_2,plain,
    ! [U_440,U_439] :
      ( ( 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_439,U_440))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_440,U_439) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_440,U_439)
        | ~ 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_439,U_440)) ) ),
    inference(variable_rename,[status(thm)],[f_130_1]) ).

fof(f_130_3,plain,
    ( ! [U_444,U_442] :
        ( 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_442,U_444))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_444,U_442) )
    & ! [U_443,U_441] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_443,U_441)
        | ~ 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_441,U_443)) ) ),
    inference(miniscope,[status(thm)],[f_130_2]) ).

fof(f_130_4,plain,
    ( ! [U_442,U_444] :
        ( 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_442,U_444))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_444,U_442) )
    & ! [U_443,U_441] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_443,U_441)
        | ~ 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_441,U_443)) ) ),
    inference(definitional_conversion,[status(esa)],[f_130_3]) ).

cnf(f_130_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_443,U_441)
    | ~ 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_441,U_443)) ),
    inference(clausify,[status(thm)],[f_130_4]) ).

cnf(f_130_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_442,U_444))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_444,U_442) ),
    inference(clausify,[status(thm)],[f_130_4]) ).

fof(f_131_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_131_2,plain,
    ! [U_445] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_445,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_131_1]) ).

fof(f_131_3,plain,
    ! [U_445] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_445,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_131_2]) ).

cnf(f_131_4,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_445,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_131_3]) ).

fof(f_132_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_132_2,plain,
    ! [U_447,U_446] :
      ( c_Groups_Ominus__class_Ominus(U_446,U_447,c_Groups_Ozero__class_Ozero(U_446)) = U_447
      | ~ class_Groups_Ogroup__add(U_446) ),
    inference(variable_rename,[status(thm)],[f_132_1]) ).

fof(f_132_3,plain,
    ! [U_447,U_446] :
      ( c_Groups_Ominus__class_Ominus(U_446,U_447,c_Groups_Ozero__class_Ozero(U_446)) = U_447
      | ~ class_Groups_Ogroup__add(U_446) ),
    inference(definitional_conversion,[status(esa)],[f_132_2]) ).

cnf(f_132_4,plain,
    ( c_Groups_Ominus__class_Ominus(U_446,U_447,c_Groups_Ozero__class_Ozero(U_446)) = U_447
    | ~ class_Groups_Ogroup__add(U_446) ),
    inference(clausify,[status(thm)],[f_132_3]) ).

fof(f_133_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_133_2,plain,
    ! [U_448] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_448,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_448,
    inference(variable_rename,[status(thm)],[f_133_1]) ).

fof(f_133_3,plain,
    ! [U_448] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_448,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_448,
    inference(definitional_conversion,[status(esa)],[f_133_2]) ).

cnf(f_133_4,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_448,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_448,
    inference(clausify,[status(thm)],[f_133_3]) ).

fof(f_134_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_134_2,plain,
    ! [U_450,U_449] :
      ( c_Groups_Ominus__class_Ominus(U_449,U_450,U_450) = c_Groups_Ozero__class_Ozero(U_449)
      | ~ class_Groups_Ogroup__add(U_449) ),
    inference(variable_rename,[status(thm)],[f_134_1]) ).

fof(f_134_3,plain,
    ! [U_449,U_450] :
      ( c_Groups_Ominus__class_Ominus(U_449,U_450,U_450) = c_Groups_Ozero__class_Ozero(U_449)
      | ~ class_Groups_Ogroup__add(U_449) ),
    inference(definitional_conversion,[status(esa)],[f_134_2]) ).

cnf(f_134_4,plain,
    ( c_Groups_Ominus__class_Ominus(U_449,U_450,U_450) = c_Groups_Ozero__class_Ozero(U_449)
    | ~ class_Groups_Ogroup__add(U_449) ),
    inference(clausify,[status(thm)],[f_134_3]) ).

fof(f_135_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_135_2,plain,
    ! [U_451] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_451,U_451) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_135_1]) ).

fof(f_135_3,plain,
    ! [U_451] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_451,U_451) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_135_2]) ).

cnf(f_135_4,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_451,U_451) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_135_3]) ).

fof(f_136_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( ( ( V_a_2 = V_b_2
          | c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) != c_Groups_Ozero__class_Ozero(T_a) )
        & ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
          | V_a_2 != V_b_2 ) )
      | ~ class_Groups_Oab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_eq__iff__diff__eq__0]) ).

fof(f_136_2,plain,
    ! [U_454,U_453,U_452] :
      ( ( ( U_453 = U_454
          | c_Groups_Ominus__class_Ominus(U_452,U_453,U_454) != c_Groups_Ozero__class_Ozero(U_452) )
        & ( c_Groups_Ominus__class_Ominus(U_452,U_453,U_454) = c_Groups_Ozero__class_Ozero(U_452)
          | U_453 != U_454 ) )
      | ~ class_Groups_Oab__group__add(U_452) ),
    inference(variable_rename,[status(thm)],[f_136_1]) ).

fof(f_136_3,plain,
    ( ! [U_452,U_453,U_454] :
        ( U_453 = U_454
        | c_Groups_Ominus__class_Ominus(U_452,U_453,U_454) != c_Groups_Ozero__class_Ozero(U_452)
        | ~ sP29(U_452,U_453,U_454) )
    & ! [U_452,U_453,U_454] :
        ( c_Groups_Ominus__class_Ominus(U_452,U_453,U_454) = c_Groups_Ozero__class_Ozero(U_452)
        | U_453 != U_454
        | ~ sP29(U_452,U_453,U_454) )
    & ! [U_452,U_453,U_454] :
        ( sP29(U_452,U_453,U_454)
        | ~ class_Groups_Oab__group__add(U_452) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP29])],[f_136_2]) ).

cnf(f_136_4,plain,
    ( sP29(U_452,U_453,U_454)
    | ~ class_Groups_Oab__group__add(U_452) ),
    inference(clausify,[status(thm)],[f_136_3]) ).

cnf(f_136_5,plain,
    ( c_Groups_Ominus__class_Ominus(U_452,U_453,U_454) = c_Groups_Ozero__class_Ozero(U_452)
    | U_453 != U_454
    | ~ sP29(U_452,U_453,U_454) ),
    inference(clausify,[status(thm)],[f_136_3]) ).

cnf(f_136_6,plain,
    ( U_453 = U_454
    | c_Groups_Ominus__class_Ominus(U_452,U_453,U_454) != c_Groups_Ozero__class_Ozero(U_452)
    | ~ sP29(U_452,U_453,U_454) ),
    inference(clausify,[status(thm)],[f_136_3]) ).

fof(f_137_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
          | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_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_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))
          | ~ c_Orderings_Oord__class_Oless(T_a,V_a_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_137_2,plain,
    ! [U_457,U_456,U_455] :
      ( ( ( c_Orderings_Oord__class_Oless(U_455,U_456,U_457)
          | ~ c_Orderings_Oord__class_Oless(U_455,c_Groups_Ominus__class_Ominus(U_455,U_456,U_457),c_Groups_Ozero__class_Ozero(U_455)) )
        & ( c_Orderings_Oord__class_Oless(U_455,c_Groups_Ominus__class_Ominus(U_455,U_456,U_457),c_Groups_Ozero__class_Ozero(U_455))
          | ~ c_Orderings_Oord__class_Oless(U_455,U_456,U_457) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_455) ),
    inference(variable_rename,[status(thm)],[f_137_1]) ).

fof(f_137_3,plain,
    ( ! [U_457,U_456,U_455] :
        ( c_Orderings_Oord__class_Oless(U_455,U_456,U_457)
        | ~ c_Orderings_Oord__class_Oless(U_455,c_Groups_Ominus__class_Ominus(U_455,U_456,U_457),c_Groups_Ozero__class_Ozero(U_455))
        | ~ sP30(U_457,U_456,U_455) )
    & ! [U_457,U_456,U_455] :
        ( c_Orderings_Oord__class_Oless(U_455,c_Groups_Ominus__class_Ominus(U_455,U_456,U_457),c_Groups_Ozero__class_Ozero(U_455))
        | ~ c_Orderings_Oord__class_Oless(U_455,U_456,U_457)
        | ~ sP30(U_457,U_456,U_455) )
    & ! [U_457,U_456,U_455] :
        ( sP30(U_457,U_456,U_455)
        | ~ class_Groups_Oordered__ab__group__add(U_455) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP30])],[f_137_2]) ).

cnf(f_137_4,plain,
    ( sP30(U_457,U_456,U_455)
    | ~ class_Groups_Oordered__ab__group__add(U_455) ),
    inference(clausify,[status(thm)],[f_137_3]) ).

cnf(f_137_5,plain,
    ( c_Orderings_Oord__class_Oless(U_455,c_Groups_Ominus__class_Ominus(U_455,U_456,U_457),c_Groups_Ozero__class_Ozero(U_455))
    | ~ c_Orderings_Oord__class_Oless(U_455,U_456,U_457)
    | ~ sP30(U_457,U_456,U_455) ),
    inference(clausify,[status(thm)],[f_137_3]) ).

cnf(f_137_6,plain,
    ( c_Orderings_Oord__class_Oless(U_455,U_456,U_457)
    | ~ c_Orderings_Oord__class_Oless(U_455,c_Groups_Ominus__class_Ominus(U_455,U_456,U_457),c_Groups_Ozero__class_Ozero(U_455))
    | ~ sP30(U_457,U_456,U_455) ),
    inference(clausify,[status(thm)],[f_137_3]) ).

fof(f_138_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_138_2,plain,
    ! [U_460,U_459,U_458] :
      ( c_Orderings_Oord__class_Oless(U_458,U_460,U_459)
      | U_459 = U_460
      | c_Orderings_Oord__class_Oless(U_458,U_459,U_460)
      | ~ class_Orderings_Olinorder(U_458) ),
    inference(variable_rename,[status(thm)],[f_138_1]) ).

fof(f_138_3,plain,
    ! [U_460,U_459,U_458] :
      ( c_Orderings_Oord__class_Oless(U_458,U_460,U_459)
      | U_459 = U_460
      | c_Orderings_Oord__class_Oless(U_458,U_459,U_460)
      | ~ class_Orderings_Olinorder(U_458) ),
    inference(definitional_conversion,[status(esa)],[f_138_2]) ).

cnf(f_138_4,plain,
    ( c_Orderings_Oord__class_Oless(U_458,U_460,U_459)
    | U_459 = U_460
    | c_Orderings_Oord__class_Oless(U_458,U_459,U_460)
    | ~ class_Orderings_Olinorder(U_458) ),
    inference(clausify,[status(thm)],[f_138_3]) ).

fof(f_139_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( ( ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
          | V_a_2 != V_b_2 )
        & ( V_a_2 = V_b_2
          | c_Groups_Ominus__class_Ominus(T_a,V_a_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_139_2,plain,
    ! [U_463,U_462,U_461] :
      ( ( ( c_Groups_Ominus__class_Ominus(U_461,U_462,U_463) = c_Groups_Ozero__class_Ozero(U_461)
          | U_462 != U_463 )
        & ( U_462 = U_463
          | c_Groups_Ominus__class_Ominus(U_461,U_462,U_463) != c_Groups_Ozero__class_Ozero(U_461) ) )
      | ~ class_Groups_Ogroup__add(U_461) ),
    inference(variable_rename,[status(thm)],[f_139_1]) ).

fof(f_139_3,plain,
    ( ! [U_461,U_462,U_463] :
        ( c_Groups_Ominus__class_Ominus(U_461,U_462,U_463) = c_Groups_Ozero__class_Ozero(U_461)
        | U_462 != U_463
        | ~ sP31(U_461,U_462,U_463) )
    & ! [U_461,U_462,U_463] :
        ( U_462 = U_463
        | c_Groups_Ominus__class_Ominus(U_461,U_462,U_463) != c_Groups_Ozero__class_Ozero(U_461)
        | ~ sP31(U_461,U_462,U_463) )
    & ! [U_461,U_462,U_463] :
        ( sP31(U_461,U_462,U_463)
        | ~ class_Groups_Ogroup__add(U_461) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP31])],[f_139_2]) ).

cnf(f_139_4,plain,
    ( sP31(U_461,U_462,U_463)
    | ~ class_Groups_Ogroup__add(U_461) ),
    inference(clausify,[status(thm)],[f_139_3]) ).

cnf(f_139_5,plain,
    ( U_462 = U_463
    | c_Groups_Ominus__class_Ominus(U_461,U_462,U_463) != c_Groups_Ozero__class_Ozero(U_461)
    | ~ sP31(U_461,U_462,U_463) ),
    inference(clausify,[status(thm)],[f_139_3]) ).

cnf(f_139_6,plain,
    ( c_Groups_Ominus__class_Ominus(U_461,U_462,U_463) = c_Groups_Ozero__class_Ozero(U_461)
    | U_462 != U_463
    | ~ sP31(U_461,U_462,U_463) ),
    inference(clausify,[status(thm)],[f_139_3]) ).

fof(f_140_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_140_2,plain,
    ! [U_466,U_465,U_464] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_464,U_465),U_466) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_464,U_466),U_465),
    inference(variable_rename,[status(thm)],[f_140_1]) ).

fof(f_140_3,plain,
    ! [U_466,U_464,U_465] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_464,U_465),U_466) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_464,U_466),U_465),
    inference(definitional_conversion,[status(esa)],[f_140_2]) ).

cnf(f_140_4,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_464,U_465),U_466) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_464,U_466),U_465),
    inference(clausify,[status(thm)],[f_140_3]) ).

fof(f_141_1,plain,
    ! [V_i_2,V_inc_2,T_a] :
      ( c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2) = V_i_2
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__aux_Osimps_I1_J]) ).

fof(f_141_2,plain,
    ! [U_469,U_468,U_467] :
      ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_467,U_468,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_469) = U_469
      | ~ class_Rings_Osemiring__1(U_467) ),
    inference(variable_rename,[status(thm)],[f_141_1]) ).

fof(f_141_3,plain,
    ! [U_467,U_468,U_469] :
      ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_467,U_468,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_469) = U_469
      | ~ class_Rings_Osemiring__1(U_467) ),
    inference(definitional_conversion,[status(esa)],[f_141_2]) ).

cnf(f_141_4,plain,
    ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_467,U_468,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_469) = U_469
    | ~ class_Rings_Osemiring__1(U_467) ),
    inference(clausify,[status(thm)],[f_141_3]) ).

fof(f_142_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_142_2,plain,
    ! [U_472,U_471,U_470] :
      ( ( ( ~ c_Orderings_Oord__class_Oless(U_470,U_472,U_471)
          | U_472 != U_471 )
        & ( U_472 = U_471
          | c_Orderings_Oord__class_Oless(U_470,U_472,U_471) ) )
      | c_Orderings_Oord__class_Oless(U_470,U_471,U_472)
      | ~ class_Orderings_Olinorder(U_470) ),
    inference(variable_rename,[status(thm)],[f_142_1]) ).

fof(f_142_3,plain,
    ( ! [U_470,U_472,U_471] :
        ( ~ c_Orderings_Oord__class_Oless(U_470,U_472,U_471)
        | U_472 != U_471
        | ~ sP32(U_470,U_472,U_471) )
    & ! [U_470,U_472,U_471] :
        ( U_472 = U_471
        | c_Orderings_Oord__class_Oless(U_470,U_472,U_471)
        | ~ sP32(U_470,U_472,U_471) )
    & ! [U_470,U_472,U_471] :
        ( sP32(U_470,U_472,U_471)
        | c_Orderings_Oord__class_Oless(U_470,U_471,U_472)
        | ~ class_Orderings_Olinorder(U_470) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP32])],[f_142_2]) ).

cnf(f_142_4,plain,
    ( sP32(U_470,U_472,U_471)
    | c_Orderings_Oord__class_Oless(U_470,U_471,U_472)
    | ~ class_Orderings_Olinorder(U_470) ),
    inference(clausify,[status(thm)],[f_142_3]) ).

cnf(f_142_5,plain,
    ( U_472 = U_471
    | c_Orderings_Oord__class_Oless(U_470,U_472,U_471)
    | ~ sP32(U_470,U_472,U_471) ),
    inference(clausify,[status(thm)],[f_142_3]) ).

cnf(f_142_6,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_470,U_472,U_471)
    | U_472 != U_471
    | ~ sP32(U_470,U_472,U_471) ),
    inference(clausify,[status(thm)],[f_142_3]) ).

fof(f_143_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_143_2,plain,
    ! [U_475,U_474,U_473] :
      ( c_Orderings_Oord__class_Oless(U_473,U_475,U_474)
      | c_Orderings_Oord__class_Oless(U_473,U_474,U_475)
      | U_474 = U_475
      | ~ class_Orderings_Olinorder(U_473) ),
    inference(variable_rename,[status(thm)],[f_143_1]) ).

fof(f_143_3,plain,
    ! [U_475,U_473,U_474] :
      ( c_Orderings_Oord__class_Oless(U_473,U_475,U_474)
      | c_Orderings_Oord__class_Oless(U_473,U_474,U_475)
      | U_474 = U_475
      | ~ class_Orderings_Olinorder(U_473) ),
    inference(definitional_conversion,[status(esa)],[f_143_2]) ).

cnf(f_143_4,plain,
    ( c_Orderings_Oord__class_Oless(U_473,U_475,U_474)
    | c_Orderings_Oord__class_Oless(U_473,U_474,U_475)
    | U_474 = U_475
    | ~ class_Orderings_Olinorder(U_473) ),
    inference(clausify,[status(thm)],[f_143_3]) ).

fof(f_144_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_144_2,plain,
    ! [U_477,U_476] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_477,U_476)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_476,U_477)
      | U_476 = U_477 ),
    inference(variable_rename,[status(thm)],[f_144_1]) ).

fof(f_144_3,plain,
    ! [U_477,U_476] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_477,U_476)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_476,U_477)
      | U_476 = U_477 ),
    inference(definitional_conversion,[status(esa)],[f_144_2]) ).

cnf(f_144_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_477,U_476)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_476,U_477)
    | U_476 = U_477 ),
    inference(clausify,[status(thm)],[f_144_3]) ).

fof(f_145_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_145_2,plain,
    ! [U_478] :
      ( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_478,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_478
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_478) ),
    inference(variable_rename,[status(thm)],[f_145_1]) ).

fof(f_145_3,plain,
    ! [U_478] :
      ( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_478,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_478
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_478) ),
    inference(definitional_conversion,[status(esa)],[f_145_2]) ).

cnf(f_145_4,plain,
    ( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_478,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_478
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_478) ),
    inference(clausify,[status(thm)],[f_145_3]) ).

fof(f_146_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_146_2,plain,
    ! [U_480,U_479] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_479,c_Nat_OSuc(U_480)),U_479)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_479) ),
    inference(variable_rename,[status(thm)],[f_146_1]) ).

fof(f_146_3,plain,
    ! [U_479,U_480] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_479,c_Nat_OSuc(U_480)),U_479)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_479) ),
    inference(definitional_conversion,[status(esa)],[f_146_2]) ).

cnf(f_146_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_479,c_Nat_OSuc(U_480)),U_479)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_479) ),
    inference(clausify,[status(thm)],[f_146_3]) ).

fof(f_147_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_147_2,plain,
    ! [U_482,U_481] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_482,U_481),U_482)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_482)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_481) ),
    inference(variable_rename,[status(thm)],[f_147_1]) ).

fof(f_147_3,plain,
    ! [U_482,U_481] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_482,U_481),U_482)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_482)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_481) ),
    inference(definitional_conversion,[status(esa)],[f_147_2]) ).

cnf(f_147_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_482,U_481),U_482)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_482)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_481) ),
    inference(clausify,[status(thm)],[f_147_3]) ).

fof(f_148_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_148_2,plain,
    ! [U_483] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_483,U_483),
    inference(variable_rename,[status(thm)],[f_148_1]) ).

fof(f_148_3,plain,
    ! [U_483] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_483,U_483),
    inference(definitional_conversion,[status(esa)],[f_148_2]) ).

cnf(f_148_4,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_483,U_483),
    inference(clausify,[status(thm)],[f_148_3]) ).

fof(f_149_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_149_2,plain,
    ! [U_485,U_484] :
      ( U_485 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_484,U_485) ),
    inference(variable_rename,[status(thm)],[f_149_1]) ).

fof(f_149_3,plain,
    ! [U_485] :
      ( ! [U_484] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_484,U_485)
      | U_485 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(miniscope,[status(thm)],[f_149_2]) ).

fof(f_149_4,plain,
    ! [U_485,U_484] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_484,U_485)
      | U_485 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(definitional_conversion,[status(esa)],[f_149_3]) ).

cnf(f_149_5,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_484,U_485)
    | U_485 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_149_4]) ).

fof(f_150_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_150_2,plain,
    ! [U_487,U_486] :
      ( U_487 != U_486
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_486,U_487) ),
    inference(variable_rename,[status(thm)],[f_150_1]) ).

fof(f_150_3,plain,
    ! [U_487,U_486] :
      ( U_487 != U_486
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_486,U_487) ),
    inference(definitional_conversion,[status(esa)],[f_150_2]) ).

cnf(f_150_4,plain,
    ( U_487 != U_486
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_486,U_487) ),
    inference(clausify,[status(thm)],[f_150_3]) ).

fof(f_151_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_151_2,plain,
    ! [U_489,U_488] :
      ( U_488 != U_489
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_488,U_489) ),
    inference(variable_rename,[status(thm)],[f_151_1]) ).

fof(f_151_3,plain,
    ! [U_489,U_488] :
      ( U_488 != U_489
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_488,U_489) ),
    inference(definitional_conversion,[status(esa)],[f_151_2]) ).

cnf(f_151_4,plain,
    ( U_488 != U_489
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_488,U_489) ),
    inference(clausify,[status(thm)],[f_151_3]) ).

fof(f_152_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_152_2,plain,
    ! [U_492,U_491,U_490] :
      ( U_491 != U_492
      | ~ c_Orderings_Oord__class_Oless(U_490,U_491,U_492)
      | ~ class_Orderings_Oorder(U_490) ),
    inference(variable_rename,[status(thm)],[f_152_1]) ).

fof(f_152_3,plain,
    ! [U_490,U_491,U_492] :
      ( U_491 != U_492
      | ~ c_Orderings_Oord__class_Oless(U_490,U_491,U_492)
      | ~ class_Orderings_Oorder(U_490) ),
    inference(definitional_conversion,[status(esa)],[f_152_2]) ).

cnf(f_152_4,plain,
    ( U_491 != U_492
    | ~ c_Orderings_Oord__class_Oless(U_490,U_491,U_492)
    | ~ class_Orderings_Oorder(U_490) ),
    inference(clausify,[status(thm)],[f_152_3]) ).

fof(f_153_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_153_2,plain,
    ! [U_495,U_494,U_493] :
      ( ~ c_Orderings_Oord__class_Oless(U_493,U_495,U_494)
      | ~ c_Orderings_Oord__class_Oless(U_493,U_494,U_495)
      | ~ class_Orderings_Opreorder(U_493) ),
    inference(variable_rename,[status(thm)],[f_153_1]) ).

fof(f_153_3,plain,
    ! [U_493,U_494,U_495] :
      ( ~ c_Orderings_Oord__class_Oless(U_493,U_495,U_494)
      | ~ c_Orderings_Oord__class_Oless(U_493,U_494,U_495)
      | ~ class_Orderings_Opreorder(U_493) ),
    inference(definitional_conversion,[status(esa)],[f_153_2]) ).

cnf(f_153_4,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_493,U_495,U_494)
    | ~ c_Orderings_Oord__class_Oless(U_493,U_494,U_495)
    | ~ class_Orderings_Opreorder(U_493) ),
    inference(clausify,[status(thm)],[f_153_3]) ).

fof(f_154_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_154_2,plain,
    ! [U_498,U_497,U_496] :
      ( ~ c_Orderings_Oord__class_Oless(U_496,U_498,U_497)
      | ~ c_Orderings_Oord__class_Oless(U_496,U_497,U_498)
      | ~ class_Orderings_Opreorder(U_496) ),
    inference(variable_rename,[status(thm)],[f_154_1]) ).

fof(f_154_3,plain,
    ! [U_498,U_496,U_497] :
      ( ~ c_Orderings_Oord__class_Oless(U_496,U_498,U_497)
      | ~ c_Orderings_Oord__class_Oless(U_496,U_497,U_498)
      | ~ class_Orderings_Opreorder(U_496) ),
    inference(definitional_conversion,[status(esa)],[f_154_2]) ).

cnf(f_154_4,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_496,U_498,U_497)
    | ~ c_Orderings_Oord__class_Oless(U_496,U_497,U_498)
    | ~ class_Orderings_Opreorder(U_496) ),
    inference(clausify,[status(thm)],[f_154_3]) ).

fof(f_155_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_155_2,plain,
    ! [U_501,U_500,U_499] :
      ( U_500 != U_501
      | ~ c_Orderings_Oord__class_Oless(U_499,U_500,U_501)
      | ~ class_Orderings_Oorder(U_499) ),
    inference(variable_rename,[status(thm)],[f_155_1]) ).

fof(f_155_3,plain,
    ! [U_499,U_501,U_500] :
      ( U_500 != U_501
      | ~ c_Orderings_Oord__class_Oless(U_499,U_500,U_501)
      | ~ class_Orderings_Oorder(U_499) ),
    inference(definitional_conversion,[status(esa)],[f_155_2]) ).

cnf(f_155_4,plain,
    ( U_500 != U_501
    | ~ c_Orderings_Oord__class_Oless(U_499,U_500,U_501)
    | ~ class_Orderings_Oorder(U_499) ),
    inference(clausify,[status(thm)],[f_155_3]) ).

fof(f_156_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_156_2,plain,
    ! [U_504,U_503,U_502] :
      ( U_504 != U_503
      | ~ c_Orderings_Oord__class_Oless(U_502,U_503,U_504)
      | ~ class_Orderings_Oorder(U_502) ),
    inference(variable_rename,[status(thm)],[f_156_1]) ).

fof(f_156_3,plain,
    ! [U_503,U_504,U_502] :
      ( U_504 != U_503
      | ~ c_Orderings_Oord__class_Oless(U_502,U_503,U_504)
      | ~ class_Orderings_Oorder(U_502) ),
    inference(definitional_conversion,[status(esa)],[f_156_2]) ).

cnf(f_156_4,plain,
    ( U_504 != U_503
    | ~ c_Orderings_Oord__class_Oless(U_502,U_503,U_504)
    | ~ class_Orderings_Oorder(U_502) ),
    inference(clausify,[status(thm)],[f_156_3]) ).

fof(f_157_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_157_2,plain,
    ! [U_507,U_506,U_505] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_505,U_507),U_506)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_505,U_506) ),
    inference(variable_rename,[status(thm)],[f_157_1]) ).

fof(f_157_3,plain,
    ! [U_505,U_506,U_507] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_505,U_507),U_506)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_505,U_506) ),
    inference(definitional_conversion,[status(esa)],[f_157_2]) ).

cnf(f_157_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_505,U_507),U_506)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_505,U_506) ),
    inference(clausify,[status(thm)],[f_157_3]) ).

fof(f_158_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_158_2,plain,
    ! [U_510,U_509,U_508] :
      ( ~ c_Orderings_Oord__class_Oless(U_508,U_510,U_509)
      | ~ c_Orderings_Oord__class_Oless(U_508,U_509,U_510)
      | ~ class_Orderings_Opreorder(U_508) ),
    inference(variable_rename,[status(thm)],[f_158_1]) ).

fof(f_158_3,plain,
    ! [U_510,U_508,U_509] :
      ( ~ c_Orderings_Oord__class_Oless(U_508,U_510,U_509)
      | ~ c_Orderings_Oord__class_Oless(U_508,U_509,U_510)
      | ~ class_Orderings_Opreorder(U_508) ),
    inference(definitional_conversion,[status(esa)],[f_158_2]) ).

cnf(f_158_4,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_508,U_510,U_509)
    | ~ c_Orderings_Oord__class_Oless(U_508,U_509,U_510)
    | ~ class_Orderings_Opreorder(U_508) ),
    inference(clausify,[status(thm)],[f_158_3]) ).

fof(f_159_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_159_2,plain,
    ! [U_513,U_512,U_511] :
      ( ~ c_Orderings_Oord__class_Oless(U_511,U_513,U_512)
      | ~ c_Orderings_Oord__class_Oless(U_511,U_512,U_513)
      | ~ class_Orderings_Oorder(U_511) ),
    inference(variable_rename,[status(thm)],[f_159_1]) ).

fof(f_159_3,plain,
    ! [U_511,U_513,U_512] :
      ( ~ c_Orderings_Oord__class_Oless(U_511,U_513,U_512)
      | ~ c_Orderings_Oord__class_Oless(U_511,U_512,U_513)
      | ~ class_Orderings_Oorder(U_511) ),
    inference(definitional_conversion,[status(esa)],[f_159_2]) ).

cnf(f_159_4,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_511,U_513,U_512)
    | ~ c_Orderings_Oord__class_Oless(U_511,U_512,U_513)
    | ~ class_Orderings_Oorder(U_511) ),
    inference(clausify,[status(thm)],[f_159_3]) ).

fof(f_160_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_160_2,plain,
    ! [U_517,U_516,U_515,U_514] :
      ( c_Orderings_Oord__class_Oless(U_514,U_515,U_517)
      | ~ c_Orderings_Oord__class_Oless(U_514,U_516,U_517)
      | U_515 != U_516
      | ~ class_Orderings_Oord(U_514) ),
    inference(variable_rename,[status(thm)],[f_160_1]) ).

fof(f_160_3,plain,
    ! [U_517,U_514,U_515,U_516] :
      ( c_Orderings_Oord__class_Oless(U_514,U_515,U_517)
      | ~ c_Orderings_Oord__class_Oless(U_514,U_516,U_517)
      | U_515 != U_516
      | ~ class_Orderings_Oord(U_514) ),
    inference(definitional_conversion,[status(esa)],[f_160_2]) ).

cnf(f_160_4,plain,
    ( c_Orderings_Oord__class_Oless(U_514,U_515,U_517)
    | ~ c_Orderings_Oord__class_Oless(U_514,U_516,U_517)
    | U_515 != U_516
    | ~ class_Orderings_Oord(U_514) ),
    inference(clausify,[status(thm)],[f_160_3]) ).

fof(f_161_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_161_2,plain,
    ! [U_521,U_520,U_519,U_518] :
      ( c_Orderings_Oord__class_Oless(U_518,U_521,U_519)
      | ~ c_Orderings_Oord__class_Oless(U_518,U_521,U_520)
      | U_519 != U_520
      | ~ class_Orderings_Oorder(U_518) ),
    inference(variable_rename,[status(thm)],[f_161_1]) ).

fof(f_161_3,plain,
    ! [U_521,U_520,U_518,U_519] :
      ( c_Orderings_Oord__class_Oless(U_518,U_521,U_519)
      | ~ c_Orderings_Oord__class_Oless(U_518,U_521,U_520)
      | U_519 != U_520
      | ~ class_Orderings_Oorder(U_518) ),
    inference(definitional_conversion,[status(esa)],[f_161_2]) ).

cnf(f_161_4,plain,
    ( c_Orderings_Oord__class_Oless(U_518,U_521,U_519)
    | ~ c_Orderings_Oord__class_Oless(U_518,U_521,U_520)
    | U_519 != U_520
    | ~ class_Orderings_Oorder(U_518) ),
    inference(clausify,[status(thm)],[f_161_3]) ).

fof(f_162_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_162_2,plain,
    ! [U_525,U_524,U_523,U_522] :
      ( c_Orderings_Oord__class_Oless(U_522,U_523,U_525)
      | U_524 != U_525
      | ~ c_Orderings_Oord__class_Oless(U_522,U_523,U_524)
      | ~ class_Orderings_Oord(U_522) ),
    inference(variable_rename,[status(thm)],[f_162_1]) ).

fof(f_162_3,plain,
    ! [U_525,U_524,U_522,U_523] :
      ( c_Orderings_Oord__class_Oless(U_522,U_523,U_525)
      | U_524 != U_525
      | ~ c_Orderings_Oord__class_Oless(U_522,U_523,U_524)
      | ~ class_Orderings_Oord(U_522) ),
    inference(definitional_conversion,[status(esa)],[f_162_2]) ).

cnf(f_162_4,plain,
    ( c_Orderings_Oord__class_Oless(U_522,U_523,U_525)
    | U_524 != U_525
    | ~ c_Orderings_Oord__class_Oless(U_522,U_523,U_524)
    | ~ class_Orderings_Oord(U_522) ),
    inference(clausify,[status(thm)],[f_162_3]) ).

fof(f_163_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_163_2,plain,
    ! [U_529,U_528,U_527,U_526] :
      ( c_Orderings_Oord__class_Oless(U_526,U_529,U_528)
      | U_527 != U_529
      | ~ c_Orderings_Oord__class_Oless(U_526,U_527,U_528)
      | ~ class_Orderings_Oorder(U_526) ),
    inference(variable_rename,[status(thm)],[f_163_1]) ).

fof(f_163_3,plain,
    ! [U_529,U_528,U_526,U_527] :
      ( c_Orderings_Oord__class_Oless(U_526,U_529,U_528)
      | U_527 != U_529
      | ~ c_Orderings_Oord__class_Oless(U_526,U_527,U_528)
      | ~ class_Orderings_Oorder(U_526) ),
    inference(definitional_conversion,[status(esa)],[f_163_2]) ).

cnf(f_163_4,plain,
    ( c_Orderings_Oord__class_Oless(U_526,U_529,U_528)
    | U_527 != U_529
    | ~ c_Orderings_Oord__class_Oless(U_526,U_527,U_528)
    | ~ class_Orderings_Oorder(U_526) ),
    inference(clausify,[status(thm)],[f_163_3]) ).

fof(f_164_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_164_2,plain,
    ! [U_533,U_532,U_531,U_530] :
      ( c_Orderings_Oord__class_Oless(U_530,U_531,U_533)
      | ~ c_Orderings_Oord__class_Oless(U_530,U_532,U_533)
      | ~ c_Orderings_Oord__class_Oless(U_530,U_531,U_532)
      | ~ class_Orderings_Opreorder(U_530) ),
    inference(variable_rename,[status(thm)],[f_164_1]) ).

fof(f_164_3,plain,
    ! [U_532,U_533,U_531,U_530] :
      ( c_Orderings_Oord__class_Oless(U_530,U_531,U_533)
      | ~ c_Orderings_Oord__class_Oless(U_530,U_532,U_533)
      | ~ c_Orderings_Oord__class_Oless(U_530,U_531,U_532)
      | ~ class_Orderings_Opreorder(U_530) ),
    inference(definitional_conversion,[status(esa)],[f_164_2]) ).

cnf(f_164_4,plain,
    ( c_Orderings_Oord__class_Oless(U_530,U_531,U_533)
    | ~ c_Orderings_Oord__class_Oless(U_530,U_532,U_533)
    | ~ c_Orderings_Oord__class_Oless(U_530,U_531,U_532)
    | ~ class_Orderings_Opreorder(U_530) ),
    inference(clausify,[status(thm)],[f_164_3]) ).

fof(f_165_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_165_2,plain,
    ! [U_537,U_536,U_535,U_534] :
      ( c_Orderings_Oord__class_Oless(U_534,U_537,U_536)
      | ~ c_Orderings_Oord__class_Oless(U_534,U_537,U_535)
      | ~ c_Orderings_Oord__class_Oless(U_534,U_535,U_536)
      | ~ class_Orderings_Oorder(U_534) ),
    inference(variable_rename,[status(thm)],[f_165_1]) ).

fof(f_165_3,plain,
    ! [U_537,U_534,U_535,U_536] :
      ( c_Orderings_Oord__class_Oless(U_534,U_537,U_536)
      | ~ c_Orderings_Oord__class_Oless(U_534,U_537,U_535)
      | ~ c_Orderings_Oord__class_Oless(U_534,U_535,U_536)
      | ~ class_Orderings_Oorder(U_534) ),
    inference(definitional_conversion,[status(esa)],[f_165_2]) ).

cnf(f_165_4,plain,
    ( c_Orderings_Oord__class_Oless(U_534,U_537,U_536)
    | ~ c_Orderings_Oord__class_Oless(U_534,U_537,U_535)
    | ~ c_Orderings_Oord__class_Oless(U_534,U_535,U_536)
    | ~ class_Orderings_Oorder(U_534) ),
    inference(clausify,[status(thm)],[f_165_3]) ).

fof(f_166_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_166_2,plain,
    ! [U_540,U_539,U_538] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_540,U_539),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_540,U_538))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_538,U_540)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_538,U_539) ),
    inference(variable_rename,[status(thm)],[f_166_1]) ).

fof(f_166_3,plain,
    ! [U_539,U_538,U_540] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_540,U_539),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_540,U_538))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_538,U_540)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_538,U_539) ),
    inference(definitional_conversion,[status(esa)],[f_166_2]) ).

cnf(f_166_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_540,U_539),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_540,U_538))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_538,U_540)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_538,U_539) ),
    inference(clausify,[status(thm)],[f_166_3]) ).

fof(f_167_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_167_2,plain,
    ! [U_543,U_542,U_541] :
      ( ~ c_Orderings_Oord__class_Oless(U_541,U_543,U_542)
      | ~ c_Orderings_Oord__class_Oless(U_541,U_542,U_543)
      | ~ class_Orderings_Opreorder(U_541) ),
    inference(variable_rename,[status(thm)],[f_167_1]) ).

fof(f_167_3,plain,
    ! [U_541,U_543,U_542] :
      ( ~ c_Orderings_Oord__class_Oless(U_541,U_543,U_542)
      | ~ c_Orderings_Oord__class_Oless(U_541,U_542,U_543)
      | ~ class_Orderings_Opreorder(U_541) ),
    inference(definitional_conversion,[status(esa)],[f_167_2]) ).

cnf(f_167_4,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_541,U_543,U_542)
    | ~ c_Orderings_Oord__class_Oless(U_541,U_542,U_543)
    | ~ class_Orderings_Opreorder(U_541) ),
    inference(clausify,[status(thm)],[f_167_3]) ).

fof(f_168_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_168_2,plain,
    ! [U_545,U_544] :
      ( U_544 = U_545
      | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_545,U_544) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_544,U_545) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_168_1]) ).

fof(f_168_3,plain,
    ! [U_544,U_545] :
      ( U_544 = U_545
      | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_545,U_544) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_544,U_545) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(definitional_conversion,[status(esa)],[f_168_2]) ).

cnf(f_168_4,plain,
    ( U_544 = U_545
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_545,U_544) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_544,U_545) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_168_3]) ).

fof(f_169_1,plain,
    ! [V_da_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( ( ( V_a_2 = V_b_2
          | V_c_2 != V_da_2 )
        & ( V_c_2 = V_da_2
          | V_a_2 != V_b_2 ) )
      | c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) != c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_da_2)
      | ~ class_Groups_Oab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__eq]) ).

fof(f_169_2,plain,
    ! [U_550,U_549,U_548,U_547,U_546] :
      ( ( ( U_547 = U_548
          | U_549 != U_550 )
        & ( U_549 = U_550
          | U_547 != U_548 ) )
      | c_Groups_Ominus__class_Ominus(U_546,U_547,U_548) != c_Groups_Ominus__class_Ominus(U_546,U_549,U_550)
      | ~ class_Groups_Oab__group__add(U_546) ),
    inference(variable_rename,[status(thm)],[f_169_1]) ).

fof(f_169_3,plain,
    ( ! [U_547,U_548,U_549,U_550] :
        ( U_547 = U_548
        | U_549 != U_550
        | ~ sP33(U_547,U_548,U_549,U_550) )
    & ! [U_547,U_548,U_549,U_550] :
        ( U_549 = U_550
        | U_547 != U_548
        | ~ sP33(U_547,U_548,U_549,U_550) )
    & ! [U_546,U_547,U_548,U_549,U_550] :
        ( sP33(U_547,U_548,U_549,U_550)
        | c_Groups_Ominus__class_Ominus(U_546,U_547,U_548) != c_Groups_Ominus__class_Ominus(U_546,U_549,U_550)
        | ~ class_Groups_Oab__group__add(U_546) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP33])],[f_169_2]) ).

cnf(f_169_4,plain,
    ( sP33(U_547,U_548,U_549,U_550)
    | c_Groups_Ominus__class_Ominus(U_546,U_547,U_548) != c_Groups_Ominus__class_Ominus(U_546,U_549,U_550)
    | ~ class_Groups_Oab__group__add(U_546) ),
    inference(clausify,[status(thm)],[f_169_3]) ).

cnf(f_169_5,plain,
    ( U_549 = U_550
    | U_547 != U_548
    | ~ sP33(U_547,U_548,U_549,U_550) ),
    inference(clausify,[status(thm)],[f_169_3]) ).

cnf(f_169_6,plain,
    ( U_547 = U_548
    | U_549 != U_550
    | ~ sP33(U_547,U_548,U_549,U_550) ),
    inference(clausify,[status(thm)],[f_169_3]) ).

fof(f_170_1,plain,
    ! [V_da_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
          | ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,V_da_2) )
        & ( c_Orderings_Oord__class_Oless(T_a,V_c_2,V_da_2)
          | ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) )
      | c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) != c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_da_2)
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less]) ).

fof(f_170_2,plain,
    ! [U_555,U_554,U_553,U_552,U_551] :
      ( ( ( c_Orderings_Oord__class_Oless(U_551,U_552,U_553)
          | ~ c_Orderings_Oord__class_Oless(U_551,U_554,U_555) )
        & ( c_Orderings_Oord__class_Oless(U_551,U_554,U_555)
          | ~ c_Orderings_Oord__class_Oless(U_551,U_552,U_553) ) )
      | c_Groups_Ominus__class_Ominus(U_551,U_552,U_553) != c_Groups_Ominus__class_Ominus(U_551,U_554,U_555)
      | ~ class_Groups_Oordered__ab__group__add(U_551) ),
    inference(variable_rename,[status(thm)],[f_170_1]) ).

fof(f_170_3,plain,
    ( ! [U_551,U_552,U_554,U_553,U_555] :
        ( c_Orderings_Oord__class_Oless(U_551,U_552,U_553)
        | ~ c_Orderings_Oord__class_Oless(U_551,U_554,U_555)
        | ~ sP34(U_551,U_552,U_554,U_553,U_555) )
    & ! [U_551,U_552,U_554,U_553,U_555] :
        ( c_Orderings_Oord__class_Oless(U_551,U_554,U_555)
        | ~ c_Orderings_Oord__class_Oless(U_551,U_552,U_553)
        | ~ sP34(U_551,U_552,U_554,U_553,U_555) )
    & ! [U_551,U_552,U_554,U_553,U_555] :
        ( sP34(U_551,U_552,U_554,U_553,U_555)
        | c_Groups_Ominus__class_Ominus(U_551,U_552,U_553) != c_Groups_Ominus__class_Ominus(U_551,U_554,U_555)
        | ~ class_Groups_Oordered__ab__group__add(U_551) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP34])],[f_170_2]) ).

cnf(f_170_4,plain,
    ( sP34(U_551,U_552,U_554,U_553,U_555)
    | c_Groups_Ominus__class_Ominus(U_551,U_552,U_553) != c_Groups_Ominus__class_Ominus(U_551,U_554,U_555)
    | ~ class_Groups_Oordered__ab__group__add(U_551) ),
    inference(clausify,[status(thm)],[f_170_3]) ).

cnf(f_170_5,plain,
    ( c_Orderings_Oord__class_Oless(U_551,U_554,U_555)
    | ~ c_Orderings_Oord__class_Oless(U_551,U_552,U_553)
    | ~ sP34(U_551,U_552,U_554,U_553,U_555) ),
    inference(clausify,[status(thm)],[f_170_3]) ).

cnf(f_170_6,plain,
    ( c_Orderings_Oord__class_Oless(U_551,U_552,U_553)
    | ~ c_Orderings_Oord__class_Oless(U_551,U_554,U_555)
    | ~ sP34(U_551,U_552,U_554,U_553,U_555) ),
    inference(clausify,[status(thm)],[f_170_3]) ).

fof(f_171_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_171_2,plain,
    ! [U_556] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_556)
      | U_556 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_171_1]) ).

fof(f_171_3,plain,
    ! [U_556] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_556)
      | U_556 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(definitional_conversion,[status(esa)],[f_171_2]) ).

cnf(f_171_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_556)
    | U_556 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_171_3]) ).

fof(f_172_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_172_2,plain,
    ! [U_559,U_558,U_557] :
      ( c_Orderings_Oord__class_Oless(U_557,U_559,U_558)
      | U_558 = U_559
      | c_Orderings_Oord__class_Oless(U_557,U_558,U_559)
      | ~ class_Orderings_Olinorder(U_557) ),
    inference(variable_rename,[status(thm)],[f_172_1]) ).

fof(f_172_3,plain,
    ! [U_558,U_557,U_559] :
      ( c_Orderings_Oord__class_Oless(U_557,U_559,U_558)
      | U_558 = U_559
      | c_Orderings_Oord__class_Oless(U_557,U_558,U_559)
      | ~ class_Orderings_Olinorder(U_557) ),
    inference(definitional_conversion,[status(esa)],[f_172_2]) ).

cnf(f_172_4,plain,
    ( c_Orderings_Oord__class_Oless(U_557,U_559,U_558)
    | U_558 = U_559
    | c_Orderings_Oord__class_Oless(U_557,U_558,U_559)
    | ~ class_Orderings_Olinorder(U_557) ),
    inference(clausify,[status(thm)],[f_172_3]) ).

fof(f_173_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_173_2,plain,
    ! [U_562,U_561,U_560] :
      ( hBOOL(hAPP(hAPP(U_562,U_561),U_560))
      | ( ~ hBOOL(hAPP(hAPP(U_562,U_561),U_560))
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_561,U_560) )
      | ( ~ hBOOL(hAPP(hAPP(U_562,U_561),U_560))
        & U_560 = U_561 )
      | ( ~ hBOOL(hAPP(hAPP(U_562,U_561),U_560))
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_560,U_561) ) ),
    inference(variable_rename,[status(thm)],[f_173_1]) ).

fof(f_173_3,plain,
    ( ! [U_560,U_561,U_562] :
        ( ~ hBOOL(hAPP(hAPP(U_562,U_561),U_560))
        | ~ sP37(U_560,U_561,U_562) )
    & ! [U_560,U_561,U_562] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_561,U_560)
        | ~ sP37(U_560,U_561,U_562) )
    & ! [U_560,U_561,U_562] :
        ( ~ hBOOL(hAPP(hAPP(U_562,U_561),U_560))
        | ~ sP36(U_560,U_561,U_562) )
    & ! [U_560,U_561,U_562] :
        ( U_560 = U_561
        | ~ sP36(U_560,U_561,U_562) )
    & ! [U_560,U_561,U_562] :
        ( ~ hBOOL(hAPP(hAPP(U_562,U_561),U_560))
        | ~ sP35(U_560,U_561,U_562) )
    & ! [U_560,U_561,U_562] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_560,U_561)
        | ~ sP35(U_560,U_561,U_562) )
    & ! [U_560,U_561,U_562] :
        ( hBOOL(hAPP(hAPP(U_562,U_561),U_560))
        | sP37(U_560,U_561,U_562)
        | sP36(U_560,U_561,U_562)
        | sP35(U_560,U_561,U_562) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP35,sP36,sP37])],[f_173_2]) ).

cnf(f_173_4,plain,
    ( hBOOL(hAPP(hAPP(U_562,U_561),U_560))
    | sP37(U_560,U_561,U_562)
    | sP36(U_560,U_561,U_562)
    | sP35(U_560,U_561,U_562) ),
    inference(clausify,[status(thm)],[f_173_3]) ).

cnf(f_173_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_560,U_561)
    | ~ sP35(U_560,U_561,U_562) ),
    inference(clausify,[status(thm)],[f_173_3]) ).

cnf(f_173_6,plain,
    ( ~ hBOOL(hAPP(hAPP(U_562,U_561),U_560))
    | ~ sP35(U_560,U_561,U_562) ),
    inference(clausify,[status(thm)],[f_173_3]) ).

cnf(f_173_7,plain,
    ( U_560 = U_561
    | ~ sP36(U_560,U_561,U_562) ),
    inference(clausify,[status(thm)],[f_173_3]) ).

cnf(f_173_8,plain,
    ( ~ hBOOL(hAPP(hAPP(U_562,U_561),U_560))
    | ~ sP36(U_560,U_561,U_562) ),
    inference(clausify,[status(thm)],[f_173_3]) ).

cnf(f_173_9,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_561,U_560)
    | ~ sP37(U_560,U_561,U_562) ),
    inference(clausify,[status(thm)],[f_173_3]) ).

cnf(f_173_10,plain,
    ( ~ hBOOL(hAPP(hAPP(U_562,U_561),U_560))
    | ~ sP37(U_560,U_561,U_562) ),
    inference(clausify,[status(thm)],[f_173_3]) ).

fof(f_174_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_174_2,plain,
    ! [U_565,U_564,U_563] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_563,U_565),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_564,U_565))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_565,U_563)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_563,U_564) ),
    inference(variable_rename,[status(thm)],[f_174_1]) ).

fof(f_174_3,plain,
    ! [U_563,U_564,U_565] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_563,U_565),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_564,U_565))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_565,U_563)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_563,U_564) ),
    inference(definitional_conversion,[status(esa)],[f_174_2]) ).

cnf(f_174_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_563,U_565),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_564,U_565))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_565,U_563)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_563,U_564) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

fof(f_175_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_175_2,plain,
    ! [U_568,U_567,U_566] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_567,U_566),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_568,U_566))
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_567,U_568) )
        & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_567,U_568)
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_567,U_566),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_568,U_566)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_566,U_568)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_566,U_567) ),
    inference(variable_rename,[status(thm)],[f_175_1]) ).

fof(f_175_3,plain,
    ( ! [U_566,U_567,U_568] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_567,U_566),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_568,U_566))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_567,U_568)
        | ~ sP38(U_566,U_567,U_568) )
    & ! [U_566,U_567,U_568] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_567,U_568)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_567,U_566),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_568,U_566))
        | ~ sP38(U_566,U_567,U_568) )
    & ! [U_566,U_567,U_568] :
        ( sP38(U_566,U_567,U_568)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_566,U_568)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_566,U_567) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP38])],[f_175_2]) ).

cnf(f_175_4,plain,
    ( sP38(U_566,U_567,U_568)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_566,U_568)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_566,U_567) ),
    inference(clausify,[status(thm)],[f_175_3]) ).

cnf(f_175_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_567,U_568)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_567,U_566),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_568,U_566))
    | ~ sP38(U_566,U_567,U_568) ),
    inference(clausify,[status(thm)],[f_175_3]) ).

cnf(f_175_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_567,U_566),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_568,U_566))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_567,U_568)
    | ~ sP38(U_566,U_567,U_568) ),
    inference(clausify,[status(thm)],[f_175_3]) ).

fof(f_176_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_176_2,plain,
    ! [U_571,U_570,U_569] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_569,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_570,U_571))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_569,U_571),U_570) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_569,U_571),U_570)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_569,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_570,U_571)) ) ),
    inference(variable_rename,[status(thm)],[f_176_1]) ).

fof(f_176_3,plain,
    ( ! [U_577,U_575,U_573] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_573,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_575,U_577))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_573,U_577),U_575) )
    & ! [U_576,U_574,U_572] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_572,U_576),U_574)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_572,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_574,U_576)) ) ),
    inference(miniscope,[status(thm)],[f_176_2]) ).

fof(f_176_4,plain,
    ( ! [U_575,U_577,U_573] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_573,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_575,U_577))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_573,U_577),U_575) )
    & ! [U_576,U_574,U_572] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_572,U_576),U_574)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_572,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_574,U_576)) ) ),
    inference(definitional_conversion,[status(esa)],[f_176_3]) ).

cnf(f_176_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_572,U_576),U_574)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_572,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_574,U_576)) ),
    inference(clausify,[status(thm)],[f_176_4]) ).

cnf(f_176_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_573,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_575,U_577))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_573,U_577),U_575) ),
    inference(clausify,[status(thm)],[f_176_4]) ).

fof(f_177_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_177_2,plain,
    ! [U_579,U_578] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_579,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_578,U_579)) = U_578
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_578,U_579) ),
    inference(variable_rename,[status(thm)],[f_177_1]) ).

fof(f_177_3,plain,
    ! [U_579,U_578] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_579,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_578,U_579)) = U_578
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_578,U_579) ),
    inference(definitional_conversion,[status(esa)],[f_177_2]) ).

cnf(f_177_4,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_579,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_578,U_579)) = U_578
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_578,U_579) ),
    inference(clausify,[status(thm)],[f_177_3]) ).

fof(f_178_1,plain,
    ! [V_a_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_a_2,V_a_2))
          | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
        & ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
          | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_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_178_2,plain,
    ! [U_581,U_580] :
      ( ( ( c_Orderings_Oord__class_Oless(U_580,c_Groups_Ozero__class_Ozero(U_580),c_Groups_Oplus__class_Oplus(U_580,U_581,U_581))
          | ~ c_Orderings_Oord__class_Oless(U_580,c_Groups_Ozero__class_Ozero(U_580),U_581) )
        & ( c_Orderings_Oord__class_Oless(U_580,c_Groups_Ozero__class_Ozero(U_580),U_581)
          | ~ c_Orderings_Oord__class_Oless(U_580,c_Groups_Ozero__class_Ozero(U_580),c_Groups_Oplus__class_Oplus(U_580,U_581,U_581)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_580) ),
    inference(variable_rename,[status(thm)],[f_178_1]) ).

fof(f_178_3,plain,
    ( ! [U_580,U_581] :
        ( c_Orderings_Oord__class_Oless(U_580,c_Groups_Ozero__class_Ozero(U_580),c_Groups_Oplus__class_Oplus(U_580,U_581,U_581))
        | ~ c_Orderings_Oord__class_Oless(U_580,c_Groups_Ozero__class_Ozero(U_580),U_581)
        | ~ sP39(U_580,U_581) )
    & ! [U_580,U_581] :
        ( c_Orderings_Oord__class_Oless(U_580,c_Groups_Ozero__class_Ozero(U_580),U_581)
        | ~ c_Orderings_Oord__class_Oless(U_580,c_Groups_Ozero__class_Ozero(U_580),c_Groups_Oplus__class_Oplus(U_580,U_581,U_581))
        | ~ sP39(U_580,U_581) )
    & ! [U_580,U_581] :
        ( sP39(U_580,U_581)
        | ~ class_Groups_Olinordered__ab__group__add(U_580) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP39])],[f_178_2]) ).

cnf(f_178_4,plain,
    ( sP39(U_580,U_581)
    | ~ class_Groups_Olinordered__ab__group__add(U_580) ),
    inference(clausify,[status(thm)],[f_178_3]) ).

cnf(f_178_5,plain,
    ( c_Orderings_Oord__class_Oless(U_580,c_Groups_Ozero__class_Ozero(U_580),U_581)
    | ~ c_Orderings_Oord__class_Oless(U_580,c_Groups_Ozero__class_Ozero(U_580),c_Groups_Oplus__class_Oplus(U_580,U_581,U_581))
    | ~ sP39(U_580,U_581) ),
    inference(clausify,[status(thm)],[f_178_3]) ).

cnf(f_178_6,plain,
    ( c_Orderings_Oord__class_Oless(U_580,c_Groups_Ozero__class_Ozero(U_580),c_Groups_Oplus__class_Oplus(U_580,U_581,U_581))
    | ~ c_Orderings_Oord__class_Oless(U_580,c_Groups_Ozero__class_Ozero(U_580),U_581)
    | ~ sP39(U_580,U_581) ),
    inference(clausify,[status(thm)],[f_178_3]) ).

fof(f_179_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
          | ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
        & ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
          | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_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_179_2,plain,
    ! [U_583,U_582] :
      ( ( ( c_Orderings_Oord__class_Oless(U_582,c_Groups_Oplus__class_Oplus(U_582,U_583,U_583),c_Groups_Ozero__class_Ozero(U_582))
          | ~ c_Orderings_Oord__class_Oless(U_582,U_583,c_Groups_Ozero__class_Ozero(U_582)) )
        & ( c_Orderings_Oord__class_Oless(U_582,U_583,c_Groups_Ozero__class_Ozero(U_582))
          | ~ c_Orderings_Oord__class_Oless(U_582,c_Groups_Oplus__class_Oplus(U_582,U_583,U_583),c_Groups_Ozero__class_Ozero(U_582)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_582) ),
    inference(variable_rename,[status(thm)],[f_179_1]) ).

fof(f_179_3,plain,
    ( ! [U_583,U_582] :
        ( c_Orderings_Oord__class_Oless(U_582,c_Groups_Oplus__class_Oplus(U_582,U_583,U_583),c_Groups_Ozero__class_Ozero(U_582))
        | ~ c_Orderings_Oord__class_Oless(U_582,U_583,c_Groups_Ozero__class_Ozero(U_582))
        | ~ sP40(U_583,U_582) )
    & ! [U_583,U_582] :
        ( c_Orderings_Oord__class_Oless(U_582,U_583,c_Groups_Ozero__class_Ozero(U_582))
        | ~ c_Orderings_Oord__class_Oless(U_582,c_Groups_Oplus__class_Oplus(U_582,U_583,U_583),c_Groups_Ozero__class_Ozero(U_582))
        | ~ sP40(U_583,U_582) )
    & ! [U_583,U_582] :
        ( sP40(U_583,U_582)
        | ~ class_Groups_Olinordered__ab__group__add(U_582) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP40])],[f_179_2]) ).

cnf(f_179_4,plain,
    ( sP40(U_583,U_582)
    | ~ class_Groups_Olinordered__ab__group__add(U_582) ),
    inference(clausify,[status(thm)],[f_179_3]) ).

cnf(f_179_5,plain,
    ( c_Orderings_Oord__class_Oless(U_582,U_583,c_Groups_Ozero__class_Ozero(U_582))
    | ~ c_Orderings_Oord__class_Oless(U_582,c_Groups_Oplus__class_Oplus(U_582,U_583,U_583),c_Groups_Ozero__class_Ozero(U_582))
    | ~ sP40(U_583,U_582) ),
    inference(clausify,[status(thm)],[f_179_3]) ).

cnf(f_179_6,plain,
    ( c_Orderings_Oord__class_Oless(U_582,c_Groups_Oplus__class_Oplus(U_582,U_583,U_583),c_Groups_Ozero__class_Ozero(U_582))
    | ~ c_Orderings_Oord__class_Oless(U_582,U_583,c_Groups_Ozero__class_Ozero(U_582))
    | ~ sP40(U_583,U_582) ),
    inference(clausify,[status(thm)],[f_179_3]) ).

fof(f_180_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_180_2,plain,
    ! [U_586,U_585,U_584] :
      ( c_Orderings_Oord__class_Oless(U_584,c_Groups_Ozero__class_Ozero(U_584),c_Groups_Oplus__class_Oplus(U_584,U_585,U_586))
      | ~ c_Orderings_Oord__class_Oless(U_584,c_Groups_Ozero__class_Ozero(U_584),U_586)
      | ~ c_Orderings_Oord__class_Oless(U_584,c_Groups_Ozero__class_Ozero(U_584),U_585)
      | ~ class_Groups_Oordered__comm__monoid__add(U_584) ),
    inference(variable_rename,[status(thm)],[f_180_1]) ).

fof(f_180_3,plain,
    ! [U_585,U_586,U_584] :
      ( c_Orderings_Oord__class_Oless(U_584,c_Groups_Ozero__class_Ozero(U_584),c_Groups_Oplus__class_Oplus(U_584,U_585,U_586))
      | ~ c_Orderings_Oord__class_Oless(U_584,c_Groups_Ozero__class_Ozero(U_584),U_586)
      | ~ c_Orderings_Oord__class_Oless(U_584,c_Groups_Ozero__class_Ozero(U_584),U_585)
      | ~ class_Groups_Oordered__comm__monoid__add(U_584) ),
    inference(definitional_conversion,[status(esa)],[f_180_2]) ).

cnf(f_180_4,plain,
    ( c_Orderings_Oord__class_Oless(U_584,c_Groups_Ozero__class_Ozero(U_584),c_Groups_Oplus__class_Oplus(U_584,U_585,U_586))
    | ~ c_Orderings_Oord__class_Oless(U_584,c_Groups_Ozero__class_Ozero(U_584),U_586)
    | ~ c_Orderings_Oord__class_Oless(U_584,c_Groups_Ozero__class_Ozero(U_584),U_585)
    | ~ class_Groups_Oordered__comm__monoid__add(U_584) ),
    inference(clausify,[status(thm)],[f_180_3]) ).

fof(f_181_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_181_2,plain,
    ! [U_589,U_588,U_587] :
      ( c_Orderings_Oord__class_Oless(U_587,c_Groups_Oplus__class_Oplus(U_587,U_588,U_589),c_Groups_Ozero__class_Ozero(U_587))
      | ~ c_Orderings_Oord__class_Oless(U_587,U_589,c_Groups_Ozero__class_Ozero(U_587))
      | ~ c_Orderings_Oord__class_Oless(U_587,U_588,c_Groups_Ozero__class_Ozero(U_587))
      | ~ class_Groups_Oordered__comm__monoid__add(U_587) ),
    inference(variable_rename,[status(thm)],[f_181_1]) ).

fof(f_181_3,plain,
    ! [U_588,U_587,U_589] :
      ( c_Orderings_Oord__class_Oless(U_587,c_Groups_Oplus__class_Oplus(U_587,U_588,U_589),c_Groups_Ozero__class_Ozero(U_587))
      | ~ c_Orderings_Oord__class_Oless(U_587,U_589,c_Groups_Ozero__class_Ozero(U_587))
      | ~ c_Orderings_Oord__class_Oless(U_587,U_588,c_Groups_Ozero__class_Ozero(U_587))
      | ~ class_Groups_Oordered__comm__monoid__add(U_587) ),
    inference(definitional_conversion,[status(esa)],[f_181_2]) ).

cnf(f_181_4,plain,
    ( c_Orderings_Oord__class_Oless(U_587,c_Groups_Oplus__class_Oplus(U_587,U_588,U_589),c_Groups_Ozero__class_Ozero(U_587))
    | ~ c_Orderings_Oord__class_Oless(U_587,U_589,c_Groups_Ozero__class_Ozero(U_587))
    | ~ c_Orderings_Oord__class_Oless(U_587,U_588,c_Groups_Ozero__class_Ozero(U_587))
    | ~ class_Groups_Oordered__comm__monoid__add(U_587) ),
    inference(clausify,[status(thm)],[f_181_3]) ).

fof(f_182_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_182_2,plain,
    ! [U_591,U_590] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_590,U_591),c_Nat_OSuc(U_590)),
    inference(variable_rename,[status(thm)],[f_182_1]) ).

fof(f_182_3,plain,
    ! [U_590,U_591] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_590,U_591),c_Nat_OSuc(U_590)),
    inference(definitional_conversion,[status(esa)],[f_182_2]) ).

cnf(f_182_4,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_590,U_591),c_Nat_OSuc(U_590)),
    inference(clausify,[status(thm)],[f_182_3]) ).

fof(f_183_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_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_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_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_183_2,plain,
    ! [U_594,U_593,U_592] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_592,U_593,U_594)
          | ~ c_Orderings_Oord__class_Oless__eq(U_592,c_Groups_Ominus__class_Ominus(U_592,U_593,U_594),c_Groups_Ozero__class_Ozero(U_592)) )
        & ( c_Orderings_Oord__class_Oless__eq(U_592,c_Groups_Ominus__class_Ominus(U_592,U_593,U_594),c_Groups_Ozero__class_Ozero(U_592))
          | ~ c_Orderings_Oord__class_Oless__eq(U_592,U_593,U_594) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_592) ),
    inference(variable_rename,[status(thm)],[f_183_1]) ).

fof(f_183_3,plain,
    ( ! [U_592,U_593,U_594] :
        ( c_Orderings_Oord__class_Oless__eq(U_592,U_593,U_594)
        | ~ c_Orderings_Oord__class_Oless__eq(U_592,c_Groups_Ominus__class_Ominus(U_592,U_593,U_594),c_Groups_Ozero__class_Ozero(U_592))
        | ~ sP41(U_592,U_593,U_594) )
    & ! [U_592,U_593,U_594] :
        ( c_Orderings_Oord__class_Oless__eq(U_592,c_Groups_Ominus__class_Ominus(U_592,U_593,U_594),c_Groups_Ozero__class_Ozero(U_592))
        | ~ c_Orderings_Oord__class_Oless__eq(U_592,U_593,U_594)
        | ~ sP41(U_592,U_593,U_594) )
    & ! [U_592,U_593,U_594] :
        ( sP41(U_592,U_593,U_594)
        | ~ class_Groups_Oordered__ab__group__add(U_592) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP41])],[f_183_2]) ).

cnf(f_183_4,plain,
    ( sP41(U_592,U_593,U_594)
    | ~ class_Groups_Oordered__ab__group__add(U_592) ),
    inference(clausify,[status(thm)],[f_183_3]) ).

cnf(f_183_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_592,c_Groups_Ominus__class_Ominus(U_592,U_593,U_594),c_Groups_Ozero__class_Ozero(U_592))
    | ~ c_Orderings_Oord__class_Oless__eq(U_592,U_593,U_594)
    | ~ sP41(U_592,U_593,U_594) ),
    inference(clausify,[status(thm)],[f_183_3]) ).

cnf(f_183_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_592,U_593,U_594)
    | ~ c_Orderings_Oord__class_Oless__eq(U_592,c_Groups_Ominus__class_Ominus(U_592,U_593,U_594),c_Groups_Ozero__class_Ozero(U_592))
    | ~ sP41(U_592,U_593,U_594) ),
    inference(clausify,[status(thm)],[f_183_3]) ).

fof(f_184_1,plain,
    ! [V_b_2,V_a_2,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))
        | ? [B_d] :
            ( ~ hBOOL(hAPP(V_P_2,B_d))
            & V_a_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_a_2,V_b_2) ) )
      & ( ( ! [B_d] :
              ( hBOOL(hAPP(V_P_2,B_d))
              | V_a_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_a_2,V_b_2) ) )
        | ~ hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__diff__split]) ).

fof(f_184_2,plain,
    ! [U_599,U_598,U_597] :
      ( ( hBOOL(hAPP(U_597,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_598,U_599)))
        | ? [U_596] :
            ( ~ hBOOL(hAPP(U_597,U_596))
            & U_598 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_599,U_596) )
        | ( ~ hBOOL(hAPP(U_597,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_598,U_599) ) )
      & ( ( ! [U_595] :
              ( hBOOL(hAPP(U_597,U_595))
              | U_598 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_599,U_595) )
          & ( hBOOL(hAPP(U_597,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_598,U_599) ) )
        | ~ hBOOL(hAPP(U_597,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_598,U_599))) ) ),
    inference(variable_rename,[status(thm)],[f_184_1]) ).

fof(f_184_3,plain,
    ( ! [U_605,U_603,U_601] :
        ( hBOOL(hAPP(U_601,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_603,U_605)))
        | ? [U_596] :
            ( ~ hBOOL(hAPP(U_601,U_596))
            & U_603 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_605,U_596) )
        | ( ~ hBOOL(hAPP(U_601,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_603,U_605) ) )
    & ! [U_604,U_602,U_600] :
        ( ( ! [U_595] :
              ( hBOOL(hAPP(U_600,U_595))
              | U_602 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_604,U_595) )
          & ( hBOOL(hAPP(U_600,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_602,U_604) ) )
        | ~ hBOOL(hAPP(U_600,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_602,U_604))) ) ),
    inference(miniscope,[status(thm)],[f_184_2]) ).

fof(f_184_4,plain,
    ( ! [U_605,U_603,U_601] :
        ( hBOOL(hAPP(U_601,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_603,U_605)))
        | ( ~ hBOOL(hAPP(U_601,sK25(U_605,U_603,U_601)))
          & U_603 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_605,sK25(U_605,U_603,U_601)) )
        | ( ~ hBOOL(hAPP(U_601,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_603,U_605) ) )
    & ! [U_604,U_602,U_600] :
        ( ( ! [U_595] :
              ( hBOOL(hAPP(U_600,U_595))
              | U_602 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_604,U_595) )
          & ( hBOOL(hAPP(U_600,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_602,U_604) ) )
        | ~ hBOOL(hAPP(U_600,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_602,U_604))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_596,sK25(U_605,U_603,U_601))],[f_184_3]) ).

fof(f_184_5,plain,
    ( ! [U_601,U_605,U_603] :
        ( ~ hBOOL(hAPP(U_601,sK25(U_605,U_603,U_601)))
        | ~ sP44(U_601,U_605,U_603) )
    & ! [U_601,U_605,U_603] :
        ( U_603 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_605,sK25(U_605,U_603,U_601))
        | ~ sP44(U_601,U_605,U_603) )
    & ! [U_601,U_605,U_603] :
        ( ~ hBOOL(hAPP(U_601,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ sP43(U_601,U_605,U_603) )
    & ! [U_601,U_605,U_603] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_603,U_605)
        | ~ sP43(U_601,U_605,U_603) )
    & ! [U_604,U_602,U_595,U_600] :
        ( hBOOL(hAPP(U_600,U_595))
        | U_602 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_604,U_595)
        | ~ sP42(U_604,U_602,U_595,U_600) )
    & ! [U_604,U_602,U_595,U_600] :
        ( hBOOL(hAPP(U_600,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_602,U_604)
        | ~ sP42(U_604,U_602,U_595,U_600) )
    & ! [U_601,U_605,U_603] :
        ( hBOOL(hAPP(U_601,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_603,U_605)))
        | sP44(U_601,U_605,U_603)
        | sP43(U_601,U_605,U_603) )
    & ! [U_604,U_602,U_595,U_600] :
        ( sP42(U_604,U_602,U_595,U_600)
        | ~ hBOOL(hAPP(U_600,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_602,U_604))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP42,sP43,sP44])],[f_184_4]) ).

cnf(f_184_6,plain,
    ( sP42(U_604,U_602,U_595,U_600)
    | ~ hBOOL(hAPP(U_600,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_602,U_604))) ),
    inference(clausify,[status(thm)],[f_184_5]) ).

cnf(f_184_7,plain,
    ( hBOOL(hAPP(U_601,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_603,U_605)))
    | sP44(U_601,U_605,U_603)
    | sP43(U_601,U_605,U_603) ),
    inference(clausify,[status(thm)],[f_184_5]) ).

cnf(f_184_8,plain,
    ( hBOOL(hAPP(U_600,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_602,U_604)
    | ~ sP42(U_604,U_602,U_595,U_600) ),
    inference(clausify,[status(thm)],[f_184_5]) ).

cnf(f_184_9,plain,
    ( hBOOL(hAPP(U_600,U_595))
    | U_602 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_604,U_595)
    | ~ sP42(U_604,U_602,U_595,U_600) ),
    inference(clausify,[status(thm)],[f_184_5]) ).

cnf(f_184_10,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_603,U_605)
    | ~ sP43(U_601,U_605,U_603) ),
    inference(clausify,[status(thm)],[f_184_5]) ).

cnf(f_184_11,plain,
    ( ~ hBOOL(hAPP(U_601,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ sP43(U_601,U_605,U_603) ),
    inference(clausify,[status(thm)],[f_184_5]) ).

cnf(f_184_12,plain,
    ( U_603 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_605,sK25(U_605,U_603,U_601))
    | ~ sP44(U_601,U_605,U_603) ),
    inference(clausify,[status(thm)],[f_184_5]) ).

cnf(f_184_13,plain,
    ( ~ hBOOL(hAPP(U_601,sK25(U_605,U_603,U_601)))
    | ~ sP44(U_601,U_605,U_603) ),
    inference(clausify,[status(thm)],[f_184_5]) ).

fof(f_185_1,plain,
    ! [V_b_2,V_a_2,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))
        | ? [B_d] :
            ( ~ hBOOL(hAPP(V_P_2,B_d))
            & V_a_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_a_2,V_b_2) ) )
      & ( ( ! [B_d] :
              ( hBOOL(hAPP(V_P_2,B_d))
              | V_a_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_a_2,V_b_2) ) )
        | ~ hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__diff__split__asm]) ).

fof(f_185_2,plain,
    ! [U_610,U_609,U_608] :
      ( ( hBOOL(hAPP(U_608,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_609,U_610)))
        | ? [U_607] :
            ( ~ hBOOL(hAPP(U_608,U_607))
            & U_609 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_610,U_607) )
        | ( ~ hBOOL(hAPP(U_608,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_609,U_610) ) )
      & ( ( ! [U_606] :
              ( hBOOL(hAPP(U_608,U_606))
              | U_609 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_610,U_606) )
          & ( hBOOL(hAPP(U_608,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_609,U_610) ) )
        | ~ hBOOL(hAPP(U_608,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_609,U_610))) ) ),
    inference(variable_rename,[status(thm)],[f_185_1]) ).

fof(f_185_3,plain,
    ( ! [U_616,U_614,U_612] :
        ( hBOOL(hAPP(U_612,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_614,U_616)))
        | ? [U_607] :
            ( ~ hBOOL(hAPP(U_612,U_607))
            & U_614 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_616,U_607) )
        | ( ~ hBOOL(hAPP(U_612,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_614,U_616) ) )
    & ! [U_615,U_613,U_611] :
        ( ( ! [U_606] :
              ( hBOOL(hAPP(U_611,U_606))
              | U_613 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_615,U_606) )
          & ( hBOOL(hAPP(U_611,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_613,U_615) ) )
        | ~ hBOOL(hAPP(U_611,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_613,U_615))) ) ),
    inference(miniscope,[status(thm)],[f_185_2]) ).

fof(f_185_4,plain,
    ( ! [U_616,U_614,U_612] :
        ( hBOOL(hAPP(U_612,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_614,U_616)))
        | ( ~ hBOOL(hAPP(U_612,sK26(U_616,U_614,U_612)))
          & U_614 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_616,sK26(U_616,U_614,U_612)) )
        | ( ~ hBOOL(hAPP(U_612,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_614,U_616) ) )
    & ! [U_615,U_613,U_611] :
        ( ( ! [U_606] :
              ( hBOOL(hAPP(U_611,U_606))
              | U_613 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_615,U_606) )
          & ( hBOOL(hAPP(U_611,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_613,U_615) ) )
        | ~ hBOOL(hAPP(U_611,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_613,U_615))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_607,sK26(U_616,U_614,U_612))],[f_185_3]) ).

fof(f_185_5,plain,
    ( ! [U_612,U_614,U_616] :
        ( ~ hBOOL(hAPP(U_612,sK26(U_616,U_614,U_612)))
        | ~ sP47(U_612,U_614,U_616) )
    & ! [U_612,U_614,U_616] :
        ( U_614 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_616,sK26(U_616,U_614,U_612))
        | ~ sP47(U_612,U_614,U_616) )
    & ! [U_612,U_614,U_616] :
        ( ~ hBOOL(hAPP(U_612,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ sP46(U_612,U_614,U_616) )
    & ! [U_612,U_614,U_616] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_614,U_616)
        | ~ sP46(U_612,U_614,U_616) )
    & ! [U_615,U_613,U_611,U_606] :
        ( hBOOL(hAPP(U_611,U_606))
        | U_613 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_615,U_606)
        | ~ sP45(U_615,U_613,U_611,U_606) )
    & ! [U_615,U_613,U_611,U_606] :
        ( hBOOL(hAPP(U_611,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_613,U_615)
        | ~ sP45(U_615,U_613,U_611,U_606) )
    & ! [U_612,U_614,U_616] :
        ( hBOOL(hAPP(U_612,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_614,U_616)))
        | sP47(U_612,U_614,U_616)
        | sP46(U_612,U_614,U_616) )
    & ! [U_615,U_613,U_611,U_606] :
        ( sP45(U_615,U_613,U_611,U_606)
        | ~ hBOOL(hAPP(U_611,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_613,U_615))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP45,sP46,sP47])],[f_185_4]) ).

cnf(f_185_6,plain,
    ( sP45(U_615,U_613,U_611,U_606)
    | ~ hBOOL(hAPP(U_611,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_613,U_615))) ),
    inference(clausify,[status(thm)],[f_185_5]) ).

cnf(f_185_7,plain,
    ( hBOOL(hAPP(U_612,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_614,U_616)))
    | sP47(U_612,U_614,U_616)
    | sP46(U_612,U_614,U_616) ),
    inference(clausify,[status(thm)],[f_185_5]) ).

cnf(f_185_8,plain,
    ( hBOOL(hAPP(U_611,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_613,U_615)
    | ~ sP45(U_615,U_613,U_611,U_606) ),
    inference(clausify,[status(thm)],[f_185_5]) ).

cnf(f_185_9,plain,
    ( hBOOL(hAPP(U_611,U_606))
    | U_613 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_615,U_606)
    | ~ sP45(U_615,U_613,U_611,U_606) ),
    inference(clausify,[status(thm)],[f_185_5]) ).

cnf(f_185_10,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_614,U_616)
    | ~ sP46(U_612,U_614,U_616) ),
    inference(clausify,[status(thm)],[f_185_5]) ).

cnf(f_185_11,plain,
    ( ~ hBOOL(hAPP(U_612,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ sP46(U_612,U_614,U_616) ),
    inference(clausify,[status(thm)],[f_185_5]) ).

cnf(f_185_12,plain,
    ( U_614 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_616,sK26(U_616,U_614,U_612))
    | ~ sP47(U_612,U_614,U_616) ),
    inference(clausify,[status(thm)],[f_185_5]) ).

cnf(f_185_13,plain,
    ( ~ hBOOL(hAPP(U_612,sK26(U_616,U_614,U_612)))
    | ~ sP47(U_612,U_614,U_616) ),
    inference(clausify,[status(thm)],[f_185_5]) ).

fof(f_186_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_186_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_186_1]) ).

cnf(f_186_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_186_2]) ).

fof(f_187_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_real__of__nat__less__iff]) ).

fof(f_187_2,plain,
    ! [U_618,U_617] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_617),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_618))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_617,U_618) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_617,U_618)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_617),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_618)) ) ),
    inference(variable_rename,[status(thm)],[f_187_1]) ).

fof(f_187_3,plain,
    ( ! [U_622,U_620] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_620),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_622))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_620,U_622) )
    & ! [U_621,U_619] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_619,U_621)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_619),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_621)) ) ),
    inference(miniscope,[status(thm)],[f_187_2]) ).

fof(f_187_4,plain,
    ( ! [U_622,U_620] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_620),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_622))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_620,U_622) )
    & ! [U_619,U_621] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_619,U_621)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_619),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_621)) ) ),
    inference(definitional_conversion,[status(esa)],[f_187_3]) ).

cnf(f_187_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_619,U_621)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_619),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_621)) ),
    inference(clausify,[status(thm)],[f_187_4]) ).

cnf(f_187_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_620),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_622))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_620,U_622) ),
    inference(clausify,[status(thm)],[f_187_4]) ).

fof(f_188_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_188_2,plain,
    ! [U_624,U_623] :
      ( ( 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_623,U_624))
        | ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_624)
          & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_623) ) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_624)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_623)
        | ~ 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_623,U_624)) ) ),
    inference(variable_rename,[status(thm)],[f_188_1]) ).

fof(f_188_3,plain,
    ( ! [U_628,U_626] :
        ( 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_626,U_628))
        | ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_628)
          & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_626) ) )
    & ! [U_627,U_625] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_627)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_625)
        | ~ 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_625,U_627)) ) ),
    inference(miniscope,[status(thm)],[f_188_2]) ).

fof(f_188_4,plain,
    ( ! [U_628,U_626] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_628)
        | ~ sP48(U_628,U_626) )
    & ! [U_628,U_626] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_626)
        | ~ sP48(U_628,U_626) )
    & ! [U_628,U_626] :
        ( 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_626,U_628))
        | sP48(U_628,U_626) )
    & ! [U_627,U_625] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_627)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_625)
        | ~ 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_625,U_627)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP48])],[f_188_3]) ).

cnf(f_188_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_627)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_625)
    | ~ 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_625,U_627)) ),
    inference(clausify,[status(thm)],[f_188_4]) ).

cnf(f_188_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_626,U_628))
    | sP48(U_628,U_626) ),
    inference(clausify,[status(thm)],[f_188_4]) ).

cnf(f_188_7,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_626)
    | ~ sP48(U_628,U_626) ),
    inference(clausify,[status(thm)],[f_188_4]) ).

cnf(f_188_8,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_628)
    | ~ sP48(U_628,U_626) ),
    inference(clausify,[status(thm)],[f_188_4]) ).

fof(f_189_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_189_2,plain,
    ! [U_630,U_629] :
      ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_629,U_630) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_629,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_630))
        | U_629 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_629,U_630) = U_630
        | U_629 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_189_1]) ).

fof(f_189_3,plain,
    ( ! [U_634,U_632] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_632,U_634) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_632,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_634))
        | U_632 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_633,U_631] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_631,U_633) = U_633
        | U_631 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_189_2]) ).

fof(f_189_4,plain,
    ( ! [U_634,U_632] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_632,U_634) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_632,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_634))
        | U_632 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_633,U_631] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_631,U_633) = U_633
        | U_631 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_189_3]) ).

cnf(f_189_5,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_631,U_633) = U_633
    | U_631 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_189_4]) ).

cnf(f_189_6,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_632,U_634) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_632,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_634))
    | U_632 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_189_4]) ).

fof(f_190_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_190_2,plain,
    ! [U_637,U_636,U_635] :
      ( c_Orderings_Oord__class_Oless(U_635,c_Groups_Ozero__class_Ozero(U_635),c_Groups_Oplus__class_Oplus(U_635,U_636,U_637))
      | ~ c_Orderings_Oord__class_Oless__eq(U_635,c_Groups_Ozero__class_Ozero(U_635),U_637)
      | ~ c_Orderings_Oord__class_Oless(U_635,c_Groups_Ozero__class_Ozero(U_635),U_636)
      | ~ class_Groups_Oordered__comm__monoid__add(U_635) ),
    inference(variable_rename,[status(thm)],[f_190_1]) ).

fof(f_190_3,plain,
    ! [U_635,U_636,U_637] :
      ( c_Orderings_Oord__class_Oless(U_635,c_Groups_Ozero__class_Ozero(U_635),c_Groups_Oplus__class_Oplus(U_635,U_636,U_637))
      | ~ c_Orderings_Oord__class_Oless__eq(U_635,c_Groups_Ozero__class_Ozero(U_635),U_637)
      | ~ c_Orderings_Oord__class_Oless(U_635,c_Groups_Ozero__class_Ozero(U_635),U_636)
      | ~ class_Groups_Oordered__comm__monoid__add(U_635) ),
    inference(definitional_conversion,[status(esa)],[f_190_2]) ).

cnf(f_190_4,plain,
    ( c_Orderings_Oord__class_Oless(U_635,c_Groups_Ozero__class_Ozero(U_635),c_Groups_Oplus__class_Oplus(U_635,U_636,U_637))
    | ~ c_Orderings_Oord__class_Oless__eq(U_635,c_Groups_Ozero__class_Ozero(U_635),U_637)
    | ~ c_Orderings_Oord__class_Oless(U_635,c_Groups_Ozero__class_Ozero(U_635),U_636)
    | ~ class_Groups_Oordered__comm__monoid__add(U_635) ),
    inference(clausify,[status(thm)],[f_190_3]) ).

fof(f_191_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_191_2,plain,
    ! [U_640,U_639,U_638] :
      ( c_Orderings_Oord__class_Oless(U_638,c_Groups_Ozero__class_Ozero(U_638),c_Groups_Oplus__class_Oplus(U_638,U_639,U_640))
      | ~ c_Orderings_Oord__class_Oless(U_638,c_Groups_Ozero__class_Ozero(U_638),U_640)
      | ~ c_Orderings_Oord__class_Oless__eq(U_638,c_Groups_Ozero__class_Ozero(U_638),U_639)
      | ~ class_Groups_Oordered__comm__monoid__add(U_638) ),
    inference(variable_rename,[status(thm)],[f_191_1]) ).

fof(f_191_3,plain,
    ! [U_638,U_639,U_640] :
      ( c_Orderings_Oord__class_Oless(U_638,c_Groups_Ozero__class_Ozero(U_638),c_Groups_Oplus__class_Oplus(U_638,U_639,U_640))
      | ~ c_Orderings_Oord__class_Oless(U_638,c_Groups_Ozero__class_Ozero(U_638),U_640)
      | ~ c_Orderings_Oord__class_Oless__eq(U_638,c_Groups_Ozero__class_Ozero(U_638),U_639)
      | ~ class_Groups_Oordered__comm__monoid__add(U_638) ),
    inference(definitional_conversion,[status(esa)],[f_191_2]) ).

cnf(f_191_4,plain,
    ( c_Orderings_Oord__class_Oless(U_638,c_Groups_Ozero__class_Ozero(U_638),c_Groups_Oplus__class_Oplus(U_638,U_639,U_640))
    | ~ c_Orderings_Oord__class_Oless(U_638,c_Groups_Ozero__class_Ozero(U_638),U_640)
    | ~ c_Orderings_Oord__class_Oless__eq(U_638,c_Groups_Ozero__class_Ozero(U_638),U_639)
    | ~ class_Groups_Oordered__comm__monoid__add(U_638) ),
    inference(clausify,[status(thm)],[f_191_3]) ).

fof(f_192_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_192_2,plain,
    ! [U_644,U_643,U_642,U_641] :
      ( c_Orderings_Oord__class_Oless(U_641,U_643,c_Groups_Oplus__class_Oplus(U_641,U_642,U_644))
      | ~ c_Orderings_Oord__class_Oless__eq(U_641,U_643,U_644)
      | ~ c_Orderings_Oord__class_Oless(U_641,c_Groups_Ozero__class_Ozero(U_641),U_642)
      | ~ class_Groups_Oordered__comm__monoid__add(U_641) ),
    inference(variable_rename,[status(thm)],[f_192_1]) ).

fof(f_192_3,plain,
    ! [U_642,U_641,U_643,U_644] :
      ( c_Orderings_Oord__class_Oless(U_641,U_643,c_Groups_Oplus__class_Oplus(U_641,U_642,U_644))
      | ~ c_Orderings_Oord__class_Oless__eq(U_641,U_643,U_644)
      | ~ c_Orderings_Oord__class_Oless(U_641,c_Groups_Ozero__class_Ozero(U_641),U_642)
      | ~ class_Groups_Oordered__comm__monoid__add(U_641) ),
    inference(definitional_conversion,[status(esa)],[f_192_2]) ).

cnf(f_192_4,plain,
    ( c_Orderings_Oord__class_Oless(U_641,U_643,c_Groups_Oplus__class_Oplus(U_641,U_642,U_644))
    | ~ c_Orderings_Oord__class_Oless__eq(U_641,U_643,U_644)
    | ~ c_Orderings_Oord__class_Oless(U_641,c_Groups_Ozero__class_Ozero(U_641),U_642)
    | ~ class_Groups_Oordered__comm__monoid__add(U_641) ),
    inference(clausify,[status(thm)],[f_192_3]) ).

fof(f_193_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_193_2,plain,
    ! [U_648,U_647,U_646,U_645] :
      ( c_Orderings_Oord__class_Oless(U_645,U_647,c_Groups_Oplus__class_Oplus(U_645,U_646,U_648))
      | ~ c_Orderings_Oord__class_Oless(U_645,U_647,U_648)
      | ~ c_Orderings_Oord__class_Oless__eq(U_645,c_Groups_Ozero__class_Ozero(U_645),U_646)
      | ~ class_Groups_Oordered__comm__monoid__add(U_645) ),
    inference(variable_rename,[status(thm)],[f_193_1]) ).

fof(f_193_3,plain,
    ! [U_645,U_648,U_647,U_646] :
      ( c_Orderings_Oord__class_Oless(U_645,U_647,c_Groups_Oplus__class_Oplus(U_645,U_646,U_648))
      | ~ c_Orderings_Oord__class_Oless(U_645,U_647,U_648)
      | ~ c_Orderings_Oord__class_Oless__eq(U_645,c_Groups_Ozero__class_Ozero(U_645),U_646)
      | ~ class_Groups_Oordered__comm__monoid__add(U_645) ),
    inference(definitional_conversion,[status(esa)],[f_193_2]) ).

cnf(f_193_4,plain,
    ( c_Orderings_Oord__class_Oless(U_645,U_647,c_Groups_Oplus__class_Oplus(U_645,U_646,U_648))
    | ~ c_Orderings_Oord__class_Oless(U_645,U_647,U_648)
    | ~ c_Orderings_Oord__class_Oless__eq(U_645,c_Groups_Ozero__class_Ozero(U_645),U_646)
    | ~ class_Groups_Oordered__comm__monoid__add(U_645) ),
    inference(clausify,[status(thm)],[f_193_3]) ).

fof(f_194_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_194_2,plain,
    ! [U_651,U_650,U_649] :
      ( c_Orderings_Oord__class_Oless(U_649,c_Groups_Oplus__class_Oplus(U_649,U_650,U_651),c_Groups_Ozero__class_Ozero(U_649))
      | ~ c_Orderings_Oord__class_Oless__eq(U_649,U_651,c_Groups_Ozero__class_Ozero(U_649))
      | ~ c_Orderings_Oord__class_Oless(U_649,U_650,c_Groups_Ozero__class_Ozero(U_649))
      | ~ class_Groups_Oordered__comm__monoid__add(U_649) ),
    inference(variable_rename,[status(thm)],[f_194_1]) ).

fof(f_194_3,plain,
    ! [U_650,U_649,U_651] :
      ( c_Orderings_Oord__class_Oless(U_649,c_Groups_Oplus__class_Oplus(U_649,U_650,U_651),c_Groups_Ozero__class_Ozero(U_649))
      | ~ c_Orderings_Oord__class_Oless__eq(U_649,U_651,c_Groups_Ozero__class_Ozero(U_649))
      | ~ c_Orderings_Oord__class_Oless(U_649,U_650,c_Groups_Ozero__class_Ozero(U_649))
      | ~ class_Groups_Oordered__comm__monoid__add(U_649) ),
    inference(definitional_conversion,[status(esa)],[f_194_2]) ).

cnf(f_194_4,plain,
    ( c_Orderings_Oord__class_Oless(U_649,c_Groups_Oplus__class_Oplus(U_649,U_650,U_651),c_Groups_Ozero__class_Ozero(U_649))
    | ~ c_Orderings_Oord__class_Oless__eq(U_649,U_651,c_Groups_Ozero__class_Ozero(U_649))
    | ~ c_Orderings_Oord__class_Oless(U_649,U_650,c_Groups_Ozero__class_Ozero(U_649))
    | ~ class_Groups_Oordered__comm__monoid__add(U_649) ),
    inference(clausify,[status(thm)],[f_194_3]) ).

fof(f_195_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_195_2,plain,
    ! [U_654,U_653,U_652] :
      ( c_Orderings_Oord__class_Oless(U_652,c_Groups_Oplus__class_Oplus(U_652,U_653,U_654),c_Groups_Ozero__class_Ozero(U_652))
      | ~ c_Orderings_Oord__class_Oless(U_652,U_654,c_Groups_Ozero__class_Ozero(U_652))
      | ~ c_Orderings_Oord__class_Oless__eq(U_652,U_653,c_Groups_Ozero__class_Ozero(U_652))
      | ~ class_Groups_Oordered__comm__monoid__add(U_652) ),
    inference(variable_rename,[status(thm)],[f_195_1]) ).

fof(f_195_3,plain,
    ! [U_652,U_653,U_654] :
      ( c_Orderings_Oord__class_Oless(U_652,c_Groups_Oplus__class_Oplus(U_652,U_653,U_654),c_Groups_Ozero__class_Ozero(U_652))
      | ~ c_Orderings_Oord__class_Oless(U_652,U_654,c_Groups_Ozero__class_Ozero(U_652))
      | ~ c_Orderings_Oord__class_Oless__eq(U_652,U_653,c_Groups_Ozero__class_Ozero(U_652))
      | ~ class_Groups_Oordered__comm__monoid__add(U_652) ),
    inference(definitional_conversion,[status(esa)],[f_195_2]) ).

cnf(f_195_4,plain,
    ( c_Orderings_Oord__class_Oless(U_652,c_Groups_Oplus__class_Oplus(U_652,U_653,U_654),c_Groups_Ozero__class_Ozero(U_652))
    | ~ c_Orderings_Oord__class_Oless(U_652,U_654,c_Groups_Ozero__class_Ozero(U_652))
    | ~ c_Orderings_Oord__class_Oless__eq(U_652,U_653,c_Groups_Ozero__class_Ozero(U_652))
    | ~ class_Groups_Oordered__comm__monoid__add(U_652) ),
    inference(clausify,[status(thm)],[f_195_3]) ).

fof(f_196_1,plain,
    ! [V_da_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,V_da_2) )
        & ( c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,V_da_2)
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) )
      | c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) != c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_da_2)
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less__eq]) ).

fof(f_196_2,plain,
    ! [U_659,U_658,U_657,U_656,U_655] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_655,U_656,U_657)
          | ~ c_Orderings_Oord__class_Oless__eq(U_655,U_658,U_659) )
        & ( c_Orderings_Oord__class_Oless__eq(U_655,U_658,U_659)
          | ~ c_Orderings_Oord__class_Oless__eq(U_655,U_656,U_657) ) )
      | c_Groups_Ominus__class_Ominus(U_655,U_656,U_657) != c_Groups_Ominus__class_Ominus(U_655,U_658,U_659)
      | ~ class_Groups_Oordered__ab__group__add(U_655) ),
    inference(variable_rename,[status(thm)],[f_196_1]) ).

fof(f_196_3,plain,
    ( ! [U_656,U_655,U_657,U_658,U_659] :
        ( c_Orderings_Oord__class_Oless__eq(U_655,U_656,U_657)
        | ~ c_Orderings_Oord__class_Oless__eq(U_655,U_658,U_659)
        | ~ sP49(U_656,U_655,U_657,U_658,U_659) )
    & ! [U_656,U_655,U_657,U_658,U_659] :
        ( c_Orderings_Oord__class_Oless__eq(U_655,U_658,U_659)
        | ~ c_Orderings_Oord__class_Oless__eq(U_655,U_656,U_657)
        | ~ sP49(U_656,U_655,U_657,U_658,U_659) )
    & ! [U_656,U_655,U_657,U_658,U_659] :
        ( sP49(U_656,U_655,U_657,U_658,U_659)
        | c_Groups_Ominus__class_Ominus(U_655,U_656,U_657) != c_Groups_Ominus__class_Ominus(U_655,U_658,U_659)
        | ~ class_Groups_Oordered__ab__group__add(U_655) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP49])],[f_196_2]) ).

cnf(f_196_4,plain,
    ( sP49(U_656,U_655,U_657,U_658,U_659)
    | c_Groups_Ominus__class_Ominus(U_655,U_656,U_657) != c_Groups_Ominus__class_Ominus(U_655,U_658,U_659)
    | ~ class_Groups_Oordered__ab__group__add(U_655) ),
    inference(clausify,[status(thm)],[f_196_3]) ).

cnf(f_196_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_655,U_658,U_659)
    | ~ c_Orderings_Oord__class_Oless__eq(U_655,U_656,U_657)
    | ~ sP49(U_656,U_655,U_657,U_658,U_659) ),
    inference(clausify,[status(thm)],[f_196_3]) ).

cnf(f_196_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_655,U_656,U_657)
    | ~ c_Orderings_Oord__class_Oless__eq(U_655,U_658,U_659)
    | ~ sP49(U_656,U_655,U_657,U_658,U_659) ),
    inference(clausify,[status(thm)],[f_196_3]) ).

fof(f_197_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_197_2,plain,
    ! [U_662,U_661,U_660] :
      ( c_Groups_Oplus__class_Oplus(U_660,c_Groups_Ominus__class_Ominus(U_660,U_661,U_662),U_662) = U_661
      | ~ class_Groups_Ogroup__add(U_660) ),
    inference(variable_rename,[status(thm)],[f_197_1]) ).

fof(f_197_3,plain,
    ! [U_662,U_661,U_660] :
      ( c_Groups_Oplus__class_Oplus(U_660,c_Groups_Ominus__class_Ominus(U_660,U_661,U_662),U_662) = U_661
      | ~ class_Groups_Ogroup__add(U_660) ),
    inference(definitional_conversion,[status(esa)],[f_197_2]) ).

cnf(f_197_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_660,c_Groups_Ominus__class_Ominus(U_660,U_661,U_662),U_662) = U_661
    | ~ class_Groups_Ogroup__add(U_660) ),
    inference(clausify,[status(thm)],[f_197_3]) ).

fof(f_198_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_198_2,plain,
    ! [U_665,U_664,U_663] :
      ( c_Groups_Ominus__class_Ominus(U_663,c_Groups_Oplus__class_Oplus(U_663,U_664,U_665),U_665) = U_664
      | ~ class_Groups_Ogroup__add(U_663) ),
    inference(variable_rename,[status(thm)],[f_198_1]) ).

fof(f_198_3,plain,
    ! [U_664,U_665,U_663] :
      ( c_Groups_Ominus__class_Ominus(U_663,c_Groups_Oplus__class_Oplus(U_663,U_664,U_665),U_665) = U_664
      | ~ class_Groups_Ogroup__add(U_663) ),
    inference(definitional_conversion,[status(esa)],[f_198_2]) ).

cnf(f_198_4,plain,
    ( c_Groups_Ominus__class_Ominus(U_663,c_Groups_Oplus__class_Oplus(U_663,U_664,U_665),U_665) = U_664
    | ~ class_Groups_Ogroup__add(U_663) ),
    inference(clausify,[status(thm)],[f_198_3]) ).

fof(f_199_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_199_2,plain,
    ! [U_668,U_667,U_666] :
      ( ( ( ~ c_Orderings_Oord__class_Oless(U_666,U_667,U_668)
          | ~ c_Orderings_Oord__class_Oless__eq(U_666,U_668,U_667) )
        & ( c_Orderings_Oord__class_Oless__eq(U_666,U_668,U_667)
          | c_Orderings_Oord__class_Oless(U_666,U_667,U_668) ) )
      | ~ class_Orderings_Olinorder(U_666) ),
    inference(variable_rename,[status(thm)],[f_199_1]) ).

fof(f_199_3,plain,
    ( ! [U_666,U_668,U_667] :
        ( ~ c_Orderings_Oord__class_Oless(U_666,U_667,U_668)
        | ~ c_Orderings_Oord__class_Oless__eq(U_666,U_668,U_667)
        | ~ sP50(U_666,U_668,U_667) )
    & ! [U_666,U_668,U_667] :
        ( c_Orderings_Oord__class_Oless__eq(U_666,U_668,U_667)
        | c_Orderings_Oord__class_Oless(U_666,U_667,U_668)
        | ~ sP50(U_666,U_668,U_667) )
    & ! [U_666,U_668,U_667] :
        ( sP50(U_666,U_668,U_667)
        | ~ class_Orderings_Olinorder(U_666) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP50])],[f_199_2]) ).

cnf(f_199_4,plain,
    ( sP50(U_666,U_668,U_667)
    | ~ class_Orderings_Olinorder(U_666) ),
    inference(clausify,[status(thm)],[f_199_3]) ).

cnf(f_199_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_666,U_668,U_667)
    | c_Orderings_Oord__class_Oless(U_666,U_667,U_668)
    | ~ sP50(U_666,U_668,U_667) ),
    inference(clausify,[status(thm)],[f_199_3]) ).

cnf(f_199_6,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_666,U_667,U_668)
    | ~ c_Orderings_Oord__class_Oless__eq(U_666,U_668,U_667)
    | ~ sP50(U_666,U_668,U_667) ),
    inference(clausify,[status(thm)],[f_199_3]) ).

fof(f_200_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_200_2,plain,
    ! [U_671,U_670,U_669] :
      ( ( ( ~ c_Orderings_Oord__class_Oless__eq(U_669,U_670,U_671)
          | ~ c_Orderings_Oord__class_Oless(U_669,U_671,U_670) )
        & ( c_Orderings_Oord__class_Oless(U_669,U_671,U_670)
          | c_Orderings_Oord__class_Oless__eq(U_669,U_670,U_671) ) )
      | ~ class_Orderings_Olinorder(U_669) ),
    inference(variable_rename,[status(thm)],[f_200_1]) ).

fof(f_200_3,plain,
    ( ! [U_671,U_670,U_669] :
        ( ~ c_Orderings_Oord__class_Oless__eq(U_669,U_670,U_671)
        | ~ c_Orderings_Oord__class_Oless(U_669,U_671,U_670)
        | ~ sP51(U_671,U_670,U_669) )
    & ! [U_671,U_670,U_669] :
        ( c_Orderings_Oord__class_Oless(U_669,U_671,U_670)
        | c_Orderings_Oord__class_Oless__eq(U_669,U_670,U_671)
        | ~ sP51(U_671,U_670,U_669) )
    & ! [U_671,U_670,U_669] :
        ( sP51(U_671,U_670,U_669)
        | ~ class_Orderings_Olinorder(U_669) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP51])],[f_200_2]) ).

cnf(f_200_4,plain,
    ( sP51(U_671,U_670,U_669)
    | ~ class_Orderings_Olinorder(U_669) ),
    inference(clausify,[status(thm)],[f_200_3]) ).

cnf(f_200_5,plain,
    ( c_Orderings_Oord__class_Oless(U_669,U_671,U_670)
    | c_Orderings_Oord__class_Oless__eq(U_669,U_670,U_671)
    | ~ sP51(U_671,U_670,U_669) ),
    inference(clausify,[status(thm)],[f_200_3]) ).

cnf(f_200_6,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(U_669,U_670,U_671)
    | ~ c_Orderings_Oord__class_Oless(U_669,U_671,U_670)
    | ~ sP51(U_671,U_670,U_669) ),
    inference(clausify,[status(thm)],[f_200_3]) ).

fof(f_201_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_201_2,plain,
    ! [U_674,U_673,U_672] :
      ( c_Orderings_Oord__class_Oless(U_672,U_674,U_673)
      | c_Orderings_Oord__class_Oless__eq(U_672,U_673,U_674)
      | ~ class_Orderings_Olinorder(U_672) ),
    inference(variable_rename,[status(thm)],[f_201_1]) ).

fof(f_201_3,plain,
    ! [U_674,U_673,U_672] :
      ( c_Orderings_Oord__class_Oless(U_672,U_674,U_673)
      | c_Orderings_Oord__class_Oless__eq(U_672,U_673,U_674)
      | ~ class_Orderings_Olinorder(U_672) ),
    inference(definitional_conversion,[status(esa)],[f_201_2]) ).

cnf(f_201_4,plain,
    ( c_Orderings_Oord__class_Oless(U_672,U_674,U_673)
    | c_Orderings_Oord__class_Oless__eq(U_672,U_673,U_674)
    | ~ class_Orderings_Olinorder(U_672) ),
    inference(clausify,[status(thm)],[f_201_3]) ).

fof(f_202_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_202_2,plain,
    ! [U_677,U_676,U_675] :
      ( ( ( c_Orderings_Oord__class_Oless(U_675,U_676,U_677)
          | U_676 = U_677
          | ~ c_Orderings_Oord__class_Oless__eq(U_675,U_676,U_677) )
        & ( ( U_676 != U_677
            & c_Orderings_Oord__class_Oless__eq(U_675,U_676,U_677) )
          | ~ c_Orderings_Oord__class_Oless(U_675,U_676,U_677) ) )
      | ~ class_Orderings_Oorder(U_675) ),
    inference(variable_rename,[status(thm)],[f_202_1]) ).

fof(f_202_3,plain,
    ( ! [U_675,U_676,U_677] :
        ( U_676 != U_677
        | ~ sP52(U_675,U_676,U_677) )
    & ! [U_675,U_676,U_677] :
        ( c_Orderings_Oord__class_Oless__eq(U_675,U_676,U_677)
        | ~ sP52(U_675,U_676,U_677) )
    & ! [U_675,U_676,U_677] :
        ( c_Orderings_Oord__class_Oless(U_675,U_676,U_677)
        | U_676 = U_677
        | ~ c_Orderings_Oord__class_Oless__eq(U_675,U_676,U_677)
        | ~ sP53(U_675,U_676,U_677) )
    & ! [U_675,U_676,U_677] :
        ( sP52(U_675,U_676,U_677)
        | ~ c_Orderings_Oord__class_Oless(U_675,U_676,U_677)
        | ~ sP53(U_675,U_676,U_677) )
    & ! [U_675,U_676,U_677] :
        ( sP53(U_675,U_676,U_677)
        | ~ class_Orderings_Oorder(U_675) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP52,sP53])],[f_202_2]) ).

cnf(f_202_4,plain,
    ( sP53(U_675,U_676,U_677)
    | ~ class_Orderings_Oorder(U_675) ),
    inference(clausify,[status(thm)],[f_202_3]) ).

cnf(f_202_5,plain,
    ( sP52(U_675,U_676,U_677)
    | ~ c_Orderings_Oord__class_Oless(U_675,U_676,U_677)
    | ~ sP53(U_675,U_676,U_677) ),
    inference(clausify,[status(thm)],[f_202_3]) ).

cnf(f_202_6,plain,
    ( c_Orderings_Oord__class_Oless(U_675,U_676,U_677)
    | U_676 = U_677
    | ~ c_Orderings_Oord__class_Oless__eq(U_675,U_676,U_677)
    | ~ sP53(U_675,U_676,U_677) ),
    inference(clausify,[status(thm)],[f_202_3]) ).

cnf(f_202_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_675,U_676,U_677)
    | ~ sP52(U_675,U_676,U_677) ),
    inference(clausify,[status(thm)],[f_202_3]) ).

cnf(f_202_8,plain,
    ( U_676 != U_677
    | ~ sP52(U_675,U_676,U_677) ),
    inference(clausify,[status(thm)],[f_202_3]) ).

fof(f_203_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_203_2,plain,
    ! [U_680,U_679,U_678] :
      ( ( ( c_Orderings_Oord__class_Oless(U_678,U_679,U_680)
          | c_Orderings_Oord__class_Oless__eq(U_678,U_680,U_679)
          | ~ c_Orderings_Oord__class_Oless__eq(U_678,U_679,U_680) )
        & ( ( ~ c_Orderings_Oord__class_Oless__eq(U_678,U_680,U_679)
            & c_Orderings_Oord__class_Oless__eq(U_678,U_679,U_680) )
          | ~ c_Orderings_Oord__class_Oless(U_678,U_679,U_680) ) )
      | ~ class_Orderings_Opreorder(U_678) ),
    inference(variable_rename,[status(thm)],[f_203_1]) ).

fof(f_203_3,plain,
    ( ! [U_680,U_679,U_678] :
        ( ~ c_Orderings_Oord__class_Oless__eq(U_678,U_680,U_679)
        | ~ sP54(U_680,U_679,U_678) )
    & ! [U_680,U_679,U_678] :
        ( c_Orderings_Oord__class_Oless__eq(U_678,U_679,U_680)
        | ~ sP54(U_680,U_679,U_678) )
    & ! [U_680,U_679,U_678] :
        ( c_Orderings_Oord__class_Oless(U_678,U_679,U_680)
        | c_Orderings_Oord__class_Oless__eq(U_678,U_680,U_679)
        | ~ c_Orderings_Oord__class_Oless__eq(U_678,U_679,U_680)
        | ~ sP55(U_680,U_679,U_678) )
    & ! [U_680,U_679,U_678] :
        ( sP54(U_680,U_679,U_678)
        | ~ c_Orderings_Oord__class_Oless(U_678,U_679,U_680)
        | ~ sP55(U_680,U_679,U_678) )
    & ! [U_680,U_679,U_678] :
        ( sP55(U_680,U_679,U_678)
        | ~ class_Orderings_Opreorder(U_678) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP54,sP55])],[f_203_2]) ).

cnf(f_203_4,plain,
    ( sP55(U_680,U_679,U_678)
    | ~ class_Orderings_Opreorder(U_678) ),
    inference(clausify,[status(thm)],[f_203_3]) ).

cnf(f_203_5,plain,
    ( sP54(U_680,U_679,U_678)
    | ~ c_Orderings_Oord__class_Oless(U_678,U_679,U_680)
    | ~ sP55(U_680,U_679,U_678) ),
    inference(clausify,[status(thm)],[f_203_3]) ).

cnf(f_203_6,plain,
    ( c_Orderings_Oord__class_Oless(U_678,U_679,U_680)
    | c_Orderings_Oord__class_Oless__eq(U_678,U_680,U_679)
    | ~ c_Orderings_Oord__class_Oless__eq(U_678,U_679,U_680)
    | ~ sP55(U_680,U_679,U_678) ),
    inference(clausify,[status(thm)],[f_203_3]) ).

cnf(f_203_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_678,U_679,U_680)
    | ~ sP54(U_680,U_679,U_678) ),
    inference(clausify,[status(thm)],[f_203_3]) ).

cnf(f_203_8,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(U_678,U_680,U_679)
    | ~ sP54(U_680,U_679,U_678) ),
    inference(clausify,[status(thm)],[f_203_3]) ).

fof(f_204_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_204_2,plain,
    ! [U_683,U_682,U_681] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_681,U_682,U_683)
          | ( U_682 != U_683
            & ~ c_Orderings_Oord__class_Oless(U_681,U_682,U_683) ) )
        & ( U_682 = U_683
          | c_Orderings_Oord__class_Oless(U_681,U_682,U_683)
          | ~ c_Orderings_Oord__class_Oless__eq(U_681,U_682,U_683) ) )
      | ~ class_Orderings_Oorder(U_681) ),
    inference(variable_rename,[status(thm)],[f_204_1]) ).

fof(f_204_3,plain,
    ( ! [U_683,U_682,U_681] :
        ( U_682 != U_683
        | ~ sP56(U_683,U_682,U_681) )
    & ! [U_683,U_682,U_681] :
        ( ~ c_Orderings_Oord__class_Oless(U_681,U_682,U_683)
        | ~ sP56(U_683,U_682,U_681) )
    & ! [U_683,U_682,U_681] :
        ( c_Orderings_Oord__class_Oless__eq(U_681,U_682,U_683)
        | sP56(U_683,U_682,U_681)
        | ~ sP57(U_683,U_682,U_681) )
    & ! [U_683,U_682,U_681] :
        ( U_682 = U_683
        | c_Orderings_Oord__class_Oless(U_681,U_682,U_683)
        | ~ c_Orderings_Oord__class_Oless__eq(U_681,U_682,U_683)
        | ~ sP57(U_683,U_682,U_681) )
    & ! [U_683,U_682,U_681] :
        ( sP57(U_683,U_682,U_681)
        | ~ class_Orderings_Oorder(U_681) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP56,sP57])],[f_204_2]) ).

cnf(f_204_4,plain,
    ( sP57(U_683,U_682,U_681)
    | ~ class_Orderings_Oorder(U_681) ),
    inference(clausify,[status(thm)],[f_204_3]) ).

cnf(f_204_5,plain,
    ( U_682 = U_683
    | c_Orderings_Oord__class_Oless(U_681,U_682,U_683)
    | ~ c_Orderings_Oord__class_Oless__eq(U_681,U_682,U_683)
    | ~ sP57(U_683,U_682,U_681) ),
    inference(clausify,[status(thm)],[f_204_3]) ).

cnf(f_204_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_681,U_682,U_683)
    | sP56(U_683,U_682,U_681)
    | ~ sP57(U_683,U_682,U_681) ),
    inference(clausify,[status(thm)],[f_204_3]) ).

cnf(f_204_7,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_681,U_682,U_683)
    | ~ sP56(U_683,U_682,U_681) ),
    inference(clausify,[status(thm)],[f_204_3]) ).

cnf(f_204_8,plain,
    ( U_682 != U_683
    | ~ sP56(U_683,U_682,U_681) ),
    inference(clausify,[status(thm)],[f_204_3]) ).

fof(f_205_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_205_2,plain,
    ! [U_686,U_685,U_684] :
      ( c_Orderings_Oord__class_Oless__eq(U_684,U_686,U_685)
      | c_Orderings_Oord__class_Oless(U_684,U_685,U_686)
      | ~ class_Orderings_Olinorder(U_684) ),
    inference(variable_rename,[status(thm)],[f_205_1]) ).

fof(f_205_3,plain,
    ! [U_684,U_685,U_686] :
      ( c_Orderings_Oord__class_Oless__eq(U_684,U_686,U_685)
      | c_Orderings_Oord__class_Oless(U_684,U_685,U_686)
      | ~ class_Orderings_Olinorder(U_684) ),
    inference(definitional_conversion,[status(esa)],[f_205_2]) ).

cnf(f_205_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_684,U_686,U_685)
    | c_Orderings_Oord__class_Oless(U_684,U_685,U_686)
    | ~ class_Orderings_Olinorder(U_684) ),
    inference(clausify,[status(thm)],[f_205_3]) ).

fof(f_206_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_206_2,plain,
    ! [U_689,U_688,U_687] :
      ( c_Orderings_Oord__class_Oless(U_687,U_689,U_688)
      | c_Orderings_Oord__class_Oless__eq(U_687,U_688,U_689)
      | ~ class_Orderings_Olinorder(U_687) ),
    inference(variable_rename,[status(thm)],[f_206_1]) ).

fof(f_206_3,plain,
    ! [U_687,U_689,U_688] :
      ( c_Orderings_Oord__class_Oless(U_687,U_689,U_688)
      | c_Orderings_Oord__class_Oless__eq(U_687,U_688,U_689)
      | ~ class_Orderings_Olinorder(U_687) ),
    inference(definitional_conversion,[status(esa)],[f_206_2]) ).

cnf(f_206_4,plain,
    ( c_Orderings_Oord__class_Oless(U_687,U_689,U_688)
    | c_Orderings_Oord__class_Oless__eq(U_687,U_688,U_689)
    | ~ class_Orderings_Olinorder(U_687) ),
    inference(clausify,[status(thm)],[f_206_3]) ).

fof(f_207_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_207_2,plain,
    ! [U_692,U_691,U_690] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_690,U_691,U_692)
          | U_691 != U_692 )
        & ( U_691 = U_692
          | ~ c_Orderings_Oord__class_Oless__eq(U_690,U_691,U_692) ) )
      | c_Orderings_Oord__class_Oless(U_690,U_691,U_692)
      | ~ class_Orderings_Olinorder(U_690) ),
    inference(variable_rename,[status(thm)],[f_207_1]) ).

fof(f_207_3,plain,
    ( ! [U_691,U_692,U_690] :
        ( c_Orderings_Oord__class_Oless__eq(U_690,U_691,U_692)
        | U_691 != U_692
        | ~ sP58(U_691,U_692,U_690) )
    & ! [U_691,U_692,U_690] :
        ( U_691 = U_692
        | ~ c_Orderings_Oord__class_Oless__eq(U_690,U_691,U_692)
        | ~ sP58(U_691,U_692,U_690) )
    & ! [U_691,U_692,U_690] :
        ( sP58(U_691,U_692,U_690)
        | c_Orderings_Oord__class_Oless(U_690,U_691,U_692)
        | ~ class_Orderings_Olinorder(U_690) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP58])],[f_207_2]) ).

cnf(f_207_4,plain,
    ( sP58(U_691,U_692,U_690)
    | c_Orderings_Oord__class_Oless(U_690,U_691,U_692)
    | ~ class_Orderings_Olinorder(U_690) ),
    inference(clausify,[status(thm)],[f_207_3]) ).

cnf(f_207_5,plain,
    ( U_691 = U_692
    | ~ c_Orderings_Oord__class_Oless__eq(U_690,U_691,U_692)
    | ~ sP58(U_691,U_692,U_690) ),
    inference(clausify,[status(thm)],[f_207_3]) ).

cnf(f_207_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_690,U_691,U_692)
    | U_691 != U_692
    | ~ sP58(U_691,U_692,U_690) ),
    inference(clausify,[status(thm)],[f_207_3]) ).

fof(f_208_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_208_2,plain,
    ! [U_695,U_694,U_693] :
      ( c_Orderings_Oord__class_Oless(U_693,U_694,U_695)
      | ~ c_Orderings_Oord__class_Oless__eq(U_693,U_694,U_695)
      | U_694 = U_695
      | ~ class_Orderings_Oorder(U_693) ),
    inference(variable_rename,[status(thm)],[f_208_1]) ).

fof(f_208_3,plain,
    ! [U_695,U_694,U_693] :
      ( c_Orderings_Oord__class_Oless(U_693,U_694,U_695)
      | ~ c_Orderings_Oord__class_Oless__eq(U_693,U_694,U_695)
      | U_694 = U_695
      | ~ class_Orderings_Oorder(U_693) ),
    inference(definitional_conversion,[status(esa)],[f_208_2]) ).

cnf(f_208_4,plain,
    ( c_Orderings_Oord__class_Oless(U_693,U_694,U_695)
    | ~ c_Orderings_Oord__class_Oless__eq(U_693,U_694,U_695)
    | U_694 = U_695
    | ~ class_Orderings_Oorder(U_693) ),
    inference(clausify,[status(thm)],[f_208_3]) ).

fof(f_209_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_209_2,plain,
    ! [U_698,U_697,U_696] :
      ( c_Orderings_Oord__class_Oless(U_696,U_698,U_697)
      | ~ c_Orderings_Oord__class_Oless__eq(U_696,U_698,U_697)
      | U_697 = U_698
      | ~ class_Orderings_Oorder(U_696) ),
    inference(variable_rename,[status(thm)],[f_209_1]) ).

fof(f_209_3,plain,
    ! [U_696,U_697,U_698] :
      ( c_Orderings_Oord__class_Oless(U_696,U_698,U_697)
      | ~ c_Orderings_Oord__class_Oless__eq(U_696,U_698,U_697)
      | U_697 = U_698
      | ~ class_Orderings_Oorder(U_696) ),
    inference(definitional_conversion,[status(esa)],[f_209_2]) ).

cnf(f_209_4,plain,
    ( c_Orderings_Oord__class_Oless(U_696,U_698,U_697)
    | ~ c_Orderings_Oord__class_Oless__eq(U_696,U_698,U_697)
    | U_697 = U_698
    | ~ class_Orderings_Oorder(U_696) ),
    inference(clausify,[status(thm)],[f_209_3]) ).

fof(f_210_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_210_2,plain,
    ! [U_701,U_700,U_699] :
      ( ~ c_Orderings_Oord__class_Oless(U_699,U_701,U_700)
      | ~ c_Orderings_Oord__class_Oless__eq(U_699,U_700,U_701)
      | ~ class_Orderings_Olinorder(U_699) ),
    inference(variable_rename,[status(thm)],[f_210_1]) ).

fof(f_210_3,plain,
    ! [U_701,U_699,U_700] :
      ( ~ c_Orderings_Oord__class_Oless(U_699,U_701,U_700)
      | ~ c_Orderings_Oord__class_Oless__eq(U_699,U_700,U_701)
      | ~ class_Orderings_Olinorder(U_699) ),
    inference(definitional_conversion,[status(esa)],[f_210_2]) ).

cnf(f_210_4,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_699,U_701,U_700)
    | ~ c_Orderings_Oord__class_Oless__eq(U_699,U_700,U_701)
    | ~ class_Orderings_Olinorder(U_699) ),
    inference(clausify,[status(thm)],[f_210_3]) ).

fof(f_211_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_211_2,plain,
    ! [U_704,U_703,U_702] :
      ( c_Orderings_Oord__class_Oless__eq(U_702,U_703,U_704)
      | ~ c_Orderings_Oord__class_Oless(U_702,U_703,U_704)
      | ~ class_Orderings_Opreorder(U_702) ),
    inference(variable_rename,[status(thm)],[f_211_1]) ).

fof(f_211_3,plain,
    ! [U_704,U_702,U_703] :
      ( c_Orderings_Oord__class_Oless__eq(U_702,U_703,U_704)
      | ~ c_Orderings_Oord__class_Oless(U_702,U_703,U_704)
      | ~ class_Orderings_Opreorder(U_702) ),
    inference(definitional_conversion,[status(esa)],[f_211_2]) ).

cnf(f_211_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_702,U_703,U_704)
    | ~ c_Orderings_Oord__class_Oless(U_702,U_703,U_704)
    | ~ class_Orderings_Opreorder(U_702) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

fof(f_212_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_212_2,plain,
    ! [U_707,U_706,U_705] :
      ( ( ( ~ c_Orderings_Oord__class_Oless(U_705,U_706,U_707)
          | U_706 != U_707 )
        & ( U_706 = U_707
          | c_Orderings_Oord__class_Oless(U_705,U_706,U_707) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(U_705,U_706,U_707)
      | ~ class_Orderings_Olinorder(U_705) ),
    inference(variable_rename,[status(thm)],[f_212_1]) ).

fof(f_212_3,plain,
    ( ! [U_705,U_706,U_707] :
        ( ~ c_Orderings_Oord__class_Oless(U_705,U_706,U_707)
        | U_706 != U_707
        | ~ sP59(U_705,U_706,U_707) )
    & ! [U_705,U_706,U_707] :
        ( U_706 = U_707
        | c_Orderings_Oord__class_Oless(U_705,U_706,U_707)
        | ~ sP59(U_705,U_706,U_707) )
    & ! [U_705,U_706,U_707] :
        ( sP59(U_705,U_706,U_707)
        | ~ c_Orderings_Oord__class_Oless__eq(U_705,U_706,U_707)
        | ~ class_Orderings_Olinorder(U_705) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP59])],[f_212_2]) ).

cnf(f_212_4,plain,
    ( sP59(U_705,U_706,U_707)
    | ~ c_Orderings_Oord__class_Oless__eq(U_705,U_706,U_707)
    | ~ class_Orderings_Olinorder(U_705) ),
    inference(clausify,[status(thm)],[f_212_3]) ).

cnf(f_212_5,plain,
    ( U_706 = U_707
    | c_Orderings_Oord__class_Oless(U_705,U_706,U_707)
    | ~ sP59(U_705,U_706,U_707) ),
    inference(clausify,[status(thm)],[f_212_3]) ).

cnf(f_212_6,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_705,U_706,U_707)
    | U_706 != U_707
    | ~ sP59(U_705,U_706,U_707) ),
    inference(clausify,[status(thm)],[f_212_3]) ).

fof(f_213_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_213_2,plain,
    ! [U_710,U_709,U_708] :
      ( U_709 = U_710
      | c_Orderings_Oord__class_Oless(U_708,U_709,U_710)
      | ~ c_Orderings_Oord__class_Oless__eq(U_708,U_709,U_710)
      | ~ class_Orderings_Oorder(U_708) ),
    inference(variable_rename,[status(thm)],[f_213_1]) ).

fof(f_213_3,plain,
    ! [U_709,U_708,U_710] :
      ( U_709 = U_710
      | c_Orderings_Oord__class_Oless(U_708,U_709,U_710)
      | ~ c_Orderings_Oord__class_Oless__eq(U_708,U_709,U_710)
      | ~ class_Orderings_Oorder(U_708) ),
    inference(definitional_conversion,[status(esa)],[f_213_2]) ).

cnf(f_213_4,plain,
    ( U_709 = U_710
    | c_Orderings_Oord__class_Oless(U_708,U_709,U_710)
    | ~ c_Orderings_Oord__class_Oless__eq(U_708,U_709,U_710)
    | ~ class_Orderings_Oorder(U_708) ),
    inference(clausify,[status(thm)],[f_213_3]) ).

fof(f_214_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_214_2,plain,
    ! [U_713,U_712,U_711] :
      ( c_Orderings_Oord__class_Oless(U_711,U_712,U_713)
      | U_712 = U_713
      | ~ c_Orderings_Oord__class_Oless__eq(U_711,U_712,U_713)
      | ~ class_Orderings_Oorder(U_711) ),
    inference(variable_rename,[status(thm)],[f_214_1]) ).

fof(f_214_3,plain,
    ! [U_711,U_712,U_713] :
      ( c_Orderings_Oord__class_Oless(U_711,U_712,U_713)
      | U_712 = U_713
      | ~ c_Orderings_Oord__class_Oless__eq(U_711,U_712,U_713)
      | ~ class_Orderings_Oorder(U_711) ),
    inference(definitional_conversion,[status(esa)],[f_214_2]) ).

cnf(f_214_4,plain,
    ( c_Orderings_Oord__class_Oless(U_711,U_712,U_713)
    | U_712 = U_713
    | ~ c_Orderings_Oord__class_Oless__eq(U_711,U_712,U_713)
    | ~ class_Orderings_Oorder(U_711) ),
    inference(clausify,[status(thm)],[f_214_3]) ).

fof(f_215_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_215_2,plain,
    ! [U_716,U_715,U_714] :
      ( c_Orderings_Oord__class_Oless(U_714,U_715,U_716)
      | U_716 = U_715
      | ~ c_Orderings_Oord__class_Oless__eq(U_714,U_715,U_716)
      | ~ class_Orderings_Oorder(U_714) ),
    inference(variable_rename,[status(thm)],[f_215_1]) ).

fof(f_215_3,plain,
    ! [U_714,U_715,U_716] :
      ( c_Orderings_Oord__class_Oless(U_714,U_715,U_716)
      | U_716 = U_715
      | ~ c_Orderings_Oord__class_Oless__eq(U_714,U_715,U_716)
      | ~ class_Orderings_Oorder(U_714) ),
    inference(definitional_conversion,[status(esa)],[f_215_2]) ).

cnf(f_215_4,plain,
    ( c_Orderings_Oord__class_Oless(U_714,U_715,U_716)
    | U_716 = U_715
    | ~ c_Orderings_Oord__class_Oless__eq(U_714,U_715,U_716)
    | ~ class_Orderings_Oorder(U_714) ),
    inference(clausify,[status(thm)],[f_215_3]) ).

fof(f_216_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_216_2,plain,
    ! [U_720,U_719,U_718,U_717] :
      ( c_Orderings_Oord__class_Oless(U_717,U_718,U_720)
      | ~ c_Orderings_Oord__class_Oless__eq(U_717,U_719,U_720)
      | ~ c_Orderings_Oord__class_Oless(U_717,U_718,U_719)
      | ~ class_Orderings_Opreorder(U_717) ),
    inference(variable_rename,[status(thm)],[f_216_1]) ).

fof(f_216_3,plain,
    ! [U_720,U_717,U_718,U_719] :
      ( c_Orderings_Oord__class_Oless(U_717,U_718,U_720)
      | ~ c_Orderings_Oord__class_Oless__eq(U_717,U_719,U_720)
      | ~ c_Orderings_Oord__class_Oless(U_717,U_718,U_719)
      | ~ class_Orderings_Opreorder(U_717) ),
    inference(definitional_conversion,[status(esa)],[f_216_2]) ).

cnf(f_216_4,plain,
    ( c_Orderings_Oord__class_Oless(U_717,U_718,U_720)
    | ~ c_Orderings_Oord__class_Oless__eq(U_717,U_719,U_720)
    | ~ c_Orderings_Oord__class_Oless(U_717,U_718,U_719)
    | ~ class_Orderings_Opreorder(U_717) ),
    inference(clausify,[status(thm)],[f_216_3]) ).

fof(f_217_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_217_2,plain,
    ! [U_724,U_723,U_722,U_721] :
      ( c_Orderings_Oord__class_Oless(U_721,U_724,U_723)
      | ~ c_Orderings_Oord__class_Oless__eq(U_721,U_724,U_722)
      | ~ c_Orderings_Oord__class_Oless(U_721,U_722,U_723)
      | ~ class_Orderings_Oorder(U_721) ),
    inference(variable_rename,[status(thm)],[f_217_1]) ).

fof(f_217_3,plain,
    ! [U_721,U_723,U_724,U_722] :
      ( c_Orderings_Oord__class_Oless(U_721,U_724,U_723)
      | ~ c_Orderings_Oord__class_Oless__eq(U_721,U_724,U_722)
      | ~ c_Orderings_Oord__class_Oless(U_721,U_722,U_723)
      | ~ class_Orderings_Oorder(U_721) ),
    inference(definitional_conversion,[status(esa)],[f_217_2]) ).

cnf(f_217_4,plain,
    ( c_Orderings_Oord__class_Oless(U_721,U_724,U_723)
    | ~ c_Orderings_Oord__class_Oless__eq(U_721,U_724,U_722)
    | ~ c_Orderings_Oord__class_Oless(U_721,U_722,U_723)
    | ~ class_Orderings_Oorder(U_721) ),
    inference(clausify,[status(thm)],[f_217_3]) ).

fof(f_218_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_218_2,plain,
    ! [U_728,U_727,U_726,U_725] :
      ( c_Orderings_Oord__class_Oless(U_725,U_726,U_728)
      | ~ c_Orderings_Oord__class_Oless(U_725,U_727,U_728)
      | ~ c_Orderings_Oord__class_Oless__eq(U_725,U_726,U_727)
      | ~ class_Orderings_Opreorder(U_725) ),
    inference(variable_rename,[status(thm)],[f_218_1]) ).

fof(f_218_3,plain,
    ! [U_726,U_727,U_725,U_728] :
      ( c_Orderings_Oord__class_Oless(U_725,U_726,U_728)
      | ~ c_Orderings_Oord__class_Oless(U_725,U_727,U_728)
      | ~ c_Orderings_Oord__class_Oless__eq(U_725,U_726,U_727)
      | ~ class_Orderings_Opreorder(U_725) ),
    inference(definitional_conversion,[status(esa)],[f_218_2]) ).

cnf(f_218_4,plain,
    ( c_Orderings_Oord__class_Oless(U_725,U_726,U_728)
    | ~ c_Orderings_Oord__class_Oless(U_725,U_727,U_728)
    | ~ c_Orderings_Oord__class_Oless__eq(U_725,U_726,U_727)
    | ~ class_Orderings_Opreorder(U_725) ),
    inference(clausify,[status(thm)],[f_218_3]) ).

fof(f_219_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_219_2,plain,
    ! [U_732,U_731,U_730,U_729] :
      ( c_Orderings_Oord__class_Oless(U_729,U_732,U_731)
      | ~ c_Orderings_Oord__class_Oless(U_729,U_732,U_730)
      | ~ c_Orderings_Oord__class_Oless__eq(U_729,U_730,U_731)
      | ~ class_Orderings_Oorder(U_729) ),
    inference(variable_rename,[status(thm)],[f_219_1]) ).

fof(f_219_3,plain,
    ! [U_732,U_731,U_729,U_730] :
      ( c_Orderings_Oord__class_Oless(U_729,U_732,U_731)
      | ~ c_Orderings_Oord__class_Oless(U_729,U_732,U_730)
      | ~ c_Orderings_Oord__class_Oless__eq(U_729,U_730,U_731)
      | ~ class_Orderings_Oorder(U_729) ),
    inference(definitional_conversion,[status(esa)],[f_219_2]) ).

cnf(f_219_4,plain,
    ( c_Orderings_Oord__class_Oless(U_729,U_732,U_731)
    | ~ c_Orderings_Oord__class_Oless(U_729,U_732,U_730)
    | ~ c_Orderings_Oord__class_Oless__eq(U_729,U_730,U_731)
    | ~ class_Orderings_Oorder(U_729) ),
    inference(clausify,[status(thm)],[f_219_3]) ).

fof(f_220_1,plain,
    ! [V_b_2,V_c_2,V_a_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
          | ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) )
        & ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
          | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2)) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right]) ).

fof(f_220_2,plain,
    ! [U_736,U_735,U_734,U_733] :
      ( ( ( c_Orderings_Oord__class_Oless(U_733,c_Groups_Oplus__class_Oplus(U_733,U_734,U_735),c_Groups_Oplus__class_Oplus(U_733,U_736,U_735))
          | ~ c_Orderings_Oord__class_Oless(U_733,U_734,U_736) )
        & ( c_Orderings_Oord__class_Oless(U_733,U_734,U_736)
          | ~ c_Orderings_Oord__class_Oless(U_733,c_Groups_Oplus__class_Oplus(U_733,U_734,U_735),c_Groups_Oplus__class_Oplus(U_733,U_736,U_735)) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_733) ),
    inference(variable_rename,[status(thm)],[f_220_1]) ).

fof(f_220_3,plain,
    ( ! [U_734,U_733,U_735,U_736] :
        ( c_Orderings_Oord__class_Oless(U_733,c_Groups_Oplus__class_Oplus(U_733,U_734,U_735),c_Groups_Oplus__class_Oplus(U_733,U_736,U_735))
        | ~ c_Orderings_Oord__class_Oless(U_733,U_734,U_736)
        | ~ sP60(U_734,U_733,U_735,U_736) )
    & ! [U_734,U_733,U_735,U_736] :
        ( c_Orderings_Oord__class_Oless(U_733,U_734,U_736)
        | ~ c_Orderings_Oord__class_Oless(U_733,c_Groups_Oplus__class_Oplus(U_733,U_734,U_735),c_Groups_Oplus__class_Oplus(U_733,U_736,U_735))
        | ~ sP60(U_734,U_733,U_735,U_736) )
    & ! [U_734,U_733,U_735,U_736] :
        ( sP60(U_734,U_733,U_735,U_736)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_733) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP60])],[f_220_2]) ).

cnf(f_220_4,plain,
    ( sP60(U_734,U_733,U_735,U_736)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_733) ),
    inference(clausify,[status(thm)],[f_220_3]) ).

cnf(f_220_5,plain,
    ( c_Orderings_Oord__class_Oless(U_733,U_734,U_736)
    | ~ c_Orderings_Oord__class_Oless(U_733,c_Groups_Oplus__class_Oplus(U_733,U_734,U_735),c_Groups_Oplus__class_Oplus(U_733,U_736,U_735))
    | ~ sP60(U_734,U_733,U_735,U_736) ),
    inference(clausify,[status(thm)],[f_220_3]) ).

cnf(f_220_6,plain,
    ( c_Orderings_Oord__class_Oless(U_733,c_Groups_Oplus__class_Oplus(U_733,U_734,U_735),c_Groups_Oplus__class_Oplus(U_733,U_736,U_735))
    | ~ c_Orderings_Oord__class_Oless(U_733,U_734,U_736)
    | ~ sP60(U_734,U_733,U_735,U_736) ),
    inference(clausify,[status(thm)],[f_220_3]) ).

fof(f_221_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))
          | ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) )
        & ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
          | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_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_221_2,plain,
    ! [U_740,U_739,U_738,U_737] :
      ( ( ( c_Orderings_Oord__class_Oless(U_737,c_Groups_Oplus__class_Oplus(U_737,U_738,U_739),c_Groups_Oplus__class_Oplus(U_737,U_738,U_740))
          | ~ c_Orderings_Oord__class_Oless(U_737,U_739,U_740) )
        & ( c_Orderings_Oord__class_Oless(U_737,U_739,U_740)
          | ~ c_Orderings_Oord__class_Oless(U_737,c_Groups_Oplus__class_Oplus(U_737,U_738,U_739),c_Groups_Oplus__class_Oplus(U_737,U_738,U_740)) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_737) ),
    inference(variable_rename,[status(thm)],[f_221_1]) ).

fof(f_221_3,plain,
    ( ! [U_740,U_737,U_738,U_739] :
        ( c_Orderings_Oord__class_Oless(U_737,c_Groups_Oplus__class_Oplus(U_737,U_738,U_739),c_Groups_Oplus__class_Oplus(U_737,U_738,U_740))
        | ~ c_Orderings_Oord__class_Oless(U_737,U_739,U_740)
        | ~ sP61(U_740,U_737,U_738,U_739) )
    & ! [U_740,U_737,U_738,U_739] :
        ( c_Orderings_Oord__class_Oless(U_737,U_739,U_740)
        | ~ c_Orderings_Oord__class_Oless(U_737,c_Groups_Oplus__class_Oplus(U_737,U_738,U_739),c_Groups_Oplus__class_Oplus(U_737,U_738,U_740))
        | ~ sP61(U_740,U_737,U_738,U_739) )
    & ! [U_740,U_737,U_738,U_739] :
        ( sP61(U_740,U_737,U_738,U_739)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_737) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP61])],[f_221_2]) ).

cnf(f_221_4,plain,
    ( sP61(U_740,U_737,U_738,U_739)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_737) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_5,plain,
    ( c_Orderings_Oord__class_Oless(U_737,U_739,U_740)
    | ~ c_Orderings_Oord__class_Oless(U_737,c_Groups_Oplus__class_Oplus(U_737,U_738,U_739),c_Groups_Oplus__class_Oplus(U_737,U_738,U_740))
    | ~ sP61(U_740,U_737,U_738,U_739) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_6,plain,
    ( c_Orderings_Oord__class_Oless(U_737,c_Groups_Oplus__class_Oplus(U_737,U_738,U_739),c_Groups_Oplus__class_Oplus(U_737,U_738,U_740))
    | ~ c_Orderings_Oord__class_Oless(U_737,U_739,U_740)
    | ~ sP61(U_740,U_737,U_738,U_739) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

fof(f_222_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_222_2,plain,
    ! [U_744,U_743,U_742,U_741] :
      ( c_Orderings_Oord__class_Oless(U_741,c_Groups_Oplus__class_Oplus(U_741,U_742,U_744),c_Groups_Oplus__class_Oplus(U_741,U_743,U_744))
      | ~ c_Orderings_Oord__class_Oless(U_741,U_742,U_743)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_741) ),
    inference(variable_rename,[status(thm)],[f_222_1]) ).

fof(f_222_3,plain,
    ! [U_743,U_744,U_741,U_742] :
      ( c_Orderings_Oord__class_Oless(U_741,c_Groups_Oplus__class_Oplus(U_741,U_742,U_744),c_Groups_Oplus__class_Oplus(U_741,U_743,U_744))
      | ~ c_Orderings_Oord__class_Oless(U_741,U_742,U_743)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_741) ),
    inference(definitional_conversion,[status(esa)],[f_222_2]) ).

cnf(f_222_4,plain,
    ( c_Orderings_Oord__class_Oless(U_741,c_Groups_Oplus__class_Oplus(U_741,U_742,U_744),c_Groups_Oplus__class_Oplus(U_741,U_743,U_744))
    | ~ c_Orderings_Oord__class_Oless(U_741,U_742,U_743)
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_741) ),
    inference(clausify,[status(thm)],[f_222_3]) ).

fof(f_223_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_223_2,plain,
    ! [U_748,U_747,U_746,U_745] :
      ( c_Orderings_Oord__class_Oless(U_745,c_Groups_Oplus__class_Oplus(U_745,U_748,U_746),c_Groups_Oplus__class_Oplus(U_745,U_748,U_747))
      | ~ c_Orderings_Oord__class_Oless(U_745,U_746,U_747)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_745) ),
    inference(variable_rename,[status(thm)],[f_223_1]) ).

fof(f_223_3,plain,
    ! [U_746,U_747,U_748,U_745] :
      ( c_Orderings_Oord__class_Oless(U_745,c_Groups_Oplus__class_Oplus(U_745,U_748,U_746),c_Groups_Oplus__class_Oplus(U_745,U_748,U_747))
      | ~ c_Orderings_Oord__class_Oless(U_745,U_746,U_747)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_745) ),
    inference(definitional_conversion,[status(esa)],[f_223_2]) ).

cnf(f_223_4,plain,
    ( c_Orderings_Oord__class_Oless(U_745,c_Groups_Oplus__class_Oplus(U_745,U_748,U_746),c_Groups_Oplus__class_Oplus(U_745,U_748,U_747))
    | ~ c_Orderings_Oord__class_Oless(U_745,U_746,U_747)
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_745) ),
    inference(clausify,[status(thm)],[f_223_3]) ).

fof(f_224_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_224_2,plain,
    ! [U_753,U_752,U_751,U_750,U_749] :
      ( c_Orderings_Oord__class_Oless(U_749,c_Groups_Oplus__class_Oplus(U_749,U_750,U_752),c_Groups_Oplus__class_Oplus(U_749,U_751,U_753))
      | ~ c_Orderings_Oord__class_Oless(U_749,U_752,U_753)
      | ~ c_Orderings_Oord__class_Oless(U_749,U_750,U_751)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_749) ),
    inference(variable_rename,[status(thm)],[f_224_1]) ).

fof(f_224_3,plain,
    ! [U_751,U_750,U_749,U_752,U_753] :
      ( c_Orderings_Oord__class_Oless(U_749,c_Groups_Oplus__class_Oplus(U_749,U_750,U_752),c_Groups_Oplus__class_Oplus(U_749,U_751,U_753))
      | ~ c_Orderings_Oord__class_Oless(U_749,U_752,U_753)
      | ~ c_Orderings_Oord__class_Oless(U_749,U_750,U_751)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_749) ),
    inference(definitional_conversion,[status(esa)],[f_224_2]) ).

cnf(f_224_4,plain,
    ( c_Orderings_Oord__class_Oless(U_749,c_Groups_Oplus__class_Oplus(U_749,U_750,U_752),c_Groups_Oplus__class_Oplus(U_749,U_751,U_753))
    | ~ c_Orderings_Oord__class_Oless(U_749,U_752,U_753)
    | ~ c_Orderings_Oord__class_Oless(U_749,U_750,U_751)
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_749) ),
    inference(clausify,[status(thm)],[f_224_3]) ).

fof(f_225_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_225_2,plain,
    ! [U_757,U_756,U_755,U_754] :
      ( c_Orderings_Oord__class_Oless(U_754,U_755,U_757)
      | ~ c_Orderings_Oord__class_Oless(U_754,c_Groups_Oplus__class_Oplus(U_754,U_755,U_756),c_Groups_Oplus__class_Oplus(U_754,U_757,U_756))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_754) ),
    inference(variable_rename,[status(thm)],[f_225_1]) ).

fof(f_225_3,plain,
    ! [U_754,U_755,U_756,U_757] :
      ( c_Orderings_Oord__class_Oless(U_754,U_755,U_757)
      | ~ c_Orderings_Oord__class_Oless(U_754,c_Groups_Oplus__class_Oplus(U_754,U_755,U_756),c_Groups_Oplus__class_Oplus(U_754,U_757,U_756))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_754) ),
    inference(definitional_conversion,[status(esa)],[f_225_2]) ).

cnf(f_225_4,plain,
    ( c_Orderings_Oord__class_Oless(U_754,U_755,U_757)
    | ~ c_Orderings_Oord__class_Oless(U_754,c_Groups_Oplus__class_Oplus(U_754,U_755,U_756),c_Groups_Oplus__class_Oplus(U_754,U_757,U_756))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_754) ),
    inference(clausify,[status(thm)],[f_225_3]) ).

fof(f_226_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_226_2,plain,
    ! [U_761,U_760,U_759,U_758] :
      ( c_Orderings_Oord__class_Oless(U_758,U_760,U_761)
      | ~ c_Orderings_Oord__class_Oless(U_758,c_Groups_Oplus__class_Oplus(U_758,U_759,U_760),c_Groups_Oplus__class_Oplus(U_758,U_759,U_761))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_758) ),
    inference(variable_rename,[status(thm)],[f_226_1]) ).

fof(f_226_3,plain,
    ! [U_758,U_759,U_760,U_761] :
      ( c_Orderings_Oord__class_Oless(U_758,U_760,U_761)
      | ~ c_Orderings_Oord__class_Oless(U_758,c_Groups_Oplus__class_Oplus(U_758,U_759,U_760),c_Groups_Oplus__class_Oplus(U_758,U_759,U_761))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_758) ),
    inference(definitional_conversion,[status(esa)],[f_226_2]) ).

cnf(f_226_4,plain,
    ( c_Orderings_Oord__class_Oless(U_758,U_760,U_761)
    | ~ c_Orderings_Oord__class_Oless(U_758,c_Groups_Oplus__class_Oplus(U_758,U_759,U_760),c_Groups_Oplus__class_Oplus(U_758,U_759,U_761))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_758) ),
    inference(clausify,[status(thm)],[f_226_3]) ).

fof(f_227_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_227_2,plain,
    ! [U_763,U_762] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_762),c_Nat_OSuc(U_763)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_762,U_763),
    inference(variable_rename,[status(thm)],[f_227_1]) ).

fof(f_227_3,plain,
    ! [U_763,U_762] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_762),c_Nat_OSuc(U_763)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_762,U_763),
    inference(definitional_conversion,[status(esa)],[f_227_2]) ).

cnf(f_227_4,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_762),c_Nat_OSuc(U_763)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_762,U_763),
    inference(clausify,[status(thm)],[f_227_3]) ).

fof(f_228_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_228_2,plain,
    ! [U_766,U_765,U_764] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_764),U_765),c_Nat_OSuc(U_766)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_764,U_765),U_766),
    inference(variable_rename,[status(thm)],[f_228_1]) ).

fof(f_228_3,plain,
    ! [U_764,U_765,U_766] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_764),U_765),c_Nat_OSuc(U_766)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_764,U_765),U_766),
    inference(definitional_conversion,[status(esa)],[f_228_2]) ).

cnf(f_228_4,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_764),U_765),c_Nat_OSuc(U_766)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_764,U_765),U_766),
    inference(clausify,[status(thm)],[f_228_3]) ).

fof(f_229_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_229_2,plain,
    ! [U_768,U_767] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_767,U_768),U_768) = U_767,
    inference(variable_rename,[status(thm)],[f_229_1]) ).

fof(f_229_3,plain,
    ! [U_767,U_768] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_767,U_768),U_768) = U_767,
    inference(definitional_conversion,[status(esa)],[f_229_2]) ).

cnf(f_229_4,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_767,U_768),U_768) = U_767,
    inference(clausify,[status(thm)],[f_229_3]) ).

fof(f_230_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_230_2,plain,
    ! [U_770,U_769] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_769,U_770),U_769) = U_770,
    inference(variable_rename,[status(thm)],[f_230_1]) ).

fof(f_230_3,plain,
    ! [U_770,U_769] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_769,U_770),U_769) = U_770,
    inference(definitional_conversion,[status(esa)],[f_230_2]) ).

cnf(f_230_4,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_769,U_770),U_769) = U_770,
    inference(clausify,[status(thm)],[f_230_3]) ).

fof(f_231_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_231_2,plain,
    ! [U_773,U_772,U_771] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_771,U_772),U_773) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_771,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_772,U_773)),
    inference(variable_rename,[status(thm)],[f_231_1]) ).

fof(f_231_3,plain,
    ! [U_772,U_771,U_773] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_771,U_772),U_773) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_771,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_772,U_773)),
    inference(definitional_conversion,[status(esa)],[f_231_2]) ).

cnf(f_231_4,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_771,U_772),U_773) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_771,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_772,U_773)),
    inference(clausify,[status(thm)],[f_231_3]) ).

fof(f_232_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_232_2,plain,
    ! [U_776,U_775,U_774] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_774,U_775),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_774,U_776)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_775,U_776),
    inference(variable_rename,[status(thm)],[f_232_1]) ).

fof(f_232_3,plain,
    ! [U_775,U_774,U_776] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_774,U_775),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_774,U_776)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_775,U_776),
    inference(definitional_conversion,[status(esa)],[f_232_2]) ).

cnf(f_232_4,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_774,U_775),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_774,U_776)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_775,U_776),
    inference(clausify,[status(thm)],[f_232_3]) ).

fof(f_233_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_233_2,plain,
    ! [U_779,U_778,U_777] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_777,U_778),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_779,U_778)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_777,U_779),
    inference(variable_rename,[status(thm)],[f_233_1]) ).

fof(f_233_3,plain,
    ! [U_778,U_777,U_779] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_777,U_778),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_779,U_778)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_777,U_779),
    inference(definitional_conversion,[status(esa)],[f_233_2]) ).

cnf(f_233_4,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_777,U_778),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_779,U_778)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_777,U_779),
    inference(clausify,[status(thm)],[f_233_3]) ).

fof(f_234_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_234_2,plain,
    ! [U_782,U_781,U_780] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_781,U_780),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_782,U_780))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_781,U_782) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_781,U_782)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_781,U_780),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_782,U_780)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_780,U_782)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_780,U_781) ),
    inference(variable_rename,[status(thm)],[f_234_1]) ).

fof(f_234_3,plain,
    ( ! [U_781,U_780,U_782] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_781,U_780),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_782,U_780))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_781,U_782)
        | ~ sP62(U_781,U_780,U_782) )
    & ! [U_781,U_780,U_782] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_781,U_782)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_781,U_780),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_782,U_780))
        | ~ sP62(U_781,U_780,U_782) )
    & ! [U_781,U_780,U_782] :
        ( sP62(U_781,U_780,U_782)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_780,U_782)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_780,U_781) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP62])],[f_234_2]) ).

cnf(f_234_4,plain,
    ( sP62(U_781,U_780,U_782)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_780,U_782)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_780,U_781) ),
    inference(clausify,[status(thm)],[f_234_3]) ).

cnf(f_234_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_781,U_782)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_781,U_780),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_782,U_780))
    | ~ sP62(U_781,U_780,U_782) ),
    inference(clausify,[status(thm)],[f_234_3]) ).

cnf(f_234_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_781,U_780),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_782,U_780))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_781,U_782)
    | ~ sP62(U_781,U_780,U_782) ),
    inference(clausify,[status(thm)],[f_234_3]) ).

fof(f_235_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_235_2,plain,
    ! [U_785,U_784,U_783] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_784,U_783),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_785,U_783)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_784,U_785)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_783,U_785)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_783,U_784) ),
    inference(variable_rename,[status(thm)],[f_235_1]) ).

fof(f_235_3,plain,
    ! [U_785,U_783,U_784] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_784,U_783),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_785,U_783)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_784,U_785)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_783,U_785)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_783,U_784) ),
    inference(definitional_conversion,[status(esa)],[f_235_2]) ).

cnf(f_235_4,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_784,U_783),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_785,U_783)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_784,U_785)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_783,U_785)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_783,U_784) ),
    inference(clausify,[status(thm)],[f_235_3]) ).

fof(f_236_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_236_2,plain,
    ! [U_788,U_787,U_786] :
      ( ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_787,U_786) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_788,U_786)
          | U_787 != U_788 )
        & ( U_787 = U_788
          | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_787,U_786) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_788,U_786) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_786,U_788)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_786,U_787) ),
    inference(variable_rename,[status(thm)],[f_236_1]) ).

fof(f_236_3,plain,
    ( ! [U_786,U_787,U_788] :
        ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_787,U_786) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_788,U_786)
        | U_787 != U_788
        | ~ sP63(U_786,U_787,U_788) )
    & ! [U_786,U_787,U_788] :
        ( U_787 = U_788
        | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_787,U_786) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_788,U_786)
        | ~ sP63(U_786,U_787,U_788) )
    & ! [U_786,U_787,U_788] :
        ( sP63(U_786,U_787,U_788)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_786,U_788)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_786,U_787) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP63])],[f_236_2]) ).

cnf(f_236_4,plain,
    ( sP63(U_786,U_787,U_788)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_786,U_788)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_786,U_787) ),
    inference(clausify,[status(thm)],[f_236_3]) ).

cnf(f_236_5,plain,
    ( U_787 = U_788
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_787,U_786) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_788,U_786)
    | ~ sP63(U_786,U_787,U_788) ),
    inference(clausify,[status(thm)],[f_236_3]) ).

cnf(f_236_6,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_787,U_786) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_788,U_786)
    | U_787 != U_788
    | ~ sP63(U_786,U_787,U_788) ),
    inference(clausify,[status(thm)],[f_236_3]) ).

fof(f_237_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_237_2,plain,
    ! [U_790,U_789] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_790,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_790,U_789)) = U_789
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_789,U_790) ),
    inference(variable_rename,[status(thm)],[f_237_1]) ).

fof(f_237_3,plain,
    ! [U_789,U_790] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_790,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_790,U_789)) = U_789
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_789,U_790) ),
    inference(definitional_conversion,[status(esa)],[f_237_2]) ).

cnf(f_237_4,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_790,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_790,U_789)) = U_789
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_789,U_790) ),
    inference(clausify,[status(thm)],[f_237_3]) ).

fof(f_238_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_238_2,plain,
    ! [U_793,U_792,U_791] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_791,U_793),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_792,U_793))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_791,U_792) ),
    inference(variable_rename,[status(thm)],[f_238_1]) ).

fof(f_238_3,plain,
    ! [U_793,U_791,U_792] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_791,U_793),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_792,U_793))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_791,U_792) ),
    inference(definitional_conversion,[status(esa)],[f_238_2]) ).

cnf(f_238_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_791,U_793),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_792,U_793))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_791,U_792) ),
    inference(clausify,[status(thm)],[f_238_3]) ).

fof(f_239_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_239_2,plain,
    ! [U_796,U_795,U_794] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_796,U_795),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_796,U_794))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_794,U_795) ),
    inference(variable_rename,[status(thm)],[f_239_1]) ).

fof(f_239_3,plain,
    ! [U_794,U_795,U_796] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_796,U_795),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_796,U_794))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_794,U_795) ),
    inference(definitional_conversion,[status(esa)],[f_239_2]) ).

cnf(f_239_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_796,U_795),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_796,U_794))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_794,U_795) ),
    inference(clausify,[status(thm)],[f_239_3]) ).

fof(f_240_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_240_2,plain,
    ! [U_798,U_797] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_797,U_798),U_797),
    inference(variable_rename,[status(thm)],[f_240_1]) ).

fof(f_240_3,plain,
    ! [U_798,U_797] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_797,U_798),U_797),
    inference(definitional_conversion,[status(esa)],[f_240_2]) ).

cnf(f_240_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_797,U_798),U_797),
    inference(clausify,[status(thm)],[f_240_3]) ).

fof(f_241_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_241_2,plain,
    ! [U_800,U_799] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_799,U_800)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_800,c_Nat_OSuc(U_799)) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_800,c_Nat_OSuc(U_799))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_799,U_800) ) ),
    inference(variable_rename,[status(thm)],[f_241_1]) ).

fof(f_241_3,plain,
    ( ! [U_804,U_802] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_802,U_804)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_804,c_Nat_OSuc(U_802)) )
    & ! [U_803,U_801] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_803,c_Nat_OSuc(U_801))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_801,U_803) ) ),
    inference(miniscope,[status(thm)],[f_241_2]) ).

fof(f_241_4,plain,
    ( ! [U_804,U_802] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_802,U_804)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_804,c_Nat_OSuc(U_802)) )
    & ! [U_803,U_801] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_803,c_Nat_OSuc(U_801))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_801,U_803) ) ),
    inference(definitional_conversion,[status(esa)],[f_241_3]) ).

cnf(f_241_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_803,c_Nat_OSuc(U_801))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_801,U_803) ),
    inference(clausify,[status(thm)],[f_241_4]) ).

cnf(f_241_6,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_802,U_804)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_804,c_Nat_OSuc(U_802)) ),
    inference(clausify,[status(thm)],[f_241_4]) ).

fof(f_242_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_242_2,plain,
    ! [U_806,U_805] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_805,c_Nat_OSuc(U_806))
        | ( U_805 != U_806
          & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_805,U_806) ) )
      & ( U_805 = U_806
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_805,U_806)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_805,c_Nat_OSuc(U_806)) ) ),
    inference(variable_rename,[status(thm)],[f_242_1]) ).

fof(f_242_3,plain,
    ( ! [U_810,U_808] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_808,c_Nat_OSuc(U_810))
        | ( U_808 != U_810
          & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_808,U_810) ) )
    & ! [U_809,U_807] :
        ( U_807 = U_809
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_807,U_809)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_807,c_Nat_OSuc(U_809)) ) ),
    inference(miniscope,[status(thm)],[f_242_2]) ).

fof(f_242_4,plain,
    ( ! [U_810,U_808] :
        ( U_808 != U_810
        | ~ sP64(U_810,U_808) )
    & ! [U_810,U_808] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_808,U_810)
        | ~ sP64(U_810,U_808) )
    & ! [U_810,U_808] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_808,c_Nat_OSuc(U_810))
        | sP64(U_810,U_808) )
    & ! [U_807,U_809] :
        ( U_807 = U_809
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_807,U_809)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_807,c_Nat_OSuc(U_809)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP64])],[f_242_3]) ).

cnf(f_242_5,plain,
    ( U_807 = U_809
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_807,U_809)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_807,c_Nat_OSuc(U_809)) ),
    inference(clausify,[status(thm)],[f_242_4]) ).

cnf(f_242_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_808,c_Nat_OSuc(U_810))
    | sP64(U_810,U_808) ),
    inference(clausify,[status(thm)],[f_242_4]) ).

cnf(f_242_7,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_808,U_810)
    | ~ sP64(U_810,U_808) ),
    inference(clausify,[status(thm)],[f_242_4]) ).

cnf(f_242_8,plain,
    ( U_808 != U_810
    | ~ sP64(U_810,U_808) ),
    inference(clausify,[status(thm)],[f_242_4]) ).

fof(f_243_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_243_2,plain,
    ! [U_812,U_811] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_811),c_Nat_OSuc(U_812))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_811,U_812) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_811,U_812)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_811),c_Nat_OSuc(U_812)) ) ),
    inference(variable_rename,[status(thm)],[f_243_1]) ).

fof(f_243_3,plain,
    ( ! [U_816,U_814] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_814),c_Nat_OSuc(U_816))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_814,U_816) )
    & ! [U_815,U_813] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_813,U_815)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_813),c_Nat_OSuc(U_815)) ) ),
    inference(miniscope,[status(thm)],[f_243_2]) ).

fof(f_243_4,plain,
    ( ! [U_816,U_814] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_814),c_Nat_OSuc(U_816))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_814,U_816) )
    & ! [U_815,U_813] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_813,U_815)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_813),c_Nat_OSuc(U_815)) ) ),
    inference(definitional_conversion,[status(esa)],[f_243_3]) ).

cnf(f_243_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_813,U_815)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_813),c_Nat_OSuc(U_815)) ),
    inference(clausify,[status(thm)],[f_243_4]) ).

cnf(f_243_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_814),c_Nat_OSuc(U_816))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_814,U_816) ),
    inference(clausify,[status(thm)],[f_243_4]) ).

fof(f_244_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_244_2,plain,
    ! [U_818,U_817] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_817,c_Nat_OSuc(U_818))
          | U_817 != U_818 )
        & ( U_817 = U_818
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_817,c_Nat_OSuc(U_818)) ) )
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_817,U_818) ),
    inference(variable_rename,[status(thm)],[f_244_1]) ).

fof(f_244_3,plain,
    ( ! [U_817,U_818] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_817,c_Nat_OSuc(U_818))
        | U_817 != U_818
        | ~ sP65(U_817,U_818) )
    & ! [U_817,U_818] :
        ( U_817 = U_818
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_817,c_Nat_OSuc(U_818))
        | ~ sP65(U_817,U_818) )
    & ! [U_817,U_818] :
        ( sP65(U_817,U_818)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_817,U_818) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP65])],[f_244_2]) ).

cnf(f_244_4,plain,
    ( sP65(U_817,U_818)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_817,U_818) ),
    inference(clausify,[status(thm)],[f_244_3]) ).

cnf(f_244_5,plain,
    ( U_817 = U_818
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_817,c_Nat_OSuc(U_818))
    | ~ sP65(U_817,U_818) ),
    inference(clausify,[status(thm)],[f_244_3]) ).

cnf(f_244_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_817,c_Nat_OSuc(U_818))
    | U_817 != U_818
    | ~ sP65(U_817,U_818) ),
    inference(clausify,[status(thm)],[f_244_3]) ).

fof(f_245_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_245_2,plain,
    ! [U_820,U_819] :
      ( U_820 = U_819
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_819,c_Nat_OSuc(U_820))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_819,U_820) ),
    inference(variable_rename,[status(thm)],[f_245_1]) ).

fof(f_245_3,plain,
    ! [U_819,U_820] :
      ( U_820 = U_819
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_819,c_Nat_OSuc(U_820))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_819,U_820) ),
    inference(definitional_conversion,[status(esa)],[f_245_2]) ).

cnf(f_245_4,plain,
    ( U_820 = U_819
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_819,c_Nat_OSuc(U_820))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_819,U_820) ),
    inference(clausify,[status(thm)],[f_245_3]) ).

fof(f_246_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_246_2,plain,
    ! [U_822,U_821] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_821,c_Nat_OSuc(U_822))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_821,U_822) ),
    inference(variable_rename,[status(thm)],[f_246_1]) ).

fof(f_246_3,plain,
    ! [U_821,U_822] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_821,c_Nat_OSuc(U_822))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_821,U_822) ),
    inference(definitional_conversion,[status(esa)],[f_246_2]) ).

cnf(f_246_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_821,c_Nat_OSuc(U_822))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_821,U_822) ),
    inference(clausify,[status(thm)],[f_246_3]) ).

fof(f_247_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_247_2,plain,
    ! [U_824,U_823] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_823),U_824)
      | c_Nat_OSuc(U_823) = U_824
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_823,U_824) ),
    inference(variable_rename,[status(thm)],[f_247_1]) ).

fof(f_247_3,plain,
    ! [U_823,U_824] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_823),U_824)
      | c_Nat_OSuc(U_823) = U_824
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_823,U_824) ),
    inference(definitional_conversion,[status(esa)],[f_247_2]) ).

cnf(f_247_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_823),U_824)
    | c_Nat_OSuc(U_823) = U_824
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_823,U_824) ),
    inference(clausify,[status(thm)],[f_247_3]) ).

fof(f_248_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_248_2,plain,
    ! [U_827,U_826,U_825] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_825),U_827)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_826,U_827)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_825,U_826) ),
    inference(variable_rename,[status(thm)],[f_248_1]) ).

fof(f_248_3,plain,
    ! [U_825,U_826,U_827] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_825),U_827)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_826,U_827)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_825,U_826) ),
    inference(definitional_conversion,[status(esa)],[f_248_2]) ).

cnf(f_248_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_825),U_827)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_826,U_827)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_825,U_826) ),
    inference(clausify,[status(thm)],[f_248_3]) ).

fof(f_249_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_249_2,plain,
    ! [U_829,U_828] :
      ( U_828 = U_829
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_828,U_829)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_828,c_Nat_OSuc(U_829)) ),
    inference(variable_rename,[status(thm)],[f_249_1]) ).

fof(f_249_3,plain,
    ! [U_828,U_829] :
      ( U_828 = U_829
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_828,U_829)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_828,c_Nat_OSuc(U_829)) ),
    inference(definitional_conversion,[status(esa)],[f_249_2]) ).

cnf(f_249_4,plain,
    ( U_828 = U_829
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_828,U_829)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_828,c_Nat_OSuc(U_829)) ),
    inference(clausify,[status(thm)],[f_249_3]) ).

fof(f_250_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_250_2,plain,
    ! [U_831,U_830] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_830,U_831)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_830),U_831) ),
    inference(variable_rename,[status(thm)],[f_250_1]) ).

fof(f_250_3,plain,
    ! [U_831,U_830] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_830,U_831)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_830),U_831) ),
    inference(definitional_conversion,[status(esa)],[f_250_2]) ).

cnf(f_250_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_830,U_831)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_830),U_831) ),
    inference(clausify,[status(thm)],[f_250_3]) ).

fof(f_251_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_251_2,plain,
    ! [U_833,U_832] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_832,U_833)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_832),c_Nat_OSuc(U_833)) ),
    inference(variable_rename,[status(thm)],[f_251_1]) ).

fof(f_251_3,plain,
    ! [U_832,U_833] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_832,U_833)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_832),c_Nat_OSuc(U_833)) ),
    inference(definitional_conversion,[status(esa)],[f_251_2]) ).

cnf(f_251_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_832,U_833)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_832),c_Nat_OSuc(U_833)) ),
    inference(clausify,[status(thm)],[f_251_3]) ).

fof(f_252_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_252_2,plain,
    ! [U_835,U_834] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_834,U_835)
        | U_834 = U_835
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_834,U_835) )
      & ( ( U_834 != U_835
          & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_834,U_835) )
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_834,U_835) ) ),
    inference(variable_rename,[status(thm)],[f_252_1]) ).

fof(f_252_3,plain,
    ( ! [U_839,U_837] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_837,U_839)
        | U_837 = U_839
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_837,U_839) )
    & ! [U_838,U_836] :
        ( ( U_836 != U_838
          & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_836,U_838) )
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_836,U_838) ) ),
    inference(miniscope,[status(thm)],[f_252_2]) ).

fof(f_252_4,plain,
    ( ! [U_836,U_838] :
        ( U_836 != U_838
        | ~ sP66(U_836,U_838) )
    & ! [U_836,U_838] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_836,U_838)
        | ~ sP66(U_836,U_838) )
    & ! [U_839,U_837] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_837,U_839)
        | U_837 = U_839
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_837,U_839) )
    & ! [U_836,U_838] :
        ( sP66(U_836,U_838)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_836,U_838) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP66])],[f_252_3]) ).

cnf(f_252_5,plain,
    ( sP66(U_836,U_838)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_836,U_838) ),
    inference(clausify,[status(thm)],[f_252_4]) ).

cnf(f_252_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_837,U_839)
    | U_837 = U_839
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_837,U_839) ),
    inference(clausify,[status(thm)],[f_252_4]) ).

cnf(f_252_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_836,U_838)
    | ~ sP66(U_836,U_838) ),
    inference(clausify,[status(thm)],[f_252_4]) ).

cnf(f_252_8,plain,
    ( U_836 != U_838
    | ~ sP66(U_836,U_838) ),
    inference(clausify,[status(thm)],[f_252_4]) ).

fof(f_253_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_253_2,plain,
    ! [U_841,U_840] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_840,U_841)
        | ( U_840 != U_841
          & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_840,U_841) ) )
      & ( U_840 = U_841
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_840,U_841)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_840,U_841) ) ),
    inference(variable_rename,[status(thm)],[f_253_1]) ).

fof(f_253_3,plain,
    ( ! [U_845,U_843] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_843,U_845)
        | ( U_843 != U_845
          & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_843,U_845) ) )
    & ! [U_844,U_842] :
        ( U_842 = U_844
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_842,U_844)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_842,U_844) ) ),
    inference(miniscope,[status(thm)],[f_253_2]) ).

fof(f_253_4,plain,
    ( ! [U_843,U_845] :
        ( U_843 != U_845
        | ~ sP67(U_843,U_845) )
    & ! [U_843,U_845] :
        ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_843,U_845)
        | ~ sP67(U_843,U_845) )
    & ! [U_843,U_845] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_843,U_845)
        | sP67(U_843,U_845) )
    & ! [U_844,U_842] :
        ( U_842 = U_844
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_842,U_844)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_842,U_844) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP67])],[f_253_3]) ).

cnf(f_253_5,plain,
    ( U_842 = U_844
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_842,U_844)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_842,U_844) ),
    inference(clausify,[status(thm)],[f_253_4]) ).

cnf(f_253_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_843,U_845)
    | sP67(U_843,U_845) ),
    inference(clausify,[status(thm)],[f_253_4]) ).

cnf(f_253_7,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_843,U_845)
    | ~ sP67(U_843,U_845) ),
    inference(clausify,[status(thm)],[f_253_4]) ).

cnf(f_253_8,plain,
    ( U_843 != U_845
    | ~ sP67(U_843,U_845) ),
    inference(clausify,[status(thm)],[f_253_4]) ).

fof(f_254_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_254_2,plain,
    ! [U_848,U_847,U_846] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_846,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_847,U_848))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_846,U_847) ),
    inference(variable_rename,[status(thm)],[f_254_1]) ).

fof(f_254_3,plain,
    ! [U_846,U_848,U_847] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_846,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_847,U_848))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_846,U_847) ),
    inference(definitional_conversion,[status(esa)],[f_254_2]) ).

cnf(f_254_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_846,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_847,U_848))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_846,U_847) ),
    inference(clausify,[status(thm)],[f_254_3]) ).

fof(f_255_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_255_2,plain,
    ! [U_851,U_850,U_849] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_849,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_851,U_850))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_849,U_850) ),
    inference(variable_rename,[status(thm)],[f_255_1]) ).

fof(f_255_3,plain,
    ! [U_851,U_850,U_849] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_849,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_851,U_850))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_849,U_850) ),
    inference(definitional_conversion,[status(esa)],[f_255_2]) ).

cnf(f_255_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_849,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_851,U_850))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_849,U_850) ),
    inference(clausify,[status(thm)],[f_255_3]) ).

fof(f_256_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_256_2,plain,
    ! [U_853,U_852] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_852,U_853),U_852),
    inference(variable_rename,[status(thm)],[f_256_1]) ).

fof(f_256_3,plain,
    ! [U_853,U_852] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_852,U_853),U_852),
    inference(definitional_conversion,[status(esa)],[f_256_2]) ).

cnf(f_256_4,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_852,U_853),U_852),
    inference(clausify,[status(thm)],[f_256_3]) ).

fof(f_257_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_257_2,plain,
    ! [U_855,U_854] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_854,U_855),U_855),
    inference(variable_rename,[status(thm)],[f_257_1]) ).

fof(f_257_3,plain,
    ! [U_855,U_854] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_854,U_855),U_855),
    inference(definitional_conversion,[status(esa)],[f_257_2]) ).

cnf(f_257_4,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_854,U_855),U_855),
    inference(clausify,[status(thm)],[f_257_3]) ).

fof(f_258_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_258_2,plain,
    ! [U_858,U_857,U_856] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_856,U_857),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_856,U_858))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_857,U_858) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_857,U_858)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_856,U_857),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_856,U_858)) ) ),
    inference(variable_rename,[status(thm)],[f_258_1]) ).

fof(f_258_3,plain,
    ( ! [U_864,U_862] :
        ( ! [U_860] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_860,U_862),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_860,U_864))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_862,U_864) )
    & ! [U_863,U_861] :
        ( ! [U_859] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_859,U_861),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_859,U_863))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_861,U_863) ) ),
    inference(miniscope,[status(thm)],[f_258_2]) ).

fof(f_258_4,plain,
    ( ! [U_864,U_862,U_860] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_860,U_862),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_860,U_864))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_862,U_864) )
    & ! [U_863,U_859,U_861] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_859,U_861),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_859,U_863))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_861,U_863) ) ),
    inference(definitional_conversion,[status(esa)],[f_258_3]) ).

cnf(f_258_5,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_859,U_861),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_859,U_863))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_861,U_863) ),
    inference(clausify,[status(thm)],[f_258_4]) ).

cnf(f_258_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_860,U_862),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_860,U_864))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_862,U_864) ),
    inference(clausify,[status(thm)],[f_258_4]) ).

fof(f_259_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_259_2,plain,
    ! [U_867,U_866,U_865] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_865,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_866,U_867))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_865,U_866) ),
    inference(variable_rename,[status(thm)],[f_259_1]) ).

fof(f_259_3,plain,
    ! [U_866,U_867,U_865] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_865,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_866,U_867))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_865,U_866) ),
    inference(definitional_conversion,[status(esa)],[f_259_2]) ).

cnf(f_259_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_865,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_866,U_867))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_865,U_866) ),
    inference(clausify,[status(thm)],[f_259_3]) ).

fof(f_260_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_260_2,plain,
    ! [U_870,U_869,U_868] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_868,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_870,U_869))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_868,U_869) ),
    inference(variable_rename,[status(thm)],[f_260_1]) ).

fof(f_260_3,plain,
    ! [U_869,U_868,U_870] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_868,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_870,U_869))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_868,U_869) ),
    inference(definitional_conversion,[status(esa)],[f_260_2]) ).

cnf(f_260_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_868,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_870,U_869))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_868,U_869) ),
    inference(clausify,[status(thm)],[f_260_3]) ).

fof(f_261_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_261_2,plain,
    ! [U_873,U_872,U_871] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_871,U_873),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_872,U_873))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_871,U_872) ),
    inference(variable_rename,[status(thm)],[f_261_1]) ).

fof(f_261_3,plain,
    ! [U_872,U_871,U_873] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_871,U_873),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_872,U_873))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_871,U_872) ),
    inference(definitional_conversion,[status(esa)],[f_261_2]) ).

cnf(f_261_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_871,U_873),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_872,U_873))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_871,U_872) ),
    inference(clausify,[status(thm)],[f_261_3]) ).

fof(f_262_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_262_2,plain,
    ! [U_877,U_876,U_875,U_874] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_874,U_876),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_875,U_877))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_876,U_877)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_874,U_875) ),
    inference(variable_rename,[status(thm)],[f_262_1]) ).

fof(f_262_3,plain,
    ! [U_874,U_875,U_876,U_877] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_874,U_876),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_875,U_877))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_876,U_877)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_874,U_875) ),
    inference(definitional_conversion,[status(esa)],[f_262_2]) ).

cnf(f_262_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_874,U_876),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_875,U_877))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_876,U_877)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_874,U_875) ),
    inference(clausify,[status(thm)],[f_262_3]) ).

fof(f_263_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_263_2,plain,
    ! [U_881,U_880,U_879,U_878] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_880,U_881)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_880,U_879) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_878,U_881)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_878,U_879) ),
    inference(variable_rename,[status(thm)],[f_263_1]) ).

fof(f_263_3,plain,
    ! [U_878,U_879,U_880,U_881] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_880,U_881)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_880,U_879) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_878,U_881)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_878,U_879) ),
    inference(definitional_conversion,[status(esa)],[f_263_2]) ).

cnf(f_263_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_880,U_881)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_880,U_879) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_878,U_881)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_878,U_879) ),
    inference(clausify,[status(thm)],[f_263_3]) ).

fof(f_264_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_264_2,plain,
    ! [U_884,U_883,U_882] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_882,U_884)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_882,U_883),U_884) ),
    inference(variable_rename,[status(thm)],[f_264_1]) ).

fof(f_264_3,plain,
    ! [U_882,U_883,U_884] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_882,U_884)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_882,U_883),U_884) ),
    inference(definitional_conversion,[status(esa)],[f_264_2]) ).

cnf(f_264_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_882,U_884)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_882,U_883),U_884) ),
    inference(clausify,[status(thm)],[f_264_3]) ).

fof(f_265_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_265_2,plain,
    ! [U_886,U_885] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_885,U_886)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_885,U_886) ),
    inference(variable_rename,[status(thm)],[f_265_1]) ).

fof(f_265_3,plain,
    ! [U_885,U_886] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_885,U_886)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_885,U_886) ),
    inference(definitional_conversion,[status(esa)],[f_265_2]) ).

cnf(f_265_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_885,U_886)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_885,U_886) ),
    inference(clausify,[status(thm)],[f_265_3]) ).

fof(f_266_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_266_2,plain,
    ! [U_888,U_887] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_887,U_888)
      | ( U_887 != U_888
        & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_887,U_888) ) ),
    inference(variable_rename,[status(thm)],[f_266_1]) ).

fof(f_266_3,plain,
    ( ! [U_887,U_888] :
        ( U_887 != U_888
        | ~ sP68(U_887,U_888) )
    & ! [U_887,U_888] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_887,U_888)
        | ~ sP68(U_887,U_888) )
    & ! [U_887,U_888] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_887,U_888)
        | sP68(U_887,U_888) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP68])],[f_266_2]) ).

cnf(f_266_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_887,U_888)
    | sP68(U_887,U_888) ),
    inference(clausify,[status(thm)],[f_266_3]) ).

cnf(f_266_5,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_887,U_888)
    | ~ sP68(U_887,U_888) ),
    inference(clausify,[status(thm)],[f_266_3]) ).

cnf(f_266_6,plain,
    ( U_887 != U_888
    | ~ sP68(U_887,U_888) ),
    inference(clausify,[status(thm)],[f_266_3]) ).

fof(f_267_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_267_2,plain,
    ! [U_890,U_889] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_889,U_890)
      | U_889 = U_890
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_889,U_890) ),
    inference(variable_rename,[status(thm)],[f_267_1]) ).

fof(f_267_3,plain,
    ! [U_890,U_889] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_889,U_890)
      | U_889 = U_890
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_889,U_890) ),
    inference(definitional_conversion,[status(esa)],[f_267_2]) ).

cnf(f_267_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_889,U_890)
    | U_889 = U_890
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_889,U_890) ),
    inference(clausify,[status(thm)],[f_267_3]) ).

fof(f_268_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_268_2,plain,
    ! [U_892,U_891] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_891,U_892)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_891,U_892) ),
    inference(variable_rename,[status(thm)],[f_268_1]) ).

fof(f_268_3,plain,
    ! [U_892,U_891] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_891,U_892)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_891,U_892) ),
    inference(definitional_conversion,[status(esa)],[f_268_2]) ).

cnf(f_268_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_891,U_892)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_891,U_892) ),
    inference(clausify,[status(thm)],[f_268_3]) ).

fof(f_269_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_269_2,plain,
    ! [U_894,U_893] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_893,U_894)
        | ( U_893 != U_894
          & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_893,U_894) ) )
      & ( U_893 = U_894
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_893,U_894)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_893,U_894) ) ),
    inference(variable_rename,[status(thm)],[f_269_1]) ).

fof(f_269_3,plain,
    ( ! [U_898,U_896] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_896,U_898)
        | ( U_896 != U_898
          & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_896,U_898) ) )
    & ! [U_897,U_895] :
        ( U_895 = U_897
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_895,U_897)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_895,U_897) ) ),
    inference(miniscope,[status(thm)],[f_269_2]) ).

fof(f_269_4,plain,
    ( ! [U_896,U_898] :
        ( U_896 != U_898
        | ~ sP69(U_896,U_898) )
    & ! [U_896,U_898] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_896,U_898)
        | ~ sP69(U_896,U_898) )
    & ! [U_896,U_898] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_896,U_898)
        | sP69(U_896,U_898) )
    & ! [U_895,U_897] :
        ( U_895 = U_897
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_895,U_897)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_895,U_897) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP69])],[f_269_3]) ).

cnf(f_269_5,plain,
    ( U_895 = U_897
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_895,U_897)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_895,U_897) ),
    inference(clausify,[status(thm)],[f_269_4]) ).

cnf(f_269_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_896,U_898)
    | sP69(U_896,U_898) ),
    inference(clausify,[status(thm)],[f_269_4]) ).

cnf(f_269_7,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_896,U_898)
    | ~ sP69(U_896,U_898) ),
    inference(clausify,[status(thm)],[f_269_4]) ).

cnf(f_269_8,plain,
    ( U_896 != U_898
    | ~ sP69(U_896,U_898) ),
    inference(clausify,[status(thm)],[f_269_4]) ).

fof(f_270_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_270_2,plain,
    ! [U_900,U_899] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_899,U_900)
        | U_899 = U_900
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_899,U_900) )
      & ( ( U_899 != U_900
          & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_899,U_900) )
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_899,U_900) ) ),
    inference(variable_rename,[status(thm)],[f_270_1]) ).

fof(f_270_3,plain,
    ( ! [U_904,U_902] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_902,U_904)
        | U_902 = U_904
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_902,U_904) )
    & ! [U_903,U_901] :
        ( ( U_901 != U_903
          & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_901,U_903) )
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_901,U_903) ) ),
    inference(miniscope,[status(thm)],[f_270_2]) ).

fof(f_270_4,plain,
    ( ! [U_901,U_903] :
        ( U_901 != U_903
        | ~ sP70(U_901,U_903) )
    & ! [U_901,U_903] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_901,U_903)
        | ~ sP70(U_901,U_903) )
    & ! [U_904,U_902] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_902,U_904)
        | U_902 = U_904
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_902,U_904) )
    & ! [U_901,U_903] :
        ( sP70(U_901,U_903)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_901,U_903) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP70])],[f_270_3]) ).

cnf(f_270_5,plain,
    ( sP70(U_901,U_903)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_901,U_903) ),
    inference(clausify,[status(thm)],[f_270_4]) ).

cnf(f_270_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_902,U_904)
    | U_902 = U_904
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_902,U_904) ),
    inference(clausify,[status(thm)],[f_270_4]) ).

cnf(f_270_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_901,U_903)
    | ~ sP70(U_901,U_903) ),
    inference(clausify,[status(thm)],[f_270_4]) ).

cnf(f_270_8,plain,
    ( U_901 != U_903
    | ~ sP70(U_901,U_903) ),
    inference(clausify,[status(thm)],[f_270_4]) ).

fof(f_271_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_271_2,plain,
    ! [U_906,U_905] :
      ( c_Groups_Oplus__class_Oplus(U_905,c_Groups_Ozero__class_Ozero(U_905),U_906) = U_906
      | ~ class_Groups_Omonoid__add(U_905) ),
    inference(variable_rename,[status(thm)],[f_271_1]) ).

fof(f_271_3,plain,
    ! [U_905,U_906] :
      ( c_Groups_Oplus__class_Oplus(U_905,c_Groups_Ozero__class_Ozero(U_905),U_906) = U_906
      | ~ class_Groups_Omonoid__add(U_905) ),
    inference(definitional_conversion,[status(esa)],[f_271_2]) ).

cnf(f_271_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_905,c_Groups_Ozero__class_Ozero(U_905),U_906) = U_906
    | ~ class_Groups_Omonoid__add(U_905) ),
    inference(clausify,[status(thm)],[f_271_3]) ).

fof(f_272_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_272_2,plain,
    ! [U_908,U_907] :
      ( c_Groups_Oplus__class_Oplus(U_907,c_Groups_Ozero__class_Ozero(U_907),U_908) = U_908
      | ~ class_Groups_Ocomm__monoid__add(U_907) ),
    inference(variable_rename,[status(thm)],[f_272_1]) ).

fof(f_272_3,plain,
    ! [U_907,U_908] :
      ( c_Groups_Oplus__class_Oplus(U_907,c_Groups_Ozero__class_Ozero(U_907),U_908) = U_908
      | ~ class_Groups_Ocomm__monoid__add(U_907) ),
    inference(definitional_conversion,[status(esa)],[f_272_2]) ).

cnf(f_272_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_907,c_Groups_Ozero__class_Ozero(U_907),U_908) = U_908
    | ~ class_Groups_Ocomm__monoid__add(U_907) ),
    inference(clausify,[status(thm)],[f_272_3]) ).

fof(f_273_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
          | c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_double__zero__sym]) ).

fof(f_273_2,plain,
    ! [U_910,U_909] :
      ( ( ( c_Groups_Ozero__class_Ozero(U_909) = c_Groups_Oplus__class_Oplus(U_909,U_910,U_910)
          | U_910 != c_Groups_Ozero__class_Ozero(U_909) )
        & ( U_910 = c_Groups_Ozero__class_Ozero(U_909)
          | c_Groups_Ozero__class_Ozero(U_909) != c_Groups_Oplus__class_Oplus(U_909,U_910,U_910) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_909) ),
    inference(variable_rename,[status(thm)],[f_273_1]) ).

fof(f_273_3,plain,
    ( ! [U_909,U_910] :
        ( c_Groups_Ozero__class_Ozero(U_909) = c_Groups_Oplus__class_Oplus(U_909,U_910,U_910)
        | U_910 != c_Groups_Ozero__class_Ozero(U_909)
        | ~ sP71(U_909,U_910) )
    & ! [U_909,U_910] :
        ( U_910 = c_Groups_Ozero__class_Ozero(U_909)
        | c_Groups_Ozero__class_Ozero(U_909) != c_Groups_Oplus__class_Oplus(U_909,U_910,U_910)
        | ~ sP71(U_909,U_910) )
    & ! [U_909,U_910] :
        ( sP71(U_909,U_910)
        | ~ class_Groups_Olinordered__ab__group__add(U_909) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP71])],[f_273_2]) ).

cnf(f_273_4,plain,
    ( sP71(U_909,U_910)
    | ~ class_Groups_Olinordered__ab__group__add(U_909) ),
    inference(clausify,[status(thm)],[f_273_3]) ).

cnf(f_273_5,plain,
    ( U_910 = c_Groups_Ozero__class_Ozero(U_909)
    | c_Groups_Ozero__class_Ozero(U_909) != c_Groups_Oplus__class_Oplus(U_909,U_910,U_910)
    | ~ sP71(U_909,U_910) ),
    inference(clausify,[status(thm)],[f_273_3]) ).

cnf(f_273_6,plain,
    ( c_Groups_Ozero__class_Ozero(U_909) = c_Groups_Oplus__class_Oplus(U_909,U_910,U_910)
    | U_910 != c_Groups_Ozero__class_Ozero(U_909)
    | ~ sP71(U_909,U_910) ),
    inference(clausify,[status(thm)],[f_273_3]) ).

fof(f_274_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_274_2,plain,
    ! [U_912,U_911] :
      ( c_Groups_Oplus__class_Oplus(U_911,U_912,c_Groups_Ozero__class_Ozero(U_911)) = U_912
      | ~ class_Groups_Omonoid__add(U_911) ),
    inference(variable_rename,[status(thm)],[f_274_1]) ).

fof(f_274_3,plain,
    ! [U_912,U_911] :
      ( c_Groups_Oplus__class_Oplus(U_911,U_912,c_Groups_Ozero__class_Ozero(U_911)) = U_912
      | ~ class_Groups_Omonoid__add(U_911) ),
    inference(definitional_conversion,[status(esa)],[f_274_2]) ).

cnf(f_274_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_911,U_912,c_Groups_Ozero__class_Ozero(U_911)) = U_912
    | ~ class_Groups_Omonoid__add(U_911) ),
    inference(clausify,[status(thm)],[f_274_3]) ).

fof(f_275_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_275_2,plain,
    ! [U_914,U_913] :
      ( c_Groups_Oplus__class_Oplus(U_913,U_914,c_Groups_Ozero__class_Ozero(U_913)) = U_914
      | ~ class_Groups_Ocomm__monoid__add(U_913) ),
    inference(variable_rename,[status(thm)],[f_275_1]) ).

fof(f_275_3,plain,
    ! [U_913,U_914] :
      ( c_Groups_Oplus__class_Oplus(U_913,U_914,c_Groups_Ozero__class_Ozero(U_913)) = U_914
      | ~ class_Groups_Ocomm__monoid__add(U_913) ),
    inference(definitional_conversion,[status(esa)],[f_275_2]) ).

cnf(f_275_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_913,U_914,c_Groups_Ozero__class_Ozero(U_913)) = U_914
    | ~ class_Groups_Ocomm__monoid__add(U_913) ),
    inference(clausify,[status(thm)],[f_275_3]) ).

fof(f_276_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_276_2,plain,
    ! [U_916,U_915] :
      ( c_Groups_Oplus__class_Oplus(U_915,c_Groups_Ozero__class_Ozero(U_915),U_916) = U_916
      | ~ class_Rings_Ocomm__semiring__1(U_915) ),
    inference(variable_rename,[status(thm)],[f_276_1]) ).

fof(f_276_3,plain,
    ! [U_915,U_916] :
      ( c_Groups_Oplus__class_Oplus(U_915,c_Groups_Ozero__class_Ozero(U_915),U_916) = U_916
      | ~ class_Rings_Ocomm__semiring__1(U_915) ),
    inference(definitional_conversion,[status(esa)],[f_276_2]) ).

cnf(f_276_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_915,c_Groups_Ozero__class_Ozero(U_915),U_916) = U_916
    | ~ class_Rings_Ocomm__semiring__1(U_915) ),
    inference(clausify,[status(thm)],[f_276_3]) ).

fof(f_277_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_277_2,plain,
    ! [U_918,U_917] :
      ( c_Groups_Oplus__class_Oplus(U_917,U_918,c_Groups_Ozero__class_Ozero(U_917)) = U_918
      | ~ class_Rings_Ocomm__semiring__1(U_917) ),
    inference(variable_rename,[status(thm)],[f_277_1]) ).

fof(f_277_3,plain,
    ! [U_917,U_918] :
      ( c_Groups_Oplus__class_Oplus(U_917,U_918,c_Groups_Ozero__class_Ozero(U_917)) = U_918
      | ~ class_Rings_Ocomm__semiring__1(U_917) ),
    inference(definitional_conversion,[status(esa)],[f_277_2]) ).

cnf(f_277_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_917,U_918,c_Groups_Ozero__class_Ozero(U_917)) = U_918
    | ~ class_Rings_Ocomm__semiring__1(U_917) ),
    inference(clausify,[status(thm)],[f_277_3]) ).

fof(f_278_1,plain,
    ! [V_a_2,V_b_2,T_a] :
      ( ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
          | V_b_2 != c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2) ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__0__iff]) ).

fof(f_278_2,plain,
    ! [U_921,U_920,U_919] :
      ( ( ( U_920 = c_Groups_Oplus__class_Oplus(U_919,U_920,U_921)
          | U_921 != c_Groups_Ozero__class_Ozero(U_919) )
        & ( U_921 = c_Groups_Ozero__class_Ozero(U_919)
          | U_920 != c_Groups_Oplus__class_Oplus(U_919,U_920,U_921) ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_919) ),
    inference(variable_rename,[status(thm)],[f_278_1]) ).

fof(f_278_3,plain,
    ( ! [U_919,U_920,U_921] :
        ( U_920 = c_Groups_Oplus__class_Oplus(U_919,U_920,U_921)
        | U_921 != c_Groups_Ozero__class_Ozero(U_919)
        | ~ sP72(U_919,U_920,U_921) )
    & ! [U_919,U_920,U_921] :
        ( U_921 = c_Groups_Ozero__class_Ozero(U_919)
        | U_920 != c_Groups_Oplus__class_Oplus(U_919,U_920,U_921)
        | ~ sP72(U_919,U_920,U_921) )
    & ! [U_919,U_920,U_921] :
        ( sP72(U_919,U_920,U_921)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_919) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP72])],[f_278_2]) ).

cnf(f_278_4,plain,
    ( sP72(U_919,U_920,U_921)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_919) ),
    inference(clausify,[status(thm)],[f_278_3]) ).

cnf(f_278_5,plain,
    ( U_921 = c_Groups_Ozero__class_Ozero(U_919)
    | U_920 != c_Groups_Oplus__class_Oplus(U_919,U_920,U_921)
    | ~ sP72(U_919,U_920,U_921) ),
    inference(clausify,[status(thm)],[f_278_3]) ).

cnf(f_278_6,plain,
    ( U_920 = c_Groups_Oplus__class_Oplus(U_919,U_920,U_921)
    | U_921 != c_Groups_Ozero__class_Ozero(U_919)
    | ~ sP72(U_919,U_920,U_921) ),
    inference(clausify,[status(thm)],[f_278_3]) ).

fof(f_279_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_279_2,plain,
    ! [U_922] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_922),
    inference(variable_rename,[status(thm)],[f_279_1]) ).

fof(f_279_3,plain,
    ! [U_922] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_922),
    inference(definitional_conversion,[status(esa)],[f_279_2]) ).

cnf(f_279_4,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_922),
    inference(clausify,[status(thm)],[f_279_3]) ).

fof(f_280_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_280_2,plain,
    ! [U_923] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_923),
    inference(variable_rename,[status(thm)],[f_280_1]) ).

fof(f_280_3,plain,
    ! [U_923] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_923),
    inference(definitional_conversion,[status(esa)],[f_280_2]) ).

cnf(f_280_4,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_923),
    inference(clausify,[status(thm)],[f_280_3]) ).

fof(f_281_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_281_2,plain,
    ! [U_924] : c_Nat_OSuc(U_924) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_281_1]) ).

fof(f_281_3,plain,
    ! [U_924] : c_Nat_OSuc(U_924) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_281_2]) ).

cnf(f_281_4,plain,
    c_Nat_OSuc(U_924) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_281_3]) ).

fof(f_282_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_282_2,plain,
    ! [U_925] : c_Nat_OSuc(U_925) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_282_1]) ).

fof(f_282_3,plain,
    ! [U_925] : c_Nat_OSuc(U_925) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_282_2]) ).

cnf(f_282_4,plain,
    c_Nat_OSuc(U_925) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_282_3]) ).

fof(f_283_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_283_2,plain,
    ! [U_926] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_926),
    inference(variable_rename,[status(thm)],[f_283_1]) ).

fof(f_283_3,plain,
    ! [U_926] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_926),
    inference(definitional_conversion,[status(esa)],[f_283_2]) ).

cnf(f_283_4,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_926),
    inference(clausify,[status(thm)],[f_283_3]) ).

fof(f_284_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_284_2,plain,
    ! [U_927] : c_Nat_OSuc(U_927) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_284_1]) ).

fof(f_284_3,plain,
    ! [U_927] : c_Nat_OSuc(U_927) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_284_2]) ).

cnf(f_284_4,plain,
    c_Nat_OSuc(U_927) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_284_3]) ).

fof(f_285_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_285_2,plain,
    ! [U_928] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_928) = U_928,
    inference(variable_rename,[status(thm)],[f_285_1]) ).

fof(f_285_3,plain,
    ! [U_928] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_928) = U_928,
    inference(definitional_conversion,[status(esa)],[f_285_2]) ).

cnf(f_285_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_928) = U_928,
    inference(clausify,[status(thm)],[f_285_3]) ).

fof(f_286_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_286_2,plain,
    ! [U_929] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_929,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_929,
    inference(variable_rename,[status(thm)],[f_286_1]) ).

fof(f_286_3,plain,
    ! [U_929] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_929,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_929,
    inference(definitional_conversion,[status(esa)],[f_286_2]) ).

cnf(f_286_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_929,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_929,
    inference(clausify,[status(thm)],[f_286_3]) ).

fof(f_287_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_287_2,plain,
    ! [U_931,U_930] :
      ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_930,U_931) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_931 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_930 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( U_931 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_930 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_930,U_931) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_287_1]) ).

fof(f_287_3,plain,
    ( ! [U_935,U_933] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_933,U_935) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_935 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_933 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_934,U_932] :
        ( ( U_934 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_932 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_932,U_934) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_287_2]) ).

fof(f_287_4,plain,
    ( ! [U_934,U_932] :
        ( U_934 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP73(U_934,U_932) )
    & ! [U_934,U_932] :
        ( U_932 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP73(U_934,U_932) )
    & ! [U_935,U_933] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_933,U_935) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_935 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_933 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_934,U_932] :
        ( sP73(U_934,U_932)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_932,U_934) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP73])],[f_287_3]) ).

cnf(f_287_5,plain,
    ( sP73(U_934,U_932)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_932,U_934) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_287_4]) ).

cnf(f_287_6,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_933,U_935) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_935 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_933 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_287_4]) ).

cnf(f_287_7,plain,
    ( U_932 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP73(U_934,U_932) ),
    inference(clausify,[status(thm)],[f_287_4]) ).

cnf(f_287_8,plain,
    ( U_934 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP73(U_934,U_932) ),
    inference(clausify,[status(thm)],[f_287_4]) ).

fof(f_288_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_288_2,plain,
    ! [U_937,U_936] :
      ( U_937 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_936,U_937) != U_936 ),
    inference(variable_rename,[status(thm)],[f_288_1]) ).

fof(f_288_3,plain,
    ! [U_937] :
      ( ! [U_936] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_936,U_937) != U_936
      | U_937 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(miniscope,[status(thm)],[f_288_2]) ).

fof(f_288_4,plain,
    ! [U_936,U_937] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_936,U_937) != U_936
      | U_937 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(definitional_conversion,[status(esa)],[f_288_3]) ).

cnf(f_288_5,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_936,U_937) != U_936
    | U_937 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_288_4]) ).

fof(f_289_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_289_2,plain,
    ! [U_938] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_938,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_938 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_938 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_938,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_289_1]) ).

fof(f_289_3,plain,
    ( ! [U_940] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_940,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_940 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_939] :
        ( U_939 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_939,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_289_2]) ).

fof(f_289_4,plain,
    ( ! [U_940] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_940,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_940 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_939] :
        ( U_939 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_939,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(definitional_conversion,[status(esa)],[f_289_3]) ).

cnf(f_289_5,plain,
    ( U_939 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_939,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_289_4]) ).

cnf(f_289_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_940,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_940 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_289_4]) ).

fof(f_290_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_290_2,plain,
    ! [U_941] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_941),
    inference(variable_rename,[status(thm)],[f_290_1]) ).

fof(f_290_3,plain,
    ! [U_941] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_941),
    inference(definitional_conversion,[status(esa)],[f_290_2]) ).

cnf(f_290_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_941),
    inference(clausify,[status(thm)],[f_290_3]) ).

fof(f_291_1,plain,
    ! [V_fa_2] :
      ( ( c_SEQ_Osubseq(V_fa_2)
        | ? [B_m,B_n] :
            ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_m),hAPP(V_fa_2,B_n))
            & c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n) ) )
      & ( ! [B_m,B_n] :
            ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_m),hAPP(V_fa_2,B_n))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n) )
        | ~ c_SEQ_Osubseq(V_fa_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_subseq__def]) ).

fof(f_291_2,plain,
    ! [U_946] :
      ( ( c_SEQ_Osubseq(U_946)
        | ? [U_945,U_944] :
            ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_946,U_945),hAPP(U_946,U_944))
            & c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_945,U_944) ) )
      & ( ! [U_943,U_942] :
            ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_946,U_943),hAPP(U_946,U_942))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_943,U_942) )
        | ~ c_SEQ_Osubseq(U_946) ) ),
    inference(variable_rename,[status(thm)],[f_291_1]) ).

fof(f_291_3,plain,
    ( ! [U_948] :
        ( c_SEQ_Osubseq(U_948)
        | ? [U_945,U_944] :
            ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_948,U_945),hAPP(U_948,U_944))
            & c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_945,U_944) ) )
    & ! [U_947] :
        ( ! [U_943,U_942] :
            ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_947,U_943),hAPP(U_947,U_942))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_943,U_942) )
        | ~ c_SEQ_Osubseq(U_947) ) ),
    inference(miniscope,[status(thm)],[f_291_2]) ).

fof(f_291_4,plain,
    ( ! [U_948] :
        ( c_SEQ_Osubseq(U_948)
        | ? [U_944] :
            ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_948,sK27(U_948)),hAPP(U_948,U_944))
            & c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK27(U_948),U_944) ) )
    & ! [U_947] :
        ( ! [U_943,U_942] :
            ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_947,U_943),hAPP(U_947,U_942))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_943,U_942) )
        | ~ c_SEQ_Osubseq(U_947) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_945,sK27(U_948))],[f_291_3]) ).

fof(f_291_5,plain,
    ( ! [U_948] :
        ( c_SEQ_Osubseq(U_948)
        | ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_948,sK27(U_948)),hAPP(U_948,sK28(U_948)))
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK27(U_948),sK28(U_948)) ) )
    & ! [U_947] :
        ( ! [U_943,U_942] :
            ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_947,U_943),hAPP(U_947,U_942))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_943,U_942) )
        | ~ c_SEQ_Osubseq(U_947) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_944,sK28(U_948))],[f_291_4]) ).

fof(f_291_6,plain,
    ( ! [U_948] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_948,sK27(U_948)),hAPP(U_948,sK28(U_948)))
        | ~ sP74(U_948) )
    & ! [U_948] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK27(U_948),sK28(U_948))
        | ~ sP74(U_948) )
    & ! [U_948] :
        ( c_SEQ_Osubseq(U_948)
        | sP74(U_948) )
    & ! [U_942,U_943,U_947] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_947,U_943),hAPP(U_947,U_942))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_943,U_942)
        | ~ c_SEQ_Osubseq(U_947) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP74])],[f_291_5]) ).

cnf(f_291_7,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_947,U_943),hAPP(U_947,U_942))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_943,U_942)
    | ~ c_SEQ_Osubseq(U_947) ),
    inference(clausify,[status(thm)],[f_291_6]) ).

cnf(f_291_8,plain,
    ( c_SEQ_Osubseq(U_948)
    | sP74(U_948) ),
    inference(clausify,[status(thm)],[f_291_6]) ).

cnf(f_291_9,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK27(U_948),sK28(U_948))
    | ~ sP74(U_948) ),
    inference(clausify,[status(thm)],[f_291_6]) ).

cnf(f_291_10,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_948,sK27(U_948)),hAPP(U_948,sK28(U_948)))
    | ~ sP74(U_948) ),
    inference(clausify,[status(thm)],[f_291_6]) ).

fof(f_292_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_292_2,plain,
    ! [U_953,U_952,U_951,U_950,U_949] :
      ( c_Orderings_Oord__class_Oless(U_949,c_Groups_Oplus__class_Oplus(U_949,U_950,U_952),c_Groups_Oplus__class_Oplus(U_949,U_951,U_953))
      | ~ c_Orderings_Oord__class_Oless__eq(U_949,U_952,U_953)
      | ~ c_Orderings_Oord__class_Oless(U_949,U_950,U_951)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_949) ),
    inference(variable_rename,[status(thm)],[f_292_1]) ).

fof(f_292_3,plain,
    ! [U_950,U_951,U_949,U_952,U_953] :
      ( c_Orderings_Oord__class_Oless(U_949,c_Groups_Oplus__class_Oplus(U_949,U_950,U_952),c_Groups_Oplus__class_Oplus(U_949,U_951,U_953))
      | ~ c_Orderings_Oord__class_Oless__eq(U_949,U_952,U_953)
      | ~ c_Orderings_Oord__class_Oless(U_949,U_950,U_951)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_949) ),
    inference(definitional_conversion,[status(esa)],[f_292_2]) ).

cnf(f_292_4,plain,
    ( c_Orderings_Oord__class_Oless(U_949,c_Groups_Oplus__class_Oplus(U_949,U_950,U_952),c_Groups_Oplus__class_Oplus(U_949,U_951,U_953))
    | ~ c_Orderings_Oord__class_Oless__eq(U_949,U_952,U_953)
    | ~ c_Orderings_Oord__class_Oless(U_949,U_950,U_951)
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_949) ),
    inference(clausify,[status(thm)],[f_292_3]) ).

fof(f_293_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_293_2,plain,
    ! [U_958,U_957,U_956,U_955,U_954] :
      ( c_Orderings_Oord__class_Oless(U_954,c_Groups_Oplus__class_Oplus(U_954,U_955,U_957),c_Groups_Oplus__class_Oplus(U_954,U_956,U_958))
      | ~ c_Orderings_Oord__class_Oless(U_954,U_957,U_958)
      | ~ c_Orderings_Oord__class_Oless__eq(U_954,U_955,U_956)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_954) ),
    inference(variable_rename,[status(thm)],[f_293_1]) ).

fof(f_293_3,plain,
    ! [U_957,U_958,U_954,U_956,U_955] :
      ( c_Orderings_Oord__class_Oless(U_954,c_Groups_Oplus__class_Oplus(U_954,U_955,U_957),c_Groups_Oplus__class_Oplus(U_954,U_956,U_958))
      | ~ c_Orderings_Oord__class_Oless(U_954,U_957,U_958)
      | ~ c_Orderings_Oord__class_Oless__eq(U_954,U_955,U_956)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_954) ),
    inference(definitional_conversion,[status(esa)],[f_293_2]) ).

cnf(f_293_4,plain,
    ( c_Orderings_Oord__class_Oless(U_954,c_Groups_Oplus__class_Oplus(U_954,U_955,U_957),c_Groups_Oplus__class_Oplus(U_954,U_956,U_958))
    | ~ c_Orderings_Oord__class_Oless(U_954,U_957,U_958)
    | ~ c_Orderings_Oord__class_Oless__eq(U_954,U_955,U_956)
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_954) ),
    inference(clausify,[status(thm)],[f_293_3]) ).

fof(f_294_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_294_2,plain,
    ! [U_960,U_959] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_960),U_959) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_960,U_959))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_959,U_960) ),
    inference(variable_rename,[status(thm)],[f_294_1]) ).

fof(f_294_3,plain,
    ! [U_960,U_959] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_960),U_959) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_960,U_959))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_959,U_960) ),
    inference(definitional_conversion,[status(esa)],[f_294_2]) ).

cnf(f_294_4,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_960),U_959) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_960,U_959))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_959,U_960) ),
    inference(clausify,[status(thm)],[f_294_3]) ).

fof(f_295_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_295_2,plain,
    ! [U_963,U_962,U_961] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_962,U_963),U_961) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_962,U_961),U_963)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_961,U_962) ),
    inference(variable_rename,[status(thm)],[f_295_1]) ).

fof(f_295_3,plain,
    ! [U_961,U_962,U_963] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_962,U_963),U_961) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_962,U_961),U_963)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_961,U_962) ),
    inference(definitional_conversion,[status(esa)],[f_295_2]) ).

cnf(f_295_4,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_962,U_963),U_961) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_962,U_961),U_963)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_961,U_962) ),
    inference(clausify,[status(thm)],[f_295_3]) ).

fof(f_296_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_296_2,plain,
    ! [U_966,U_965,U_964] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_965,U_964),U_966) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_965,U_966),U_964)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_964,U_965) ),
    inference(variable_rename,[status(thm)],[f_296_1]) ).

fof(f_296_3,plain,
    ! [U_964,U_965,U_966] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_965,U_964),U_966) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_965,U_966),U_964)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_964,U_965) ),
    inference(definitional_conversion,[status(esa)],[f_296_2]) ).

cnf(f_296_4,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_965,U_964),U_966) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_965,U_966),U_964)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_964,U_965) ),
    inference(clausify,[status(thm)],[f_296_3]) ).

fof(f_297_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_297_2,plain,
    ! [U_969,U_968,U_967] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_969,U_968),U_967) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_969,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_968,U_967))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_967,U_968) ),
    inference(variable_rename,[status(thm)],[f_297_1]) ).

fof(f_297_3,plain,
    ! [U_968,U_967,U_969] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_969,U_968),U_967) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_969,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_968,U_967))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_967,U_968) ),
    inference(definitional_conversion,[status(esa)],[f_297_2]) ).

cnf(f_297_4,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_969,U_968),U_967) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_969,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_968,U_967))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_967,U_968) ),
    inference(clausify,[status(thm)],[f_297_3]) ).

fof(f_298_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_298_2,plain,
    ! [U_972,U_971,U_970] :
      ( ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_971,U_970) = U_972
          | U_971 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_972,U_970) )
        & ( U_971 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_972,U_970)
          | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_971,U_970) != U_972 ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_970,U_971) ),
    inference(variable_rename,[status(thm)],[f_298_1]) ).

fof(f_298_3,plain,
    ( ! [U_970,U_971,U_972] :
        ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_971,U_970) = U_972
        | U_971 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_972,U_970)
        | ~ sP75(U_970,U_971,U_972) )
    & ! [U_970,U_971,U_972] :
        ( U_971 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_972,U_970)
        | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_971,U_970) != U_972
        | ~ sP75(U_970,U_971,U_972) )
    & ! [U_970,U_971,U_972] :
        ( sP75(U_970,U_971,U_972)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_970,U_971) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP75])],[f_298_2]) ).

cnf(f_298_4,plain,
    ( sP75(U_970,U_971,U_972)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_970,U_971) ),
    inference(clausify,[status(thm)],[f_298_3]) ).

cnf(f_298_5,plain,
    ( U_971 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_972,U_970)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_971,U_970) != U_972
    | ~ sP75(U_970,U_971,U_972) ),
    inference(clausify,[status(thm)],[f_298_3]) ).

cnf(f_298_6,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_971,U_970) = U_972
    | U_971 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_972,U_970)
    | ~ sP75(U_970,U_971,U_972) ),
    inference(clausify,[status(thm)],[f_298_3]) ).

fof(f_299_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_299_2,plain,
    ! [U_974,U_973] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_974,U_973),U_973) = U_974
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_973,U_974) ),
    inference(variable_rename,[status(thm)],[f_299_1]) ).

fof(f_299_3,plain,
    ! [U_973,U_974] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_974,U_973),U_973) = U_974
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_973,U_974) ),
    inference(definitional_conversion,[status(esa)],[f_299_2]) ).

cnf(f_299_4,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_974,U_973),U_973) = U_974
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_973,U_974) ),
    inference(clausify,[status(thm)],[f_299_3]) ).

fof(f_300_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_300_2,plain,
    ! [U_977,U_976,U_975] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_977,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_976,U_975))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_977,U_975),U_976) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_977,U_975),U_976)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_977,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_976,U_975)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_975,U_976) ),
    inference(variable_rename,[status(thm)],[f_300_1]) ).

fof(f_300_3,plain,
    ( ! [U_976,U_977,U_975] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_977,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_976,U_975))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_977,U_975),U_976)
        | ~ sP76(U_976,U_977,U_975) )
    & ! [U_976,U_977,U_975] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_977,U_975),U_976)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_977,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_976,U_975))
        | ~ sP76(U_976,U_977,U_975) )
    & ! [U_976,U_977,U_975] :
        ( sP76(U_976,U_977,U_975)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_975,U_976) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP76])],[f_300_2]) ).

cnf(f_300_4,plain,
    ( sP76(U_976,U_977,U_975)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_975,U_976) ),
    inference(clausify,[status(thm)],[f_300_3]) ).

cnf(f_300_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_977,U_975),U_976)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_977,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_976,U_975))
    | ~ sP76(U_976,U_977,U_975) ),
    inference(clausify,[status(thm)],[f_300_3]) ).

cnf(f_300_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_977,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_976,U_975))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_977,U_975),U_976)
    | ~ sP76(U_976,U_977,U_975) ),
    inference(clausify,[status(thm)],[f_300_3]) ).

fof(f_301_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_301_2,plain,
    ! [U_980,U_979,U_978] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_980,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_979,U_978)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_980,U_979),U_978)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_978,U_979) ),
    inference(variable_rename,[status(thm)],[f_301_1]) ).

fof(f_301_3,plain,
    ! [U_980,U_979,U_978] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_980,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_979,U_978)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_980,U_979),U_978)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_978,U_979) ),
    inference(definitional_conversion,[status(esa)],[f_301_2]) ).

cnf(f_301_4,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_980,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_979,U_978)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_980,U_979),U_978)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_978,U_979) ),
    inference(clausify,[status(thm)],[f_301_3]) ).

fof(f_302_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_302_2,plain,
    ! [U_982,U_981] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_981,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_982,U_981)) = U_982
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_981,U_982) ),
    inference(variable_rename,[status(thm)],[f_302_1]) ).

fof(f_302_3,plain,
    ! [U_982,U_981] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_981,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_982,U_981)) = U_982
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_981,U_982) ),
    inference(definitional_conversion,[status(esa)],[f_302_2]) ).

cnf(f_302_4,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_981,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_982,U_981)) = U_982
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_981,U_982) ),
    inference(clausify,[status(thm)],[f_302_3]) ).

fof(f_303_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_303_2,plain,
    ! [U_985,U_984,U_983] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_985,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_984,U_985),U_983))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_983,U_984) ),
    inference(variable_rename,[status(thm)],[f_303_1]) ).

fof(f_303_3,plain,
    ! [U_984,U_983,U_985] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_985,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_984,U_985),U_983))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_983,U_984) ),
    inference(definitional_conversion,[status(esa)],[f_303_2]) ).

cnf(f_303_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_985,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_984,U_985),U_983))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_983,U_984) ),
    inference(clausify,[status(thm)],[f_303_3]) ).

fof(f_304_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_304_2,plain,
    ! [U_988,U_987,U_986] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_986,U_987),U_988)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_986,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_988,U_987)) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_986,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_988,U_987))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_986,U_987),U_988) ) ),
    inference(variable_rename,[status(thm)],[f_304_1]) ).

fof(f_304_3,plain,
    ( ! [U_994,U_992,U_990] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_990,U_992),U_994)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_990,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_994,U_992)) )
    & ! [U_993,U_991,U_989] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_989,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_993,U_991))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_989,U_991),U_993) ) ),
    inference(miniscope,[status(thm)],[f_304_2]) ).

fof(f_304_4,plain,
    ( ! [U_994,U_992,U_990] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_990,U_992),U_994)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_990,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_994,U_992)) )
    & ! [U_989,U_991,U_993] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_989,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_993,U_991))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_989,U_991),U_993) ) ),
    inference(definitional_conversion,[status(esa)],[f_304_3]) ).

cnf(f_304_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_989,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_993,U_991))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_989,U_991),U_993) ),
    inference(clausify,[status(thm)],[f_304_4]) ).

cnf(f_304_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_990,U_992),U_994)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_990,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_994,U_992)) ),
    inference(clausify,[status(thm)],[f_304_4]) ).

fof(f_305_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_305_2,plain,
    ! [U_997,U_996,U_995] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_997,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_996,U_995)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_997,U_995),U_996)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_995,U_996) ),
    inference(variable_rename,[status(thm)],[f_305_1]) ).

fof(f_305_3,plain,
    ! [U_997,U_996,U_995] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_997,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_996,U_995)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_997,U_995),U_996)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_995,U_996) ),
    inference(definitional_conversion,[status(esa)],[f_305_2]) ).

cnf(f_305_4,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_997,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_996,U_995)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_997,U_995),U_996)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_995,U_996) ),
    inference(clausify,[status(thm)],[f_305_3]) ).

fof(f_306_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_306_2,plain,
    ! [U_999,U_998] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_998,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_998,U_999))),
    inference(variable_rename,[status(thm)],[f_306_1]) ).

fof(f_306_3,plain,
    ! [U_998,U_999] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_998,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_998,U_999))),
    inference(definitional_conversion,[status(esa)],[f_306_2]) ).

cnf(f_306_4,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_998,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_998,U_999))),
    inference(clausify,[status(thm)],[f_306_3]) ).

fof(f_307_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_307_2,plain,
    ! [U_1001,U_1000] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1000,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1001,U_1000))),
    inference(variable_rename,[status(thm)],[f_307_1]) ).

fof(f_307_3,plain,
    ! [U_1000,U_1001] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1000,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1001,U_1000))),
    inference(definitional_conversion,[status(esa)],[f_307_2]) ).

cnf(f_307_4,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1000,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1001,U_1000))),
    inference(clausify,[status(thm)],[f_307_3]) ).

fof(f_308_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_308_2,plain,
    ! [U_1005,U_1004] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1004,U_1005)
        | ! [U_1003] : U_1005 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1004,U_1003)) )
      & ( ? [U_1002] : U_1005 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1004,U_1002))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1004,U_1005) ) ),
    inference(variable_rename,[status(thm)],[f_308_1]) ).

fof(f_308_3,plain,
    ( ! [U_1009,U_1007] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1007,U_1009)
        | ! [U_1003] : U_1009 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1007,U_1003)) )
    & ! [U_1008,U_1006] :
        ( ? [U_1002] : U_1008 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1006,U_1002))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1006,U_1008) ) ),
    inference(miniscope,[status(thm)],[f_308_2]) ).

fof(f_308_4,plain,
    ( ! [U_1009,U_1007] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1007,U_1009)
        | ! [U_1003] : U_1009 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1007,U_1003)) )
    & ! [U_1008,U_1006] :
        ( U_1008 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1006,sK29(U_1008,U_1006)))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1006,U_1008) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_1002,sK29(U_1008,U_1006))],[f_308_3]) ).

fof(f_308_5,plain,
    ( ! [U_1003,U_1009,U_1007] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1007,U_1009)
        | U_1009 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1007,U_1003)) )
    & ! [U_1008,U_1006] :
        ( U_1008 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1006,sK29(U_1008,U_1006)))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1006,U_1008) ) ),
    inference(definitional_conversion,[status(esa)],[f_308_4]) ).

cnf(f_308_6,plain,
    ( U_1008 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1006,sK29(U_1008,U_1006)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1006,U_1008) ),
    inference(clausify,[status(thm)],[f_308_5]) ).

cnf(f_308_7,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1007,U_1009)
    | U_1009 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1007,U_1003)) ),
    inference(clausify,[status(thm)],[f_308_5]) ).

fof(f_309_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_309_2,plain,
    ! [U_1011,U_1010] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1010,U_1011)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1010),U_1011) ),
    inference(variable_rename,[status(thm)],[f_309_1]) ).

fof(f_309_3,plain,
    ! [U_1011,U_1010] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1010,U_1011)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1010),U_1011) ),
    inference(definitional_conversion,[status(esa)],[f_309_2]) ).

cnf(f_309_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1010,U_1011)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1010),U_1011) ),
    inference(clausify,[status(thm)],[f_309_3]) ).

fof(f_310_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_310_2,plain,
    ! [U_1013,U_1012] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1013,c_Nat_OSuc(U_1012))
          | U_1013 != U_1012 )
        & ( U_1013 = U_1012
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1013,c_Nat_OSuc(U_1012)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1012,U_1013) ),
    inference(variable_rename,[status(thm)],[f_310_1]) ).

fof(f_310_3,plain,
    ( ! [U_1013,U_1012] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1013,c_Nat_OSuc(U_1012))
        | U_1013 != U_1012
        | ~ sP77(U_1013,U_1012) )
    & ! [U_1013,U_1012] :
        ( U_1013 = U_1012
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1013,c_Nat_OSuc(U_1012))
        | ~ sP77(U_1013,U_1012) )
    & ! [U_1013,U_1012] :
        ( sP77(U_1013,U_1012)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1012,U_1013) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP77])],[f_310_2]) ).

cnf(f_310_4,plain,
    ( sP77(U_1013,U_1012)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1012,U_1013) ),
    inference(clausify,[status(thm)],[f_310_3]) ).

cnf(f_310_5,plain,
    ( U_1013 = U_1012
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1013,c_Nat_OSuc(U_1012))
    | ~ sP77(U_1013,U_1012) ),
    inference(clausify,[status(thm)],[f_310_3]) ).

cnf(f_310_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1013,c_Nat_OSuc(U_1012))
    | U_1013 != U_1012
    | ~ sP77(U_1013,U_1012) ),
    inference(clausify,[status(thm)],[f_310_3]) ).

fof(f_311_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_311_2,plain,
    ! [U_1015,U_1014] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1014),U_1015)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1014,U_1015) ),
    inference(variable_rename,[status(thm)],[f_311_1]) ).

fof(f_311_3,plain,
    ! [U_1014,U_1015] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1014),U_1015)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1014,U_1015) ),
    inference(definitional_conversion,[status(esa)],[f_311_2]) ).

cnf(f_311_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1014),U_1015)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1014,U_1015) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

fof(f_312_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_312_2,plain,
    ! [U_1017,U_1016] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1016,c_Nat_OSuc(U_1017))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1016,U_1017) ),
    inference(variable_rename,[status(thm)],[f_312_1]) ).

fof(f_312_3,plain,
    ! [U_1016,U_1017] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1016,c_Nat_OSuc(U_1017))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1016,U_1017) ),
    inference(definitional_conversion,[status(esa)],[f_312_2]) ).

cnf(f_312_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1016,c_Nat_OSuc(U_1017))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1016,U_1017) ),
    inference(clausify,[status(thm)],[f_312_3]) ).

fof(f_313_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_313_2,plain,
    ! [U_1019,U_1018] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1018),U_1019)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1018,U_1019) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1018,U_1019)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1018),U_1019) ) ),
    inference(variable_rename,[status(thm)],[f_313_1]) ).

fof(f_313_3,plain,
    ( ! [U_1023,U_1021] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1021),U_1023)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1021,U_1023) )
    & ! [U_1022,U_1020] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1020,U_1022)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1020),U_1022) ) ),
    inference(miniscope,[status(thm)],[f_313_2]) ).

fof(f_313_4,plain,
    ( ! [U_1023,U_1021] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1021),U_1023)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1021,U_1023) )
    & ! [U_1022,U_1020] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1020,U_1022)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1020),U_1022) ) ),
    inference(definitional_conversion,[status(esa)],[f_313_3]) ).

cnf(f_313_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1020,U_1022)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1020),U_1022) ),
    inference(clausify,[status(thm)],[f_313_4]) ).

cnf(f_313_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1021),U_1023)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1021,U_1023) ),
    inference(clausify,[status(thm)],[f_313_4]) ).

fof(f_314_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_314_2,plain,
    ! [U_1025,U_1024] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1024,c_Nat_OSuc(U_1025))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1024,U_1025) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1024,U_1025)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1024,c_Nat_OSuc(U_1025)) ) ),
    inference(variable_rename,[status(thm)],[f_314_1]) ).

fof(f_314_3,plain,
    ( ! [U_1029,U_1027] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1027,c_Nat_OSuc(U_1029))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1027,U_1029) )
    & ! [U_1028,U_1026] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1026,U_1028)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1026,c_Nat_OSuc(U_1028)) ) ),
    inference(miniscope,[status(thm)],[f_314_2]) ).

fof(f_314_4,plain,
    ( ! [U_1029,U_1027] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1027,c_Nat_OSuc(U_1029))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1027,U_1029) )
    & ! [U_1026,U_1028] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1026,U_1028)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1026,c_Nat_OSuc(U_1028)) ) ),
    inference(definitional_conversion,[status(esa)],[f_314_3]) ).

cnf(f_314_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1026,U_1028)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1026,c_Nat_OSuc(U_1028)) ),
    inference(clausify,[status(thm)],[f_314_4]) ).

cnf(f_314_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1027,c_Nat_OSuc(U_1029))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1027,U_1029) ),
    inference(clausify,[status(thm)],[f_314_4]) ).

fof(f_315_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_315_2,plain,
    ! [U_1031,U_1030] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1030,U_1031)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1030),U_1031) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1030),U_1031)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1030,U_1031) ) ),
    inference(variable_rename,[status(thm)],[f_315_1]) ).

fof(f_315_3,plain,
    ( ! [U_1035,U_1033] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1033,U_1035)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1033),U_1035) )
    & ! [U_1034,U_1032] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1032),U_1034)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1032,U_1034) ) ),
    inference(miniscope,[status(thm)],[f_315_2]) ).

fof(f_315_4,plain,
    ( ! [U_1035,U_1033] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1033,U_1035)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1033),U_1035) )
    & ! [U_1032,U_1034] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1032),U_1034)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1032,U_1034) ) ),
    inference(definitional_conversion,[status(esa)],[f_315_3]) ).

cnf(f_315_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1032),U_1034)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1032,U_1034) ),
    inference(clausify,[status(thm)],[f_315_4]) ).

cnf(f_315_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1033,U_1035)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1033),U_1035) ),
    inference(clausify,[status(thm)],[f_315_4]) ).

fof(f_316_1,plain,
    ! [V_a_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_a_2,V_a_2))
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
        & ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_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_316_2,plain,
    ! [U_1037,U_1036] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_1036,c_Groups_Ozero__class_Ozero(U_1036),c_Groups_Oplus__class_Oplus(U_1036,U_1037,U_1037))
          | ~ c_Orderings_Oord__class_Oless__eq(U_1036,c_Groups_Ozero__class_Ozero(U_1036),U_1037) )
        & ( c_Orderings_Oord__class_Oless__eq(U_1036,c_Groups_Ozero__class_Ozero(U_1036),U_1037)
          | ~ c_Orderings_Oord__class_Oless__eq(U_1036,c_Groups_Ozero__class_Ozero(U_1036),c_Groups_Oplus__class_Oplus(U_1036,U_1037,U_1037)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_1036) ),
    inference(variable_rename,[status(thm)],[f_316_1]) ).

fof(f_316_3,plain,
    ( ! [U_1036,U_1037] :
        ( c_Orderings_Oord__class_Oless__eq(U_1036,c_Groups_Ozero__class_Ozero(U_1036),c_Groups_Oplus__class_Oplus(U_1036,U_1037,U_1037))
        | ~ c_Orderings_Oord__class_Oless__eq(U_1036,c_Groups_Ozero__class_Ozero(U_1036),U_1037)
        | ~ sP78(U_1036,U_1037) )
    & ! [U_1036,U_1037] :
        ( c_Orderings_Oord__class_Oless__eq(U_1036,c_Groups_Ozero__class_Ozero(U_1036),U_1037)
        | ~ c_Orderings_Oord__class_Oless__eq(U_1036,c_Groups_Ozero__class_Ozero(U_1036),c_Groups_Oplus__class_Oplus(U_1036,U_1037,U_1037))
        | ~ sP78(U_1036,U_1037) )
    & ! [U_1036,U_1037] :
        ( sP78(U_1036,U_1037)
        | ~ class_Groups_Olinordered__ab__group__add(U_1036) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP78])],[f_316_2]) ).

cnf(f_316_4,plain,
    ( sP78(U_1036,U_1037)
    | ~ class_Groups_Olinordered__ab__group__add(U_1036) ),
    inference(clausify,[status(thm)],[f_316_3]) ).

cnf(f_316_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1036,c_Groups_Ozero__class_Ozero(U_1036),U_1037)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1036,c_Groups_Ozero__class_Ozero(U_1036),c_Groups_Oplus__class_Oplus(U_1036,U_1037,U_1037))
    | ~ sP78(U_1036,U_1037) ),
    inference(clausify,[status(thm)],[f_316_3]) ).

cnf(f_316_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1036,c_Groups_Ozero__class_Ozero(U_1036),c_Groups_Oplus__class_Oplus(U_1036,U_1037,U_1037))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1036,c_Groups_Ozero__class_Ozero(U_1036),U_1037)
    | ~ sP78(U_1036,U_1037) ),
    inference(clausify,[status(thm)],[f_316_3]) ).

fof(f_317_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
        & ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_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_317_2,plain,
    ! [U_1039,U_1038] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_1038,c_Groups_Oplus__class_Oplus(U_1038,U_1039,U_1039),c_Groups_Ozero__class_Ozero(U_1038))
          | ~ c_Orderings_Oord__class_Oless__eq(U_1038,U_1039,c_Groups_Ozero__class_Ozero(U_1038)) )
        & ( c_Orderings_Oord__class_Oless__eq(U_1038,U_1039,c_Groups_Ozero__class_Ozero(U_1038))
          | ~ c_Orderings_Oord__class_Oless__eq(U_1038,c_Groups_Oplus__class_Oplus(U_1038,U_1039,U_1039),c_Groups_Ozero__class_Ozero(U_1038)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_1038) ),
    inference(variable_rename,[status(thm)],[f_317_1]) ).

fof(f_317_3,plain,
    ( ! [U_1039,U_1038] :
        ( c_Orderings_Oord__class_Oless__eq(U_1038,c_Groups_Oplus__class_Oplus(U_1038,U_1039,U_1039),c_Groups_Ozero__class_Ozero(U_1038))
        | ~ c_Orderings_Oord__class_Oless__eq(U_1038,U_1039,c_Groups_Ozero__class_Ozero(U_1038))
        | ~ sP79(U_1039,U_1038) )
    & ! [U_1039,U_1038] :
        ( c_Orderings_Oord__class_Oless__eq(U_1038,U_1039,c_Groups_Ozero__class_Ozero(U_1038))
        | ~ c_Orderings_Oord__class_Oless__eq(U_1038,c_Groups_Oplus__class_Oplus(U_1038,U_1039,U_1039),c_Groups_Ozero__class_Ozero(U_1038))
        | ~ sP79(U_1039,U_1038) )
    & ! [U_1039,U_1038] :
        ( sP79(U_1039,U_1038)
        | ~ class_Groups_Olinordered__ab__group__add(U_1038) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP79])],[f_317_2]) ).

cnf(f_317_4,plain,
    ( sP79(U_1039,U_1038)
    | ~ class_Groups_Olinordered__ab__group__add(U_1038) ),
    inference(clausify,[status(thm)],[f_317_3]) ).

cnf(f_317_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1038,U_1039,c_Groups_Ozero__class_Ozero(U_1038))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1038,c_Groups_Oplus__class_Oplus(U_1038,U_1039,U_1039),c_Groups_Ozero__class_Ozero(U_1038))
    | ~ sP79(U_1039,U_1038) ),
    inference(clausify,[status(thm)],[f_317_3]) ).

cnf(f_317_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1038,c_Groups_Oplus__class_Oplus(U_1038,U_1039,U_1039),c_Groups_Ozero__class_Ozero(U_1038))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1038,U_1039,c_Groups_Ozero__class_Ozero(U_1038))
    | ~ sP79(U_1039,U_1038) ),
    inference(clausify,[status(thm)],[f_317_3]) ).

fof(f_318_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_318_2,plain,
    ! [U_1042,U_1041,U_1040] :
      ( c_Orderings_Oord__class_Oless__eq(U_1040,c_Groups_Ozero__class_Ozero(U_1040),c_Groups_Oplus__class_Oplus(U_1040,U_1041,U_1042))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1040,c_Groups_Ozero__class_Ozero(U_1040),U_1042)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1040,c_Groups_Ozero__class_Ozero(U_1040),U_1041)
      | ~ class_Groups_Oordered__comm__monoid__add(U_1040) ),
    inference(variable_rename,[status(thm)],[f_318_1]) ).

fof(f_318_3,plain,
    ! [U_1041,U_1042,U_1040] :
      ( c_Orderings_Oord__class_Oless__eq(U_1040,c_Groups_Ozero__class_Ozero(U_1040),c_Groups_Oplus__class_Oplus(U_1040,U_1041,U_1042))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1040,c_Groups_Ozero__class_Ozero(U_1040),U_1042)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1040,c_Groups_Ozero__class_Ozero(U_1040),U_1041)
      | ~ class_Groups_Oordered__comm__monoid__add(U_1040) ),
    inference(definitional_conversion,[status(esa)],[f_318_2]) ).

cnf(f_318_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1040,c_Groups_Ozero__class_Ozero(U_1040),c_Groups_Oplus__class_Oplus(U_1040,U_1041,U_1042))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1040,c_Groups_Ozero__class_Ozero(U_1040),U_1042)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1040,c_Groups_Ozero__class_Ozero(U_1040),U_1041)
    | ~ class_Groups_Oordered__comm__monoid__add(U_1040) ),
    inference(clausify,[status(thm)],[f_318_3]) ).

fof(f_319_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_319_2,plain,
    ! [U_1045,U_1044,U_1043] :
      ( ( ( c_Groups_Oplus__class_Oplus(U_1043,U_1044,U_1045) = c_Groups_Ozero__class_Ozero(U_1043)
          | U_1045 != c_Groups_Ozero__class_Ozero(U_1043)
          | U_1044 != c_Groups_Ozero__class_Ozero(U_1043) )
        & ( ( U_1045 = c_Groups_Ozero__class_Ozero(U_1043)
            & U_1044 = c_Groups_Ozero__class_Ozero(U_1043) )
          | c_Groups_Oplus__class_Oplus(U_1043,U_1044,U_1045) != c_Groups_Ozero__class_Ozero(U_1043) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(U_1043,c_Groups_Ozero__class_Ozero(U_1043),U_1045)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1043,c_Groups_Ozero__class_Ozero(U_1043),U_1044)
      | ~ class_Groups_Oordered__comm__monoid__add(U_1043) ),
    inference(variable_rename,[status(thm)],[f_319_1]) ).

fof(f_319_3,plain,
    ( ! [U_1045,U_1043,U_1044] :
        ( U_1045 = c_Groups_Ozero__class_Ozero(U_1043)
        | ~ sP80(U_1045,U_1043,U_1044) )
    & ! [U_1045,U_1043,U_1044] :
        ( U_1044 = c_Groups_Ozero__class_Ozero(U_1043)
        | ~ sP80(U_1045,U_1043,U_1044) )
    & ! [U_1045,U_1043,U_1044] :
        ( c_Groups_Oplus__class_Oplus(U_1043,U_1044,U_1045) = c_Groups_Ozero__class_Ozero(U_1043)
        | U_1045 != c_Groups_Ozero__class_Ozero(U_1043)
        | U_1044 != c_Groups_Ozero__class_Ozero(U_1043)
        | ~ sP81(U_1045,U_1043,U_1044) )
    & ! [U_1045,U_1043,U_1044] :
        ( sP80(U_1045,U_1043,U_1044)
        | c_Groups_Oplus__class_Oplus(U_1043,U_1044,U_1045) != c_Groups_Ozero__class_Ozero(U_1043)
        | ~ sP81(U_1045,U_1043,U_1044) )
    & ! [U_1045,U_1043,U_1044] :
        ( sP81(U_1045,U_1043,U_1044)
        | ~ c_Orderings_Oord__class_Oless__eq(U_1043,c_Groups_Ozero__class_Ozero(U_1043),U_1045)
        | ~ c_Orderings_Oord__class_Oless__eq(U_1043,c_Groups_Ozero__class_Ozero(U_1043),U_1044)
        | ~ class_Groups_Oordered__comm__monoid__add(U_1043) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP80,sP81])],[f_319_2]) ).

cnf(f_319_4,plain,
    ( sP81(U_1045,U_1043,U_1044)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1043,c_Groups_Ozero__class_Ozero(U_1043),U_1045)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1043,c_Groups_Ozero__class_Ozero(U_1043),U_1044)
    | ~ class_Groups_Oordered__comm__monoid__add(U_1043) ),
    inference(clausify,[status(thm)],[f_319_3]) ).

cnf(f_319_5,plain,
    ( sP80(U_1045,U_1043,U_1044)
    | c_Groups_Oplus__class_Oplus(U_1043,U_1044,U_1045) != c_Groups_Ozero__class_Ozero(U_1043)
    | ~ sP81(U_1045,U_1043,U_1044) ),
    inference(clausify,[status(thm)],[f_319_3]) ).

cnf(f_319_6,plain,
    ( c_Groups_Oplus__class_Oplus(U_1043,U_1044,U_1045) = c_Groups_Ozero__class_Ozero(U_1043)
    | U_1045 != c_Groups_Ozero__class_Ozero(U_1043)
    | U_1044 != c_Groups_Ozero__class_Ozero(U_1043)
    | ~ sP81(U_1045,U_1043,U_1044) ),
    inference(clausify,[status(thm)],[f_319_3]) ).

cnf(f_319_7,plain,
    ( U_1044 = c_Groups_Ozero__class_Ozero(U_1043)
    | ~ sP80(U_1045,U_1043,U_1044) ),
    inference(clausify,[status(thm)],[f_319_3]) ).

cnf(f_319_8,plain,
    ( U_1045 = c_Groups_Ozero__class_Ozero(U_1043)
    | ~ sP80(U_1045,U_1043,U_1044) ),
    inference(clausify,[status(thm)],[f_319_3]) ).

fof(f_320_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_320_2,plain,
    ! [U_1049,U_1048,U_1047,U_1046] :
      ( c_Orderings_Oord__class_Oless__eq(U_1046,U_1048,c_Groups_Oplus__class_Oplus(U_1046,U_1047,U_1049))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1046,U_1048,U_1049)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1046,c_Groups_Ozero__class_Ozero(U_1046),U_1047)
      | ~ class_Groups_Oordered__comm__monoid__add(U_1046) ),
    inference(variable_rename,[status(thm)],[f_320_1]) ).

fof(f_320_3,plain,
    ! [U_1047,U_1049,U_1048,U_1046] :
      ( c_Orderings_Oord__class_Oless__eq(U_1046,U_1048,c_Groups_Oplus__class_Oplus(U_1046,U_1047,U_1049))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1046,U_1048,U_1049)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1046,c_Groups_Ozero__class_Ozero(U_1046),U_1047)
      | ~ class_Groups_Oordered__comm__monoid__add(U_1046) ),
    inference(definitional_conversion,[status(esa)],[f_320_2]) ).

cnf(f_320_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1046,U_1048,c_Groups_Oplus__class_Oplus(U_1046,U_1047,U_1049))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1046,U_1048,U_1049)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1046,c_Groups_Ozero__class_Ozero(U_1046),U_1047)
    | ~ class_Groups_Oordered__comm__monoid__add(U_1046) ),
    inference(clausify,[status(thm)],[f_320_3]) ).

fof(f_321_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_321_2,plain,
    ! [U_1053,U_1052,U_1051,U_1050] :
      ( c_Orderings_Oord__class_Oless__eq(U_1050,U_1052,c_Groups_Oplus__class_Oplus(U_1050,U_1053,U_1051))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1050,U_1052,U_1053)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1050,c_Groups_Ozero__class_Ozero(U_1050),U_1051)
      | ~ class_Groups_Oordered__comm__monoid__add(U_1050) ),
    inference(variable_rename,[status(thm)],[f_321_1]) ).

fof(f_321_3,plain,
    ! [U_1053,U_1050,U_1051,U_1052] :
      ( c_Orderings_Oord__class_Oless__eq(U_1050,U_1052,c_Groups_Oplus__class_Oplus(U_1050,U_1053,U_1051))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1050,U_1052,U_1053)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1050,c_Groups_Ozero__class_Ozero(U_1050),U_1051)
      | ~ class_Groups_Oordered__comm__monoid__add(U_1050) ),
    inference(definitional_conversion,[status(esa)],[f_321_2]) ).

cnf(f_321_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1050,U_1052,c_Groups_Oplus__class_Oplus(U_1050,U_1053,U_1051))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1050,U_1052,U_1053)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1050,c_Groups_Ozero__class_Ozero(U_1050),U_1051)
    | ~ class_Groups_Oordered__comm__monoid__add(U_1050) ),
    inference(clausify,[status(thm)],[f_321_3]) ).

fof(f_322_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_322_2,plain,
    ! [U_1056,U_1055,U_1054] :
      ( c_Orderings_Oord__class_Oless__eq(U_1054,c_Groups_Oplus__class_Oplus(U_1054,U_1055,U_1056),c_Groups_Ozero__class_Ozero(U_1054))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1054,U_1056,c_Groups_Ozero__class_Ozero(U_1054))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1054,U_1055,c_Groups_Ozero__class_Ozero(U_1054))
      | ~ class_Groups_Oordered__comm__monoid__add(U_1054) ),
    inference(variable_rename,[status(thm)],[f_322_1]) ).

fof(f_322_3,plain,
    ! [U_1054,U_1055,U_1056] :
      ( c_Orderings_Oord__class_Oless__eq(U_1054,c_Groups_Oplus__class_Oplus(U_1054,U_1055,U_1056),c_Groups_Ozero__class_Ozero(U_1054))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1054,U_1056,c_Groups_Ozero__class_Ozero(U_1054))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1054,U_1055,c_Groups_Ozero__class_Ozero(U_1054))
      | ~ class_Groups_Oordered__comm__monoid__add(U_1054) ),
    inference(definitional_conversion,[status(esa)],[f_322_2]) ).

cnf(f_322_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1054,c_Groups_Oplus__class_Oplus(U_1054,U_1055,U_1056),c_Groups_Ozero__class_Ozero(U_1054))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1054,U_1056,c_Groups_Ozero__class_Ozero(U_1054))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1054,U_1055,c_Groups_Ozero__class_Ozero(U_1054))
    | ~ class_Groups_Oordered__comm__monoid__add(U_1054) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

fof(f_323_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_323_2,plain,
    ! [U_1057] : c_Nat_OSuc(U_1057) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_1057),
    inference(variable_rename,[status(thm)],[f_323_1]) ).

fof(f_323_3,plain,
    ! [U_1057] : c_Nat_OSuc(U_1057) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_1057),
    inference(definitional_conversion,[status(esa)],[f_323_2]) ).

cnf(f_323_4,plain,
    c_Nat_OSuc(U_1057) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_1057),
    inference(clausify,[status(thm)],[f_323_3]) ).

fof(f_324_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_324_2,plain,
    ! [U_1058] : c_Nat_OSuc(U_1058) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1058,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_324_1]) ).

fof(f_324_3,plain,
    ! [U_1058] : c_Nat_OSuc(U_1058) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1058,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_324_2]) ).

cnf(f_324_4,plain,
    c_Nat_OSuc(U_1058) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1058,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_324_3]) ).

fof(f_325_1,plain,
    hAPP(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_325_2,plain,
    hAPP(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_325_1]) ).

cnf(f_325_3,plain,
    hAPP(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_325_2]) ).

fof(f_326_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_326_2,plain,
    ! [U_1060,U_1059] :
      ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1059,U_1060)
        | ( ( U_1060 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | U_1059 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( U_1060 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_1059 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
      & ( ( U_1060 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_1059 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( U_1060 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_1059 = 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_1059,U_1060) ) ),
    inference(variable_rename,[status(thm)],[f_326_1]) ).

fof(f_326_3,plain,
    ( ! [U_1064,U_1062] :
        ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1062,U_1064)
        | ( ( U_1064 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | U_1062 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( U_1064 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_1062 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
    & ! [U_1063,U_1061] :
        ( ( U_1063 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_1061 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( U_1063 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_1061 = 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_1061,U_1063) ) ),
    inference(miniscope,[status(thm)],[f_326_2]) ).

fof(f_326_4,plain,
    ( ! [U_1062,U_1064] :
        ( U_1064 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_1062 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP84(U_1062,U_1064) )
    & ! [U_1062,U_1064] :
        ( U_1064 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_1062 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP84(U_1062,U_1064) )
    & ! [U_1063,U_1061] :
        ( U_1063 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP83(U_1063,U_1061) )
    & ! [U_1063,U_1061] :
        ( U_1061 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP83(U_1063,U_1061) )
    & ! [U_1063,U_1061] :
        ( U_1063 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP82(U_1063,U_1061) )
    & ! [U_1063,U_1061] :
        ( U_1061 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP82(U_1063,U_1061) )
    & ! [U_1062,U_1064] :
        ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1062,U_1064)
        | sP84(U_1062,U_1064) )
    & ! [U_1063,U_1061] :
        ( sP83(U_1063,U_1061)
        | sP82(U_1063,U_1061)
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1061,U_1063) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP82,sP83,sP84])],[f_326_3]) ).

cnf(f_326_5,plain,
    ( sP83(U_1063,U_1061)
    | sP82(U_1063,U_1061)
    | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1061,U_1063) ),
    inference(clausify,[status(thm)],[f_326_4]) ).

cnf(f_326_6,plain,
    ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1062,U_1064)
    | sP84(U_1062,U_1064) ),
    inference(clausify,[status(thm)],[f_326_4]) ).

cnf(f_326_7,plain,
    ( U_1061 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP82(U_1063,U_1061) ),
    inference(clausify,[status(thm)],[f_326_4]) ).

cnf(f_326_8,plain,
    ( U_1063 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP82(U_1063,U_1061) ),
    inference(clausify,[status(thm)],[f_326_4]) ).

cnf(f_326_9,plain,
    ( U_1061 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP83(U_1063,U_1061) ),
    inference(clausify,[status(thm)],[f_326_4]) ).

cnf(f_326_10,plain,
    ( U_1063 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP83(U_1063,U_1061) ),
    inference(clausify,[status(thm)],[f_326_4]) ).

cnf(f_326_11,plain,
    ( U_1064 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_1062 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP84(U_1062,U_1064) ),
    inference(clausify,[status(thm)],[f_326_4]) ).

cnf(f_326_12,plain,
    ( U_1064 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_1062 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP84(U_1062,U_1064) ),
    inference(clausify,[status(thm)],[f_326_4]) ).

fof(f_327_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_327_2,plain,
    ! [U_1066,U_1065] :
      ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1065,U_1066) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( ( U_1066 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | U_1065 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( U_1066 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_1065 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
      & ( ( U_1066 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_1065 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( U_1066 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_1065 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1065,U_1066) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_327_1]) ).

fof(f_327_3,plain,
    ( ! [U_1070,U_1068] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1068,U_1070) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( ( U_1070 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | U_1068 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( U_1070 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_1068 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
    & ! [U_1069,U_1067] :
        ( ( U_1069 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_1067 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( U_1069 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_1067 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1067,U_1069) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_327_2]) ).

fof(f_327_4,plain,
    ( ! [U_1068,U_1070] :
        ( U_1070 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_1068 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP87(U_1068,U_1070) )
    & ! [U_1068,U_1070] :
        ( U_1070 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_1068 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP87(U_1068,U_1070) )
    & ! [U_1067,U_1069] :
        ( U_1069 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP86(U_1067,U_1069) )
    & ! [U_1067,U_1069] :
        ( U_1067 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP86(U_1067,U_1069) )
    & ! [U_1067,U_1069] :
        ( U_1069 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP85(U_1067,U_1069) )
    & ! [U_1067,U_1069] :
        ( U_1067 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP85(U_1067,U_1069) )
    & ! [U_1068,U_1070] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1068,U_1070) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | sP87(U_1068,U_1070) )
    & ! [U_1067,U_1069] :
        ( sP86(U_1067,U_1069)
        | sP85(U_1067,U_1069)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1067,U_1069) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP85,sP86,sP87])],[f_327_3]) ).

cnf(f_327_5,plain,
    ( sP86(U_1067,U_1069)
    | sP85(U_1067,U_1069)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1067,U_1069) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_327_4]) ).

cnf(f_327_6,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1068,U_1070) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | sP87(U_1068,U_1070) ),
    inference(clausify,[status(thm)],[f_327_4]) ).

cnf(f_327_7,plain,
    ( U_1067 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP85(U_1067,U_1069) ),
    inference(clausify,[status(thm)],[f_327_4]) ).

cnf(f_327_8,plain,
    ( U_1069 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP85(U_1067,U_1069) ),
    inference(clausify,[status(thm)],[f_327_4]) ).

cnf(f_327_9,plain,
    ( U_1067 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP86(U_1067,U_1069) ),
    inference(clausify,[status(thm)],[f_327_4]) ).

cnf(f_327_10,plain,
    ( U_1069 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP86(U_1067,U_1069) ),
    inference(clausify,[status(thm)],[f_327_4]) ).

cnf(f_327_11,plain,
    ( U_1070 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_1068 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP87(U_1068,U_1070) ),
    inference(clausify,[status(thm)],[f_327_4]) ).

cnf(f_327_12,plain,
    ( U_1070 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_1068 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP87(U_1068,U_1070) ),
    inference(clausify,[status(thm)],[f_327_4]) ).

fof(f_328_1,plain,
    ! [V_fa_2] :
      ( ( c_SEQ_Osubseq(V_fa_2)
        | ? [B_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_n),hAPP(V_fa_2,c_Nat_OSuc(B_n))) )
      & ( ! [B_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_n),hAPP(V_fa_2,c_Nat_OSuc(B_n)))
        | ~ c_SEQ_Osubseq(V_fa_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_subseq__Suc__iff]) ).

fof(f_328_2,plain,
    ! [U_1073] :
      ( ( c_SEQ_Osubseq(U_1073)
        | ? [U_1072] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1073,U_1072),hAPP(U_1073,c_Nat_OSuc(U_1072))) )
      & ( ! [U_1071] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1073,U_1071),hAPP(U_1073,c_Nat_OSuc(U_1071)))
        | ~ c_SEQ_Osubseq(U_1073) ) ),
    inference(variable_rename,[status(thm)],[f_328_1]) ).

fof(f_328_3,plain,
    ( ! [U_1075] :
        ( c_SEQ_Osubseq(U_1075)
        | ? [U_1072] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1075,U_1072),hAPP(U_1075,c_Nat_OSuc(U_1072))) )
    & ! [U_1074] :
        ( ! [U_1071] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1074,U_1071),hAPP(U_1074,c_Nat_OSuc(U_1071)))
        | ~ c_SEQ_Osubseq(U_1074) ) ),
    inference(miniscope,[status(thm)],[f_328_2]) ).

fof(f_328_4,plain,
    ( ! [U_1075] :
        ( c_SEQ_Osubseq(U_1075)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1075,sK30(U_1075)),hAPP(U_1075,c_Nat_OSuc(sK30(U_1075)))) )
    & ! [U_1074] :
        ( ! [U_1071] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1074,U_1071),hAPP(U_1074,c_Nat_OSuc(U_1071)))
        | ~ c_SEQ_Osubseq(U_1074) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_1072,sK30(U_1075))],[f_328_3]) ).

fof(f_328_5,plain,
    ( ! [U_1075] :
        ( c_SEQ_Osubseq(U_1075)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1075,sK30(U_1075)),hAPP(U_1075,c_Nat_OSuc(sK30(U_1075)))) )
    & ! [U_1074,U_1071] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1074,U_1071),hAPP(U_1074,c_Nat_OSuc(U_1071)))
        | ~ c_SEQ_Osubseq(U_1074) ) ),
    inference(definitional_conversion,[status(esa)],[f_328_4]) ).

cnf(f_328_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1074,U_1071),hAPP(U_1074,c_Nat_OSuc(U_1071)))
    | ~ c_SEQ_Osubseq(U_1074) ),
    inference(clausify,[status(thm)],[f_328_5]) ).

cnf(f_328_7,plain,
    ( c_SEQ_Osubseq(U_1075)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1075,sK30(U_1075)),hAPP(U_1075,c_Nat_OSuc(sK30(U_1075)))) ),
    inference(clausify,[status(thm)],[f_328_5]) ).

fof(f_329_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_329_2,plain,
    ! [U_1078,U_1077,U_1076] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1078,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1077,U_1076))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1078,U_1076),c_Nat_OSuc(U_1077))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1076,U_1077) ),
    inference(variable_rename,[status(thm)],[f_329_1]) ).

fof(f_329_3,plain,
    ! [U_1077,U_1076,U_1078] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1078,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1077,U_1076))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1078,U_1076),c_Nat_OSuc(U_1077))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1076,U_1077) ),
    inference(definitional_conversion,[status(esa)],[f_329_2]) ).

cnf(f_329_4,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1078,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1077,U_1076))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1078,U_1076),c_Nat_OSuc(U_1077))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1076,U_1077) ),
    inference(clausify,[status(thm)],[f_329_3]) ).

fof(f_330_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_330_2,plain,
    ! [U_1079] :
      ( c_Orderings_Oord__class_Oless(U_1079,c_Groups_Ozero__class_Ozero(U_1079),c_Groups_Oplus__class_Oplus(U_1079,c_Groups_Oone__class_Oone(U_1079),c_Groups_Oone__class_Oone(U_1079)))
      | ~ class_Rings_Olinordered__semidom(U_1079) ),
    inference(variable_rename,[status(thm)],[f_330_1]) ).

fof(f_330_3,plain,
    ! [U_1079] :
      ( c_Orderings_Oord__class_Oless(U_1079,c_Groups_Ozero__class_Ozero(U_1079),c_Groups_Oplus__class_Oplus(U_1079,c_Groups_Oone__class_Oone(U_1079),c_Groups_Oone__class_Oone(U_1079)))
      | ~ class_Rings_Olinordered__semidom(U_1079) ),
    inference(definitional_conversion,[status(esa)],[f_330_2]) ).

cnf(f_330_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1079,c_Groups_Ozero__class_Ozero(U_1079),c_Groups_Oplus__class_Oplus(U_1079,c_Groups_Oone__class_Oone(U_1079),c_Groups_Oone__class_Oone(U_1079)))
    | ~ class_Rings_Olinordered__semidom(U_1079) ),
    inference(clausify,[status(thm)],[f_330_3]) ).

fof(f_331_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_331_2,plain,
    ! [U_1080] :
      ( U_1080 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | U_1080 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1080,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    inference(variable_rename,[status(thm)],[f_331_1]) ).

fof(f_331_3,plain,
    ! [U_1080] :
      ( U_1080 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | U_1080 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1080,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    inference(definitional_conversion,[status(esa)],[f_331_2]) ).

cnf(f_331_4,plain,
    ( U_1080 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_1080 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1080,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    inference(clausify,[status(thm)],[f_331_3]) ).

fof(f_332_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_332_2,plain,
    ! [U_1082,U_1081] :
      ( c_Orderings_Oord__class_Oless(U_1081,U_1082,c_Groups_Oplus__class_Oplus(U_1081,U_1082,c_Groups_Oone__class_Oone(U_1081)))
      | ~ class_Rings_Olinordered__semidom(U_1081) ),
    inference(variable_rename,[status(thm)],[f_332_1]) ).

fof(f_332_3,plain,
    ! [U_1081,U_1082] :
      ( c_Orderings_Oord__class_Oless(U_1081,U_1082,c_Groups_Oplus__class_Oplus(U_1081,U_1082,c_Groups_Oone__class_Oone(U_1081)))
      | ~ class_Rings_Olinordered__semidom(U_1081) ),
    inference(definitional_conversion,[status(esa)],[f_332_2]) ).

cnf(f_332_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1081,U_1082,c_Groups_Oplus__class_Oplus(U_1081,U_1082,c_Groups_Oone__class_Oone(U_1081)))
    | ~ class_Rings_Olinordered__semidom(U_1081) ),
    inference(clausify,[status(thm)],[f_332_3]) ).

fof(f_333_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_333_2,plain,
    ! [U_1083] :
      ( ~ c_Orderings_Oord__class_Oless(U_1083,c_Groups_Oone__class_Oone(U_1083),c_Groups_Ozero__class_Ozero(U_1083))
      | ~ class_Rings_Olinordered__semidom(U_1083) ),
    inference(variable_rename,[status(thm)],[f_333_1]) ).

fof(f_333_3,plain,
    ! [U_1083] :
      ( ~ c_Orderings_Oord__class_Oless(U_1083,c_Groups_Oone__class_Oone(U_1083),c_Groups_Ozero__class_Ozero(U_1083))
      | ~ class_Rings_Olinordered__semidom(U_1083) ),
    inference(definitional_conversion,[status(esa)],[f_333_2]) ).

cnf(f_333_4,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_1083,c_Groups_Oone__class_Oone(U_1083),c_Groups_Ozero__class_Ozero(U_1083))
    | ~ class_Rings_Olinordered__semidom(U_1083) ),
    inference(clausify,[status(thm)],[f_333_3]) ).

fof(f_334_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_334_2,plain,
    ! [U_1084] :
      ( c_Orderings_Oord__class_Oless(U_1084,c_Groups_Ozero__class_Ozero(U_1084),c_Groups_Oone__class_Oone(U_1084))
      | ~ class_Rings_Olinordered__semidom(U_1084) ),
    inference(variable_rename,[status(thm)],[f_334_1]) ).

fof(f_334_3,plain,
    ! [U_1084] :
      ( c_Orderings_Oord__class_Oless(U_1084,c_Groups_Ozero__class_Ozero(U_1084),c_Groups_Oone__class_Oone(U_1084))
      | ~ class_Rings_Olinordered__semidom(U_1084) ),
    inference(definitional_conversion,[status(esa)],[f_334_2]) ).

cnf(f_334_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1084,c_Groups_Ozero__class_Ozero(U_1084),c_Groups_Oone__class_Oone(U_1084))
    | ~ class_Rings_Olinordered__semidom(U_1084) ),
    inference(clausify,[status(thm)],[f_334_3]) ).

fof(f_335_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_335_2,plain,
    ! [U_1085] :
      ( c_Orderings_Oord__class_Oless__eq(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_335_1]) ).

fof(f_335_3,plain,
    ! [U_1085] :
      ( c_Orderings_Oord__class_Oless__eq(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_335_2]) ).

cnf(f_335_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(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_335_3]) ).

fof(f_336_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_336_2,plain,
    ! [U_1086] :
      ( ~ c_Orderings_Oord__class_Oless__eq(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_336_1]) ).

fof(f_336_3,plain,
    ! [U_1086] :
      ( ~ c_Orderings_Oord__class_Oless__eq(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_336_2]) ).

cnf(f_336_4,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(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_336_3]) ).

fof(f_337_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_337_2,plain,
    ! [U_1090,U_1089,U_1088,U_1087] :
      ( c_Orderings_Oord__class_Oless(U_1087,U_1089,c_Groups_Oplus__class_Oplus(U_1087,U_1088,U_1090))
      | ~ c_Orderings_Oord__class_Oless(U_1087,U_1089,U_1090)
      | ~ c_Orderings_Oord__class_Oless(U_1087,c_Groups_Ozero__class_Ozero(U_1087),U_1088)
      | ~ class_Rings_Olinordered__semidom(U_1087) ),
    inference(variable_rename,[status(thm)],[f_337_1]) ).

fof(f_337_3,plain,
    ! [U_1087,U_1088,U_1089,U_1090] :
      ( c_Orderings_Oord__class_Oless(U_1087,U_1089,c_Groups_Oplus__class_Oplus(U_1087,U_1088,U_1090))
      | ~ c_Orderings_Oord__class_Oless(U_1087,U_1089,U_1090)
      | ~ c_Orderings_Oord__class_Oless(U_1087,c_Groups_Ozero__class_Ozero(U_1087),U_1088)
      | ~ class_Rings_Olinordered__semidom(U_1087) ),
    inference(definitional_conversion,[status(esa)],[f_337_2]) ).

cnf(f_337_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1087,U_1089,c_Groups_Oplus__class_Oplus(U_1087,U_1088,U_1090))
    | ~ c_Orderings_Oord__class_Oless(U_1087,U_1089,U_1090)
    | ~ c_Orderings_Oord__class_Oless(U_1087,c_Groups_Ozero__class_Ozero(U_1087),U_1088)
    | ~ class_Rings_Olinordered__semidom(U_1087) ),
    inference(clausify,[status(thm)],[f_337_3]) ).

fof(f_338_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
          | ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
        & ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
          | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_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_338_2,plain,
    ! [U_1092,U_1091] :
      ( ( ( c_Orderings_Oord__class_Oless(U_1091,c_Groups_Oplus__class_Oplus(U_1091,U_1092,U_1092),c_Groups_Ozero__class_Ozero(U_1091))
          | ~ c_Orderings_Oord__class_Oless(U_1091,U_1092,c_Groups_Ozero__class_Ozero(U_1091)) )
        & ( c_Orderings_Oord__class_Oless(U_1091,U_1092,c_Groups_Ozero__class_Ozero(U_1091))
          | ~ c_Orderings_Oord__class_Oless(U_1091,c_Groups_Oplus__class_Oplus(U_1091,U_1092,U_1092),c_Groups_Ozero__class_Ozero(U_1091)) ) )
      | ~ class_Rings_Olinordered__idom(U_1091) ),
    inference(variable_rename,[status(thm)],[f_338_1]) ).

fof(f_338_3,plain,
    ( ! [U_1092,U_1091] :
        ( c_Orderings_Oord__class_Oless(U_1091,c_Groups_Oplus__class_Oplus(U_1091,U_1092,U_1092),c_Groups_Ozero__class_Ozero(U_1091))
        | ~ c_Orderings_Oord__class_Oless(U_1091,U_1092,c_Groups_Ozero__class_Ozero(U_1091))
        | ~ sP88(U_1092,U_1091) )
    & ! [U_1092,U_1091] :
        ( c_Orderings_Oord__class_Oless(U_1091,U_1092,c_Groups_Ozero__class_Ozero(U_1091))
        | ~ c_Orderings_Oord__class_Oless(U_1091,c_Groups_Oplus__class_Oplus(U_1091,U_1092,U_1092),c_Groups_Ozero__class_Ozero(U_1091))
        | ~ sP88(U_1092,U_1091) )
    & ! [U_1092,U_1091] :
        ( sP88(U_1092,U_1091)
        | ~ class_Rings_Olinordered__idom(U_1091) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP88])],[f_338_2]) ).

cnf(f_338_4,plain,
    ( sP88(U_1092,U_1091)
    | ~ class_Rings_Olinordered__idom(U_1091) ),
    inference(clausify,[status(thm)],[f_338_3]) ).

cnf(f_338_5,plain,
    ( c_Orderings_Oord__class_Oless(U_1091,U_1092,c_Groups_Ozero__class_Ozero(U_1091))
    | ~ c_Orderings_Oord__class_Oless(U_1091,c_Groups_Oplus__class_Oplus(U_1091,U_1092,U_1092),c_Groups_Ozero__class_Ozero(U_1091))
    | ~ sP88(U_1092,U_1091) ),
    inference(clausify,[status(thm)],[f_338_3]) ).

cnf(f_338_6,plain,
    ( c_Orderings_Oord__class_Oless(U_1091,c_Groups_Oplus__class_Oplus(U_1091,U_1092,U_1092),c_Groups_Ozero__class_Ozero(U_1091))
    | ~ c_Orderings_Oord__class_Oless(U_1091,U_1092,c_Groups_Ozero__class_Ozero(U_1091))
    | ~ sP88(U_1092,U_1091) ),
    inference(clausify,[status(thm)],[f_338_3]) ).

fof(f_339_1,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____),
    inference(fof_nnf,[status(thm)],[fact_d_I1_J]) ).

fof(f_339_2,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____),
    inference(definitional_conversion,[status(esa)],[f_339_1]) ).

cnf(f_339_3,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____),
    inference(clausify,[status(thm)],[f_339_2]) ).

fof(f_340_1,plain,
    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_rp]) ).

fof(f_340_2,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r),
    inference(definitional_conversion,[status(esa)],[f_340_1]) ).

cnf(f_340_3,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r),
    inference(clausify,[status(thm)],[f_340_2]) ).

fof(f_341_1,plain,
    ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)),
    inference(fof_nnf,[status(thm)],[fact_real__of__nat__ge__zero]) ).

fof(f_341_2,plain,
    ! [U_1093] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1093)),
    inference(variable_rename,[status(thm)],[f_341_1]) ).

fof(f_341_3,plain,
    ! [U_1093] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1093)),
    inference(definitional_conversion,[status(esa)],[f_341_2]) ).

cnf(f_341_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1093)),
    inference(clausify,[status(thm)],[f_341_3]) ).

fof(f_342_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_342_2,plain,
    ! [U_1095,U_1094] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1094,U_1095)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1094,U_1095),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_1094,U_1095),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1094,U_1095) ) ),
    inference(variable_rename,[status(thm)],[f_342_1]) ).

fof(f_342_3,plain,
    ( ! [U_1099,U_1097] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1097,U_1099)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1097,U_1099),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
    & ! [U_1098,U_1096] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1096,U_1098),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1096,U_1098) ) ),
    inference(miniscope,[status(thm)],[f_342_2]) ).

fof(f_342_4,plain,
    ( ! [U_1099,U_1097] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1097,U_1099)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1097,U_1099),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
    & ! [U_1096,U_1098] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1096,U_1098),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1096,U_1098) ) ),
    inference(definitional_conversion,[status(esa)],[f_342_3]) ).

cnf(f_342_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1096,U_1098),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1096,U_1098) ),
    inference(clausify,[status(thm)],[f_342_4]) ).

cnf(f_342_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1097,U_1099)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1097,U_1099),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(clausify,[status(thm)],[f_342_4]) ).

fof(f_343_1,plain,
    ! [V_ga_2,V_fa_2,T_a,T_b] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_fa_2,V_ga_2)
          | c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_ga_2,V_fa_2)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2,V_ga_2) )
        & ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_ga_2,V_fa_2)
            & c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2,V_ga_2) )
          | ~ c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_fa_2,V_ga_2) ) )
      | ~ class_Orderings_Oord(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__fun__def]) ).

fof(f_343_2,plain,
    ! [U_1103,U_1102,U_1101,U_1100] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_fun(U_1101,U_1100),U_1102,U_1103)
          | c_Orderings_Oord__class_Oless__eq(tc_fun(U_1101,U_1100),U_1103,U_1102)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1101,U_1100),U_1102,U_1103) )
        & ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1101,U_1100),U_1103,U_1102)
            & c_Orderings_Oord__class_Oless__eq(tc_fun(U_1101,U_1100),U_1102,U_1103) )
          | ~ c_Orderings_Oord__class_Oless(tc_fun(U_1101,U_1100),U_1102,U_1103) ) )
      | ~ class_Orderings_Oord(U_1100) ),
    inference(variable_rename,[status(thm)],[f_343_1]) ).

fof(f_343_3,plain,
    ( ! [U_1100,U_1102,U_1103,U_1101] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1101,U_1100),U_1103,U_1102)
        | ~ sP89(U_1100,U_1102,U_1103,U_1101) )
    & ! [U_1100,U_1102,U_1103,U_1101] :
        ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_1101,U_1100),U_1102,U_1103)
        | ~ sP89(U_1100,U_1102,U_1103,U_1101) )
    & ! [U_1100,U_1102,U_1103,U_1101] :
        ( c_Orderings_Oord__class_Oless(tc_fun(U_1101,U_1100),U_1102,U_1103)
        | c_Orderings_Oord__class_Oless__eq(tc_fun(U_1101,U_1100),U_1103,U_1102)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1101,U_1100),U_1102,U_1103)
        | ~ sP90(U_1100,U_1102,U_1103,U_1101) )
    & ! [U_1100,U_1102,U_1103,U_1101] :
        ( sP89(U_1100,U_1102,U_1103,U_1101)
        | ~ c_Orderings_Oord__class_Oless(tc_fun(U_1101,U_1100),U_1102,U_1103)
        | ~ sP90(U_1100,U_1102,U_1103,U_1101) )
    & ! [U_1100,U_1102,U_1103,U_1101] :
        ( sP90(U_1100,U_1102,U_1103,U_1101)
        | ~ class_Orderings_Oord(U_1100) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP89,sP90])],[f_343_2]) ).

cnf(f_343_4,plain,
    ( sP90(U_1100,U_1102,U_1103,U_1101)
    | ~ class_Orderings_Oord(U_1100) ),
    inference(clausify,[status(thm)],[f_343_3]) ).

cnf(f_343_5,plain,
    ( sP89(U_1100,U_1102,U_1103,U_1101)
    | ~ c_Orderings_Oord__class_Oless(tc_fun(U_1101,U_1100),U_1102,U_1103)
    | ~ sP90(U_1100,U_1102,U_1103,U_1101) ),
    inference(clausify,[status(thm)],[f_343_3]) ).

cnf(f_343_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_fun(U_1101,U_1100),U_1102,U_1103)
    | c_Orderings_Oord__class_Oless__eq(tc_fun(U_1101,U_1100),U_1103,U_1102)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1101,U_1100),U_1102,U_1103)
    | ~ sP90(U_1100,U_1102,U_1103,U_1101) ),
    inference(clausify,[status(thm)],[f_343_3]) ).

cnf(f_343_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_1101,U_1100),U_1102,U_1103)
    | ~ sP89(U_1100,U_1102,U_1103,U_1101) ),
    inference(clausify,[status(thm)],[f_343_3]) ).

cnf(f_343_8,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1101,U_1100),U_1103,U_1102)
    | ~ sP89(U_1100,U_1102,U_1103,U_1101) ),
    inference(clausify,[status(thm)],[f_343_3]) ).

fof(f_344_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_344_2,plain,
    c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_344_1]) ).

cnf(f_344_3,plain,
    c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_344_2]) ).

fof(f_345_1,plain,
    hAPP(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_345_2,plain,
    hAPP(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_345_1]) ).

cnf(f_345_3,plain,
    hAPP(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_345_2]) ).

fof(f_346_1,plain,
    ! [V_n_2] :
      ( ( hAPP(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)
        | hAPP(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_346_2,plain,
    ! [U_1104] :
      ( ( hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1104) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | U_1104 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_1104 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1104) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(variable_rename,[status(thm)],[f_346_1]) ).

fof(f_346_3,plain,
    ( ! [U_1106] :
        ( hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1106) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | U_1106 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_1105] :
        ( U_1105 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1105) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(miniscope,[status(thm)],[f_346_2]) ).

fof(f_346_4,plain,
    ( ! [U_1106] :
        ( hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1106) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | U_1106 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_1105] :
        ( U_1105 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1105) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(definitional_conversion,[status(esa)],[f_346_3]) ).

cnf(f_346_5,plain,
    ( U_1105 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1105) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(clausify,[status(thm)],[f_346_4]) ).

cnf(f_346_6,plain,
    ( hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1106) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | U_1106 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_346_4]) ).

fof(f_347_1,plain,
    ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(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_347_2,plain,
    ! [U_1107] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1107),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    inference(variable_rename,[status(thm)],[f_347_1]) ).

fof(f_347_3,plain,
    ! [U_1107] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1107),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    inference(definitional_conversion,[status(esa)],[f_347_2]) ).

cnf(f_347_4,plain,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1107),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    inference(clausify,[status(thm)],[f_347_3]) ).

fof(f_348_1,plain,
    ! [V_m,V_n] :
      ( hAPP(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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m),hAPP(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_348_2,plain,
    ! [U_1109,U_1108] :
      ( hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1109,U_1108)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1109),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1108))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1108,U_1109) ),
    inference(variable_rename,[status(thm)],[f_348_1]) ).

fof(f_348_3,plain,
    ! [U_1108,U_1109] :
      ( hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1109,U_1108)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1109),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1108))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1108,U_1109) ),
    inference(definitional_conversion,[status(esa)],[f_348_2]) ).

cnf(f_348_4,plain,
    ( hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1109,U_1108)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1109),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1108))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1108,U_1109) ),
    inference(clausify,[status(thm)],[f_348_3]) ).

fof(f_349_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_349_2,plain,
    ! [U_1112,U_1111,U_1110] :
      ( c_Orderings_Oord__class_Oless(U_1110,U_1112,U_1111)
      | c_Orderings_Oord__class_Oless(U_1110,U_1111,U_1112)
      | U_1111 = U_1112
      | ~ class_Rings_Olinordered__idom(U_1110) ),
    inference(variable_rename,[status(thm)],[f_349_1]) ).

fof(f_349_3,plain,
    ! [U_1110,U_1112,U_1111] :
      ( c_Orderings_Oord__class_Oless(U_1110,U_1112,U_1111)
      | c_Orderings_Oord__class_Oless(U_1110,U_1111,U_1112)
      | U_1111 = U_1112
      | ~ class_Rings_Olinordered__idom(U_1110) ),
    inference(definitional_conversion,[status(esa)],[f_349_2]) ).

cnf(f_349_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1110,U_1112,U_1111)
    | c_Orderings_Oord__class_Oless(U_1110,U_1111,U_1112)
    | U_1111 = U_1112
    | ~ class_Rings_Olinordered__idom(U_1110) ),
    inference(clausify,[status(thm)],[f_349_3]) ).

fof(f_350_1,plain,
    ! [V_n_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(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,hAPP(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_350_2,plain,
    ! [U_1113] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1113),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | U_1113 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_1113 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1113),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
    inference(variable_rename,[status(thm)],[f_350_1]) ).

fof(f_350_3,plain,
    ( ! [U_1115] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1115),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | U_1115 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_1114] :
        ( U_1114 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1114),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
    inference(miniscope,[status(thm)],[f_350_2]) ).

fof(f_350_4,plain,
    ( ! [U_1115] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1115),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | U_1115 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_1114] :
        ( U_1114 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1114),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
    inference(definitional_conversion,[status(esa)],[f_350_3]) ).

cnf(f_350_5,plain,
    ( U_1114 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1114),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(clausify,[status(thm)],[f_350_4]) ).

cnf(f_350_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1115),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | U_1115 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_350_4]) ).

fof(f_351_1,plain,
    ! [V_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(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_351_2,plain,
    ! [U_1116] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_1116))),
    inference(variable_rename,[status(thm)],[f_351_1]) ).

fof(f_351_3,plain,
    ! [U_1116] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_1116))),
    inference(definitional_conversion,[status(esa)],[f_351_2]) ).

cnf(f_351_4,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_1116))),
    inference(clausify,[status(thm)],[f_351_3]) ).

fof(f_352_1,plain,
    ! [V_n_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(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),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_real__of__nat__gt__zero__cancel__iff]) ).

fof(f_352_2,plain,
    ! [U_1117] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1117))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1117) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1117)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1117)) ) ),
    inference(variable_rename,[status(thm)],[f_352_1]) ).

fof(f_352_3,plain,
    ( ! [U_1119] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1119))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1119) )
    & ! [U_1118] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1118)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1118)) ) ),
    inference(miniscope,[status(thm)],[f_352_2]) ).

fof(f_352_4,plain,
    ( ! [U_1119] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1119))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1119) )
    & ! [U_1118] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1118)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1118)) ) ),
    inference(definitional_conversion,[status(esa)],[f_352_3]) ).

cnf(f_352_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1118)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1118)) ),
    inference(clausify,[status(thm)],[f_352_4]) ).

cnf(f_352_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1119))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1119) ),
    inference(clausify,[status(thm)],[f_352_4]) ).

fof(f_353_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
          | c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_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_353_2,plain,
    ! [U_1121,U_1120] :
      ( ( ( c_Groups_Oplus__class_Oplus(U_1120,U_1121,U_1121) = c_Groups_Ozero__class_Ozero(U_1120)
          | U_1121 != c_Groups_Ozero__class_Ozero(U_1120) )
        & ( U_1121 = c_Groups_Ozero__class_Ozero(U_1120)
          | c_Groups_Oplus__class_Oplus(U_1120,U_1121,U_1121) != c_Groups_Ozero__class_Ozero(U_1120) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_1120) ),
    inference(variable_rename,[status(thm)],[f_353_1]) ).

fof(f_353_3,plain,
    ( ! [U_1120,U_1121] :
        ( c_Groups_Oplus__class_Oplus(U_1120,U_1121,U_1121) = c_Groups_Ozero__class_Ozero(U_1120)
        | U_1121 != c_Groups_Ozero__class_Ozero(U_1120)
        | ~ sP91(U_1120,U_1121) )
    & ! [U_1120,U_1121] :
        ( U_1121 = c_Groups_Ozero__class_Ozero(U_1120)
        | c_Groups_Oplus__class_Oplus(U_1120,U_1121,U_1121) != c_Groups_Ozero__class_Ozero(U_1120)
        | ~ sP91(U_1120,U_1121) )
    & ! [U_1120,U_1121] :
        ( sP91(U_1120,U_1121)
        | ~ class_Groups_Olinordered__ab__group__add(U_1120) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP91])],[f_353_2]) ).

cnf(f_353_4,plain,
    ( sP91(U_1120,U_1121)
    | ~ class_Groups_Olinordered__ab__group__add(U_1120) ),
    inference(clausify,[status(thm)],[f_353_3]) ).

cnf(f_353_5,plain,
    ( U_1121 = c_Groups_Ozero__class_Ozero(U_1120)
    | c_Groups_Oplus__class_Oplus(U_1120,U_1121,U_1121) != c_Groups_Ozero__class_Ozero(U_1120)
    | ~ sP91(U_1120,U_1121) ),
    inference(clausify,[status(thm)],[f_353_3]) ).

cnf(f_353_6,plain,
    ( c_Groups_Oplus__class_Oplus(U_1120,U_1121,U_1121) = c_Groups_Ozero__class_Ozero(U_1120)
    | U_1121 != c_Groups_Ozero__class_Ozero(U_1120)
    | ~ sP91(U_1120,U_1121) ),
    inference(clausify,[status(thm)],[f_353_3]) ).

fof(f_354_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_354_2,plain,
    ! [U_1122] :
      ( c_Groups_Oone__class_Oone(U_1122) != c_Groups_Ozero__class_Ozero(U_1122)
      | ~ class_Rings_Ozero__neq__one(U_1122) ),
    inference(variable_rename,[status(thm)],[f_354_1]) ).

fof(f_354_3,plain,
    ! [U_1122] :
      ( c_Groups_Oone__class_Oone(U_1122) != c_Groups_Ozero__class_Ozero(U_1122)
      | ~ class_Rings_Ozero__neq__one(U_1122) ),
    inference(definitional_conversion,[status(esa)],[f_354_2]) ).

cnf(f_354_4,plain,
    ( c_Groups_Oone__class_Oone(U_1122) != c_Groups_Ozero__class_Ozero(U_1122)
    | ~ class_Rings_Ozero__neq__one(U_1122) ),
    inference(clausify,[status(thm)],[f_354_3]) ).

fof(f_355_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_355_2,plain,
    ! [U_1123] :
      ( c_Groups_Ozero__class_Ozero(U_1123) != c_Groups_Oone__class_Oone(U_1123)
      | ~ class_Rings_Ozero__neq__one(U_1123) ),
    inference(variable_rename,[status(thm)],[f_355_1]) ).

fof(f_355_3,plain,
    ! [U_1123] :
      ( c_Groups_Ozero__class_Ozero(U_1123) != c_Groups_Oone__class_Oone(U_1123)
      | ~ class_Rings_Ozero__neq__one(U_1123) ),
    inference(definitional_conversion,[status(esa)],[f_355_2]) ).

cnf(f_355_4,plain,
    ( c_Groups_Ozero__class_Ozero(U_1123) != c_Groups_Oone__class_Oone(U_1123)
    | ~ class_Rings_Ozero__neq__one(U_1123) ),
    inference(clausify,[status(thm)],[f_355_3]) ).

fof(f_356_1,plain,
    ! [V_e,V_x,V_m] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_m)),V_e)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_m,V_e))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_m,V_x) ),
    inference(fof_nnf,[status(thm)],[fact_ath]) ).

fof(f_356_2,plain,
    ! [U_1126,U_1125,U_1124] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1125,U_1124)),U_1126)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1125,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1124,U_1126))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1124,U_1125) ),
    inference(variable_rename,[status(thm)],[f_356_1]) ).

fof(f_356_3,plain,
    ! [U_1124,U_1125,U_1126] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1125,U_1124)),U_1126)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1125,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1124,U_1126))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1124,U_1125) ),
    inference(definitional_conversion,[status(esa)],[f_356_2]) ).

cnf(f_356_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1125,U_1124)),U_1126)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1125,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1124,U_1126))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1124,U_1125) ),
    inference(clausify,[status(thm)],[f_356_3]) ).

fof(f_357_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_357_2,plain,
    ! [U_1131,U_1130,U_1129,U_1128,U_1127] :
      ( c_Groups_Ominus__class_Ominus(U_1127,c_Groups_Oplus__class_Oplus(U_1127,U_1128,U_1129),c_Groups_Oplus__class_Oplus(U_1127,U_1130,U_1131)) = c_Groups_Oplus__class_Oplus(U_1127,c_Groups_Ominus__class_Ominus(U_1127,U_1128,U_1130),c_Groups_Ominus__class_Ominus(U_1127,U_1129,U_1131))
      | ~ class_Groups_Oab__group__add(U_1127) ),
    inference(variable_rename,[status(thm)],[f_357_1]) ).

fof(f_357_3,plain,
    ! [U_1128,U_1127,U_1129,U_1130,U_1131] :
      ( c_Groups_Ominus__class_Ominus(U_1127,c_Groups_Oplus__class_Oplus(U_1127,U_1128,U_1129),c_Groups_Oplus__class_Oplus(U_1127,U_1130,U_1131)) = c_Groups_Oplus__class_Oplus(U_1127,c_Groups_Ominus__class_Ominus(U_1127,U_1128,U_1130),c_Groups_Ominus__class_Ominus(U_1127,U_1129,U_1131))
      | ~ class_Groups_Oab__group__add(U_1127) ),
    inference(definitional_conversion,[status(esa)],[f_357_2]) ).

cnf(f_357_4,plain,
    ( c_Groups_Ominus__class_Ominus(U_1127,c_Groups_Oplus__class_Oplus(U_1127,U_1128,U_1129),c_Groups_Oplus__class_Oplus(U_1127,U_1130,U_1131)) = c_Groups_Oplus__class_Oplus(U_1127,c_Groups_Ominus__class_Ominus(U_1127,U_1128,U_1130),c_Groups_Ominus__class_Ominus(U_1127,U_1129,U_1131))
    | ~ class_Groups_Oab__group__add(U_1127) ),
    inference(clausify,[status(thm)],[f_357_3]) ).

fof(f_358_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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n),V_x) ),
    inference(fof_nnf,[status(thm)],[fact_natceiling__eq]) ).

fof(f_358_2,plain,
    ! [U_1133,U_1132] :
      ( c_RComplete_Onatceiling(U_1133) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1132,c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1133,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1132),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1132),U_1133) ),
    inference(variable_rename,[status(thm)],[f_358_1]) ).

fof(f_358_3,plain,
    ! [U_1133,U_1132] :
      ( c_RComplete_Onatceiling(U_1133) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1132,c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1133,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1132),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1132),U_1133) ),
    inference(definitional_conversion,[status(esa)],[f_358_2]) ).

cnf(f_358_4,plain,
    ( c_RComplete_Onatceiling(U_1133) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1132,c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1133,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1132),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1132),U_1133) ),
    inference(clausify,[status(thm)],[f_358_3]) ).

fof(f_359_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_359_2,plain,
    ! [U_1137,U_1136] :
      ( ? [U_1135] :
          ( hBOOL(hAPP(U_1136,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1135,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
          & ! [U_1134] :
              ( ~ hBOOL(hAPP(U_1136,U_1134))
              | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1134,U_1135) )
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1135,U_1137) )
      | ~ hBOOL(hAPP(U_1136,U_1137))
      | hBOOL(hAPP(U_1136,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(variable_rename,[status(thm)],[f_359_1]) ).

fof(f_359_3,plain,
    ! [U_1137,U_1136] :
      ( ( hBOOL(hAPP(U_1136,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK31(U_1137,U_1136),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        & ! [U_1134] :
            ( ~ hBOOL(hAPP(U_1136,U_1134))
            | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1134,sK31(U_1137,U_1136)) )
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK31(U_1137,U_1136),U_1137) )
      | ~ hBOOL(hAPP(U_1136,U_1137))
      | hBOOL(hAPP(U_1136,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_1135,sK31(U_1137,U_1136))],[f_359_2]) ).

fof(f_359_4,plain,
    ( ! [U_1134,U_1136,U_1137] :
        ( hBOOL(hAPP(U_1136,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK31(U_1137,U_1136),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | ~ sP92(U_1134,U_1136,U_1137) )
    & ! [U_1134,U_1136,U_1137] :
        ( ~ hBOOL(hAPP(U_1136,U_1134))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1134,sK31(U_1137,U_1136))
        | ~ sP92(U_1134,U_1136,U_1137) )
    & ! [U_1134,U_1136,U_1137] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK31(U_1137,U_1136),U_1137)
        | ~ sP92(U_1134,U_1136,U_1137) )
    & ! [U_1134,U_1136,U_1137] :
        ( sP92(U_1134,U_1136,U_1137)
        | ~ hBOOL(hAPP(U_1136,U_1137))
        | hBOOL(hAPP(U_1136,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP92])],[f_359_3]) ).

cnf(f_359_5,plain,
    ( sP92(U_1134,U_1136,U_1137)
    | ~ hBOOL(hAPP(U_1136,U_1137))
    | hBOOL(hAPP(U_1136,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_359_4]) ).

cnf(f_359_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK31(U_1137,U_1136),U_1137)
    | ~ sP92(U_1134,U_1136,U_1137) ),
    inference(clausify,[status(thm)],[f_359_4]) ).

cnf(f_359_7,plain,
    ( ~ hBOOL(hAPP(U_1136,U_1134))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1134,sK31(U_1137,U_1136))
    | ~ sP92(U_1134,U_1136,U_1137) ),
    inference(clausify,[status(thm)],[f_359_4]) ).

cnf(f_359_8,plain,
    ( hBOOL(hAPP(U_1136,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK31(U_1137,U_1136),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ sP92(U_1134,U_1136,U_1137) ),
    inference(clausify,[status(thm)],[f_359_4]) ).

fof(f_360_1,plain,
    ! [V_v] :
      ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) ),
    inference(fof_nnf,[status(thm)],[fact_expand__Suc]) ).

fof(f_360_2,plain,
    ! [U_1138] :
      ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1138) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1138),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1138)) ),
    inference(variable_rename,[status(thm)],[f_360_1]) ).

fof(f_360_3,plain,
    ! [U_1138] :
      ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1138) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1138),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1138)) ),
    inference(definitional_conversion,[status(esa)],[f_360_2]) ).

cnf(f_360_4,plain,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1138) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1138),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1138)) ),
    inference(clausify,[status(thm)],[f_360_3]) ).

fof(f_361_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_361_2,plain,
    ! [U_1140,U_1139] :
      ( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(U_1139,U_1140) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | U_1140 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1139)) )
        & ( U_1140 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1139))
          | c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(U_1139,U_1140) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ class_Groups_Ozero(U_1139) ),
    inference(variable_rename,[status(thm)],[f_361_1]) ).

fof(f_361_3,plain,
    ( ! [U_1140,U_1139] :
        ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(U_1139,U_1140) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_1140 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1139))
        | ~ sP93(U_1140,U_1139) )
    & ! [U_1140,U_1139] :
        ( U_1140 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1139))
        | c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(U_1139,U_1140) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP93(U_1140,U_1139) )
    & ! [U_1140,U_1139] :
        ( sP93(U_1140,U_1139)
        | ~ class_Groups_Ozero(U_1139) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP93])],[f_361_2]) ).

cnf(f_361_4,plain,
    ( sP93(U_1140,U_1139)
    | ~ class_Groups_Ozero(U_1139) ),
    inference(clausify,[status(thm)],[f_361_3]) ).

cnf(f_361_5,plain,
    ( U_1140 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1139))
    | c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(U_1139,U_1140) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP93(U_1140,U_1139) ),
    inference(clausify,[status(thm)],[f_361_3]) ).

cnf(f_361_6,plain,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(U_1139,U_1140) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_1140 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1139))
    | ~ sP93(U_1140,U_1139) ),
    inference(clausify,[status(thm)],[f_361_3]) ).

fof(f_362_1,plain,
    ! [T_a] :
      ( c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a)
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__one]) ).

fof(f_362_2,plain,
    ! [U_1141] :
      ( c_Groups_Oabs__class_Oabs(U_1141,c_Groups_Oone__class_Oone(U_1141)) = c_Groups_Oone__class_Oone(U_1141)
      | ~ class_Rings_Olinordered__idom(U_1141) ),
    inference(variable_rename,[status(thm)],[f_362_1]) ).

fof(f_362_3,plain,
    ! [U_1141] :
      ( c_Groups_Oabs__class_Oabs(U_1141,c_Groups_Oone__class_Oone(U_1141)) = c_Groups_Oone__class_Oone(U_1141)
      | ~ class_Rings_Olinordered__idom(U_1141) ),
    inference(definitional_conversion,[status(esa)],[f_362_2]) ).

cnf(f_362_4,plain,
    ( c_Groups_Oabs__class_Oabs(U_1141,c_Groups_Oone__class_Oone(U_1141)) = c_Groups_Oone__class_Oone(U_1141)
    | ~ class_Rings_Olinordered__idom(U_1141) ),
    inference(clausify,[status(thm)],[f_362_3]) ).

fof(f_363_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_363_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_363_1]) ).

cnf(f_363_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_363_2]) ).

fof(f_364_1,plain,
    ! [V_x_2,V_wa_2,T_a] :
      ( ( ( c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = V_x_2
          | V_x_2 != c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) )
        & ( V_x_2 = c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)
          | c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) != V_x_2 ) )
      | ~ class_Int_Onumber(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_number__of__reorient]) ).

fof(f_364_2,plain,
    ! [U_1144,U_1143,U_1142] :
      ( ( ( c_Int_Onumber__class_Onumber__of(U_1142,U_1143) = U_1144
          | U_1144 != c_Int_Onumber__class_Onumber__of(U_1142,U_1143) )
        & ( U_1144 = c_Int_Onumber__class_Onumber__of(U_1142,U_1143)
          | c_Int_Onumber__class_Onumber__of(U_1142,U_1143) != U_1144 ) )
      | ~ class_Int_Onumber(U_1142) ),
    inference(variable_rename,[status(thm)],[f_364_1]) ).

fof(f_364_3,plain,
    ( ! [U_1144,U_1143,U_1142] :
        ( c_Int_Onumber__class_Onumber__of(U_1142,U_1143) = U_1144
        | U_1144 != c_Int_Onumber__class_Onumber__of(U_1142,U_1143)
        | ~ sP94(U_1144,U_1143,U_1142) )
    & ! [U_1144,U_1143,U_1142] :
        ( U_1144 = c_Int_Onumber__class_Onumber__of(U_1142,U_1143)
        | c_Int_Onumber__class_Onumber__of(U_1142,U_1143) != U_1144
        | ~ sP94(U_1144,U_1143,U_1142) )
    & ! [U_1144,U_1143,U_1142] :
        ( sP94(U_1144,U_1143,U_1142)
        | ~ class_Int_Onumber(U_1142) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP94])],[f_364_2]) ).

cnf(f_364_4,plain,
    ( sP94(U_1144,U_1143,U_1142)
    | ~ class_Int_Onumber(U_1142) ),
    inference(clausify,[status(thm)],[f_364_3]) ).

cnf(f_364_5,plain,
    ( U_1144 = c_Int_Onumber__class_Onumber__of(U_1142,U_1143)
    | c_Int_Onumber__class_Onumber__of(U_1142,U_1143) != U_1144
    | ~ sP94(U_1144,U_1143,U_1142) ),
    inference(clausify,[status(thm)],[f_364_3]) ).

cnf(f_364_6,plain,
    ( c_Int_Onumber__class_Onumber__of(U_1142,U_1143) = U_1144
    | U_1144 != c_Int_Onumber__class_Onumber__of(U_1142,U_1143)
    | ~ sP94(U_1144,U_1143,U_1142) ),
    inference(clausify,[status(thm)],[f_364_3]) ).

fof(f_365_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( c_Int_Onumber__class_Onumber__of(T_a,V_x_2) = c_Int_Onumber__class_Onumber__of(T_a,V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | c_Int_Onumber__class_Onumber__of(T_a,V_x_2) != c_Int_Onumber__class_Onumber__of(T_a,V_y_2) ) )
      | ~ class_Int_Oring__char__0(T_a)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_eq__number__of]) ).

fof(f_365_2,plain,
    ! [U_1147,U_1146,U_1145] :
      ( ( ( c_Int_Onumber__class_Onumber__of(U_1145,U_1146) = c_Int_Onumber__class_Onumber__of(U_1145,U_1147)
          | U_1146 != U_1147 )
        & ( U_1146 = U_1147
          | c_Int_Onumber__class_Onumber__of(U_1145,U_1146) != c_Int_Onumber__class_Onumber__of(U_1145,U_1147) ) )
      | ~ class_Int_Oring__char__0(U_1145)
      | ~ class_Int_Onumber__ring(U_1145) ),
    inference(variable_rename,[status(thm)],[f_365_1]) ).

fof(f_365_3,plain,
    ( ! [U_1147,U_1146,U_1145] :
        ( c_Int_Onumber__class_Onumber__of(U_1145,U_1146) = c_Int_Onumber__class_Onumber__of(U_1145,U_1147)
        | U_1146 != U_1147
        | ~ sP95(U_1147,U_1146,U_1145) )
    & ! [U_1147,U_1146,U_1145] :
        ( U_1146 = U_1147
        | c_Int_Onumber__class_Onumber__of(U_1145,U_1146) != c_Int_Onumber__class_Onumber__of(U_1145,U_1147)
        | ~ sP95(U_1147,U_1146,U_1145) )
    & ! [U_1147,U_1146,U_1145] :
        ( sP95(U_1147,U_1146,U_1145)
        | ~ class_Int_Oring__char__0(U_1145)
        | ~ class_Int_Onumber__ring(U_1145) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP95])],[f_365_2]) ).

cnf(f_365_4,plain,
    ( sP95(U_1147,U_1146,U_1145)
    | ~ class_Int_Oring__char__0(U_1145)
    | ~ class_Int_Onumber__ring(U_1145) ),
    inference(clausify,[status(thm)],[f_365_3]) ).

cnf(f_365_5,plain,
    ( U_1146 = U_1147
    | c_Int_Onumber__class_Onumber__of(U_1145,U_1146) != c_Int_Onumber__class_Onumber__of(U_1145,U_1147)
    | ~ sP95(U_1147,U_1146,U_1145) ),
    inference(clausify,[status(thm)],[f_365_3]) ).

cnf(f_365_6,plain,
    ( c_Int_Onumber__class_Onumber__of(U_1145,U_1146) = c_Int_Onumber__class_Onumber__of(U_1145,U_1147)
    | U_1146 != U_1147
    | ~ sP95(U_1147,U_1146,U_1145) ),
    inference(clausify,[status(thm)],[f_365_3]) ).

fof(f_366_1,plain,
    ! [V_n] : c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)) = V_n,
    inference(fof_nnf,[status(thm)],[fact_natceiling__real__of__nat]) ).

fof(f_366_2,plain,
    ! [U_1148] : c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1148)) = U_1148,
    inference(variable_rename,[status(thm)],[f_366_1]) ).

fof(f_366_3,plain,
    ! [U_1148] : c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1148)) = U_1148,
    inference(definitional_conversion,[status(esa)],[f_366_2]) ).

cnf(f_366_4,plain,
    c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1148)) = U_1148,
    inference(clausify,[status(thm)],[f_366_3]) ).

fof(f_367_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( c_Groups_Oabs__class_Oabs(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
          | c_Groups_Oabs__class_Oabs(T_a,V_a_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__eq__0]) ).

fof(f_367_2,plain,
    ! [U_1150,U_1149] :
      ( ( ( c_Groups_Oabs__class_Oabs(U_1149,U_1150) = c_Groups_Ozero__class_Ozero(U_1149)
          | U_1150 != c_Groups_Ozero__class_Ozero(U_1149) )
        & ( U_1150 = c_Groups_Ozero__class_Ozero(U_1149)
          | c_Groups_Oabs__class_Oabs(U_1149,U_1150) != c_Groups_Ozero__class_Ozero(U_1149) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(U_1149) ),
    inference(variable_rename,[status(thm)],[f_367_1]) ).

fof(f_367_3,plain,
    ( ! [U_1150,U_1149] :
        ( c_Groups_Oabs__class_Oabs(U_1149,U_1150) = c_Groups_Ozero__class_Ozero(U_1149)
        | U_1150 != c_Groups_Ozero__class_Ozero(U_1149)
        | ~ sP96(U_1150,U_1149) )
    & ! [U_1150,U_1149] :
        ( U_1150 = c_Groups_Ozero__class_Ozero(U_1149)
        | c_Groups_Oabs__class_Oabs(U_1149,U_1150) != c_Groups_Ozero__class_Ozero(U_1149)
        | ~ sP96(U_1150,U_1149) )
    & ! [U_1150,U_1149] :
        ( sP96(U_1150,U_1149)
        | ~ class_Groups_Oordered__ab__group__add__abs(U_1149) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP96])],[f_367_2]) ).

cnf(f_367_4,plain,
    ( sP96(U_1150,U_1149)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_1149) ),
    inference(clausify,[status(thm)],[f_367_3]) ).

cnf(f_367_5,plain,
    ( U_1150 = c_Groups_Ozero__class_Ozero(U_1149)
    | c_Groups_Oabs__class_Oabs(U_1149,U_1150) != c_Groups_Ozero__class_Ozero(U_1149)
    | ~ sP96(U_1150,U_1149) ),
    inference(clausify,[status(thm)],[f_367_3]) ).

cnf(f_367_6,plain,
    ( c_Groups_Oabs__class_Oabs(U_1149,U_1150) = c_Groups_Ozero__class_Ozero(U_1149)
    | U_1150 != c_Groups_Ozero__class_Ozero(U_1149)
    | ~ sP96(U_1150,U_1149) ),
    inference(clausify,[status(thm)],[f_367_3]) ).

fof(f_368_1,plain,
    ! [T_a] :
      ( c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__zero]) ).

fof(f_368_2,plain,
    ! [U_1151] :
      ( c_Groups_Oabs__class_Oabs(U_1151,c_Groups_Ozero__class_Ozero(U_1151)) = c_Groups_Ozero__class_Ozero(U_1151)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_1151) ),
    inference(variable_rename,[status(thm)],[f_368_1]) ).

fof(f_368_3,plain,
    ! [U_1151] :
      ( c_Groups_Oabs__class_Oabs(U_1151,c_Groups_Ozero__class_Ozero(U_1151)) = c_Groups_Ozero__class_Ozero(U_1151)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_1151) ),
    inference(definitional_conversion,[status(esa)],[f_368_2]) ).

cnf(f_368_4,plain,
    ( c_Groups_Oabs__class_Oabs(U_1151,c_Groups_Ozero__class_Ozero(U_1151)) = c_Groups_Ozero__class_Ozero(U_1151)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_1151) ),
    inference(clausify,[status(thm)],[f_368_3]) ).

fof(f_369_1,plain,
    ! [V_b,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_Oabs__class_Oabs(T_a,V_a),V_b)
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__le__D1]) ).

fof(f_369_2,plain,
    ! [U_1154,U_1153,U_1152] :
      ( c_Orderings_Oord__class_Oless__eq(U_1152,U_1153,U_1154)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1152,c_Groups_Oabs__class_Oabs(U_1152,U_1153),U_1154)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_1152) ),
    inference(variable_rename,[status(thm)],[f_369_1]) ).

fof(f_369_3,plain,
    ! [U_1152,U_1154,U_1153] :
      ( c_Orderings_Oord__class_Oless__eq(U_1152,U_1153,U_1154)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1152,c_Groups_Oabs__class_Oabs(U_1152,U_1153),U_1154)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_1152) ),
    inference(definitional_conversion,[status(esa)],[f_369_2]) ).

cnf(f_369_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1152,U_1153,U_1154)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1152,c_Groups_Oabs__class_Oabs(U_1152,U_1153),U_1154)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_1152) ),
    inference(clausify,[status(thm)],[f_369_3]) ).

fof(f_370_1,plain,
    ! [V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oabs__class_Oabs(T_a,V_a))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__ge__self]) ).

fof(f_370_2,plain,
    ! [U_1156,U_1155] :
      ( c_Orderings_Oord__class_Oless__eq(U_1155,U_1156,c_Groups_Oabs__class_Oabs(U_1155,U_1156))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_1155) ),
    inference(variable_rename,[status(thm)],[f_370_1]) ).

fof(f_370_3,plain,
    ! [U_1156,U_1155] :
      ( c_Orderings_Oord__class_Oless__eq(U_1155,U_1156,c_Groups_Oabs__class_Oabs(U_1155,U_1156))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_1155) ),
    inference(definitional_conversion,[status(esa)],[f_370_2]) ).

cnf(f_370_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1155,U_1156,c_Groups_Oabs__class_Oabs(U_1155,U_1156))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_1155) ),
    inference(clausify,[status(thm)],[f_370_3]) ).

fof(f_371_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__add__abs]) ).

fof(f_371_2,plain,
    ! [U_1159,U_1158,U_1157] :
      ( c_Groups_Oabs__class_Oabs(U_1157,c_Groups_Oplus__class_Oplus(U_1157,c_Groups_Oabs__class_Oabs(U_1157,U_1158),c_Groups_Oabs__class_Oabs(U_1157,U_1159))) = c_Groups_Oplus__class_Oplus(U_1157,c_Groups_Oabs__class_Oabs(U_1157,U_1158),c_Groups_Oabs__class_Oabs(U_1157,U_1159))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_1157) ),
    inference(variable_rename,[status(thm)],[f_371_1]) ).

fof(f_371_3,plain,
    ! [U_1157,U_1158,U_1159] :
      ( c_Groups_Oabs__class_Oabs(U_1157,c_Groups_Oplus__class_Oplus(U_1157,c_Groups_Oabs__class_Oabs(U_1157,U_1158),c_Groups_Oabs__class_Oabs(U_1157,U_1159))) = c_Groups_Oplus__class_Oplus(U_1157,c_Groups_Oabs__class_Oabs(U_1157,U_1158),c_Groups_Oabs__class_Oabs(U_1157,U_1159))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_1157) ),
    inference(definitional_conversion,[status(esa)],[f_371_2]) ).

cnf(f_371_4,plain,
    ( c_Groups_Oabs__class_Oabs(U_1157,c_Groups_Oplus__class_Oplus(U_1157,c_Groups_Oabs__class_Oabs(U_1157,U_1158),c_Groups_Oabs__class_Oabs(U_1157,U_1159))) = c_Groups_Oplus__class_Oplus(U_1157,c_Groups_Oabs__class_Oabs(U_1157,U_1158),c_Groups_Oabs__class_Oabs(U_1157,U_1159))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_1157) ),
    inference(clausify,[status(thm)],[f_371_3]) ).

fof(f_372_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__minus__commute]) ).

fof(f_372_2,plain,
    ! [U_1162,U_1161,U_1160] :
      ( c_Groups_Oabs__class_Oabs(U_1160,c_Groups_Ominus__class_Ominus(U_1160,U_1161,U_1162)) = c_Groups_Oabs__class_Oabs(U_1160,c_Groups_Ominus__class_Ominus(U_1160,U_1162,U_1161))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_1160) ),
    inference(variable_rename,[status(thm)],[f_372_1]) ).

fof(f_372_3,plain,
    ! [U_1160,U_1161,U_1162] :
      ( c_Groups_Oabs__class_Oabs(U_1160,c_Groups_Ominus__class_Ominus(U_1160,U_1161,U_1162)) = c_Groups_Oabs__class_Oabs(U_1160,c_Groups_Ominus__class_Ominus(U_1160,U_1162,U_1161))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_1160) ),
    inference(definitional_conversion,[status(esa)],[f_372_2]) ).

cnf(f_372_4,plain,
    ( c_Groups_Oabs__class_Oabs(U_1160,c_Groups_Ominus__class_Ominus(U_1160,U_1161,U_1162)) = c_Groups_Oabs__class_Oabs(U_1160,c_Groups_Ominus__class_Ominus(U_1160,U_1162,U_1161))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_1160) ),
    inference(clausify,[status(thm)],[f_372_3]) ).

fof(f_373_1,plain,
    ! [V_a,T_a] :
      ( c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) = c_Groups_Oabs__class_Oabs(T_a,V_a)
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__idempotent]) ).

fof(f_373_2,plain,
    ! [U_1164,U_1163] :
      ( c_Groups_Oabs__class_Oabs(U_1163,c_Groups_Oabs__class_Oabs(U_1163,U_1164)) = c_Groups_Oabs__class_Oabs(U_1163,U_1164)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_1163) ),
    inference(variable_rename,[status(thm)],[f_373_1]) ).

fof(f_373_3,plain,
    ! [U_1164,U_1163] :
      ( c_Groups_Oabs__class_Oabs(U_1163,c_Groups_Oabs__class_Oabs(U_1163,U_1164)) = c_Groups_Oabs__class_Oabs(U_1163,U_1164)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_1163) ),
    inference(definitional_conversion,[status(esa)],[f_373_2]) ).

cnf(f_373_4,plain,
    ( c_Groups_Oabs__class_Oabs(U_1163,c_Groups_Oabs__class_Oabs(U_1163,U_1164)) = c_Groups_Oabs__class_Oabs(U_1163,U_1164)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_1163) ),
    inference(clausify,[status(thm)],[f_373_3]) ).

fof(f_374_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,V_y_2) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,V_y_2)
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Int_Onumber__class_Onumber__of(T_a,V_y_2)) ) )
      | ~ class_Rings_Olinordered__idom(T_a)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__number__of]) ).

fof(f_374_2,plain,
    ! [U_1167,U_1166,U_1165] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_1165,c_Int_Onumber__class_Onumber__of(U_1165,U_1166),c_Int_Onumber__class_Onumber__of(U_1165,U_1167))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1166,U_1167) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1166,U_1167)
          | ~ c_Orderings_Oord__class_Oless__eq(U_1165,c_Int_Onumber__class_Onumber__of(U_1165,U_1166),c_Int_Onumber__class_Onumber__of(U_1165,U_1167)) ) )
      | ~ class_Rings_Olinordered__idom(U_1165)
      | ~ class_Int_Onumber__ring(U_1165) ),
    inference(variable_rename,[status(thm)],[f_374_1]) ).

fof(f_374_3,plain,
    ( ! [U_1165,U_1166,U_1167] :
        ( c_Orderings_Oord__class_Oless__eq(U_1165,c_Int_Onumber__class_Onumber__of(U_1165,U_1166),c_Int_Onumber__class_Onumber__of(U_1165,U_1167))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1166,U_1167)
        | ~ sP97(U_1165,U_1166,U_1167) )
    & ! [U_1165,U_1166,U_1167] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1166,U_1167)
        | ~ c_Orderings_Oord__class_Oless__eq(U_1165,c_Int_Onumber__class_Onumber__of(U_1165,U_1166),c_Int_Onumber__class_Onumber__of(U_1165,U_1167))
        | ~ sP97(U_1165,U_1166,U_1167) )
    & ! [U_1165,U_1166,U_1167] :
        ( sP97(U_1165,U_1166,U_1167)
        | ~ class_Rings_Olinordered__idom(U_1165)
        | ~ class_Int_Onumber__ring(U_1165) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP97])],[f_374_2]) ).

cnf(f_374_4,plain,
    ( sP97(U_1165,U_1166,U_1167)
    | ~ class_Rings_Olinordered__idom(U_1165)
    | ~ class_Int_Onumber__ring(U_1165) ),
    inference(clausify,[status(thm)],[f_374_3]) ).

cnf(f_374_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1166,U_1167)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1165,c_Int_Onumber__class_Onumber__of(U_1165,U_1166),c_Int_Onumber__class_Onumber__of(U_1165,U_1167))
    | ~ sP97(U_1165,U_1166,U_1167) ),
    inference(clausify,[status(thm)],[f_374_3]) ).

cnf(f_374_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1165,c_Int_Onumber__class_Onumber__of(U_1165,U_1166),c_Int_Onumber__class_Onumber__of(U_1165,U_1167))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1166,U_1167)
    | ~ sP97(U_1165,U_1166,U_1167) ),
    inference(clausify,[status(thm)],[f_374_3]) ).

fof(f_375_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
          | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,V_y_2) )
        & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,V_y_2)
          | ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Int_Onumber__class_Onumber__of(T_a,V_y_2)) ) )
      | ~ class_Rings_Olinordered__idom(T_a)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__number__of]) ).

fof(f_375_2,plain,
    ! [U_1170,U_1169,U_1168] :
      ( ( ( c_Orderings_Oord__class_Oless(U_1168,c_Int_Onumber__class_Onumber__of(U_1168,U_1169),c_Int_Onumber__class_Onumber__of(U_1168,U_1170))
          | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1169,U_1170) )
        & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1169,U_1170)
          | ~ c_Orderings_Oord__class_Oless(U_1168,c_Int_Onumber__class_Onumber__of(U_1168,U_1169),c_Int_Onumber__class_Onumber__of(U_1168,U_1170)) ) )
      | ~ class_Rings_Olinordered__idom(U_1168)
      | ~ class_Int_Onumber__ring(U_1168) ),
    inference(variable_rename,[status(thm)],[f_375_1]) ).

fof(f_375_3,plain,
    ( ! [U_1170,U_1169,U_1168] :
        ( c_Orderings_Oord__class_Oless(U_1168,c_Int_Onumber__class_Onumber__of(U_1168,U_1169),c_Int_Onumber__class_Onumber__of(U_1168,U_1170))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1169,U_1170)
        | ~ sP98(U_1170,U_1169,U_1168) )
    & ! [U_1170,U_1169,U_1168] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1169,U_1170)
        | ~ c_Orderings_Oord__class_Oless(U_1168,c_Int_Onumber__class_Onumber__of(U_1168,U_1169),c_Int_Onumber__class_Onumber__of(U_1168,U_1170))
        | ~ sP98(U_1170,U_1169,U_1168) )
    & ! [U_1170,U_1169,U_1168] :
        ( sP98(U_1170,U_1169,U_1168)
        | ~ class_Rings_Olinordered__idom(U_1168)
        | ~ class_Int_Onumber__ring(U_1168) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP98])],[f_375_2]) ).

cnf(f_375_4,plain,
    ( sP98(U_1170,U_1169,U_1168)
    | ~ class_Rings_Olinordered__idom(U_1168)
    | ~ class_Int_Onumber__ring(U_1168) ),
    inference(clausify,[status(thm)],[f_375_3]) ).

cnf(f_375_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1169,U_1170)
    | ~ c_Orderings_Oord__class_Oless(U_1168,c_Int_Onumber__class_Onumber__of(U_1168,U_1169),c_Int_Onumber__class_Onumber__of(U_1168,U_1170))
    | ~ sP98(U_1170,U_1169,U_1168) ),
    inference(clausify,[status(thm)],[f_375_3]) ).

cnf(f_375_6,plain,
    ( c_Orderings_Oord__class_Oless(U_1168,c_Int_Onumber__class_Onumber__of(U_1168,U_1169),c_Int_Onumber__class_Onumber__of(U_1168,U_1170))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1169,U_1170)
    | ~ sP98(U_1170,U_1169,U_1168) ),
    inference(clausify,[status(thm)],[f_375_3]) ).

fof(f_376_1,plain,
    ! [V_z,V_w,V_v,T_a] :
      ( c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_z)) = c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)),V_z)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__number__of__left]) ).

fof(f_376_2,plain,
    ! [U_1174,U_1173,U_1172,U_1171] :
      ( c_Groups_Oplus__class_Oplus(U_1171,c_Int_Onumber__class_Onumber__of(U_1171,U_1172),c_Groups_Oplus__class_Oplus(U_1171,c_Int_Onumber__class_Onumber__of(U_1171,U_1173),U_1174)) = c_Groups_Oplus__class_Oplus(U_1171,c_Int_Onumber__class_Onumber__of(U_1171,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1172,U_1173)),U_1174)
      | ~ class_Int_Onumber__ring(U_1171) ),
    inference(variable_rename,[status(thm)],[f_376_1]) ).

fof(f_376_3,plain,
    ! [U_1174,U_1172,U_1171,U_1173] :
      ( c_Groups_Oplus__class_Oplus(U_1171,c_Int_Onumber__class_Onumber__of(U_1171,U_1172),c_Groups_Oplus__class_Oplus(U_1171,c_Int_Onumber__class_Onumber__of(U_1171,U_1173),U_1174)) = c_Groups_Oplus__class_Oplus(U_1171,c_Int_Onumber__class_Onumber__of(U_1171,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1172,U_1173)),U_1174)
      | ~ class_Int_Onumber__ring(U_1171) ),
    inference(definitional_conversion,[status(esa)],[f_376_2]) ).

cnf(f_376_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_1171,c_Int_Onumber__class_Onumber__of(U_1171,U_1172),c_Groups_Oplus__class_Oplus(U_1171,c_Int_Onumber__class_Onumber__of(U_1171,U_1173),U_1174)) = c_Groups_Oplus__class_Oplus(U_1171,c_Int_Onumber__class_Onumber__of(U_1171,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1172,U_1173)),U_1174)
    | ~ class_Int_Onumber__ring(U_1171) ),
    inference(clausify,[status(thm)],[f_376_3]) ).

fof(f_377_1,plain,
    ! [V_w,V_v,T_a] :
      ( c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__number__of__eq]) ).

fof(f_377_2,plain,
    ! [U_1177,U_1176,U_1175] :
      ( c_Groups_Oplus__class_Oplus(U_1175,c_Int_Onumber__class_Onumber__of(U_1175,U_1176),c_Int_Onumber__class_Onumber__of(U_1175,U_1177)) = c_Int_Onumber__class_Onumber__of(U_1175,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1176,U_1177))
      | ~ class_Int_Onumber__ring(U_1175) ),
    inference(variable_rename,[status(thm)],[f_377_1]) ).

fof(f_377_3,plain,
    ! [U_1175,U_1176,U_1177] :
      ( c_Groups_Oplus__class_Oplus(U_1175,c_Int_Onumber__class_Onumber__of(U_1175,U_1176),c_Int_Onumber__class_Onumber__of(U_1175,U_1177)) = c_Int_Onumber__class_Onumber__of(U_1175,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1176,U_1177))
      | ~ class_Int_Onumber__ring(U_1175) ),
    inference(definitional_conversion,[status(esa)],[f_377_2]) ).

cnf(f_377_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_1175,c_Int_Onumber__class_Onumber__of(U_1175,U_1176),c_Int_Onumber__class_Onumber__of(U_1175,U_1177)) = c_Int_Onumber__class_Onumber__of(U_1175,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1176,U_1177))
    | ~ class_Int_Onumber__ring(U_1175) ),
    inference(clausify,[status(thm)],[f_377_3]) ).

fof(f_378_1,plain,
    ! [V_w,V_v,T_a] :
      ( c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)) = c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_number__of__add]) ).

fof(f_378_2,plain,
    ! [U_1180,U_1179,U_1178] :
      ( c_Int_Onumber__class_Onumber__of(U_1178,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1179,U_1180)) = c_Groups_Oplus__class_Oplus(U_1178,c_Int_Onumber__class_Onumber__of(U_1178,U_1179),c_Int_Onumber__class_Onumber__of(U_1178,U_1180))
      | ~ class_Int_Onumber__ring(U_1178) ),
    inference(variable_rename,[status(thm)],[f_378_1]) ).

fof(f_378_3,plain,
    ! [U_1178,U_1179,U_1180] :
      ( c_Int_Onumber__class_Onumber__of(U_1178,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1179,U_1180)) = c_Groups_Oplus__class_Oplus(U_1178,c_Int_Onumber__class_Onumber__of(U_1178,U_1179),c_Int_Onumber__class_Onumber__of(U_1178,U_1180))
      | ~ class_Int_Onumber__ring(U_1178) ),
    inference(definitional_conversion,[status(esa)],[f_378_2]) ).

cnf(f_378_4,plain,
    ( c_Int_Onumber__class_Onumber__of(U_1178,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1179,U_1180)) = c_Groups_Oplus__class_Oplus(U_1178,c_Int_Onumber__class_Onumber__of(U_1178,U_1179),c_Int_Onumber__class_Onumber__of(U_1178,U_1180))
    | ~ class_Int_Onumber__ring(U_1178) ),
    inference(clausify,[status(thm)],[f_378_3]) ).

fof(f_379_1,plain,
    ! [V_w,V_v,T_a] :
      ( c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_v,V_w)) = c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_number__of__diff]) ).

fof(f_379_2,plain,
    ! [U_1183,U_1182,U_1181] :
      ( c_Int_Onumber__class_Onumber__of(U_1181,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1182,U_1183)) = c_Groups_Ominus__class_Ominus(U_1181,c_Int_Onumber__class_Onumber__of(U_1181,U_1182),c_Int_Onumber__class_Onumber__of(U_1181,U_1183))
      | ~ class_Int_Onumber__ring(U_1181) ),
    inference(variable_rename,[status(thm)],[f_379_1]) ).

fof(f_379_3,plain,
    ! [U_1181,U_1182,U_1183] :
      ( c_Int_Onumber__class_Onumber__of(U_1181,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1182,U_1183)) = c_Groups_Ominus__class_Ominus(U_1181,c_Int_Onumber__class_Onumber__of(U_1181,U_1182),c_Int_Onumber__class_Onumber__of(U_1181,U_1183))
      | ~ class_Int_Onumber__ring(U_1181) ),
    inference(definitional_conversion,[status(esa)],[f_379_2]) ).

cnf(f_379_4,plain,
    ( c_Int_Onumber__class_Onumber__of(U_1181,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1182,U_1183)) = c_Groups_Ominus__class_Ominus(U_1181,c_Int_Onumber__class_Onumber__of(U_1181,U_1182),c_Int_Onumber__class_Onumber__of(U_1181,U_1183))
    | ~ class_Int_Onumber__ring(U_1181) ),
    inference(clausify,[status(thm)],[f_379_3]) ).

fof(f_380_1,plain,
    ! [V_x] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_x)) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_x),
    inference(fof_nnf,[status(thm)],[fact_abs__real__of__nat__cancel]) ).

fof(f_380_2,plain,
    ! [U_1184] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1184)) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1184),
    inference(variable_rename,[status(thm)],[f_380_1]) ).

fof(f_380_3,plain,
    ! [U_1184] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1184)) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1184),
    inference(definitional_conversion,[status(esa)],[f_380_2]) ).

cnf(f_380_4,plain,
    c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1184)) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1184),
    inference(clausify,[status(thm)],[f_380_3]) ).

fof(f_381_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_381_2,plain,
    ! [U_1185] :
      ( c_RComplete_Onatceiling(U_1185) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1185,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(variable_rename,[status(thm)],[f_381_1]) ).

fof(f_381_3,plain,
    ! [U_1185] :
      ( c_RComplete_Onatceiling(U_1185) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1185,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(definitional_conversion,[status(esa)],[f_381_2]) ).

cnf(f_381_4,plain,
    ( c_RComplete_Onatceiling(U_1185) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1185,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(clausify,[status(thm)],[f_381_3]) ).

fof(f_382_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_382_2,plain,
    ! [U_1186] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(U_1186)),
    inference(variable_rename,[status(thm)],[f_382_1]) ).

fof(f_382_3,plain,
    ! [U_1186] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(U_1186)),
    inference(definitional_conversion,[status(esa)],[f_382_2]) ).

cnf(f_382_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(U_1186)),
    inference(clausify,[status(thm)],[f_382_3]) ).

fof(f_383_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_383_2,plain,
    ! [U_1188,U_1187] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1187),c_RComplete_Onatceiling(U_1188))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1187,U_1188) ),
    inference(variable_rename,[status(thm)],[f_383_1]) ).

fof(f_383_3,plain,
    ! [U_1187,U_1188] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1187),c_RComplete_Onatceiling(U_1188))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1187,U_1188) ),
    inference(definitional_conversion,[status(esa)],[f_383_2]) ).

cnf(f_383_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1187),c_RComplete_Onatceiling(U_1188))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1187,U_1188) ),
    inference(clausify,[status(thm)],[f_383_3]) ).

fof(f_384_1,plain,
    ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatceiling(V_x))),
    inference(fof_nnf,[status(thm)],[fact_real__natceiling__ge]) ).

fof(f_384_2,plain,
    ! [U_1189] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1189,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatceiling(U_1189))),
    inference(variable_rename,[status(thm)],[f_384_1]) ).

fof(f_384_3,plain,
    ! [U_1189] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1189,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatceiling(U_1189))),
    inference(definitional_conversion,[status(esa)],[f_384_2]) ).

cnf(f_384_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1189,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatceiling(U_1189))),
    inference(clausify,[status(thm)],[f_384_3]) ).

fof(f_385_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_385_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_385_1]) ).

cnf(f_385_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_385_2]) ).

fof(f_386_1,plain,
    ! [V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__ge__zero]) ).

fof(f_386_2,plain,
    ! [U_1191,U_1190] :
      ( c_Orderings_Oord__class_Oless__eq(U_1190,c_Groups_Ozero__class_Ozero(U_1190),c_Groups_Oabs__class_Oabs(U_1190,U_1191))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_1190) ),
    inference(variable_rename,[status(thm)],[f_386_1]) ).

fof(f_386_3,plain,
    ! [U_1190,U_1191] :
      ( c_Orderings_Oord__class_Oless__eq(U_1190,c_Groups_Ozero__class_Ozero(U_1190),c_Groups_Oabs__class_Oabs(U_1190,U_1191))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_1190) ),
    inference(definitional_conversion,[status(esa)],[f_386_2]) ).

cnf(f_386_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1190,c_Groups_Ozero__class_Ozero(U_1190),c_Groups_Oabs__class_Oabs(U_1190,U_1191))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_1190) ),
    inference(clausify,[status(thm)],[f_386_3]) ).

fof(f_387_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__le__zero__iff]) ).

fof(f_387_2,plain,
    ! [U_1193,U_1192] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_1192,c_Groups_Oabs__class_Oabs(U_1192,U_1193),c_Groups_Ozero__class_Ozero(U_1192))
          | U_1193 != c_Groups_Ozero__class_Ozero(U_1192) )
        & ( U_1193 = c_Groups_Ozero__class_Ozero(U_1192)
          | ~ c_Orderings_Oord__class_Oless__eq(U_1192,c_Groups_Oabs__class_Oabs(U_1192,U_1193),c_Groups_Ozero__class_Ozero(U_1192)) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(U_1192) ),
    inference(variable_rename,[status(thm)],[f_387_1]) ).

fof(f_387_3,plain,
    ( ! [U_1192,U_1193] :
        ( c_Orderings_Oord__class_Oless__eq(U_1192,c_Groups_Oabs__class_Oabs(U_1192,U_1193),c_Groups_Ozero__class_Ozero(U_1192))
        | U_1193 != c_Groups_Ozero__class_Ozero(U_1192)
        | ~ sP99(U_1192,U_1193) )
    & ! [U_1192,U_1193] :
        ( U_1193 = c_Groups_Ozero__class_Ozero(U_1192)
        | ~ c_Orderings_Oord__class_Oless__eq(U_1192,c_Groups_Oabs__class_Oabs(U_1192,U_1193),c_Groups_Ozero__class_Ozero(U_1192))
        | ~ sP99(U_1192,U_1193) )
    & ! [U_1192,U_1193] :
        ( sP99(U_1192,U_1193)
        | ~ class_Groups_Oordered__ab__group__add__abs(U_1192) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP99])],[f_387_2]) ).

cnf(f_387_4,plain,
    ( sP99(U_1192,U_1193)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_1192) ),
    inference(clausify,[status(thm)],[f_387_3]) ).

cnf(f_387_5,plain,
    ( U_1193 = c_Groups_Ozero__class_Ozero(U_1192)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1192,c_Groups_Oabs__class_Oabs(U_1192,U_1193),c_Groups_Ozero__class_Ozero(U_1192))
    | ~ sP99(U_1192,U_1193) ),
    inference(clausify,[status(thm)],[f_387_3]) ).

cnf(f_387_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1192,c_Groups_Oabs__class_Oabs(U_1192,U_1193),c_Groups_Ozero__class_Ozero(U_1192))
    | U_1193 != c_Groups_Ozero__class_Ozero(U_1192)
    | ~ sP99(U_1192,U_1193) ),
    inference(clausify,[status(thm)],[f_387_3]) ).

fof(f_388_1,plain,
    ! [V_a,T_a] :
      ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__of__nonneg]) ).

fof(f_388_2,plain,
    ! [U_1195,U_1194] :
      ( c_Groups_Oabs__class_Oabs(U_1194,U_1195) = U_1195
      | ~ c_Orderings_Oord__class_Oless__eq(U_1194,c_Groups_Ozero__class_Ozero(U_1194),U_1195)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_1194) ),
    inference(variable_rename,[status(thm)],[f_388_1]) ).

fof(f_388_3,plain,
    ! [U_1195,U_1194] :
      ( c_Groups_Oabs__class_Oabs(U_1194,U_1195) = U_1195
      | ~ c_Orderings_Oord__class_Oless__eq(U_1194,c_Groups_Ozero__class_Ozero(U_1194),U_1195)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_1194) ),
    inference(definitional_conversion,[status(esa)],[f_388_2]) ).

cnf(f_388_4,plain,
    ( c_Groups_Oabs__class_Oabs(U_1194,U_1195) = U_1195
    | ~ c_Orderings_Oord__class_Oless__eq(U_1194,c_Groups_Ozero__class_Ozero(U_1194),U_1195)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_1194) ),
    inference(clausify,[status(thm)],[f_388_3]) ).

fof(f_389_1,plain,
    ! [V_a,T_a] :
      ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__not__less__zero]) ).

fof(f_389_2,plain,
    ! [U_1197,U_1196] :
      ( ~ c_Orderings_Oord__class_Oless(U_1196,c_Groups_Oabs__class_Oabs(U_1196,U_1197),c_Groups_Ozero__class_Ozero(U_1196))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_1196) ),
    inference(variable_rename,[status(thm)],[f_389_1]) ).

fof(f_389_3,plain,
    ! [U_1196,U_1197] :
      ( ~ c_Orderings_Oord__class_Oless(U_1196,c_Groups_Oabs__class_Oabs(U_1196,U_1197),c_Groups_Ozero__class_Ozero(U_1196))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_1196) ),
    inference(definitional_conversion,[status(esa)],[f_389_2]) ).

cnf(f_389_4,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_1196,c_Groups_Oabs__class_Oabs(U_1196,U_1197),c_Groups_Ozero__class_Ozero(U_1196))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_1196) ),
    inference(clausify,[status(thm)],[f_389_3]) ).

fof(f_390_1,plain,
    ! [V_a_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a_2))
          | V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
        & ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a)
          | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a_2)) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__abs__iff]) ).

fof(f_390_2,plain,
    ! [U_1199,U_1198] :
      ( ( ( c_Orderings_Oord__class_Oless(U_1198,c_Groups_Ozero__class_Ozero(U_1198),c_Groups_Oabs__class_Oabs(U_1198,U_1199))
          | U_1199 = c_Groups_Ozero__class_Ozero(U_1198) )
        & ( U_1199 != c_Groups_Ozero__class_Ozero(U_1198)
          | ~ c_Orderings_Oord__class_Oless(U_1198,c_Groups_Ozero__class_Ozero(U_1198),c_Groups_Oabs__class_Oabs(U_1198,U_1199)) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(U_1198) ),
    inference(variable_rename,[status(thm)],[f_390_1]) ).

fof(f_390_3,plain,
    ( ! [U_1198,U_1199] :
        ( c_Orderings_Oord__class_Oless(U_1198,c_Groups_Ozero__class_Ozero(U_1198),c_Groups_Oabs__class_Oabs(U_1198,U_1199))
        | U_1199 = c_Groups_Ozero__class_Ozero(U_1198)
        | ~ sP100(U_1198,U_1199) )
    & ! [U_1198,U_1199] :
        ( U_1199 != c_Groups_Ozero__class_Ozero(U_1198)
        | ~ c_Orderings_Oord__class_Oless(U_1198,c_Groups_Ozero__class_Ozero(U_1198),c_Groups_Oabs__class_Oabs(U_1198,U_1199))
        | ~ sP100(U_1198,U_1199) )
    & ! [U_1198,U_1199] :
        ( sP100(U_1198,U_1199)
        | ~ class_Groups_Oordered__ab__group__add__abs(U_1198) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP100])],[f_390_2]) ).

cnf(f_390_4,plain,
    ( sP100(U_1198,U_1199)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_1198) ),
    inference(clausify,[status(thm)],[f_390_3]) ).

cnf(f_390_5,plain,
    ( U_1199 != c_Groups_Ozero__class_Ozero(U_1198)
    | ~ c_Orderings_Oord__class_Oless(U_1198,c_Groups_Ozero__class_Ozero(U_1198),c_Groups_Oabs__class_Oabs(U_1198,U_1199))
    | ~ sP100(U_1198,U_1199) ),
    inference(clausify,[status(thm)],[f_390_3]) ).

cnf(f_390_6,plain,
    ( c_Orderings_Oord__class_Oless(U_1198,c_Groups_Ozero__class_Ozero(U_1198),c_Groups_Oabs__class_Oabs(U_1198,U_1199))
    | U_1199 = c_Groups_Ozero__class_Ozero(U_1198)
    | ~ sP100(U_1198,U_1199) ),
    inference(clausify,[status(thm)],[f_390_3]) ).

fof(f_391_1,plain,
    ! [V_a,T_a] :
      ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__of__pos]) ).

fof(f_391_2,plain,
    ! [U_1201,U_1200] :
      ( c_Groups_Oabs__class_Oabs(U_1200,U_1201) = U_1201
      | ~ c_Orderings_Oord__class_Oless(U_1200,c_Groups_Ozero__class_Ozero(U_1200),U_1201)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_1200) ),
    inference(variable_rename,[status(thm)],[f_391_1]) ).

fof(f_391_3,plain,
    ! [U_1201,U_1200] :
      ( c_Groups_Oabs__class_Oabs(U_1200,U_1201) = U_1201
      | ~ c_Orderings_Oord__class_Oless(U_1200,c_Groups_Ozero__class_Ozero(U_1200),U_1201)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_1200) ),
    inference(definitional_conversion,[status(esa)],[f_391_2]) ).

cnf(f_391_4,plain,
    ( c_Groups_Oabs__class_Oabs(U_1200,U_1201) = U_1201
    | ~ c_Orderings_Oord__class_Oless(U_1200,c_Groups_Ozero__class_Ozero(U_1200),U_1201)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_1200) ),
    inference(clausify,[status(thm)],[f_391_3]) ).

fof(f_392_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq]) ).

fof(f_392_2,plain,
    ! [U_1204,U_1203,U_1202] :
      ( c_Orderings_Oord__class_Oless__eq(U_1202,c_Groups_Oabs__class_Oabs(U_1202,c_Groups_Oplus__class_Oplus(U_1202,U_1203,U_1204)),c_Groups_Oplus__class_Oplus(U_1202,c_Groups_Oabs__class_Oabs(U_1202,U_1203),c_Groups_Oabs__class_Oabs(U_1202,U_1204)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_1202) ),
    inference(variable_rename,[status(thm)],[f_392_1]) ).

fof(f_392_3,plain,
    ! [U_1202,U_1203,U_1204] :
      ( c_Orderings_Oord__class_Oless__eq(U_1202,c_Groups_Oabs__class_Oabs(U_1202,c_Groups_Oplus__class_Oplus(U_1202,U_1203,U_1204)),c_Groups_Oplus__class_Oplus(U_1202,c_Groups_Oabs__class_Oabs(U_1202,U_1203),c_Groups_Oabs__class_Oabs(U_1202,U_1204)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_1202) ),
    inference(definitional_conversion,[status(esa)],[f_392_2]) ).

cnf(f_392_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1202,c_Groups_Oabs__class_Oabs(U_1202,c_Groups_Oplus__class_Oplus(U_1202,U_1203,U_1204)),c_Groups_Oplus__class_Oplus(U_1202,c_Groups_Oabs__class_Oabs(U_1202,U_1203),c_Groups_Oabs__class_Oabs(U_1202,U_1204)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_1202) ),
    inference(clausify,[status(thm)],[f_392_3]) ).

fof(f_393_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq3]) ).

fof(f_393_2,plain,
    ! [U_1207,U_1206,U_1205] :
      ( c_Orderings_Oord__class_Oless__eq(U_1205,c_Groups_Oabs__class_Oabs(U_1205,c_Groups_Ominus__class_Ominus(U_1205,c_Groups_Oabs__class_Oabs(U_1205,U_1206),c_Groups_Oabs__class_Oabs(U_1205,U_1207))),c_Groups_Oabs__class_Oabs(U_1205,c_Groups_Ominus__class_Ominus(U_1205,U_1206,U_1207)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_1205) ),
    inference(variable_rename,[status(thm)],[f_393_1]) ).

fof(f_393_3,plain,
    ! [U_1205,U_1206,U_1207] :
      ( c_Orderings_Oord__class_Oless__eq(U_1205,c_Groups_Oabs__class_Oabs(U_1205,c_Groups_Ominus__class_Ominus(U_1205,c_Groups_Oabs__class_Oabs(U_1205,U_1206),c_Groups_Oabs__class_Oabs(U_1205,U_1207))),c_Groups_Oabs__class_Oabs(U_1205,c_Groups_Ominus__class_Ominus(U_1205,U_1206,U_1207)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_1205) ),
    inference(definitional_conversion,[status(esa)],[f_393_2]) ).

cnf(f_393_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1205,c_Groups_Oabs__class_Oabs(U_1205,c_Groups_Ominus__class_Ominus(U_1205,c_Groups_Oabs__class_Oabs(U_1205,U_1206),c_Groups_Oabs__class_Oabs(U_1205,U_1207))),c_Groups_Oabs__class_Oabs(U_1205,c_Groups_Ominus__class_Ominus(U_1205,U_1206,U_1207)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_1205) ),
    inference(clausify,[status(thm)],[f_393_3]) ).

fof(f_394_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2]) ).

fof(f_394_2,plain,
    ! [U_1210,U_1209,U_1208] :
      ( c_Orderings_Oord__class_Oless__eq(U_1208,c_Groups_Ominus__class_Ominus(U_1208,c_Groups_Oabs__class_Oabs(U_1208,U_1209),c_Groups_Oabs__class_Oabs(U_1208,U_1210)),c_Groups_Oabs__class_Oabs(U_1208,c_Groups_Ominus__class_Ominus(U_1208,U_1209,U_1210)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_1208) ),
    inference(variable_rename,[status(thm)],[f_394_1]) ).

fof(f_394_3,plain,
    ! [U_1208,U_1209,U_1210] :
      ( c_Orderings_Oord__class_Oless__eq(U_1208,c_Groups_Ominus__class_Ominus(U_1208,c_Groups_Oabs__class_Oabs(U_1208,U_1209),c_Groups_Oabs__class_Oabs(U_1208,U_1210)),c_Groups_Oabs__class_Oabs(U_1208,c_Groups_Ominus__class_Ominus(U_1208,U_1209,U_1210)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_1208) ),
    inference(definitional_conversion,[status(esa)],[f_394_2]) ).

cnf(f_394_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1208,c_Groups_Ominus__class_Ominus(U_1208,c_Groups_Oabs__class_Oabs(U_1208,U_1209),c_Groups_Oabs__class_Oabs(U_1208,U_1210)),c_Groups_Oabs__class_Oabs(U_1208,c_Groups_Ominus__class_Ominus(U_1208,U_1209,U_1210)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_1208) ),
    inference(clausify,[status(thm)],[f_394_3]) ).

fof(f_395_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2__sym]) ).

fof(f_395_2,plain,
    ! [U_1213,U_1212,U_1211] :
      ( c_Orderings_Oord__class_Oless__eq(U_1211,c_Groups_Ominus__class_Ominus(U_1211,c_Groups_Oabs__class_Oabs(U_1211,U_1212),c_Groups_Oabs__class_Oabs(U_1211,U_1213)),c_Groups_Oabs__class_Oabs(U_1211,c_Groups_Ominus__class_Ominus(U_1211,U_1213,U_1212)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_1211) ),
    inference(variable_rename,[status(thm)],[f_395_1]) ).

fof(f_395_3,plain,
    ! [U_1211,U_1212,U_1213] :
      ( c_Orderings_Oord__class_Oless__eq(U_1211,c_Groups_Ominus__class_Ominus(U_1211,c_Groups_Oabs__class_Oabs(U_1211,U_1212),c_Groups_Oabs__class_Oabs(U_1211,U_1213)),c_Groups_Oabs__class_Oabs(U_1211,c_Groups_Ominus__class_Ominus(U_1211,U_1213,U_1212)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_1211) ),
    inference(definitional_conversion,[status(esa)],[f_395_2]) ).

cnf(f_395_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1211,c_Groups_Ominus__class_Ominus(U_1211,c_Groups_Oabs__class_Oabs(U_1211,U_1212),c_Groups_Oabs__class_Oabs(U_1211,U_1213)),c_Groups_Oabs__class_Oabs(U_1211,c_Groups_Ominus__class_Ominus(U_1211,U_1213,U_1212)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_1211) ),
    inference(clausify,[status(thm)],[f_395_3]) ).

fof(f_396_1,plain,
    ! [V_ra_2,V_a_2,V_x_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x_2,V_a_2)),V_ra_2)
          | ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ra_2))
          | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ra_2),V_x_2) )
        & ( ( c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ra_2))
            & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ra_2),V_x_2) )
          | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x_2,V_a_2)),V_ra_2) ) )
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__diff__less__iff]) ).

fof(f_396_2,plain,
    ! [U_1217,U_1216,U_1215,U_1214] :
      ( ( ( c_Orderings_Oord__class_Oless(U_1214,c_Groups_Oabs__class_Oabs(U_1214,c_Groups_Ominus__class_Ominus(U_1214,U_1215,U_1216)),U_1217)
          | ~ c_Orderings_Oord__class_Oless(U_1214,U_1215,c_Groups_Oplus__class_Oplus(U_1214,U_1216,U_1217))
          | ~ c_Orderings_Oord__class_Oless(U_1214,c_Groups_Ominus__class_Ominus(U_1214,U_1216,U_1217),U_1215) )
        & ( ( c_Orderings_Oord__class_Oless(U_1214,U_1215,c_Groups_Oplus__class_Oplus(U_1214,U_1216,U_1217))
            & c_Orderings_Oord__class_Oless(U_1214,c_Groups_Ominus__class_Ominus(U_1214,U_1216,U_1217),U_1215) )
          | ~ c_Orderings_Oord__class_Oless(U_1214,c_Groups_Oabs__class_Oabs(U_1214,c_Groups_Ominus__class_Ominus(U_1214,U_1215,U_1216)),U_1217) ) )
      | ~ class_Rings_Olinordered__idom(U_1214) ),
    inference(variable_rename,[status(thm)],[f_396_1]) ).

fof(f_396_3,plain,
    ( ! [U_1215,U_1216,U_1214,U_1217] :
        ( c_Orderings_Oord__class_Oless(U_1214,U_1215,c_Groups_Oplus__class_Oplus(U_1214,U_1216,U_1217))
        | ~ sP101(U_1215,U_1216,U_1214,U_1217) )
    & ! [U_1215,U_1216,U_1214,U_1217] :
        ( c_Orderings_Oord__class_Oless(U_1214,c_Groups_Ominus__class_Ominus(U_1214,U_1216,U_1217),U_1215)
        | ~ sP101(U_1215,U_1216,U_1214,U_1217) )
    & ! [U_1215,U_1216,U_1214,U_1217] :
        ( c_Orderings_Oord__class_Oless(U_1214,c_Groups_Oabs__class_Oabs(U_1214,c_Groups_Ominus__class_Ominus(U_1214,U_1215,U_1216)),U_1217)
        | ~ c_Orderings_Oord__class_Oless(U_1214,U_1215,c_Groups_Oplus__class_Oplus(U_1214,U_1216,U_1217))
        | ~ c_Orderings_Oord__class_Oless(U_1214,c_Groups_Ominus__class_Ominus(U_1214,U_1216,U_1217),U_1215)
        | ~ sP102(U_1215,U_1216,U_1214,U_1217) )
    & ! [U_1215,U_1216,U_1214,U_1217] :
        ( sP101(U_1215,U_1216,U_1214,U_1217)
        | ~ c_Orderings_Oord__class_Oless(U_1214,c_Groups_Oabs__class_Oabs(U_1214,c_Groups_Ominus__class_Ominus(U_1214,U_1215,U_1216)),U_1217)
        | ~ sP102(U_1215,U_1216,U_1214,U_1217) )
    & ! [U_1215,U_1216,U_1214,U_1217] :
        ( sP102(U_1215,U_1216,U_1214,U_1217)
        | ~ class_Rings_Olinordered__idom(U_1214) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP101,sP102])],[f_396_2]) ).

cnf(f_396_4,plain,
    ( sP102(U_1215,U_1216,U_1214,U_1217)
    | ~ class_Rings_Olinordered__idom(U_1214) ),
    inference(clausify,[status(thm)],[f_396_3]) ).

cnf(f_396_5,plain,
    ( sP101(U_1215,U_1216,U_1214,U_1217)
    | ~ c_Orderings_Oord__class_Oless(U_1214,c_Groups_Oabs__class_Oabs(U_1214,c_Groups_Ominus__class_Ominus(U_1214,U_1215,U_1216)),U_1217)
    | ~ sP102(U_1215,U_1216,U_1214,U_1217) ),
    inference(clausify,[status(thm)],[f_396_3]) ).

cnf(f_396_6,plain,
    ( c_Orderings_Oord__class_Oless(U_1214,c_Groups_Oabs__class_Oabs(U_1214,c_Groups_Ominus__class_Ominus(U_1214,U_1215,U_1216)),U_1217)
    | ~ c_Orderings_Oord__class_Oless(U_1214,U_1215,c_Groups_Oplus__class_Oplus(U_1214,U_1216,U_1217))
    | ~ c_Orderings_Oord__class_Oless(U_1214,c_Groups_Ominus__class_Ominus(U_1214,U_1216,U_1217),U_1215)
    | ~ sP102(U_1215,U_1216,U_1214,U_1217) ),
    inference(clausify,[status(thm)],[f_396_3]) ).

cnf(f_396_7,plain,
    ( c_Orderings_Oord__class_Oless(U_1214,c_Groups_Ominus__class_Ominus(U_1214,U_1216,U_1217),U_1215)
    | ~ sP101(U_1215,U_1216,U_1214,U_1217) ),
    inference(clausify,[status(thm)],[f_396_3]) ).

cnf(f_396_8,plain,
    ( c_Orderings_Oord__class_Oless(U_1214,U_1215,c_Groups_Oplus__class_Oplus(U_1214,U_1216,U_1217))
    | ~ sP101(U_1215,U_1216,U_1214,U_1217) ),
    inference(clausify,[status(thm)],[f_396_3]) ).

fof(f_397_1,plain,
    ! [V_wa_2,V_v_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
          | c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Int_Onumber__class_Onumber__of(T_a,V_v_2)) )
        & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Int_Onumber__class_Onumber__of(T_a,V_v_2))
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) ) )
      | ~ class_Orderings_Olinorder(T_a)
      | ~ class_Int_Onumber(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__number__of__eq__not__less]) ).

fof(f_397_2,plain,
    ! [U_1220,U_1219,U_1218] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_1218,c_Int_Onumber__class_Onumber__of(U_1218,U_1219),c_Int_Onumber__class_Onumber__of(U_1218,U_1220))
          | c_Orderings_Oord__class_Oless(U_1218,c_Int_Onumber__class_Onumber__of(U_1218,U_1220),c_Int_Onumber__class_Onumber__of(U_1218,U_1219)) )
        & ( ~ c_Orderings_Oord__class_Oless(U_1218,c_Int_Onumber__class_Onumber__of(U_1218,U_1220),c_Int_Onumber__class_Onumber__of(U_1218,U_1219))
          | ~ c_Orderings_Oord__class_Oless__eq(U_1218,c_Int_Onumber__class_Onumber__of(U_1218,U_1219),c_Int_Onumber__class_Onumber__of(U_1218,U_1220)) ) )
      | ~ class_Orderings_Olinorder(U_1218)
      | ~ class_Int_Onumber(U_1218) ),
    inference(variable_rename,[status(thm)],[f_397_1]) ).

fof(f_397_3,plain,
    ( ! [U_1220,U_1218,U_1219] :
        ( c_Orderings_Oord__class_Oless__eq(U_1218,c_Int_Onumber__class_Onumber__of(U_1218,U_1219),c_Int_Onumber__class_Onumber__of(U_1218,U_1220))
        | c_Orderings_Oord__class_Oless(U_1218,c_Int_Onumber__class_Onumber__of(U_1218,U_1220),c_Int_Onumber__class_Onumber__of(U_1218,U_1219))
        | ~ sP103(U_1220,U_1218,U_1219) )
    & ! [U_1220,U_1218,U_1219] :
        ( ~ c_Orderings_Oord__class_Oless(U_1218,c_Int_Onumber__class_Onumber__of(U_1218,U_1220),c_Int_Onumber__class_Onumber__of(U_1218,U_1219))
        | ~ c_Orderings_Oord__class_Oless__eq(U_1218,c_Int_Onumber__class_Onumber__of(U_1218,U_1219),c_Int_Onumber__class_Onumber__of(U_1218,U_1220))
        | ~ sP103(U_1220,U_1218,U_1219) )
    & ! [U_1220,U_1218,U_1219] :
        ( sP103(U_1220,U_1218,U_1219)
        | ~ class_Orderings_Olinorder(U_1218)
        | ~ class_Int_Onumber(U_1218) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP103])],[f_397_2]) ).

cnf(f_397_4,plain,
    ( sP103(U_1220,U_1218,U_1219)
    | ~ class_Orderings_Olinorder(U_1218)
    | ~ class_Int_Onumber(U_1218) ),
    inference(clausify,[status(thm)],[f_397_3]) ).

cnf(f_397_5,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_1218,c_Int_Onumber__class_Onumber__of(U_1218,U_1220),c_Int_Onumber__class_Onumber__of(U_1218,U_1219))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1218,c_Int_Onumber__class_Onumber__of(U_1218,U_1219),c_Int_Onumber__class_Onumber__of(U_1218,U_1220))
    | ~ sP103(U_1220,U_1218,U_1219) ),
    inference(clausify,[status(thm)],[f_397_3]) ).

cnf(f_397_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1218,c_Int_Onumber__class_Onumber__of(U_1218,U_1219),c_Int_Onumber__class_Onumber__of(U_1218,U_1220))
    | c_Orderings_Oord__class_Oless(U_1218,c_Int_Onumber__class_Onumber__of(U_1218,U_1220),c_Int_Onumber__class_Onumber__of(U_1218,U_1219))
    | ~ sP103(U_1220,U_1218,U_1219) ),
    inference(clausify,[status(thm)],[f_397_3]) ).

fof(f_398_1,plain,
    ! [V_c,V_w,V_v,T_a] :
      ( c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_c)) = c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)),V_c)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__number__of__diff1]) ).

fof(f_398_2,plain,
    ! [U_1224,U_1223,U_1222,U_1221] :
      ( c_Groups_Oplus__class_Oplus(U_1221,c_Int_Onumber__class_Onumber__of(U_1221,U_1222),c_Groups_Ominus__class_Ominus(U_1221,c_Int_Onumber__class_Onumber__of(U_1221,U_1223),U_1224)) = c_Groups_Ominus__class_Ominus(U_1221,c_Int_Onumber__class_Onumber__of(U_1221,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1222,U_1223)),U_1224)
      | ~ class_Int_Onumber__ring(U_1221) ),
    inference(variable_rename,[status(thm)],[f_398_1]) ).

fof(f_398_3,plain,
    ! [U_1224,U_1222,U_1221,U_1223] :
      ( c_Groups_Oplus__class_Oplus(U_1221,c_Int_Onumber__class_Onumber__of(U_1221,U_1222),c_Groups_Ominus__class_Ominus(U_1221,c_Int_Onumber__class_Onumber__of(U_1221,U_1223),U_1224)) = c_Groups_Ominus__class_Ominus(U_1221,c_Int_Onumber__class_Onumber__of(U_1221,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1222,U_1223)),U_1224)
      | ~ class_Int_Onumber__ring(U_1221) ),
    inference(definitional_conversion,[status(esa)],[f_398_2]) ).

cnf(f_398_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_1221,c_Int_Onumber__class_Onumber__of(U_1221,U_1222),c_Groups_Ominus__class_Ominus(U_1221,c_Int_Onumber__class_Onumber__of(U_1221,U_1223),U_1224)) = c_Groups_Ominus__class_Ominus(U_1221,c_Int_Onumber__class_Onumber__of(U_1221,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1222,U_1223)),U_1224)
    | ~ class_Int_Onumber__ring(U_1221) ),
    inference(clausify,[status(thm)],[f_398_3]) ).

fof(f_399_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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a)) ),
    inference(fof_nnf,[status(thm)],[fact_natceiling__le]) ).

fof(f_399_2,plain,
    ! [U_1226,U_1225] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1225),U_1226)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1225,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1226)) ),
    inference(variable_rename,[status(thm)],[f_399_1]) ).

fof(f_399_3,plain,
    ! [U_1226,U_1225] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1225),U_1226)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1225,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1226)) ),
    inference(definitional_conversion,[status(esa)],[f_399_2]) ).

cnf(f_399_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1225),U_1226)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1225,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1226)) ),
    inference(clausify,[status(thm)],[f_399_3]) ).

fof(f_400_1,plain,
    ! [V_a_2,V_x_2] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_2)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a_2)) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a_2))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_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_400_2,plain,
    ! [U_1228,U_1227] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1227),U_1228)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1227,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1228)) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1227,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1228))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1227),U_1228) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1227) ),
    inference(variable_rename,[status(thm)],[f_400_1]) ).

fof(f_400_3,plain,
    ( ! [U_1228,U_1227] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1227),U_1228)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1227,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1228))
        | ~ sP104(U_1228,U_1227) )
    & ! [U_1228,U_1227] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1227,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1228))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1227),U_1228)
        | ~ sP104(U_1228,U_1227) )
    & ! [U_1228,U_1227] :
        ( sP104(U_1228,U_1227)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1227) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP104])],[f_400_2]) ).

cnf(f_400_4,plain,
    ( sP104(U_1228,U_1227)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1227) ),
    inference(clausify,[status(thm)],[f_400_3]) ).

cnf(f_400_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1227,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1228))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1227),U_1228)
    | ~ sP104(U_1228,U_1227) ),
    inference(clausify,[status(thm)],[f_400_3]) ).

cnf(f_400_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1227),U_1228)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1227,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1228))
    | ~ sP104(U_1228,U_1227) ),
    inference(clausify,[status(thm)],[f_400_3]) ).

fof(f_401_1,plain,
    ! [V_x,V_a] :
      ( c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,hAPP(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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a),V_x) ),
    inference(fof_nnf,[status(thm)],[fact_natceiling__subtract]) ).

fof(f_401_2,plain,
    ! [U_1230,U_1229] :
      ( c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1230,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1229))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(U_1230),U_1229)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1229),U_1230) ),
    inference(variable_rename,[status(thm)],[f_401_1]) ).

fof(f_401_3,plain,
    ! [U_1230,U_1229] :
      ( c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1230,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1229))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(U_1230),U_1229)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1229),U_1230) ),
    inference(definitional_conversion,[status(esa)],[f_401_2]) ).

cnf(f_401_4,plain,
    ( c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1230,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1229))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(U_1230),U_1229)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1229),U_1230) ),
    inference(clausify,[status(thm)],[f_401_3]) ).

fof(f_402_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq4]) ).

fof(f_402_2,plain,
    ! [U_1233,U_1232,U_1231] :
      ( c_Orderings_Oord__class_Oless__eq(U_1231,c_Groups_Oabs__class_Oabs(U_1231,c_Groups_Ominus__class_Ominus(U_1231,U_1232,U_1233)),c_Groups_Oplus__class_Oplus(U_1231,c_Groups_Oabs__class_Oabs(U_1231,U_1232),c_Groups_Oabs__class_Oabs(U_1231,U_1233)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_1231) ),
    inference(variable_rename,[status(thm)],[f_402_1]) ).

fof(f_402_3,plain,
    ! [U_1231,U_1232,U_1233] :
      ( c_Orderings_Oord__class_Oless__eq(U_1231,c_Groups_Oabs__class_Oabs(U_1231,c_Groups_Ominus__class_Ominus(U_1231,U_1232,U_1233)),c_Groups_Oplus__class_Oplus(U_1231,c_Groups_Oabs__class_Oabs(U_1231,U_1232),c_Groups_Oabs__class_Oabs(U_1231,U_1233)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_1231) ),
    inference(definitional_conversion,[status(esa)],[f_402_2]) ).

cnf(f_402_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1231,c_Groups_Oabs__class_Oabs(U_1231,c_Groups_Ominus__class_Ominus(U_1231,U_1232,U_1233)),c_Groups_Oplus__class_Oplus(U_1231,c_Groups_Oabs__class_Oabs(U_1231,U_1232),c_Groups_Oabs__class_Oabs(U_1231,U_1233)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_1231) ),
    inference(clausify,[status(thm)],[f_402_3]) ).

fof(f_403_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(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(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d))))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__diff__triangle__ineq]) ).

fof(f_403_2,plain,
    ! [U_1238,U_1237,U_1236,U_1235,U_1234] :
      ( c_Orderings_Oord__class_Oless__eq(U_1234,c_Groups_Oabs__class_Oabs(U_1234,c_Groups_Ominus__class_Ominus(U_1234,c_Groups_Oplus__class_Oplus(U_1234,U_1235,U_1236),c_Groups_Oplus__class_Oplus(U_1234,U_1237,U_1238))),c_Groups_Oplus__class_Oplus(U_1234,c_Groups_Oabs__class_Oabs(U_1234,c_Groups_Ominus__class_Ominus(U_1234,U_1235,U_1237)),c_Groups_Oabs__class_Oabs(U_1234,c_Groups_Ominus__class_Ominus(U_1234,U_1236,U_1238))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_1234) ),
    inference(variable_rename,[status(thm)],[f_403_1]) ).

fof(f_403_3,plain,
    ! [U_1234,U_1235,U_1236,U_1237,U_1238] :
      ( c_Orderings_Oord__class_Oless__eq(U_1234,c_Groups_Oabs__class_Oabs(U_1234,c_Groups_Ominus__class_Ominus(U_1234,c_Groups_Oplus__class_Oplus(U_1234,U_1235,U_1236),c_Groups_Oplus__class_Oplus(U_1234,U_1237,U_1238))),c_Groups_Oplus__class_Oplus(U_1234,c_Groups_Oabs__class_Oabs(U_1234,c_Groups_Ominus__class_Ominus(U_1234,U_1235,U_1237)),c_Groups_Oabs__class_Oabs(U_1234,c_Groups_Ominus__class_Ominus(U_1234,U_1236,U_1238))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_1234) ),
    inference(definitional_conversion,[status(esa)],[f_403_2]) ).

cnf(f_403_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1234,c_Groups_Oabs__class_Oabs(U_1234,c_Groups_Ominus__class_Ominus(U_1234,c_Groups_Oplus__class_Oplus(U_1234,U_1235,U_1236),c_Groups_Oplus__class_Oplus(U_1234,U_1237,U_1238))),c_Groups_Oplus__class_Oplus(U_1234,c_Groups_Oabs__class_Oabs(U_1234,c_Groups_Ominus__class_Ominus(U_1234,U_1235,U_1237)),c_Groups_Oabs__class_Oabs(U_1234,c_Groups_Ominus__class_Ominus(U_1234,U_1236,U_1238))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_1234) ),
    inference(clausify,[status(thm)],[f_403_3]) ).

fof(f_404_1,plain,
    ! [V_x] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x),
    inference(fof_nnf,[status(thm)],[fact_abs__add__one__not__less__self]) ).

fof(f_404_2,plain,
    ! [U_1239] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1239),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_1239),
    inference(variable_rename,[status(thm)],[f_404_1]) ).

fof(f_404_3,plain,
    ! [U_1239] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1239),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_1239),
    inference(definitional_conversion,[status(esa)],[f_404_2]) ).

cnf(f_404_4,plain,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1239),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_1239),
    inference(clausify,[status(thm)],[f_404_3]) ).

fof(f_405_1,plain,
    ! [V_x] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x))),
    inference(fof_nnf,[status(thm)],[fact_abs__add__one__gt__zero]) ).

fof(f_405_2,plain,
    ! [U_1240] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1240))),
    inference(variable_rename,[status(thm)],[f_405_1]) ).

fof(f_405_3,plain,
    ! [U_1240] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1240))),
    inference(definitional_conversion,[status(esa)],[f_405_2]) ).

cnf(f_405_4,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,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1240))),
    inference(clausify,[status(thm)],[f_405_3]) ).

fof(f_406_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_406_2,plain,
    ! [U_1241] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1241),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1241,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1241,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1241),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_406_1]) ).

fof(f_406_3,plain,
    ( ! [U_1243] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1243),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1243,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
    & ! [U_1242] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1242,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1242),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_406_2]) ).

fof(f_406_4,plain,
    ( ! [U_1243] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1243),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1243,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
    & ! [U_1242] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1242,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1242),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    inference(definitional_conversion,[status(esa)],[f_406_3]) ).

cnf(f_406_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1242,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1242),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_406_4]) ).

cnf(f_406_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1243),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1243,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
    inference(clausify,[status(thm)],[f_406_4]) ).

fof(f_407_1,plain,
    ! [V_a,V_x] :
      ( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,hAPP(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_407_2,plain,
    ! [U_1245,U_1244] :
      ( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1244,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1245))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(U_1244),U_1245)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1244) ),
    inference(variable_rename,[status(thm)],[f_407_1]) ).

fof(f_407_3,plain,
    ! [U_1244,U_1245] :
      ( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1244,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1245))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(U_1244),U_1245)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1244) ),
    inference(definitional_conversion,[status(esa)],[f_407_2]) ).

cnf(f_407_4,plain,
    ( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1244,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1245))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(U_1244),U_1245)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1244) ),
    inference(clausify,[status(thm)],[f_407_3]) ).

fof(f_408_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_408_2,plain,
    ! [U_1246] :
      ( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1246,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(U_1246),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_1246) ),
    inference(variable_rename,[status(thm)],[f_408_1]) ).

fof(f_408_3,plain,
    ! [U_1246] :
      ( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1246,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(U_1246),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_1246) ),
    inference(definitional_conversion,[status(esa)],[f_408_2]) ).

cnf(f_408_4,plain,
    ( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1246,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(U_1246),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_1246) ),
    inference(clausify,[status(thm)],[f_408_3]) ).

fof(f_409_1,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),v_r),
    inference(fof_nnf,[status(thm)],[fact_wr]) ).

fof(f_409_2,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),v_r),
    inference(definitional_conversion,[status(esa)],[f_409_1]) ).

cnf(f_409_3,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),v_r),
    inference(clausify,[status(thm)],[f_409_2]) ).

fof(f_410_1,plain,
    ! [V_r] :
      ( ? [B_n] :
          ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,hAPP(c_RealDef_Oreal(tc_Nat_Onat),B_n))
          & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(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_410_2,plain,
    ! [U_1248] :
      ( ? [U_1247] :
          ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1248,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1247))
          & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1247,c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_1248) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1248) ),
    inference(variable_rename,[status(thm)],[f_410_1]) ).

fof(f_410_3,plain,
    ! [U_1248] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1248,hAPP(c_RealDef_Oreal(tc_Nat_Onat),sK32(U_1248)))
        & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,sK32(U_1248),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_1248) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1248) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_1247,sK32(U_1248))],[f_410_2]) ).

fof(f_410_4,plain,
    ( ! [U_1248] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1248,hAPP(c_RealDef_Oreal(tc_Nat_Onat),sK32(U_1248)))
        | ~ sP105(U_1248) )
    & ! [U_1248] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,sK32(U_1248),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_1248)
        | ~ sP105(U_1248) )
    & ! [U_1248] :
        ( sP105(U_1248)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1248) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP105])],[f_410_3]) ).

cnf(f_410_5,plain,
    ( sP105(U_1248)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1248) ),
    inference(clausify,[status(thm)],[f_410_4]) ).

cnf(f_410_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,sK32(U_1248),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_1248)
    | ~ sP105(U_1248) ),
    inference(clausify,[status(thm)],[f_410_4]) ).

cnf(f_410_7,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1248,hAPP(c_RealDef_Oreal(tc_Nat_Onat),sK32(U_1248)))
    | ~ sP105(U_1248) ),
    inference(clausify,[status(thm)],[f_410_4]) ).

fof(f_411_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_411_2,plain,
    ! [U_1249] :
      ( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1249,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_1249),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_1249) ),
    inference(variable_rename,[status(thm)],[f_411_1]) ).

fof(f_411_3,plain,
    ! [U_1249] :
      ( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1249,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_1249),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_1249) ),
    inference(definitional_conversion,[status(esa)],[f_411_2]) ).

cnf(f_411_4,plain,
    ( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1249,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_1249),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_1249) ),
    inference(clausify,[status(thm)],[f_411_3]) ).

fof(f_412_1,plain,
    ! [V_b,V_x,V_a] :
      ( ? [B_d] :
          ( ! [B_y] :
              ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B_y,V_b)
                & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_a,B_y) )
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,B_y)),B_d) )
          & 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,V_x,V_b)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,V_x) ),
    inference(fof_nnf,[status(thm)],[fact_lemma__interval]) ).

fof(f_412_2,plain,
    ! [U_1254,U_1253,U_1252] :
      ( ? [U_1251] :
          ( ! [U_1250] :
              ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1250,U_1254)
                & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1252,U_1250) )
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1253,U_1250)),U_1251) )
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1251) )
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1253,U_1254)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1252,U_1253) ),
    inference(variable_rename,[status(thm)],[f_412_1]) ).

fof(f_412_3,plain,
    ! [U_1254,U_1253,U_1252] :
      ( ( ! [U_1250] :
            ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1250,U_1254)
              & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1252,U_1250) )
            | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1253,U_1250)),sK33(U_1254,U_1253,U_1252)) )
        & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK33(U_1254,U_1253,U_1252)) )
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1253,U_1254)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1252,U_1253) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_1251,sK33(U_1254,U_1253,U_1252))],[f_412_2]) ).

fof(f_412_4,plain,
    ( ! [U_1250,U_1252,U_1254] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1250,U_1254)
        | ~ sP106(U_1250,U_1252,U_1254) )
    & ! [U_1250,U_1252,U_1254] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1252,U_1250)
        | ~ sP106(U_1250,U_1252,U_1254) )
    & ! [U_1250,U_1252,U_1253,U_1254] :
        ( sP106(U_1250,U_1252,U_1254)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1253,U_1250)),sK33(U_1254,U_1253,U_1252))
        | ~ sP107(U_1250,U_1252,U_1253,U_1254) )
    & ! [U_1250,U_1252,U_1253,U_1254] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK33(U_1254,U_1253,U_1252))
        | ~ sP107(U_1250,U_1252,U_1253,U_1254) )
    & ! [U_1250,U_1252,U_1253,U_1254] :
        ( sP107(U_1250,U_1252,U_1253,U_1254)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1253,U_1254)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1252,U_1253) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP106,sP107])],[f_412_3]) ).

cnf(f_412_5,plain,
    ( sP107(U_1250,U_1252,U_1253,U_1254)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1253,U_1254)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1252,U_1253) ),
    inference(clausify,[status(thm)],[f_412_4]) ).

cnf(f_412_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK33(U_1254,U_1253,U_1252))
    | ~ sP107(U_1250,U_1252,U_1253,U_1254) ),
    inference(clausify,[status(thm)],[f_412_4]) ).

cnf(f_412_7,plain,
    ( sP106(U_1250,U_1252,U_1254)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1253,U_1250)),sK33(U_1254,U_1253,U_1252))
    | ~ sP107(U_1250,U_1252,U_1253,U_1254) ),
    inference(clausify,[status(thm)],[f_412_4]) ).

cnf(f_412_8,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1252,U_1250)
    | ~ sP106(U_1250,U_1252,U_1254) ),
    inference(clausify,[status(thm)],[f_412_4]) ).

cnf(f_412_9,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1250,U_1254)
    | ~ sP106(U_1250,U_1252,U_1254) ),
    inference(clausify,[status(thm)],[f_412_4]) ).

fof(f_413_1,plain,
    ! [V_r] :
      ( ? [B_n] :
          ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(B_n)))
          & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),B_n),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__Archimedean6a]) ).

fof(f_413_2,plain,
    ! [U_1256] :
      ( ? [U_1255] :
          ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1256,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_1255)))
          & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1255),U_1256) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1256) ),
    inference(variable_rename,[status(thm)],[f_413_1]) ).

fof(f_413_3,plain,
    ! [U_1256] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1256,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(sK34(U_1256))))
        & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),sK34(U_1256)),U_1256) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1256) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_1255,sK34(U_1256))],[f_413_2]) ).

fof(f_413_4,plain,
    ( ! [U_1256] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1256,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(sK34(U_1256))))
        | ~ sP108(U_1256) )
    & ! [U_1256] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),sK34(U_1256)),U_1256)
        | ~ sP108(U_1256) )
    & ! [U_1256] :
        ( sP108(U_1256)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1256) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP108])],[f_413_3]) ).

cnf(f_413_5,plain,
    ( sP108(U_1256)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1256) ),
    inference(clausify,[status(thm)],[f_413_4]) ).

cnf(f_413_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),sK34(U_1256)),U_1256)
    | ~ sP108(U_1256) ),
    inference(clausify,[status(thm)],[f_413_4]) ).

cnf(f_413_7,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1256,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(sK34(U_1256))))
    | ~ sP108(U_1256) ),
    inference(clausify,[status(thm)],[f_413_4]) ).

fof(f_414_1,plain,
    ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_g____(B_n)),v_r),
    inference(fof_nnf,[status(thm)],[fact_g_I1_J]) ).

fof(f_414_2,plain,
    ! [U_1257] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_g____(U_1257)),v_r),
    inference(variable_rename,[status(thm)],[f_414_1]) ).

fof(f_414_3,plain,
    ! [U_1257] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_g____(U_1257)),v_r),
    inference(definitional_conversion,[status(esa)],[f_414_2]) ).

cnf(f_414_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_g____(U_1257)),v_r),
    inference(clausify,[status(thm)],[f_414_3]) ).

fof(f_415_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_415_2,plain,
    ! [U_1258] : 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_1258),U_1258) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_415_1]) ).

fof(f_415_3,plain,
    ! [U_1258] : 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_1258),U_1258) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_415_2]) ).

cnf(f_415_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_1258),U_1258) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_415_3]) ).

fof(f_416_1,plain,
    ! [V_za_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_za_2)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_za_2) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_za_2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_za_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_int__one__le__iff__zero__less]) ).

fof(f_416_2,plain,
    ! [U_1259] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_1259)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1259) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1259)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_1259) ) ),
    inference(variable_rename,[status(thm)],[f_416_1]) ).

fof(f_416_3,plain,
    ( ! [U_1261] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_1261)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1261) )
    & ! [U_1260] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1260)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_1260) ) ),
    inference(miniscope,[status(thm)],[f_416_2]) ).

fof(f_416_4,plain,
    ( ! [U_1261] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_1261)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1261) )
    & ! [U_1260] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1260)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_1260) ) ),
    inference(definitional_conversion,[status(esa)],[f_416_3]) ).

cnf(f_416_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1260)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_1260) ),
    inference(clausify,[status(thm)],[f_416_4]) ).

cnf(f_416_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_1261)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1261) ),
    inference(clausify,[status(thm)],[f_416_4]) ).

fof(f_417_1,plain,
    ! [V_za_2,V_wa_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_wa_2,V_za_2) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_wa_2,V_za_2)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zle__add1__eq__le]) ).

fof(f_417_2,plain,
    ! [U_1263,U_1262] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1262,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1263,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1262,U_1263) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1262,U_1263)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1262,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1263,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_417_1]) ).

fof(f_417_3,plain,
    ( ! [U_1267,U_1265] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1265,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1267,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1265,U_1267) )
    & ! [U_1266,U_1264] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1264,U_1266)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1264,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1266,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_417_2]) ).

fof(f_417_4,plain,
    ( ! [U_1267,U_1265] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1265,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1267,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1265,U_1267) )
    & ! [U_1264,U_1266] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1264,U_1266)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1264,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1266,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa)],[f_417_3]) ).

cnf(f_417_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1264,U_1266)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1264,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1266,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_417_4]) ).

cnf(f_417_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1265,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1267,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1265,U_1267) ),
    inference(clausify,[status(thm)],[f_417_4]) ).

fof(f_418_1,plain,
    ! [V_za_2,V_wa_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_wa_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_wa_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zle__diff1__eq]) ).

fof(f_418_2,plain,
    ! [U_1269,U_1268] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1268,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1269,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1268,U_1269) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1268,U_1269)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1268,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1269,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_418_1]) ).

fof(f_418_3,plain,
    ( ! [U_1273,U_1271] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1271,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1273,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1271,U_1273) )
    & ! [U_1272,U_1270] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1270,U_1272)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1270,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1272,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_418_2]) ).

fof(f_418_4,plain,
    ( ! [U_1273,U_1271] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1271,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1273,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1271,U_1273) )
    & ! [U_1270,U_1272] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1270,U_1272)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1270,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1272,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa)],[f_418_3]) ).

cnf(f_418_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1270,U_1272)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1270,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1272,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_418_4]) ).

cnf(f_418_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1271,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1273,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1271,U_1273) ),
    inference(clausify,[status(thm)],[f_418_4]) ).

fof(f_419_1,plain,
    ! [V_za_2,V_wa_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ( V_wa_2 != V_za_2
          & ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2) ) )
      & ( V_wa_2 = V_za_2
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zless__add1__eq]) ).

fof(f_419_2,plain,
    ! [U_1275,U_1274] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1274,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1275,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ( U_1274 != U_1275
          & ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1274,U_1275) ) )
      & ( U_1274 = U_1275
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1274,U_1275)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1274,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1275,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_419_1]) ).

fof(f_419_3,plain,
    ( ! [U_1279,U_1277] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1277,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1279,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ( U_1277 != U_1279
          & ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1277,U_1279) ) )
    & ! [U_1278,U_1276] :
        ( U_1276 = U_1278
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1276,U_1278)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1276,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1278,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_419_2]) ).

fof(f_419_4,plain,
    ( ! [U_1279,U_1277] :
        ( U_1277 != U_1279
        | ~ sP109(U_1279,U_1277) )
    & ! [U_1279,U_1277] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1277,U_1279)
        | ~ sP109(U_1279,U_1277) )
    & ! [U_1279,U_1277] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1277,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1279,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | sP109(U_1279,U_1277) )
    & ! [U_1276,U_1278] :
        ( U_1276 = U_1278
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1276,U_1278)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1276,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1278,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP109])],[f_419_3]) ).

cnf(f_419_5,plain,
    ( U_1276 = U_1278
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1276,U_1278)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1276,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1278,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_419_4]) ).

cnf(f_419_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1277,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1279,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | sP109(U_1279,U_1277) ),
    inference(clausify,[status(thm)],[f_419_4]) ).

cnf(f_419_7,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1277,U_1279)
    | ~ sP109(U_1279,U_1277) ),
    inference(clausify,[status(thm)],[f_419_4]) ).

cnf(f_419_8,plain,
    ( U_1277 != U_1279
    | ~ sP109(U_1279,U_1277) ),
    inference(clausify,[status(thm)],[f_419_4]) ).

fof(f_420_1,plain,
    ! [V_za_2,V_wa_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_wa_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_za_2)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_wa_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_za_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_add1__zle__eq]) ).

fof(f_420_2,plain,
    ! [U_1281,U_1280] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1280,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1281)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1280,U_1281) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1280,U_1281)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1280,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1281) ) ),
    inference(variable_rename,[status(thm)],[f_420_1]) ).

fof(f_420_3,plain,
    ( ! [U_1285,U_1283] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1283,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1285)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1283,U_1285) )
    & ! [U_1284,U_1282] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1282,U_1284)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1282,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1284) ) ),
    inference(miniscope,[status(thm)],[f_420_2]) ).

fof(f_420_4,plain,
    ( ! [U_1285,U_1283] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1283,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1285)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1283,U_1285) )
    & ! [U_1282,U_1284] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1282,U_1284)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1282,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1284) ) ),
    inference(definitional_conversion,[status(esa)],[f_420_3]) ).

cnf(f_420_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1282,U_1284)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1282,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1284) ),
    inference(clausify,[status(thm)],[f_420_4]) ).

cnf(f_420_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1283,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1285)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1283,U_1285) ),
    inference(clausify,[status(thm)],[f_420_4]) ).

fof(f_421_1,plain,
    ! [V_za_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_za_2),V_za_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_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_za_2),V_za_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    inference(fof_nnf,[status(thm)],[fact_odd__less__0]) ).

fof(f_421_2,plain,
    ! [U_1286] :
      ( ( 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_1286),U_1286),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1286,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1286,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_1286),U_1286),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    inference(variable_rename,[status(thm)],[f_421_1]) ).

fof(f_421_3,plain,
    ( ! [U_1288] :
        ( 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_1288),U_1288),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1288,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    & ! [U_1287] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1287,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_1287),U_1287),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    inference(miniscope,[status(thm)],[f_421_2]) ).

fof(f_421_4,plain,
    ( ! [U_1288] :
        ( 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_1288),U_1288),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1288,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    & ! [U_1287] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1287,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_1287),U_1287),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    inference(definitional_conversion,[status(esa)],[f_421_3]) ).

cnf(f_421_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1287,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_1287),U_1287),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(clausify,[status(thm)],[f_421_4]) ).

cnf(f_421_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_1288),U_1288),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1288,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(clausify,[status(thm)],[f_421_4]) ).

fof(f_422_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_422_2,plain,
    ! [U_1289] :
      ( 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_1289))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1289) ),
    inference(variable_rename,[status(thm)],[f_422_1]) ).

fof(f_422_3,plain,
    ! [U_1289] :
      ( 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_1289))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1289) ),
    inference(definitional_conversion,[status(esa)],[f_422_2]) ).

cnf(f_422_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_1289))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1289) ),
    inference(clausify,[status(thm)],[f_422_3]) ).

fof(f_423_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_423_2,plain,
    ! [U_1291,U_1290] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1290,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1291)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1290,U_1291) ),
    inference(variable_rename,[status(thm)],[f_423_1]) ).

fof(f_423_3,plain,
    ! [U_1291,U_1290] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1290,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1291)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1290,U_1291) ),
    inference(definitional_conversion,[status(esa)],[f_423_2]) ).

cnf(f_423_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1290,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1291)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1290,U_1291) ),
    inference(clausify,[status(thm)],[f_423_3]) ).

fof(f_424_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_424_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_424_1]) ).

cnf(f_424_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_424_2]) ).

fof(f_425_1,plain,
    ! [V_za_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_za_2),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | V_za_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( V_za_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_za_2),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
    inference(fof_nnf,[status(thm)],[fact_zabs__less__one__iff]) ).

fof(f_425_2,plain,
    ! [U_1292] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_1292),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | U_1292 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( U_1292 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_1292),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
    inference(variable_rename,[status(thm)],[f_425_1]) ).

fof(f_425_3,plain,
    ( ! [U_1294] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_1294),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | U_1294 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_1293] :
        ( U_1293 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_1293),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
    inference(miniscope,[status(thm)],[f_425_2]) ).

fof(f_425_4,plain,
    ( ! [U_1294] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_1294),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | U_1294 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_1293] :
        ( U_1293 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_1293),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
    inference(definitional_conversion,[status(esa)],[f_425_3]) ).

cnf(f_425_5,plain,
    ( U_1293 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_1293),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    inference(clausify,[status(thm)],[f_425_4]) ).

cnf(f_425_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_1294),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | U_1294 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_425_4]) ).

fof(f_426_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__number__of__int__code]) ).

fof(f_426_2,plain,
    ! [U_1296,U_1295] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1295),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1296))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1295,U_1296) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1295,U_1296)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1295),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1296)) ) ),
    inference(variable_rename,[status(thm)],[f_426_1]) ).

fof(f_426_3,plain,
    ( ! [U_1300,U_1298] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1298),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1300))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1298,U_1300) )
    & ! [U_1299,U_1297] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1297,U_1299)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1297),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1299)) ) ),
    inference(miniscope,[status(thm)],[f_426_2]) ).

fof(f_426_4,plain,
    ( ! [U_1298,U_1300] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1298),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1300))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1298,U_1300) )
    & ! [U_1299,U_1297] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1297,U_1299)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1297),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1299)) ) ),
    inference(definitional_conversion,[status(esa)],[f_426_3]) ).

cnf(f_426_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1297,U_1299)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1297),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1299)) ),
    inference(clausify,[status(thm)],[f_426_4]) ).

cnf(f_426_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1298),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1300))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1298,U_1300) ),
    inference(clausify,[status(thm)],[f_426_4]) ).

fof(f_427_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_427_2,plain,
    ! [U_1302,U_1301] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1302,U_1301)
      | U_1301 = U_1302
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1301,U_1302) ),
    inference(variable_rename,[status(thm)],[f_427_1]) ).

fof(f_427_3,plain,
    ! [U_1301,U_1302] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1302,U_1301)
      | U_1301 = U_1302
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1301,U_1302) ),
    inference(definitional_conversion,[status(esa)],[f_427_2]) ).

cnf(f_427_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1302,U_1301)
    | U_1301 = U_1302
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1301,U_1302) ),
    inference(clausify,[status(thm)],[f_427_3]) ).

fof(f_428_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_428_2,plain,
    ! [U_1304,U_1303] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1303,U_1304)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1303,U_1304),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_1303,U_1304),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1303,U_1304) ) ),
    inference(variable_rename,[status(thm)],[f_428_1]) ).

fof(f_428_3,plain,
    ( ! [U_1308,U_1306] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1306,U_1308)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1306,U_1308),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    & ! [U_1307,U_1305] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1305,U_1307),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1305,U_1307) ) ),
    inference(miniscope,[status(thm)],[f_428_2]) ).

fof(f_428_4,plain,
    ( ! [U_1308,U_1306] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1306,U_1308)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1306,U_1308),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    & ! [U_1305,U_1307] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1305,U_1307),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1305,U_1307) ) ),
    inference(definitional_conversion,[status(esa)],[f_428_3]) ).

cnf(f_428_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1305,U_1307),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1305,U_1307) ),
    inference(clausify,[status(thm)],[f_428_4]) ).

cnf(f_428_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1306,U_1308)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1306,U_1308),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(clausify,[status(thm)],[f_428_4]) ).

fof(f_429_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_429_2,plain,
    ! [U_1312,U_1311,U_1310,U_1309] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1309,U_1311),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1310,U_1312))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1311,U_1312)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1309,U_1310) ),
    inference(variable_rename,[status(thm)],[f_429_1]) ).

fof(f_429_3,plain,
    ! [U_1310,U_1309,U_1311,U_1312] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1309,U_1311),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1310,U_1312))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1311,U_1312)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1309,U_1310) ),
    inference(definitional_conversion,[status(esa)],[f_429_2]) ).

cnf(f_429_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1309,U_1311),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1310,U_1312))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1311,U_1312)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1309,U_1310) ),
    inference(clausify,[status(thm)],[f_429_3]) ).

fof(f_430_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_430_2,plain,
    ! [U_1315,U_1314,U_1313] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1313,U_1315),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1314,U_1315))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1313,U_1314) ),
    inference(variable_rename,[status(thm)],[f_430_1]) ).

fof(f_430_3,plain,
    ! [U_1315,U_1313,U_1314] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1313,U_1315),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1314,U_1315))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1313,U_1314) ),
    inference(definitional_conversion,[status(esa)],[f_430_2]) ).

cnf(f_430_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1313,U_1315),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1314,U_1315))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1313,U_1314) ),
    inference(clausify,[status(thm)],[f_430_3]) ).

fof(f_431_1,plain,
    ! [V_wa_2,V_za_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,V_wa_2)
        | V_za_2 = V_wa_2
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_za_2,V_wa_2) )
      & ( ( V_za_2 != V_wa_2
          & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_za_2,V_wa_2) )
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,V_wa_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_zless__le]) ).

fof(f_431_2,plain,
    ! [U_1317,U_1316] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1316,U_1317)
        | U_1316 = U_1317
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1316,U_1317) )
      & ( ( U_1316 != U_1317
          & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1316,U_1317) )
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1316,U_1317) ) ),
    inference(variable_rename,[status(thm)],[f_431_1]) ).

fof(f_431_3,plain,
    ( ! [U_1321,U_1319] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1319,U_1321)
        | U_1319 = U_1321
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1319,U_1321) )
    & ! [U_1320,U_1318] :
        ( ( U_1318 != U_1320
          & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1318,U_1320) )
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1318,U_1320) ) ),
    inference(miniscope,[status(thm)],[f_431_2]) ).

fof(f_431_4,plain,
    ( ! [U_1318,U_1320] :
        ( U_1318 != U_1320
        | ~ sP110(U_1318,U_1320) )
    & ! [U_1318,U_1320] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1318,U_1320)
        | ~ sP110(U_1318,U_1320) )
    & ! [U_1321,U_1319] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1319,U_1321)
        | U_1319 = U_1321
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1319,U_1321) )
    & ! [U_1318,U_1320] :
        ( sP110(U_1318,U_1320)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1318,U_1320) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP110])],[f_431_3]) ).

cnf(f_431_5,plain,
    ( sP110(U_1318,U_1320)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1318,U_1320) ),
    inference(clausify,[status(thm)],[f_431_4]) ).

cnf(f_431_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1319,U_1321)
    | U_1319 = U_1321
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1319,U_1321) ),
    inference(clausify,[status(thm)],[f_431_4]) ).

cnf(f_431_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1318,U_1320)
    | ~ sP110(U_1318,U_1320) ),
    inference(clausify,[status(thm)],[f_431_4]) ).

cnf(f_431_8,plain,
    ( U_1318 != U_1320
    | ~ sP110(U_1318,U_1320) ),
    inference(clausify,[status(thm)],[f_431_4]) ).

fof(f_432_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_432_2,plain,
    ! [U_1322] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1322,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_1322,
    inference(variable_rename,[status(thm)],[f_432_1]) ).

fof(f_432_3,plain,
    ! [U_1322] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1322,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_1322,
    inference(definitional_conversion,[status(esa)],[f_432_2]) ).

cnf(f_432_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1322,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_1322,
    inference(clausify,[status(thm)],[f_432_3]) ).

fof(f_433_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_433_2,plain,
    ! [U_1323] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1323) = U_1323,
    inference(variable_rename,[status(thm)],[f_433_1]) ).

fof(f_433_3,plain,
    ! [U_1323] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1323) = U_1323,
    inference(definitional_conversion,[status(esa)],[f_433_2]) ).

cnf(f_433_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1323) = U_1323,
    inference(clausify,[status(thm)],[f_433_3]) ).

fof(f_434_1,plain,
    ! [V_w,V_v] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)),
    inference(fof_nnf,[status(thm)],[fact_plus__numeral__code_I9_J]) ).

fof(f_434_2,plain,
    ! [U_1325,U_1324] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1324),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1325)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1324,U_1325)),
    inference(variable_rename,[status(thm)],[f_434_1]) ).

fof(f_434_3,plain,
    ! [U_1324,U_1325] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1324),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1325)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1324,U_1325)),
    inference(definitional_conversion,[status(esa)],[f_434_2]) ).

cnf(f_434_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1324),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1325)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1324,U_1325)),
    inference(clausify,[status(thm)],[f_434_3]) ).

fof(f_435_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__eq__number__of__int__code]) ).

fof(f_435_2,plain,
    ! [U_1327,U_1326] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1326),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1327))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1326,U_1327) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1326,U_1327)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1326),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1327)) ) ),
    inference(variable_rename,[status(thm)],[f_435_1]) ).

fof(f_435_3,plain,
    ( ! [U_1331,U_1329] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1329),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1331))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1329,U_1331) )
    & ! [U_1330,U_1328] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1328,U_1330)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1328),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1330)) ) ),
    inference(miniscope,[status(thm)],[f_435_2]) ).

fof(f_435_4,plain,
    ( ! [U_1331,U_1329] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1329),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1331))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1329,U_1331) )
    & ! [U_1330,U_1328] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1328,U_1330)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1328),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1330)) ) ),
    inference(definitional_conversion,[status(esa)],[f_435_3]) ).

cnf(f_435_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1328,U_1330)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1328),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1330)) ),
    inference(clausify,[status(thm)],[f_435_4]) ).

cnf(f_435_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1329),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1331))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1329,U_1331) ),
    inference(clausify,[status(thm)],[f_435_4]) ).

fof(f_436_1,plain,
    ! [V_n] : c_RComplete_Onatfloor(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_n)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_n),
    inference(fof_nnf,[status(thm)],[fact_natfloor__number__of__eq]) ).

fof(f_436_2,plain,
    ! [U_1332] : c_RComplete_Onatfloor(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_1332)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1332),
    inference(variable_rename,[status(thm)],[f_436_1]) ).

fof(f_436_3,plain,
    ! [U_1332] : c_RComplete_Onatfloor(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_1332)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1332),
    inference(definitional_conversion,[status(esa)],[f_436_2]) ).

cnf(f_436_4,plain,
    c_RComplete_Onatfloor(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_1332)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1332),
    inference(clausify,[status(thm)],[f_436_3]) ).

fof(f_437_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_437_2,plain,
    ! [U_1334,U_1333] :
      ( U_1333 = U_1334
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1334,U_1333)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1333,U_1334) ),
    inference(variable_rename,[status(thm)],[f_437_1]) ).

fof(f_437_3,plain,
    ! [U_1334,U_1333] :
      ( U_1333 = U_1334
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1334,U_1333)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1333,U_1334) ),
    inference(definitional_conversion,[status(esa)],[f_437_2]) ).

cnf(f_437_4,plain,
    ( U_1333 = U_1334
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1334,U_1333)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1333,U_1334) ),
    inference(clausify,[status(thm)],[f_437_3]) ).

fof(f_438_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_438_2,plain,
    ! [U_1337,U_1336,U_1335] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1335,U_1337)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1336,U_1337)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1335,U_1336) ),
    inference(variable_rename,[status(thm)],[f_438_1]) ).

fof(f_438_3,plain,
    ! [U_1336,U_1337,U_1335] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1335,U_1337)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1336,U_1337)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1335,U_1336) ),
    inference(definitional_conversion,[status(esa)],[f_438_2]) ).

cnf(f_438_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1335,U_1337)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1336,U_1337)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1335,U_1336) ),
    inference(clausify,[status(thm)],[f_438_3]) ).

fof(f_439_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_439_2,plain,
    ! [U_1340,U_1339,U_1338] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1340,U_1338),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1340,U_1339))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1338,U_1339) ),
    inference(variable_rename,[status(thm)],[f_439_1]) ).

fof(f_439_3,plain,
    ! [U_1339,U_1338,U_1340] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1340,U_1338),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1340,U_1339))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1338,U_1339) ),
    inference(definitional_conversion,[status(esa)],[f_439_2]) ).

cnf(f_439_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1340,U_1338),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1340,U_1339))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1338,U_1339) ),
    inference(clausify,[status(thm)],[f_439_3]) ).

fof(f_440_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_440_2,plain,
    ! [U_1343,U_1342,U_1341] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1341,U_1342),U_1343) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1341,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1342,U_1343)),
    inference(variable_rename,[status(thm)],[f_440_1]) ).

fof(f_440_3,plain,
    ! [U_1341,U_1342,U_1343] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1341,U_1342),U_1343) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1341,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1342,U_1343)),
    inference(definitional_conversion,[status(esa)],[f_440_2]) ).

cnf(f_440_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1341,U_1342),U_1343) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1341,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1342,U_1343)),
    inference(clausify,[status(thm)],[f_440_3]) ).

fof(f_441_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_441_2,plain,
    ! [U_1346,U_1345,U_1344] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1344,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1345,U_1346)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1345,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1344,U_1346)),
    inference(variable_rename,[status(thm)],[f_441_1]) ).

fof(f_441_3,plain,
    ! [U_1344,U_1345,U_1346] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1344,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1345,U_1346)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1345,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1344,U_1346)),
    inference(definitional_conversion,[status(esa)],[f_441_2]) ).

cnf(f_441_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1344,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1345,U_1346)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1345,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1344,U_1346)),
    inference(clausify,[status(thm)],[f_441_3]) ).

fof(f_442_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_442_2,plain,
    ! [U_1348,U_1347] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1348,U_1347)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1347,U_1348) ),
    inference(variable_rename,[status(thm)],[f_442_1]) ).

fof(f_442_3,plain,
    ! [U_1348,U_1347] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1348,U_1347)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1347,U_1348) ),
    inference(definitional_conversion,[status(esa)],[f_442_2]) ).

cnf(f_442_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1348,U_1347)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1347,U_1348) ),
    inference(clausify,[status(thm)],[f_442_3]) ).

fof(f_443_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_443_2,plain,
    ! [U_1350,U_1349] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1349,U_1350) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1350,U_1349),
    inference(variable_rename,[status(thm)],[f_443_1]) ).

fof(f_443_3,plain,
    ! [U_1350,U_1349] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1349,U_1350) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1350,U_1349),
    inference(definitional_conversion,[status(esa)],[f_443_2]) ).

cnf(f_443_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1349,U_1350) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1350,U_1349),
    inference(clausify,[status(thm)],[f_443_3]) ).

fof(f_444_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_444_2,plain,
    ! [U_1351] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1351,U_1351),
    inference(variable_rename,[status(thm)],[f_444_1]) ).

fof(f_444_3,plain,
    ! [U_1351] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1351,U_1351),
    inference(definitional_conversion,[status(esa)],[f_444_2]) ).

cnf(f_444_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1351,U_1351),
    inference(clausify,[status(thm)],[f_444_3]) ).

fof(f_445_1,plain,
    ! [V_n] : c_RComplete_Onatfloor(hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)) = V_n,
    inference(fof_nnf,[status(thm)],[fact_natfloor__real__of__nat]) ).

fof(f_445_2,plain,
    ! [U_1352] : c_RComplete_Onatfloor(hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1352)) = U_1352,
    inference(variable_rename,[status(thm)],[f_445_1]) ).

fof(f_445_3,plain,
    ! [U_1352] : c_RComplete_Onatfloor(hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1352)) = U_1352,
    inference(definitional_conversion,[status(esa)],[f_445_2]) ).

cnf(f_445_4,plain,
    c_RComplete_Onatfloor(hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1352)) = U_1352,
    inference(clausify,[status(thm)],[f_445_3]) ).

fof(f_446_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_446_2,plain,
    ! [U_1354,U_1353] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1353),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_1353,U_1354)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1354))),
    inference(variable_rename,[status(thm)],[f_446_1]) ).

fof(f_446_3,plain,
    ! [U_1353,U_1354] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1353),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_1353,U_1354)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1354))),
    inference(definitional_conversion,[status(esa)],[f_446_2]) ).

cnf(f_446_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1353),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_1353,U_1354)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1354))),
    inference(clausify,[status(thm)],[f_446_3]) ).

fof(f_447_1,plain,
    ! [V_n] : c_RComplete_Onatceiling(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_n)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_n),
    inference(fof_nnf,[status(thm)],[fact_natceiling__number__of__eq]) ).

fof(f_447_2,plain,
    ! [U_1355] : c_RComplete_Onatceiling(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_1355)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1355),
    inference(variable_rename,[status(thm)],[f_447_1]) ).

fof(f_447_3,plain,
    ! [U_1355] : c_RComplete_Onatceiling(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_1355)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1355),
    inference(definitional_conversion,[status(esa)],[f_447_2]) ).

cnf(f_447_4,plain,
    c_RComplete_Onatceiling(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_1355)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1355),
    inference(clausify,[status(thm)],[f_447_3]) ).

fof(f_448_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_448_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_448_1]) ).

cnf(f_448_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_448_2]) ).

fof(f_449_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_449_2,plain,
    ! [U_1356] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(U_1356)),
    inference(variable_rename,[status(thm)],[f_449_1]) ).

fof(f_449_3,plain,
    ! [U_1356] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(U_1356)),
    inference(definitional_conversion,[status(esa)],[f_449_2]) ).

cnf(f_449_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(U_1356)),
    inference(clausify,[status(thm)],[f_449_3]) ).

fof(f_450_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_450_2,plain,
    ! [U_1358,U_1357] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(U_1357),c_RComplete_Onatfloor(U_1358))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1357,U_1358) ),
    inference(variable_rename,[status(thm)],[f_450_1]) ).

fof(f_450_3,plain,
    ! [U_1357,U_1358] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(U_1357),c_RComplete_Onatfloor(U_1358))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1357,U_1358) ),
    inference(definitional_conversion,[status(esa)],[f_450_2]) ).

cnf(f_450_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(U_1357),c_RComplete_Onatfloor(U_1358))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1357,U_1358) ),
    inference(clausify,[status(thm)],[f_450_3]) ).

fof(f_451_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_451_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_451_1]) ).

cnf(f_451_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_451_2]) ).

fof(f_452_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_452_2,plain,
    ! [U_1359] :
      ( c_RComplete_Onatfloor(U_1359) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1359,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(variable_rename,[status(thm)],[f_452_1]) ).

fof(f_452_3,plain,
    ! [U_1359] :
      ( c_RComplete_Onatfloor(U_1359) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1359,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(definitional_conversion,[status(esa)],[f_452_2]) ).

cnf(f_452_4,plain,
    ( c_RComplete_Onatfloor(U_1359) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1359,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(clausify,[status(thm)],[f_452_3]) ).

fof(f_453_1,plain,
    ! [V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(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_453_2,plain,
    ! [U_1360] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(U_1360)),U_1360)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1360) ),
    inference(variable_rename,[status(thm)],[f_453_1]) ).

fof(f_453_3,plain,
    ! [U_1360] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(U_1360)),U_1360)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1360) ),
    inference(definitional_conversion,[status(esa)],[f_453_2]) ).

cnf(f_453_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(U_1360)),U_1360)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1360) ),
    inference(clausify,[status(thm)],[f_453_3]) ).

fof(f_454_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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_x),V_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__natfloor]) ).

fof(f_454_2,plain,
    ! [U_1362,U_1361] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1361,c_RComplete_Onatfloor(U_1362))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1361),U_1362) ),
    inference(variable_rename,[status(thm)],[f_454_1]) ).

fof(f_454_3,plain,
    ! [U_1361,U_1362] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1361,c_RComplete_Onatfloor(U_1362))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1361),U_1362) ),
    inference(definitional_conversion,[status(esa)],[f_454_2]) ).

cnf(f_454_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1361,c_RComplete_Onatfloor(U_1362))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1361),U_1362) ),
    inference(clausify,[status(thm)],[f_454_3]) ).

fof(f_455_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)),hAPP(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)),hAPP(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_455_2,plain,
    ! [U_1372,U_1371] :
      ( ( ( ? [U_1370] :
              ( ! [U_1369] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1371,hAPP(U_1372,U_1369)),U_1370)
              & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1370) )
          | ! [U_1368] :
            ? [U_1367] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1371,hAPP(U_1372,U_1367)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_1368))) )
        & ( ? [U_1366] :
            ! [U_1365] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1371,hAPP(U_1372,U_1365)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_1366)))
          | ! [U_1364] :
              ( ? [U_1363] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1371,hAPP(U_1372,U_1363)),U_1364)
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1364) ) ) )
      | ~ class_RealVector_Oreal__normed__vector(U_1371) ),
    inference(variable_rename,[status(thm)],[f_455_1]) ).

fof(f_455_3,plain,
    ! [U_1372,U_1371] :
      ( ( ( ? [U_1370] :
              ( ! [U_1369] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1371,hAPP(U_1372,U_1369)),U_1370)
              & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1370) )
          | ! [U_1368] :
            ? [U_1367] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1371,hAPP(U_1372,U_1367)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_1368))) )
        & ( ? [U_1366] :
            ! [U_1365] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1371,hAPP(U_1372,U_1365)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_1366)))
          | ! [U_1364] :
              ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1371,hAPP(U_1372,sK35(U_1372,U_1371,U_1364))),U_1364)
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1364) ) ) )
      | ~ class_RealVector_Oreal__normed__vector(U_1371) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_1363,sK35(U_1372,U_1371,U_1364))],[f_455_2]) ).

fof(f_455_4,plain,
    ! [U_1372,U_1371] :
      ( ( ( ? [U_1370] :
              ( ! [U_1369] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1371,hAPP(U_1372,U_1369)),U_1370)
              & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1370) )
          | ! [U_1368] :
            ? [U_1367] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1371,hAPP(U_1372,U_1367)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_1368))) )
        & ( ! [U_1365] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1371,hAPP(U_1372,U_1365)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(sK36(U_1372,U_1371))))
          | ! [U_1364] :
              ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1371,hAPP(U_1372,sK35(U_1372,U_1371,U_1364))),U_1364)
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1364) ) ) )
      | ~ class_RealVector_Oreal__normed__vector(U_1371) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_1366,sK36(U_1372,U_1371))],[f_455_3]) ).

fof(f_455_5,plain,
    ! [U_1372,U_1371] :
      ( ( ( ? [U_1370] :
              ( ! [U_1369] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1371,hAPP(U_1372,U_1369)),U_1370)
              & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1370) )
          | ! [U_1368] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1371,hAPP(U_1372,sK37(U_1372,U_1371,U_1368))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_1368))) )
        & ( ! [U_1365] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1371,hAPP(U_1372,U_1365)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(sK36(U_1372,U_1371))))
          | ! [U_1364] :
              ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1371,hAPP(U_1372,sK35(U_1372,U_1371,U_1364))),U_1364)
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1364) ) ) )
      | ~ class_RealVector_Oreal__normed__vector(U_1371) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_1367,sK37(U_1372,U_1371,U_1368))],[f_455_4]) ).

fof(f_455_6,plain,
    ! [U_1372,U_1371] :
      ( ( ( ( ! [U_1369] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1371,hAPP(U_1372,U_1369)),sK38(U_1372,U_1371))
            & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK38(U_1372,U_1371)) )
          | ! [U_1368] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1371,hAPP(U_1372,sK37(U_1372,U_1371,U_1368))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_1368))) )
        & ( ! [U_1365] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1371,hAPP(U_1372,U_1365)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(sK36(U_1372,U_1371))))
          | ! [U_1364] :
              ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1371,hAPP(U_1372,sK35(U_1372,U_1371,U_1364))),U_1364)
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1364) ) ) )
      | ~ class_RealVector_Oreal__normed__vector(U_1371) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_1370,sK38(U_1372,U_1371))],[f_455_5]) ).

fof(f_455_7,plain,
    ( ! [U_1369,U_1371,U_1372] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1371,hAPP(U_1372,U_1369)),sK38(U_1372,U_1371))
        | ~ sP111(U_1369,U_1371,U_1372) )
    & ! [U_1369,U_1371,U_1372] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK38(U_1372,U_1371))
        | ~ sP111(U_1369,U_1371,U_1372) )
    & ! [U_1364,U_1365,U_1368,U_1369,U_1371,U_1372] :
        ( sP111(U_1369,U_1371,U_1372)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1371,hAPP(U_1372,sK37(U_1372,U_1371,U_1368))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_1368)))
        | ~ sP112(U_1364,U_1365,U_1368,U_1369,U_1371,U_1372) )
    & ! [U_1364,U_1365,U_1368,U_1369,U_1371,U_1372] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1371,hAPP(U_1372,U_1365)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(sK36(U_1372,U_1371))))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1371,hAPP(U_1372,sK35(U_1372,U_1371,U_1364))),U_1364)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1364)
        | ~ sP112(U_1364,U_1365,U_1368,U_1369,U_1371,U_1372) )
    & ! [U_1364,U_1365,U_1368,U_1369,U_1371,U_1372] :
        ( sP112(U_1364,U_1365,U_1368,U_1369,U_1371,U_1372)
        | ~ class_RealVector_Oreal__normed__vector(U_1371) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP111,sP112])],[f_455_6]) ).

cnf(f_455_8,plain,
    ( sP112(U_1364,U_1365,U_1368,U_1369,U_1371,U_1372)
    | ~ class_RealVector_Oreal__normed__vector(U_1371) ),
    inference(clausify,[status(thm)],[f_455_7]) ).

cnf(f_455_9,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1371,hAPP(U_1372,U_1365)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(sK36(U_1372,U_1371))))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1371,hAPP(U_1372,sK35(U_1372,U_1371,U_1364))),U_1364)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1364)
    | ~ sP112(U_1364,U_1365,U_1368,U_1369,U_1371,U_1372) ),
    inference(clausify,[status(thm)],[f_455_7]) ).

cnf(f_455_10,plain,
    ( sP111(U_1369,U_1371,U_1372)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1371,hAPP(U_1372,sK37(U_1372,U_1371,U_1368))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_1368)))
    | ~ sP112(U_1364,U_1365,U_1368,U_1369,U_1371,U_1372) ),
    inference(clausify,[status(thm)],[f_455_7]) ).

cnf(f_455_11,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK38(U_1372,U_1371))
    | ~ sP111(U_1369,U_1371,U_1372) ),
    inference(clausify,[status(thm)],[f_455_7]) ).

cnf(f_455_12,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1371,hAPP(U_1372,U_1369)),sK38(U_1372,U_1371))
    | ~ sP111(U_1369,U_1371,U_1372) ),
    inference(clausify,[status(thm)],[f_455_7]) ).

fof(f_456_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)),hAPP(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)),hAPP(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_456_2,plain,
    ! [U_1382,U_1381] :
      ( ( ( ? [U_1380] :
              ( ! [U_1379] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1381,hAPP(U_1382,U_1379)),U_1380)
              & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1380) )
          | ! [U_1378] :
            ? [U_1377] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1381,hAPP(U_1382,U_1377)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_1378))) )
        & ( ? [U_1376] :
            ! [U_1375] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1381,hAPP(U_1382,U_1375)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_1376)))
          | ! [U_1374] :
              ( ? [U_1373] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1381,hAPP(U_1382,U_1373)),U_1374)
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1374) ) ) )
      | ~ class_RealVector_Oreal__normed__vector(U_1381) ),
    inference(variable_rename,[status(thm)],[f_456_1]) ).

fof(f_456_3,plain,
    ! [U_1382,U_1381] :
      ( ( ( ? [U_1380] :
              ( ! [U_1379] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1381,hAPP(U_1382,U_1379)),U_1380)
              & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1380) )
          | ! [U_1378] :
            ? [U_1377] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1381,hAPP(U_1382,U_1377)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_1378))) )
        & ( ? [U_1376] :
            ! [U_1375] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1381,hAPP(U_1382,U_1375)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_1376)))
          | ! [U_1374] :
              ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1381,hAPP(U_1382,sK39(U_1382,U_1381,U_1374))),U_1374)
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1374) ) ) )
      | ~ class_RealVector_Oreal__normed__vector(U_1381) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_1373,sK39(U_1382,U_1381,U_1374))],[f_456_2]) ).

fof(f_456_4,plain,
    ! [U_1382,U_1381] :
      ( ( ( ? [U_1380] :
              ( ! [U_1379] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1381,hAPP(U_1382,U_1379)),U_1380)
              & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1380) )
          | ! [U_1378] :
            ? [U_1377] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1381,hAPP(U_1382,U_1377)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_1378))) )
        & ( ! [U_1375] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1381,hAPP(U_1382,U_1375)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(sK40(U_1382,U_1381))))
          | ! [U_1374] :
              ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1381,hAPP(U_1382,sK39(U_1382,U_1381,U_1374))),U_1374)
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1374) ) ) )
      | ~ class_RealVector_Oreal__normed__vector(U_1381) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_1376,sK40(U_1382,U_1381))],[f_456_3]) ).

fof(f_456_5,plain,
    ! [U_1382,U_1381] :
      ( ( ( ? [U_1380] :
              ( ! [U_1379] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1381,hAPP(U_1382,U_1379)),U_1380)
              & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1380) )
          | ! [U_1378] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1381,hAPP(U_1382,sK41(U_1382,U_1381,U_1378))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_1378))) )
        & ( ! [U_1375] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1381,hAPP(U_1382,U_1375)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(sK40(U_1382,U_1381))))
          | ! [U_1374] :
              ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1381,hAPP(U_1382,sK39(U_1382,U_1381,U_1374))),U_1374)
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1374) ) ) )
      | ~ class_RealVector_Oreal__normed__vector(U_1381) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_1377,sK41(U_1382,U_1381,U_1378))],[f_456_4]) ).

fof(f_456_6,plain,
    ! [U_1382,U_1381] :
      ( ( ( ( ! [U_1379] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1381,hAPP(U_1382,U_1379)),sK42(U_1382,U_1381))
            & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK42(U_1382,U_1381)) )
          | ! [U_1378] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1381,hAPP(U_1382,sK41(U_1382,U_1381,U_1378))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_1378))) )
        & ( ! [U_1375] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1381,hAPP(U_1382,U_1375)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(sK40(U_1382,U_1381))))
          | ! [U_1374] :
              ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1381,hAPP(U_1382,sK39(U_1382,U_1381,U_1374))),U_1374)
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1374) ) ) )
      | ~ class_RealVector_Oreal__normed__vector(U_1381) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_1380,sK42(U_1382,U_1381))],[f_456_5]) ).

fof(f_456_7,plain,
    ( ! [U_1381,U_1382,U_1379] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1381,hAPP(U_1382,U_1379)),sK42(U_1382,U_1381))
        | ~ sP113(U_1381,U_1382,U_1379) )
    & ! [U_1381,U_1382,U_1379] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK42(U_1382,U_1381))
        | ~ sP113(U_1381,U_1382,U_1379) )
    & ! [U_1378,U_1381,U_1382,U_1379,U_1374,U_1375] :
        ( sP113(U_1381,U_1382,U_1379)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1381,hAPP(U_1382,sK41(U_1382,U_1381,U_1378))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_1378)))
        | ~ sP114(U_1378,U_1381,U_1382,U_1379,U_1374,U_1375) )
    & ! [U_1378,U_1381,U_1382,U_1379,U_1374,U_1375] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1381,hAPP(U_1382,U_1375)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(sK40(U_1382,U_1381))))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1381,hAPP(U_1382,sK39(U_1382,U_1381,U_1374))),U_1374)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1374)
        | ~ sP114(U_1378,U_1381,U_1382,U_1379,U_1374,U_1375) )
    & ! [U_1378,U_1381,U_1382,U_1379,U_1374,U_1375] :
        ( sP114(U_1378,U_1381,U_1382,U_1379,U_1374,U_1375)
        | ~ class_RealVector_Oreal__normed__vector(U_1381) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP113,sP114])],[f_456_6]) ).

cnf(f_456_8,plain,
    ( sP114(U_1378,U_1381,U_1382,U_1379,U_1374,U_1375)
    | ~ class_RealVector_Oreal__normed__vector(U_1381) ),
    inference(clausify,[status(thm)],[f_456_7]) ).

cnf(f_456_9,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1381,hAPP(U_1382,U_1375)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(sK40(U_1382,U_1381))))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1381,hAPP(U_1382,sK39(U_1382,U_1381,U_1374))),U_1374)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1374)
    | ~ sP114(U_1378,U_1381,U_1382,U_1379,U_1374,U_1375) ),
    inference(clausify,[status(thm)],[f_456_7]) ).

cnf(f_456_10,plain,
    ( sP113(U_1381,U_1382,U_1379)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1381,hAPP(U_1382,sK41(U_1382,U_1381,U_1378))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_1378)))
    | ~ sP114(U_1378,U_1381,U_1382,U_1379,U_1374,U_1375) ),
    inference(clausify,[status(thm)],[f_456_7]) ).

cnf(f_456_11,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK42(U_1382,U_1381))
    | ~ sP113(U_1381,U_1382,U_1379) ),
    inference(clausify,[status(thm)],[f_456_7]) ).

cnf(f_456_12,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1381,hAPP(U_1382,U_1379)),sK42(U_1382,U_1381))
    | ~ sP113(U_1381,U_1382,U_1379) ),
    inference(clausify,[status(thm)],[f_456_7]) ).

fof(f_457_1,plain,
    ! [V_a_2,V_x_2] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_a_2,c_RComplete_Onatfloor(V_x_2))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a_2),V_x_2) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a_2),V_x_2)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_a_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_457_2,plain,
    ! [U_1384,U_1383] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1384,c_RComplete_Onatfloor(U_1383))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1384),U_1383) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1384),U_1383)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1384,c_RComplete_Onatfloor(U_1383)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1383) ),
    inference(variable_rename,[status(thm)],[f_457_1]) ).

fof(f_457_3,plain,
    ( ! [U_1383,U_1384] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1384,c_RComplete_Onatfloor(U_1383))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1384),U_1383)
        | ~ sP115(U_1383,U_1384) )
    & ! [U_1383,U_1384] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1384),U_1383)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1384,c_RComplete_Onatfloor(U_1383))
        | ~ sP115(U_1383,U_1384) )
    & ! [U_1383,U_1384] :
        ( sP115(U_1383,U_1384)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1383) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP115])],[f_457_2]) ).

cnf(f_457_4,plain,
    ( sP115(U_1383,U_1384)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1383) ),
    inference(clausify,[status(thm)],[f_457_3]) ).

cnf(f_457_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1384),U_1383)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1384,c_RComplete_Onatfloor(U_1383))
    | ~ sP115(U_1383,U_1384) ),
    inference(clausify,[status(thm)],[f_457_3]) ).

cnf(f_457_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1384,c_RComplete_Onatfloor(U_1383))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1384),U_1383)
    | ~ sP115(U_1383,U_1384) ),
    inference(clausify,[status(thm)],[f_457_3]) ).

fof(f_458_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_458_2,plain,
    ! [U_1385] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(U_1385))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1385) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1385)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(U_1385)) ) ),
    inference(variable_rename,[status(thm)],[f_458_1]) ).

fof(f_458_3,plain,
    ( ! [U_1387] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(U_1387))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1387) )
    & ! [U_1386] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1386)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(U_1386)) ) ),
    inference(miniscope,[status(thm)],[f_458_2]) ).

fof(f_458_4,plain,
    ( ! [U_1387] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(U_1387))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1387) )
    & ! [U_1386] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1386)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(U_1386)) ) ),
    inference(definitional_conversion,[status(esa)],[f_458_3]) ).

cnf(f_458_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1386)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(U_1386)) ),
    inference(clausify,[status(thm)],[f_458_4]) ).

cnf(f_458_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(U_1387))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1387) ),
    inference(clausify,[status(thm)],[f_458_4]) ).

fof(f_459_1,plain,
    ! [V_x] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(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_459_2,plain,
    ! [U_1388] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1388,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(U_1388)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
    inference(variable_rename,[status(thm)],[f_459_1]) ).

fof(f_459_3,plain,
    ! [U_1388] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1388,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(U_1388)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
    inference(definitional_conversion,[status(esa)],[f_459_2]) ).

cnf(f_459_4,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1388,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(U_1388)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
    inference(clausify,[status(thm)],[f_459_3]) ).

fof(f_460_1,plain,
    ! [V_x,V_a] :
      ( c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,hAPP(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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a),V_x) ),
    inference(fof_nnf,[status(thm)],[fact_natfloor__subtract]) ).

fof(f_460_2,plain,
    ! [U_1390,U_1389] :
      ( c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1390,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1389))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(U_1390),U_1389)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1389),U_1390) ),
    inference(variable_rename,[status(thm)],[f_460_1]) ).

fof(f_460_3,plain,
    ! [U_1390,U_1389] :
      ( c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1390,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1389))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(U_1390),U_1389)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1389),U_1390) ),
    inference(definitional_conversion,[status(esa)],[f_460_2]) ).

cnf(f_460_4,plain,
    ( c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1390,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1389))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(U_1390),U_1389)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1389),U_1390) ),
    inference(clausify,[status(thm)],[f_460_3]) ).

fof(f_461_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)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(V_x))),
    inference(fof_nnf,[status(thm)],[fact_real__natfloor__gt__diff__one]) ).

fof(f_461_2,plain,
    ! [U_1391] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1391,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(U_1391))),
    inference(variable_rename,[status(thm)],[f_461_1]) ).

fof(f_461_3,plain,
    ! [U_1391] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1391,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(U_1391))),
    inference(definitional_conversion,[status(esa)],[f_461_2]) ).

cnf(f_461_4,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1391,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(U_1391))),
    inference(clausify,[status(thm)],[f_461_3]) ).

fof(f_462_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,hAPP(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_462_2,plain,
    ! [U_1393,U_1392] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(U_1392),U_1393)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1392,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1393))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1392) ),
    inference(variable_rename,[status(thm)],[f_462_1]) ).

fof(f_462_3,plain,
    ! [U_1392,U_1393] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(U_1392),U_1393)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1392,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1393))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1392) ),
    inference(definitional_conversion,[status(esa)],[f_462_2]) ).

cnf(f_462_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(U_1392),U_1393)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1392,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1393))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1392) ),
    inference(clausify,[status(thm)],[f_462_3]) ).

fof(f_463_1,plain,
    ! [V_a,V_x] :
      ( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,hAPP(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_463_2,plain,
    ! [U_1395,U_1394] :
      ( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1394,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1395))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_1394),U_1395)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1394) ),
    inference(variable_rename,[status(thm)],[f_463_1]) ).

fof(f_463_3,plain,
    ! [U_1395,U_1394] :
      ( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1394,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1395))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_1394),U_1395)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1394) ),
    inference(definitional_conversion,[status(esa)],[f_463_2]) ).

cnf(f_463_4,plain,
    ( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1394,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1395))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_1394),U_1395)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1394) ),
    inference(clausify,[status(thm)],[f_463_3]) ).

fof(f_464_1,plain,
    ! [V_n,V_z] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z,hAPP(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_464_2,plain,
    ! [U_1397,U_1396] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1396,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1397))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_1396),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_1397) ),
    inference(variable_rename,[status(thm)],[f_464_1]) ).

fof(f_464_3,plain,
    ! [U_1397,U_1396] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1396,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1397))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_1396),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_1397) ),
    inference(definitional_conversion,[status(esa)],[f_464_2]) ).

cnf(f_464_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1396,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1397))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_1396),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_1397) ),
    inference(clausify,[status(thm)],[f_464_3]) ).

fof(f_465_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,hAPP(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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n),V_x) ),
    inference(fof_nnf,[status(thm)],[fact_natfloor__eq]) ).

fof(f_465_2,plain,
    ! [U_1399,U_1398] :
      ( c_RComplete_Onatfloor(U_1399) = U_1398
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1399,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1398),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1398),U_1399) ),
    inference(variable_rename,[status(thm)],[f_465_1]) ).

fof(f_465_3,plain,
    ! [U_1398,U_1399] :
      ( c_RComplete_Onatfloor(U_1399) = U_1398
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1399,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1398),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1398),U_1399) ),
    inference(definitional_conversion,[status(esa)],[f_465_2]) ).

cnf(f_465_4,plain,
    ( c_RComplete_Onatfloor(U_1399) = U_1398
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1399,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1398),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_1398),U_1399) ),
    inference(clausify,[status(thm)],[f_465_3]) ).

fof(f_466_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(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__ineq3]) ).

fof(f_466_2,plain,
    ! [U_1402,U_1401,U_1400] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1400,U_1401),c_RealVector_Onorm__class_Onorm(U_1400,U_1402))),c_RealVector_Onorm__class_Onorm(U_1400,c_Groups_Ominus__class_Ominus(U_1400,U_1401,U_1402)))
      | ~ class_RealVector_Oreal__normed__vector(U_1400) ),
    inference(variable_rename,[status(thm)],[f_466_1]) ).

fof(f_466_3,plain,
    ! [U_1400,U_1401,U_1402] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1400,U_1401),c_RealVector_Onorm__class_Onorm(U_1400,U_1402))),c_RealVector_Onorm__class_Onorm(U_1400,c_Groups_Ominus__class_Ominus(U_1400,U_1401,U_1402)))
      | ~ class_RealVector_Oreal__normed__vector(U_1400) ),
    inference(definitional_conversion,[status(esa)],[f_466_2]) ).

cnf(f_466_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1400,U_1401),c_RealVector_Onorm__class_Onorm(U_1400,U_1402))),c_RealVector_Onorm__class_Onorm(U_1400,c_Groups_Ominus__class_Ominus(U_1400,U_1401,U_1402)))
    | ~ class_RealVector_Oreal__normed__vector(U_1400) ),
    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__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_467_2,plain,
    ! [U_1407,U_1406,U_1405,U_1404,U_1403] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1403,c_Groups_Ominus__class_Ominus(U_1403,c_Groups_Oplus__class_Oplus(U_1403,U_1404,U_1405),c_Groups_Oplus__class_Oplus(U_1403,U_1406,U_1407))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1403,c_Groups_Ominus__class_Ominus(U_1403,U_1404,U_1406)),c_RealVector_Onorm__class_Onorm(U_1403,c_Groups_Ominus__class_Ominus(U_1403,U_1405,U_1407))))
      | ~ class_RealVector_Oreal__normed__vector(U_1403) ),
    inference(variable_rename,[status(thm)],[f_467_1]) ).

fof(f_467_3,plain,
    ! [U_1403,U_1404,U_1405,U_1406,U_1407] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1403,c_Groups_Ominus__class_Ominus(U_1403,c_Groups_Oplus__class_Oplus(U_1403,U_1404,U_1405),c_Groups_Oplus__class_Oplus(U_1403,U_1406,U_1407))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1403,c_Groups_Ominus__class_Ominus(U_1403,U_1404,U_1406)),c_RealVector_Onorm__class_Onorm(U_1403,c_Groups_Ominus__class_Ominus(U_1403,U_1405,U_1407))))
      | ~ class_RealVector_Oreal__normed__vector(U_1403) ),
    inference(definitional_conversion,[status(esa)],[f_467_2]) ).

cnf(f_467_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1403,c_Groups_Ominus__class_Ominus(U_1403,c_Groups_Oplus__class_Oplus(U_1403,U_1404,U_1405),c_Groups_Oplus__class_Oplus(U_1403,U_1406,U_1407))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1403,c_Groups_Ominus__class_Ominus(U_1403,U_1404,U_1406)),c_RealVector_Onorm__class_Onorm(U_1403,c_Groups_Ominus__class_Ominus(U_1403,U_1405,U_1407))))
    | ~ class_RealVector_Oreal__normed__vector(U_1403) ),
    inference(clausify,[status(thm)],[f_467_3]) ).

fof(f_468_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_468_2,plain,
    ! [U_1410,U_1409,U_1408] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1408,U_1409),c_RealVector_Onorm__class_Onorm(U_1408,U_1410)),c_RealVector_Onorm__class_Onorm(U_1408,c_Groups_Ominus__class_Ominus(U_1408,U_1409,U_1410)))
      | ~ class_RealVector_Oreal__normed__vector(U_1408) ),
    inference(variable_rename,[status(thm)],[f_468_1]) ).

fof(f_468_3,plain,
    ! [U_1409,U_1408,U_1410] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1408,U_1409),c_RealVector_Onorm__class_Onorm(U_1408,U_1410)),c_RealVector_Onorm__class_Onorm(U_1408,c_Groups_Ominus__class_Ominus(U_1408,U_1409,U_1410)))
      | ~ class_RealVector_Oreal__normed__vector(U_1408) ),
    inference(definitional_conversion,[status(esa)],[f_468_2]) ).

cnf(f_468_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_1408,U_1409),c_RealVector_Onorm__class_Onorm(U_1408,U_1410)),c_RealVector_Onorm__class_Onorm(U_1408,c_Groups_Ominus__class_Ominus(U_1408,U_1409,U_1410)))
    | ~ class_RealVector_Oreal__normed__vector(U_1408) ),
    inference(clausify,[status(thm)],[f_468_3]) ).

fof(f_469_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_469_2,plain,
    ! [U_1413,U_1412,U_1411] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1411,U_1412),c_RealVector_Onorm__class_Onorm(U_1411,U_1413)),c_RealVector_Onorm__class_Onorm(U_1411,c_Groups_Oplus__class_Oplus(U_1411,U_1412,U_1413)))
      | ~ class_RealVector_Oreal__normed__vector(U_1411) ),
    inference(variable_rename,[status(thm)],[f_469_1]) ).

fof(f_469_3,plain,
    ! [U_1411,U_1412,U_1413] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1411,U_1412),c_RealVector_Onorm__class_Onorm(U_1411,U_1413)),c_RealVector_Onorm__class_Onorm(U_1411,c_Groups_Oplus__class_Oplus(U_1411,U_1412,U_1413)))
      | ~ class_RealVector_Oreal__normed__vector(U_1411) ),
    inference(definitional_conversion,[status(esa)],[f_469_2]) ).

cnf(f_469_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_1411,U_1412),c_RealVector_Onorm__class_Onorm(U_1411,U_1413)),c_RealVector_Onorm__class_Onorm(U_1411,c_Groups_Oplus__class_Oplus(U_1411,U_1412,U_1413)))
    | ~ class_RealVector_Oreal__normed__vector(U_1411) ),
    inference(clausify,[status(thm)],[f_469_3]) ).

fof(f_470_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_470_2,plain,
    ! [U_1416,U_1415,U_1414] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1414,c_Groups_Ominus__class_Ominus(U_1414,U_1415,U_1416)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1414,U_1415),c_RealVector_Onorm__class_Onorm(U_1414,U_1416)))
      | ~ class_RealVector_Oreal__normed__vector(U_1414) ),
    inference(variable_rename,[status(thm)],[f_470_1]) ).

fof(f_470_3,plain,
    ! [U_1414,U_1415,U_1416] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1414,c_Groups_Ominus__class_Ominus(U_1414,U_1415,U_1416)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1414,U_1415),c_RealVector_Onorm__class_Onorm(U_1414,U_1416)))
      | ~ class_RealVector_Oreal__normed__vector(U_1414) ),
    inference(definitional_conversion,[status(esa)],[f_470_2]) ).

cnf(f_470_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1414,c_Groups_Ominus__class_Ominus(U_1414,U_1415,U_1416)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1414,U_1415),c_RealVector_Onorm__class_Onorm(U_1414,U_1416)))
    | ~ class_RealVector_Oreal__normed__vector(U_1414) ),
    inference(clausify,[status(thm)],[f_470_3]) ).

fof(f_471_1,plain,
    ! [B_n] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,B_n)),v_z____)),v_d____)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_N1____,B_n) ),
    inference(fof_nnf,[status(thm)],[fact_N1]) ).

fof(f_471_2,plain,
    ! [U_1417] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,U_1417)),v_z____)),v_d____)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_N1____,U_1417) ),
    inference(variable_rename,[status(thm)],[f_471_1]) ).

fof(f_471_3,plain,
    ! [U_1417] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,U_1417)),v_z____)),v_d____)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_N1____,U_1417) ),
    inference(definitional_conversion,[status(esa)],[f_471_2]) ).

cnf(f_471_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,v_g____(hAPP(v_f____,U_1417)),v_z____)),v_d____)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_N1____,U_1417) ),
    inference(clausify,[status(thm)],[f_471_3]) ).

fof(f_472_1,plain,
    ! [V_k] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k) = V_k,
    inference(fof_nnf,[status(thm)],[fact_number__of__is__id]) ).

fof(f_472_2,plain,
    ! [U_1418] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1418) = U_1418,
    inference(variable_rename,[status(thm)],[f_472_1]) ).

fof(f_472_3,plain,
    ! [U_1418] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1418) = U_1418,
    inference(definitional_conversion,[status(esa)],[f_472_2]) ).

cnf(f_472_4,plain,
    c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1418) = U_1418,
    inference(clausify,[status(thm)],[f_472_3]) ).

fof(f_473_1,plain,
    ! [V_r] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r),
    inference(fof_nnf,[status(thm)],[fact_real__norm__def]) ).

fof(f_473_2,plain,
    ! [U_1419] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,U_1419) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1419),
    inference(variable_rename,[status(thm)],[f_473_1]) ).

fof(f_473_3,plain,
    ! [U_1419] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,U_1419) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1419),
    inference(definitional_conversion,[status(esa)],[f_473_2]) ).

cnf(f_473_4,plain,
    c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,U_1419) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1419),
    inference(clausify,[status(thm)],[f_473_3]) ).

fof(f_474_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_474_2,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_474_1]) ).

cnf(f_474_3,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_474_2]) ).

fof(f_475_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_475_2,plain,
    ! [U_1422,U_1421,U_1420] :
      ( c_RealVector_Onorm__class_Onorm(U_1420,c_Groups_Ominus__class_Ominus(U_1420,U_1421,U_1422)) = c_RealVector_Onorm__class_Onorm(U_1420,c_Groups_Ominus__class_Ominus(U_1420,U_1422,U_1421))
      | ~ class_RealVector_Oreal__normed__vector(U_1420) ),
    inference(variable_rename,[status(thm)],[f_475_1]) ).

fof(f_475_3,plain,
    ! [U_1420,U_1421,U_1422] :
      ( c_RealVector_Onorm__class_Onorm(U_1420,c_Groups_Ominus__class_Ominus(U_1420,U_1421,U_1422)) = c_RealVector_Onorm__class_Onorm(U_1420,c_Groups_Ominus__class_Ominus(U_1420,U_1422,U_1421))
      | ~ class_RealVector_Oreal__normed__vector(U_1420) ),
    inference(definitional_conversion,[status(esa)],[f_475_2]) ).

cnf(f_475_4,plain,
    ( c_RealVector_Onorm__class_Onorm(U_1420,c_Groups_Ominus__class_Ominus(U_1420,U_1421,U_1422)) = c_RealVector_Onorm__class_Onorm(U_1420,c_Groups_Ominus__class_Ominus(U_1420,U_1422,U_1421))
    | ~ class_RealVector_Oreal__normed__vector(U_1420) ),
    inference(clausify,[status(thm)],[f_475_3]) ).

fof(f_476_1,plain,
    ! [V_a,T_a] :
      ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a)) = c_RealVector_Onorm__class_Onorm(T_a,V_a)
      | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__norm__cancel]) ).

fof(f_476_2,plain,
    ! [U_1424,U_1423] :
      ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1423,U_1424)) = c_RealVector_Onorm__class_Onorm(U_1423,U_1424)
      | ~ class_RealVector_Oreal__normed__vector(U_1423) ),
    inference(variable_rename,[status(thm)],[f_476_1]) ).

fof(f_476_3,plain,
    ! [U_1424,U_1423] :
      ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1423,U_1424)) = c_RealVector_Onorm__class_Onorm(U_1423,U_1424)
      | ~ class_RealVector_Oreal__normed__vector(U_1423) ),
    inference(definitional_conversion,[status(esa)],[f_476_2]) ).

cnf(f_476_4,plain,
    ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1423,U_1424)) = c_RealVector_Onorm__class_Onorm(U_1423,U_1424)
    | ~ class_RealVector_Oreal__normed__vector(U_1423) ),
    inference(clausify,[status(thm)],[f_476_3]) ).

fof(f_477_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_477_2,plain,
    ! [U_1426,U_1425] :
      ( ( ( c_RealVector_Onorm__class_Onorm(U_1425,U_1426) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
          | U_1426 != c_Groups_Ozero__class_Ozero(U_1425) )
        & ( U_1426 = c_Groups_Ozero__class_Ozero(U_1425)
          | c_RealVector_Onorm__class_Onorm(U_1425,U_1426) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
      | ~ class_RealVector_Oreal__normed__vector(U_1425) ),
    inference(variable_rename,[status(thm)],[f_477_1]) ).

fof(f_477_3,plain,
    ( ! [U_1425,U_1426] :
        ( c_RealVector_Onorm__class_Onorm(U_1425,U_1426) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | U_1426 != c_Groups_Ozero__class_Ozero(U_1425)
        | ~ sP116(U_1425,U_1426) )
    & ! [U_1425,U_1426] :
        ( U_1426 = c_Groups_Ozero__class_Ozero(U_1425)
        | c_RealVector_Onorm__class_Onorm(U_1425,U_1426) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | ~ sP116(U_1425,U_1426) )
    & ! [U_1425,U_1426] :
        ( sP116(U_1425,U_1426)
        | ~ class_RealVector_Oreal__normed__vector(U_1425) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP116])],[f_477_2]) ).

cnf(f_477_4,plain,
    ( sP116(U_1425,U_1426)
    | ~ class_RealVector_Oreal__normed__vector(U_1425) ),
    inference(clausify,[status(thm)],[f_477_3]) ).

cnf(f_477_5,plain,
    ( U_1426 = c_Groups_Ozero__class_Ozero(U_1425)
    | c_RealVector_Onorm__class_Onorm(U_1425,U_1426) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | ~ sP116(U_1425,U_1426) ),
    inference(clausify,[status(thm)],[f_477_3]) ).

cnf(f_477_6,plain,
    ( c_RealVector_Onorm__class_Onorm(U_1425,U_1426) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | U_1426 != c_Groups_Ozero__class_Ozero(U_1425)
    | ~ sP116(U_1425,U_1426) ),
    inference(clausify,[status(thm)],[f_477_3]) ).

fof(f_478_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_478_2,plain,
    ! [U_1427] :
      ( c_RealVector_Onorm__class_Onorm(U_1427,c_Groups_Ozero__class_Ozero(U_1427)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
      | ~ class_RealVector_Oreal__normed__vector(U_1427) ),
    inference(variable_rename,[status(thm)],[f_478_1]) ).

fof(f_478_3,plain,
    ! [U_1427] :
      ( c_RealVector_Onorm__class_Onorm(U_1427,c_Groups_Ozero__class_Ozero(U_1427)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
      | ~ class_RealVector_Oreal__normed__vector(U_1427) ),
    inference(definitional_conversion,[status(esa)],[f_478_2]) ).

cnf(f_478_4,plain,
    ( c_RealVector_Onorm__class_Onorm(U_1427,c_Groups_Ozero__class_Ozero(U_1427)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | ~ class_RealVector_Oreal__normed__vector(U_1427) ),
    inference(clausify,[status(thm)],[f_478_3]) ).

fof(f_479_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_479_2,plain,
    ! [U_1429,U_1428] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1428,U_1429))
      | ~ class_RealVector_Oreal__normed__vector(U_1428) ),
    inference(variable_rename,[status(thm)],[f_479_1]) ).

fof(f_479_3,plain,
    ! [U_1428,U_1429] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1428,U_1429))
      | ~ class_RealVector_Oreal__normed__vector(U_1428) ),
    inference(definitional_conversion,[status(esa)],[f_479_2]) ).

cnf(f_479_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_1428,U_1429))
    | ~ class_RealVector_Oreal__normed__vector(U_1428) ),
    inference(clausify,[status(thm)],[f_479_3]) ).

fof(f_480_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_480_2,plain,
    ! [U_1431,U_1430] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1430,U_1431),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
      | ~ class_RealVector_Oreal__normed__vector(U_1430) ),
    inference(variable_rename,[status(thm)],[f_480_1]) ).

fof(f_480_3,plain,
    ! [U_1431,U_1430] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1430,U_1431),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
      | ~ class_RealVector_Oreal__normed__vector(U_1430) ),
    inference(definitional_conversion,[status(esa)],[f_480_2]) ).

cnf(f_480_4,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1430,U_1431),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | ~ class_RealVector_Oreal__normed__vector(U_1430) ),
    inference(clausify,[status(thm)],[f_480_3]) ).

fof(f_481_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_481_2,plain,
    ! [U_1432] :
      ( c_RealVector_Onorm__class_Onorm(U_1432,c_Groups_Oone__class_Oone(U_1432)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
      | ~ class_RealVector_Oreal__normed__algebra__1(U_1432) ),
    inference(variable_rename,[status(thm)],[f_481_1]) ).

fof(f_481_3,plain,
    ! [U_1432] :
      ( c_RealVector_Onorm__class_Onorm(U_1432,c_Groups_Oone__class_Oone(U_1432)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
      | ~ class_RealVector_Oreal__normed__algebra__1(U_1432) ),
    inference(definitional_conversion,[status(esa)],[f_481_2]) ).

cnf(f_481_4,plain,
    ( c_RealVector_Onorm__class_Onorm(U_1432,c_Groups_Oone__class_Oone(U_1432)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
    | ~ class_RealVector_Oreal__normed__algebra__1(U_1432) ),
    inference(clausify,[status(thm)],[f_481_3]) ).

fof(f_482_1,plain,
    ! [V_w,T_a] :
      ( c_RealVector_Onorm__class_Onorm(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_w))
      | ~ class_RealVector_Oreal__normed__algebra__1(T_a)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_norm__number__of]) ).

fof(f_482_2,plain,
    ! [U_1434,U_1433] :
      ( c_RealVector_Onorm__class_Onorm(U_1433,c_Int_Onumber__class_Onumber__of(U_1433,U_1434)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_1434))
      | ~ class_RealVector_Oreal__normed__algebra__1(U_1433)
      | ~ class_Int_Onumber__ring(U_1433) ),
    inference(variable_rename,[status(thm)],[f_482_1]) ).

fof(f_482_3,plain,
    ! [U_1433,U_1434] :
      ( c_RealVector_Onorm__class_Onorm(U_1433,c_Int_Onumber__class_Onumber__of(U_1433,U_1434)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_1434))
      | ~ class_RealVector_Oreal__normed__algebra__1(U_1433)
      | ~ class_Int_Onumber__ring(U_1433) ),
    inference(definitional_conversion,[status(esa)],[f_482_2]) ).

cnf(f_482_4,plain,
    ( c_RealVector_Onorm__class_Onorm(U_1433,c_Int_Onumber__class_Onumber__of(U_1433,U_1434)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_1434))
    | ~ class_RealVector_Oreal__normed__algebra__1(U_1433)
    | ~ class_Int_Onumber__ring(U_1433) ),
    inference(clausify,[status(thm)],[f_482_3]) ).

fof(f_483_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_483_2,plain,
    ! [U_1436,U_1435] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1435,U_1436),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
          | U_1436 != c_Groups_Ozero__class_Ozero(U_1435) )
        & ( U_1436 = c_Groups_Ozero__class_Ozero(U_1435)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1435,U_1436),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
      | ~ class_RealVector_Oreal__normed__vector(U_1435) ),
    inference(variable_rename,[status(thm)],[f_483_1]) ).

fof(f_483_3,plain,
    ( ! [U_1436,U_1435] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1435,U_1436),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | U_1436 != c_Groups_Ozero__class_Ozero(U_1435)
        | ~ sP117(U_1436,U_1435) )
    & ! [U_1436,U_1435] :
        ( U_1436 = c_Groups_Ozero__class_Ozero(U_1435)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1435,U_1436),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ sP117(U_1436,U_1435) )
    & ! [U_1436,U_1435] :
        ( sP117(U_1436,U_1435)
        | ~ class_RealVector_Oreal__normed__vector(U_1435) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP117])],[f_483_2]) ).

cnf(f_483_4,plain,
    ( sP117(U_1436,U_1435)
    | ~ class_RealVector_Oreal__normed__vector(U_1435) ),
    inference(clausify,[status(thm)],[f_483_3]) ).

cnf(f_483_5,plain,
    ( U_1436 = c_Groups_Ozero__class_Ozero(U_1435)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1435,U_1436),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | ~ sP117(U_1436,U_1435) ),
    inference(clausify,[status(thm)],[f_483_3]) ).

cnf(f_483_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1435,U_1436),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | U_1436 != c_Groups_Ozero__class_Ozero(U_1435)
    | ~ sP117(U_1436,U_1435) ),
    inference(clausify,[status(thm)],[f_483_3]) ).

fof(f_484_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_484_2,plain,
    ! [U_1438,U_1437] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1437,U_1438))
          | U_1438 = c_Groups_Ozero__class_Ozero(U_1437) )
        & ( U_1438 != c_Groups_Ozero__class_Ozero(U_1437)
          | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1437,U_1438)) ) )
      | ~ class_RealVector_Oreal__normed__vector(U_1437) ),
    inference(variable_rename,[status(thm)],[f_484_1]) ).

fof(f_484_3,plain,
    ( ! [U_1438,U_1437] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1437,U_1438))
        | U_1438 = c_Groups_Ozero__class_Ozero(U_1437)
        | ~ sP118(U_1438,U_1437) )
    & ! [U_1438,U_1437] :
        ( U_1438 != c_Groups_Ozero__class_Ozero(U_1437)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1437,U_1438))
        | ~ sP118(U_1438,U_1437) )
    & ! [U_1438,U_1437] :
        ( sP118(U_1438,U_1437)
        | ~ class_RealVector_Oreal__normed__vector(U_1437) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP118])],[f_484_2]) ).

cnf(f_484_4,plain,
    ( sP118(U_1438,U_1437)
    | ~ class_RealVector_Oreal__normed__vector(U_1437) ),
    inference(clausify,[status(thm)],[f_484_3]) ).

cnf(f_484_5,plain,
    ( U_1438 != c_Groups_Ozero__class_Ozero(U_1437)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1437,U_1438))
    | ~ sP118(U_1438,U_1437) ),
    inference(clausify,[status(thm)],[f_484_3]) ).

cnf(f_484_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1437,U_1438))
    | U_1438 = c_Groups_Ozero__class_Ozero(U_1437)
    | ~ sP118(U_1438,U_1437) ),
    inference(clausify,[status(thm)],[f_484_3]) ).

fof(f_485_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_485_2,plain,
    ! [U_1441,U_1440,U_1439] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1439,c_Groups_Oplus__class_Oplus(U_1439,U_1440,U_1441)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1439,U_1440),c_RealVector_Onorm__class_Onorm(U_1439,U_1441)))
      | ~ class_RealVector_Oreal__normed__vector(U_1439) ),
    inference(variable_rename,[status(thm)],[f_485_1]) ).

fof(f_485_3,plain,
    ! [U_1439,U_1440,U_1441] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1439,c_Groups_Oplus__class_Oplus(U_1439,U_1440,U_1441)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1439,U_1440),c_RealVector_Onorm__class_Onorm(U_1439,U_1441)))
      | ~ class_RealVector_Oreal__normed__vector(U_1439) ),
    inference(definitional_conversion,[status(esa)],[f_485_2]) ).

cnf(f_485_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1439,c_Groups_Oplus__class_Oplus(U_1439,U_1440,U_1441)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1439,U_1440),c_RealVector_Onorm__class_Onorm(U_1439,U_1441)))
    | ~ class_RealVector_Oreal__normed__vector(U_1439) ),
    inference(clausify,[status(thm)],[f_485_3]) ).

fof(f_486_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_486_2,plain,
    ! [U_1446,U_1445,U_1444,U_1443,U_1442] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1442,c_Groups_Oplus__class_Oplus(U_1442,U_1443,U_1445)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1444,U_1446))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1442,U_1445),U_1446)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1442,U_1443),U_1444)
      | ~ class_RealVector_Oreal__normed__vector(U_1442) ),
    inference(variable_rename,[status(thm)],[f_486_1]) ).

fof(f_486_3,plain,
    ! [U_1442,U_1443,U_1444,U_1445,U_1446] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1442,c_Groups_Oplus__class_Oplus(U_1442,U_1443,U_1445)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1444,U_1446))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1442,U_1445),U_1446)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1442,U_1443),U_1444)
      | ~ class_RealVector_Oreal__normed__vector(U_1442) ),
    inference(definitional_conversion,[status(esa)],[f_486_2]) ).

cnf(f_486_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1442,c_Groups_Oplus__class_Oplus(U_1442,U_1443,U_1445)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1444,U_1446))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1442,U_1445),U_1446)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1442,U_1443),U_1444)
    | ~ class_RealVector_Oreal__normed__vector(U_1442) ),
    inference(clausify,[status(thm)],[f_486_3]) ).

fof(f_487_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_487_2,plain,
    ! [U_1448,U_1447] : 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_1447,U_1448)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1447)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1448)),
    inference(variable_rename,[status(thm)],[f_487_1]) ).

fof(f_487_3,plain,
    ! [U_1447,U_1448] : 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_1447,U_1448)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1447)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1448)),
    inference(definitional_conversion,[status(esa)],[f_487_2]) ).

cnf(f_487_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_1447,U_1448)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1447)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1448)),
    inference(clausify,[status(thm)],[f_487_3]) ).

fof(f_488_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_488_2,plain,
    ! [U_1450,U_1449] :
      ( 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_1449,U_1450))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1450)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1449) ),
    inference(variable_rename,[status(thm)],[f_488_1]) ).

fof(f_488_3,plain,
    ! [U_1449,U_1450] :
      ( 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_1449,U_1450))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1450)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1449) ),
    inference(definitional_conversion,[status(esa)],[f_488_2]) ).

cnf(f_488_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_1449,U_1450))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1450)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1449) ),
    inference(clausify,[status(thm)],[f_488_3]) ).

fof(f_489_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_489_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_489_1]) ).

cnf(f_489_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_489_2]) ).

fof(f_490_1,plain,
    ! [B_e] :
      ( ? [B_N] :
        ! [B_n] :
          ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,B_n)),v_z____)),B_e)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_N,B_n) )
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_e) ),
    inference(fof_nnf,[status(thm)],[fact_fz_I2_J]) ).

fof(f_490_2,plain,
    ! [U_1453] :
      ( ? [U_1452] :
        ! [U_1451] :
          ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,U_1451)),v_z____)),U_1453)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1452,U_1451) )
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1453) ),
    inference(variable_rename,[status(thm)],[f_490_1]) ).

fof(f_490_3,plain,
    ! [U_1453] :
      ( ! [U_1451] :
          ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,U_1451)),v_z____)),U_1453)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK43(U_1453),U_1451) )
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1453) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_1452,sK43(U_1453))],[f_490_2]) ).

fof(f_490_4,plain,
    ! [U_1451,U_1453] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,U_1451)),v_z____)),U_1453)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK43(U_1453),U_1451)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1453) ),
    inference(definitional_conversion,[status(esa)],[f_490_3]) ).

cnf(f_490_5,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,v_g____(hAPP(v_f____,U_1451)),v_z____)),U_1453)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK43(U_1453),U_1451)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1453) ),
    inference(clausify,[status(thm)],[f_490_4]) ).

fof(f_491_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_491_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_491_1]) ).

cnf(f_491_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_491_2]) ).

fof(f_492_1,plain,
    ? [B_N] :
    ! [B_n] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,B_n)),v_z____)),v_d____)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_N,B_n) ),
    inference(fof_nnf,[status(thm)],[fact__096EX_AN_O_AALL_An_062_061N_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ad_096]) ).

fof(f_492_2,plain,
    ? [U_1455] :
    ! [U_1454] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,U_1454)),v_z____)),v_d____)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1455,U_1454) ),
    inference(variable_rename,[status(thm)],[f_492_1]) ).

fof(f_492_3,plain,
    ! [U_1454] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,U_1454)),v_z____)),v_d____)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK44,U_1454) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_1455,sK44)],[f_492_2]) ).

fof(f_492_4,plain,
    ! [U_1454] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,U_1454)),v_z____)),v_d____)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK44,U_1454) ),
    inference(definitional_conversion,[status(esa)],[f_492_3]) ).

cnf(f_492_5,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,v_g____(hAPP(v_f____,U_1454)),v_z____)),v_d____)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK44,U_1454) ),
    inference(clausify,[status(thm)],[f_492_4]) ).

fof(f_493_1,plain,
    ? [B_N1] :
    ! [B_n] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,B_n)),v_z____)),v_d____)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_N1,B_n) ),
    inference(fof_nnf,[status(thm)],[fact__096_B_Bthesis_O_A_I_B_BN1_O_AALL_An_062_061N1_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ad_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096]) ).

fof(f_493_2,plain,
    ? [U_1457] :
    ! [U_1456] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,U_1456)),v_z____)),v_d____)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1457,U_1456) ),
    inference(variable_rename,[status(thm)],[f_493_1]) ).

fof(f_493_3,plain,
    ! [U_1456] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,U_1456)),v_z____)),v_d____)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK45,U_1456) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_1457,sK45)],[f_493_2]) ).

fof(f_493_4,plain,
    ! [U_1456] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,U_1456)),v_z____)),v_d____)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK45,U_1456) ),
    inference(definitional_conversion,[status(esa)],[f_493_3]) ).

cnf(f_493_5,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,v_g____(hAPP(v_f____,U_1456)),v_z____)),v_d____)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK45,U_1456) ),
    inference(clausify,[status(thm)],[f_493_4]) ).

fof(f_494_1,plain,
    ! [V_x,V_n] :
      ( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_n))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_n))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
      | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_natceiling__add__number__of]) ).

fof(f_494_2,plain,
    ! [U_1459,U_1458] :
      ( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1459,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_1458))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(U_1459),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1458))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1459)
      | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1458)) ),
    inference(variable_rename,[status(thm)],[f_494_1]) ).

fof(f_494_3,plain,
    ! [U_1458,U_1459] :
      ( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1459,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_1458))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(U_1459),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1458))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1459)
      | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1458)) ),
    inference(definitional_conversion,[status(esa)],[f_494_2]) ).

cnf(f_494_4,plain,
    ( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1459,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_1458))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(U_1459),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1458))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1459)
    | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1458)) ),
    inference(clausify,[status(thm)],[f_494_3]) ).

fof(f_495_1,plain,
    ! [V_x,V_n] :
      ( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_n))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_n))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
      | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_natfloor__add__number__of]) ).

fof(f_495_2,plain,
    ! [U_1461,U_1460] :
      ( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1461,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_1460))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_1461),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1460))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1461)
      | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1460)) ),
    inference(variable_rename,[status(thm)],[f_495_1]) ).

fof(f_495_3,plain,
    ! [U_1460,U_1461] :
      ( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1461,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_1460))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_1461),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1460))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1461)
      | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1460)) ),
    inference(definitional_conversion,[status(esa)],[f_495_2]) ).

cnf(f_495_4,plain,
    ( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1461,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_1460))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_1461),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1460))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1461)
    | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1460)) ),
    inference(clausify,[status(thm)],[f_495_3]) ).

fof(f_496_1,plain,
    ~ c_Nat__Numeral_Oneg(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(fof_nnf,[status(thm)],[fact_not__neg__0]) ).

fof(f_496_2,plain,
    ~ c_Nat__Numeral_Oneg(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(definitional_conversion,[status(esa)],[f_496_1]) ).

cnf(f_496_3,plain,
    ~ c_Nat__Numeral_Oneg(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_496_2]) ).

fof(f_497_1,plain,
    ~ c_Nat__Numeral_Oneg(c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(fof_nnf,[status(thm)],[fact_not__neg__1]) ).

fof(f_497_2,plain,
    ~ c_Nat__Numeral_Oneg(c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(definitional_conversion,[status(esa)],[f_497_1]) ).

cnf(f_497_3,plain,
    ~ c_Nat__Numeral_Oneg(c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_497_2]) ).

fof(f_498_1,plain,
    ! [V_x_2] :
      ( ( ~ c_Nat__Numeral_Oneg(V_x_2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x_2) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x_2)
        | c_Nat__Numeral_Oneg(V_x_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_not__neg__eq__ge__0]) ).

fof(f_498_2,plain,
    ! [U_1462] :
      ( ( ~ c_Nat__Numeral_Oneg(U_1462)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1462) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1462)
        | c_Nat__Numeral_Oneg(U_1462) ) ),
    inference(variable_rename,[status(thm)],[f_498_1]) ).

fof(f_498_3,plain,
    ( ! [U_1464] :
        ( ~ c_Nat__Numeral_Oneg(U_1464)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1464) )
    & ! [U_1463] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1463)
        | c_Nat__Numeral_Oneg(U_1463) ) ),
    inference(miniscope,[status(thm)],[f_498_2]) ).

fof(f_498_4,plain,
    ( ! [U_1464] :
        ( ~ c_Nat__Numeral_Oneg(U_1464)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1464) )
    & ! [U_1463] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1463)
        | c_Nat__Numeral_Oneg(U_1463) ) ),
    inference(definitional_conversion,[status(esa)],[f_498_3]) ).

cnf(f_498_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1463)
    | c_Nat__Numeral_Oneg(U_1463) ),
    inference(clausify,[status(thm)],[f_498_4]) ).

cnf(f_498_6,plain,
    ( ~ c_Nat__Numeral_Oneg(U_1464)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1464) ),
    inference(clausify,[status(thm)],[f_498_4]) ).

fof(f_499_1,plain,
    ! [V_Z_2] :
      ( ( c_Nat__Numeral_Oneg(V_Z_2)
        | ~ 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_Nat__Numeral_Oneg(V_Z_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_neg__def]) ).

fof(f_499_2,plain,
    ! [U_1465] :
      ( ( c_Nat__Numeral_Oneg(U_1465)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1465,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1465,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Nat__Numeral_Oneg(U_1465) ) ),
    inference(variable_rename,[status(thm)],[f_499_1]) ).

fof(f_499_3,plain,
    ( ! [U_1467] :
        ( c_Nat__Numeral_Oneg(U_1467)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1467,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    & ! [U_1466] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1466,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Nat__Numeral_Oneg(U_1466) ) ),
    inference(miniscope,[status(thm)],[f_499_2]) ).

fof(f_499_4,plain,
    ( ! [U_1467] :
        ( c_Nat__Numeral_Oneg(U_1467)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1467,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    & ! [U_1466] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1466,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Nat__Numeral_Oneg(U_1466) ) ),
    inference(definitional_conversion,[status(esa)],[f_499_3]) ).

cnf(f_499_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1466,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Nat__Numeral_Oneg(U_1466) ),
    inference(clausify,[status(thm)],[f_499_4]) ).

cnf(f_499_6,plain,
    ( c_Nat__Numeral_Oneg(U_1467)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1467,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(clausify,[status(thm)],[f_499_4]) ).

fof(f_500_1,plain,
    ! [V_v] :
      ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v)) ),
    inference(fof_nnf,[status(thm)],[fact_neg__imp__number__of__eq__0]) ).

fof(f_500_2,plain,
    ! [U_1468] :
      ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1468) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1468)) ),
    inference(variable_rename,[status(thm)],[f_500_1]) ).

fof(f_500_3,plain,
    ! [U_1468] :
      ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1468) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1468)) ),
    inference(definitional_conversion,[status(esa)],[f_500_2]) ).

cnf(f_500_4,plain,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1468) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1468)) ),
    inference(clausify,[status(thm)],[f_500_3]) ).

fof(f_501_1,plain,
    ! [V_v_H_2,V_v_2] :
      ( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2)
        | ( ( ( V_v_2 != V_v_H_2
              & ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H_2)) )
            | ( c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              & c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H_2)) ) )
          & ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_2)) )
        | ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
          & c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_2)) ) )
      & ( ( ( ( ( V_v_2 = V_v_H_2
                | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H_2)) )
              & ( c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H_2)) ) )
            | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_2)) )
          & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
            | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_2)) ) )
        | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_eq__nat__number__of]) ).

fof(f_501_2,plain,
    ! [U_1470,U_1469] :
      ( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1469) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1470)
        | ( ( ( U_1469 != U_1470
              & ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1470)) )
            | ( c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1469) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              & c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1470)) ) )
          & ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1469)) )
        | ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1470),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
          & c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1469)) ) )
      & ( ( ( ( ( U_1469 = U_1470
                | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1470)) )
              & ( c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1469) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1470)) ) )
            | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1469)) )
          & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1470),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
            | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1469)) ) )
        | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1469) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1470) ) ),
    inference(variable_rename,[status(thm)],[f_501_1]) ).

fof(f_501_3,plain,
    ( ! [U_1474,U_1472] :
        ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1472) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1474)
        | ( ( ( U_1472 != U_1474
              & ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1474)) )
            | ( c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1472) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              & c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1474)) ) )
          & ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1472)) )
        | ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1474),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
          & c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1472)) ) )
    & ! [U_1473,U_1471] :
        ( ( ( ( ( U_1471 = U_1473
                | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1473)) )
              & ( c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1471) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1473)) ) )
            | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1471)) )
          & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1473),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
            | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1471)) ) )
        | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1471) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1473) ) ),
    inference(miniscope,[status(thm)],[f_501_2]) ).

fof(f_501_4,plain,
    ( ! [U_1472,U_1474] :
        ( U_1472 != U_1474
        | ~ sP123(U_1472,U_1474) )
    & ! [U_1472,U_1474] :
        ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1474))
        | ~ sP123(U_1472,U_1474) )
    & ! [U_1472,U_1474] :
        ( c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1472) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP122(U_1472,U_1474) )
    & ! [U_1472,U_1474] :
        ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1474))
        | ~ sP122(U_1472,U_1474) )
    & ! [U_1472,U_1474] :
        ( sP123(U_1472,U_1474)
        | sP122(U_1472,U_1474)
        | ~ sP124(U_1472,U_1474) )
    & ! [U_1472,U_1474] :
        ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1472))
        | ~ sP124(U_1472,U_1474) )
    & ! [U_1472,U_1474] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1474),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ sP121(U_1472,U_1474) )
    & ! [U_1472,U_1474] :
        ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1472))
        | ~ sP121(U_1472,U_1474) )
    & ! [U_1471,U_1473] :
        ( U_1471 = U_1473
        | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1473))
        | ~ sP119(U_1471,U_1473) )
    & ! [U_1471,U_1473] :
        ( c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1471) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1473))
        | ~ sP119(U_1471,U_1473) )
    & ! [U_1471,U_1473] :
        ( sP119(U_1471,U_1473)
        | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1471))
        | ~ sP120(U_1471,U_1473) )
    & ! [U_1471,U_1473] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1473),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1471))
        | ~ sP120(U_1471,U_1473) )
    & ! [U_1472,U_1474] :
        ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1472) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1474)
        | sP124(U_1472,U_1474)
        | sP121(U_1472,U_1474) )
    & ! [U_1471,U_1473] :
        ( sP120(U_1471,U_1473)
        | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1471) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1473) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP119,sP120,sP121,sP122,sP123,sP124])],[f_501_3]) ).

cnf(f_501_5,plain,
    ( sP120(U_1471,U_1473)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1471) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1473) ),
    inference(clausify,[status(thm)],[f_501_4]) ).

cnf(f_501_6,plain,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1472) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1474)
    | sP124(U_1472,U_1474)
    | sP121(U_1472,U_1474) ),
    inference(clausify,[status(thm)],[f_501_4]) ).

cnf(f_501_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1473),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1471))
    | ~ sP120(U_1471,U_1473) ),
    inference(clausify,[status(thm)],[f_501_4]) ).

cnf(f_501_8,plain,
    ( sP119(U_1471,U_1473)
    | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1471))
    | ~ sP120(U_1471,U_1473) ),
    inference(clausify,[status(thm)],[f_501_4]) ).

cnf(f_501_9,plain,
    ( c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1471) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1473))
    | ~ sP119(U_1471,U_1473) ),
    inference(clausify,[status(thm)],[f_501_4]) ).

cnf(f_501_10,plain,
    ( U_1471 = U_1473
    | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1473))
    | ~ sP119(U_1471,U_1473) ),
    inference(clausify,[status(thm)],[f_501_4]) ).

cnf(f_501_11,plain,
    ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1472))
    | ~ sP121(U_1472,U_1474) ),
    inference(clausify,[status(thm)],[f_501_4]) ).

cnf(f_501_12,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1474),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ sP121(U_1472,U_1474) ),
    inference(clausify,[status(thm)],[f_501_4]) ).

cnf(f_501_13,plain,
    ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1472))
    | ~ sP124(U_1472,U_1474) ),
    inference(clausify,[status(thm)],[f_501_4]) ).

cnf(f_501_14,plain,
    ( sP123(U_1472,U_1474)
    | sP122(U_1472,U_1474)
    | ~ sP124(U_1472,U_1474) ),
    inference(clausify,[status(thm)],[f_501_4]) ).

cnf(f_501_15,plain,
    ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1474))
    | ~ sP122(U_1472,U_1474) ),
    inference(clausify,[status(thm)],[f_501_4]) ).

cnf(f_501_16,plain,
    ( c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1472) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP122(U_1472,U_1474) ),
    inference(clausify,[status(thm)],[f_501_4]) ).

cnf(f_501_17,plain,
    ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1474))
    | ~ sP123(U_1472,U_1474) ),
    inference(clausify,[status(thm)],[f_501_4]) ).

cnf(f_501_18,plain,
    ( U_1472 != U_1474
    | ~ sP123(U_1472,U_1474) ),
    inference(clausify,[status(thm)],[f_501_4]) ).

fof(f_502_1,plain,
    ! [V_k,V_v_H,V_v] :
      ( ( ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H),V_k)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_v_H)),V_k)
            | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H)) )
          & ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H),V_k)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),V_k)
            | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H)) ) )
        | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v)) )
      & ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H),V_k)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H),V_k)
        | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v)) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__number__of__add__left]) ).

fof(f_502_2,plain,
    ! [U_1477,U_1476,U_1475] :
      ( ( ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1475),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1476),U_1477)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1475,U_1476)),U_1477)
            | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1476)) )
          & ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1475),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1476),U_1477)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1475),U_1477)
            | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1476)) ) )
        | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1475)) )
      & ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1475),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1476),U_1477)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1476),U_1477)
        | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1475)) ) ),
    inference(variable_rename,[status(thm)],[f_502_1]) ).

fof(f_502_3,plain,
    ( ! [U_1483,U_1481,U_1479] :
        ( ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1479),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1481),U_1483)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1479,U_1481)),U_1483)
            | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1481)) )
          & ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1479),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1481),U_1483)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1479),U_1483)
            | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1481)) ) )
        | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1479)) )
    & ! [U_1482,U_1480,U_1478] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1478),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1480),U_1482)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1480),U_1482)
        | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1478)) ) ),
    inference(miniscope,[status(thm)],[f_502_2]) ).

fof(f_502_4,plain,
    ( ! [U_1481,U_1479,U_1483] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1479),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1481),U_1483)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1479,U_1481)),U_1483)
        | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1481))
        | ~ sP125(U_1481,U_1479,U_1483) )
    & ! [U_1481,U_1479,U_1483] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1479),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1481),U_1483)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1479),U_1483)
        | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1481))
        | ~ sP125(U_1481,U_1479,U_1483) )
    & ! [U_1481,U_1479,U_1483] :
        ( sP125(U_1481,U_1479,U_1483)
        | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1479)) )
    & ! [U_1478,U_1482,U_1480] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1478),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1480),U_1482)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1480),U_1482)
        | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1478)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP125])],[f_502_3]) ).

cnf(f_502_5,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1478),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1480),U_1482)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1480),U_1482)
    | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1478)) ),
    inference(clausify,[status(thm)],[f_502_4]) ).

cnf(f_502_6,plain,
    ( sP125(U_1481,U_1479,U_1483)
    | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1479)) ),
    inference(clausify,[status(thm)],[f_502_4]) ).

cnf(f_502_7,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1479),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1481),U_1483)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1479),U_1483)
    | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1481))
    | ~ sP125(U_1481,U_1479,U_1483) ),
    inference(clausify,[status(thm)],[f_502_4]) ).

cnf(f_502_8,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1479),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1481),U_1483)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1479,U_1481)),U_1483)
    | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1481))
    | ~ sP125(U_1481,U_1479,U_1483) ),
    inference(clausify,[status(thm)],[f_502_4]) ).

fof(f_503_1,plain,
    ! [V_v] :
      ( ( hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_v)
        | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v)) )
      & ( hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v)) ) ),
    inference(fof_nnf,[status(thm)],[fact_real__of__nat__number__of]) ).

fof(f_503_2,plain,
    ! [U_1484] :
      ( ( hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1484)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_1484)
        | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1484)) )
      & ( hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1484)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1484)) ) ),
    inference(variable_rename,[status(thm)],[f_503_1]) ).

fof(f_503_3,plain,
    ( ! [U_1486] :
        ( hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1486)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_1486)
        | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1486)) )
    & ! [U_1485] :
        ( hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1485)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1485)) ) ),
    inference(miniscope,[status(thm)],[f_503_2]) ).

fof(f_503_4,plain,
    ( ! [U_1486] :
        ( hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1486)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_1486)
        | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1486)) )
    & ! [U_1485] :
        ( hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1485)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1485)) ) ),
    inference(definitional_conversion,[status(esa)],[f_503_3]) ).

cnf(f_503_5,plain,
    ( hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1485)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1485)) ),
    inference(clausify,[status(thm)],[f_503_4]) ).

cnf(f_503_6,plain,
    ( hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1486)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_1486)
    | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1486)) ),
    inference(clausify,[status(thm)],[f_503_4]) ).

fof(f_504_1,plain,
    ! [V_x_2,V_n_2] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_n_2),c_RComplete_Onatfloor(V_x_2))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_n_2),V_x_2) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_n_2),V_x_2)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_n_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)
      | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_n_2)) ),
    inference(fof_nnf,[status(thm)],[fact_le__natfloor__eq__number__of]) ).

fof(f_504_2,plain,
    ! [U_1488,U_1487] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1487),c_RComplete_Onatfloor(U_1488))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_1487),U_1488) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_1487),U_1488)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1487),c_RComplete_Onatfloor(U_1488)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1488)
      | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1487)) ),
    inference(variable_rename,[status(thm)],[f_504_1]) ).

fof(f_504_3,plain,
    ( ! [U_1487,U_1488] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1487),c_RComplete_Onatfloor(U_1488))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_1487),U_1488)
        | ~ sP126(U_1487,U_1488) )
    & ! [U_1487,U_1488] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_1487),U_1488)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1487),c_RComplete_Onatfloor(U_1488))
        | ~ sP126(U_1487,U_1488) )
    & ! [U_1487,U_1488] :
        ( sP126(U_1487,U_1488)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1488)
        | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1487)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP126])],[f_504_2]) ).

cnf(f_504_4,plain,
    ( sP126(U_1487,U_1488)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1488)
    | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1487)) ),
    inference(clausify,[status(thm)],[f_504_3]) ).

cnf(f_504_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_1487),U_1488)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1487),c_RComplete_Onatfloor(U_1488))
    | ~ sP126(U_1487,U_1488) ),
    inference(clausify,[status(thm)],[f_504_3]) ).

cnf(f_504_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1487),c_RComplete_Onatfloor(U_1488))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_1487),U_1488)
    | ~ sP126(U_1487,U_1488) ),
    inference(clausify,[status(thm)],[f_504_3]) ).

fof(f_505_1,plain,
    ! [V_x_2,V_n_2] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_n_2))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_n_2)) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_n_2))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_n_2)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
      | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_n_2)) ),
    inference(fof_nnf,[status(thm)],[fact_natceiling__le__eq__number__of]) ).

fof(f_505_2,plain,
    ! [U_1490,U_1489] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1490),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1489))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1490,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_1489)) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1490,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_1489))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1490),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1489)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1490)
      | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1489)) ),
    inference(variable_rename,[status(thm)],[f_505_1]) ).

fof(f_505_3,plain,
    ( ! [U_1489,U_1490] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1490),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1489))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1490,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_1489))
        | ~ sP127(U_1489,U_1490) )
    & ! [U_1489,U_1490] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1490,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_1489))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1490),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1489))
        | ~ sP127(U_1489,U_1490) )
    & ! [U_1489,U_1490] :
        ( sP127(U_1489,U_1490)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1490)
        | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1489)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP127])],[f_505_2]) ).

cnf(f_505_4,plain,
    ( sP127(U_1489,U_1490)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1490)
    | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1489)) ),
    inference(clausify,[status(thm)],[f_505_3]) ).

cnf(f_505_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1490,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_1489))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1490),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1489))
    | ~ sP127(U_1489,U_1490) ),
    inference(clausify,[status(thm)],[f_505_3]) ).

cnf(f_505_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1490),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1489))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1490,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_1489))
    | ~ sP127(U_1489,U_1490) ),
    inference(clausify,[status(thm)],[f_505_3]) ).

fof(f_506_1,plain,
    ! [V_n,V_v] :
      ( ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),V_n)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(V_v)),V_n)
        | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v)) )
      & ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),V_n)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n)
        | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__nat__number__of__add]) ).

fof(f_506_2,plain,
    ! [U_1492,U_1491] :
      ( ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1491),U_1492)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(U_1491)),U_1492)
        | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1491)) )
      & ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1491),U_1492)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_1492)
        | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1491)) ) ),
    inference(variable_rename,[status(thm)],[f_506_1]) ).

fof(f_506_3,plain,
    ( ! [U_1496,U_1494] :
        ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1494),U_1496)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(U_1494)),U_1496)
        | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1494)) )
    & ! [U_1495,U_1493] :
        ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1493),U_1495)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_1495)
        | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1493)) ) ),
    inference(miniscope,[status(thm)],[f_506_2]) ).

fof(f_506_4,plain,
    ( ! [U_1494,U_1496] :
        ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1494),U_1496)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(U_1494)),U_1496)
        | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1494)) )
    & ! [U_1493,U_1495] :
        ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1493),U_1495)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_1495)
        | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1493)) ) ),
    inference(definitional_conversion,[status(esa)],[f_506_3]) ).

cnf(f_506_5,plain,
    ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1493),U_1495)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_1495)
    | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1493)) ),
    inference(clausify,[status(thm)],[f_506_4]) ).

cnf(f_506_6,plain,
    ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1494),U_1496)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(U_1494)),U_1496)
    | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1494)) ),
    inference(clausify,[status(thm)],[f_506_4]) ).

fof(f_507_1,plain,
    ! [V_v] :
      ( ( c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(V_v))
        | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v)) )
      & ( c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__nat__number__of]) ).

fof(f_507_2,plain,
    ! [U_1497] :
      ( ( c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1497)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(U_1497))
        | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1497)) )
      & ( c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1497)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1497)) ) ),
    inference(variable_rename,[status(thm)],[f_507_1]) ).

fof(f_507_3,plain,
    ( ! [U_1499] :
        ( c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1499)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(U_1499))
        | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1499)) )
    & ! [U_1498] :
        ( c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1498)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1498)) ) ),
    inference(miniscope,[status(thm)],[f_507_2]) ).

fof(f_507_4,plain,
    ( ! [U_1499] :
        ( c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1499)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(U_1499))
        | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1499)) )
    & ! [U_1498] :
        ( c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1498)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1498)) ) ),
    inference(definitional_conversion,[status(esa)],[f_507_3]) ).

cnf(f_507_5,plain,
    ( c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1498)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1498)) ),
    inference(clausify,[status(thm)],[f_507_4]) ).

cnf(f_507_6,plain,
    ( c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1499)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(U_1499))
    | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1499)) ),
    inference(clausify,[status(thm)],[f_507_4]) ).

fof(f_508_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_508_2,plain,
    ! [U_1505,U_1504,U_1503,U_1502] :
      ( ! [U_1501] :
          ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1502,hAPP(U_1505,U_1501)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1502,hAPP(U_1505,U_1504))))
          | ~ c_Orderings_Oord__class_Oless__eq(U_1503,U_1504,U_1501) )
      | ? [U_1500] :
          ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1502,c_Groups_Ominus__class_Ominus(U_1502,hAPP(U_1505,U_1504),hAPP(U_1505,U_1500))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
          & c_Orderings_Oord__class_Oless__eq(U_1503,U_1504,U_1500) )
      | ~ class_Orderings_Oord(U_1503)
      | ~ class_RealVector_Oreal__normed__vector(U_1502) ),
    inference(variable_rename,[status(thm)],[f_508_1]) ).

fof(f_508_3,plain,
    ! [U_1505,U_1504,U_1503,U_1502] :
      ( ! [U_1501] :
          ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1502,hAPP(U_1505,U_1501)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1502,hAPP(U_1505,U_1504))))
          | ~ c_Orderings_Oord__class_Oless__eq(U_1503,U_1504,U_1501) )
      | ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1502,c_Groups_Ominus__class_Ominus(U_1502,hAPP(U_1505,U_1504),hAPP(U_1505,sK46(U_1505,U_1504,U_1503,U_1502)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
        & c_Orderings_Oord__class_Oless__eq(U_1503,U_1504,sK46(U_1505,U_1504,U_1503,U_1502)) )
      | ~ class_Orderings_Oord(U_1503)
      | ~ class_RealVector_Oreal__normed__vector(U_1502) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_1500,sK46(U_1505,U_1504,U_1503,U_1502))],[f_508_2]) ).

fof(f_508_4,plain,
    ( ! [U_1502,U_1503,U_1504,U_1505] :
        ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1502,c_Groups_Ominus__class_Ominus(U_1502,hAPP(U_1505,U_1504),hAPP(U_1505,sK46(U_1505,U_1504,U_1503,U_1502)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
        | ~ sP128(U_1502,U_1503,U_1504,U_1505) )
    & ! [U_1502,U_1503,U_1504,U_1505] :
        ( c_Orderings_Oord__class_Oless__eq(U_1503,U_1504,sK46(U_1505,U_1504,U_1503,U_1502))
        | ~ sP128(U_1502,U_1503,U_1504,U_1505) )
    & ! [U_1501,U_1502,U_1503,U_1504,U_1505] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1502,hAPP(U_1505,U_1501)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1502,hAPP(U_1505,U_1504))))
        | ~ c_Orderings_Oord__class_Oless__eq(U_1503,U_1504,U_1501)
        | sP128(U_1502,U_1503,U_1504,U_1505)
        | ~ class_Orderings_Oord(U_1503)
        | ~ class_RealVector_Oreal__normed__vector(U_1502) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP128])],[f_508_3]) ).

cnf(f_508_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1502,hAPP(U_1505,U_1501)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1502,hAPP(U_1505,U_1504))))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1503,U_1504,U_1501)
    | sP128(U_1502,U_1503,U_1504,U_1505)
    | ~ class_Orderings_Oord(U_1503)
    | ~ class_RealVector_Oreal__normed__vector(U_1502) ),
    inference(clausify,[status(thm)],[f_508_4]) ).

cnf(f_508_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1503,U_1504,sK46(U_1505,U_1504,U_1503,U_1502))
    | ~ sP128(U_1502,U_1503,U_1504,U_1505) ),
    inference(clausify,[status(thm)],[f_508_4]) ).

cnf(f_508_7,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1502,c_Groups_Ominus__class_Ominus(U_1502,hAPP(U_1505,U_1504),hAPP(U_1505,sK46(U_1505,U_1504,U_1503,U_1502)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    | ~ sP128(U_1502,U_1503,U_1504,U_1505) ),
    inference(clausify,[status(thm)],[f_508_4]) ).

fof(f_509_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_509_2,plain,
    ! [U_1506] :
      ( 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_1506,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_1506,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_1506,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_1506,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_1506) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
    inference(variable_rename,[status(thm)],[f_509_1]) ).

fof(f_509_3,plain,
    ! [U_1506] :
      ( 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_1506,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_1506,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_1506,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_1506,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_1506) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
    inference(definitional_conversion,[status(esa)],[f_509_2]) ).

cnf(f_509_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_1506,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_1506,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_1506,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_1506,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_1506) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
    inference(clausify,[status(thm)],[f_509_3]) ).

fof(f_510_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_510_2,plain,
    c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_510_1]) ).

cnf(f_510_3,plain,
    c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_510_2]) ).

fof(f_511_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_511_2,plain,
    c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_511_1]) ).

cnf(f_511_3,plain,
    c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_511_2]) ).

fof(f_512_1,plain,
    ! [V_w] : c_Complex_Oii != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,V_w),
    inference(fof_nnf,[status(thm)],[fact_complex__i__not__number__of]) ).

fof(f_512_2,plain,
    ! [U_1507] : c_Complex_Oii != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,U_1507),
    inference(variable_rename,[status(thm)],[f_512_1]) ).

fof(f_512_3,plain,
    ! [U_1507] : c_Complex_Oii != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,U_1507),
    inference(definitional_conversion,[status(esa)],[f_512_2]) ).

cnf(f_512_4,plain,
    c_Complex_Oii != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,U_1507),
    inference(clausify,[status(thm)],[f_512_3]) ).

fof(f_513_1,plain,
    ! [V_k] : c_Int_Osucc(V_k) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(fof_nnf,[status(thm)],[fact_succ__def]) ).

fof(f_513_2,plain,
    ! [U_1508] : c_Int_Osucc(U_1508) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1508,c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(variable_rename,[status(thm)],[f_513_1]) ).

fof(f_513_3,plain,
    ! [U_1508] : c_Int_Osucc(U_1508) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1508,c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(definitional_conversion,[status(esa)],[f_513_2]) ).

cnf(f_513_4,plain,
    c_Int_Osucc(U_1508) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1508,c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_513_3]) ).

fof(f_514_1,plain,
    ! [V_k,T_a] :
      ( c_Int_Onumber__class_Onumber__of(T_a,c_Int_Osucc(V_k)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_k))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_number__of__succ]) ).

fof(f_514_2,plain,
    ! [U_1510,U_1509] :
      ( c_Int_Onumber__class_Onumber__of(U_1509,c_Int_Osucc(U_1510)) = c_Groups_Oplus__class_Oplus(U_1509,c_Groups_Oone__class_Oone(U_1509),c_Int_Onumber__class_Onumber__of(U_1509,U_1510))
      | ~ class_Int_Onumber__ring(U_1509) ),
    inference(variable_rename,[status(thm)],[f_514_1]) ).

fof(f_514_3,plain,
    ! [U_1510,U_1509] :
      ( c_Int_Onumber__class_Onumber__of(U_1509,c_Int_Osucc(U_1510)) = c_Groups_Oplus__class_Oplus(U_1509,c_Groups_Oone__class_Oone(U_1509),c_Int_Onumber__class_Onumber__of(U_1509,U_1510))
      | ~ class_Int_Onumber__ring(U_1509) ),
    inference(definitional_conversion,[status(esa)],[f_514_2]) ).

cnf(f_514_4,plain,
    ( c_Int_Onumber__class_Onumber__of(U_1509,c_Int_Osucc(U_1510)) = c_Groups_Oplus__class_Oplus(U_1509,c_Groups_Oone__class_Oone(U_1509),c_Int_Onumber__class_Onumber__of(U_1509,U_1510))
    | ~ class_Int_Onumber__ring(U_1509) ),
    inference(clausify,[status(thm)],[f_514_3]) ).

fof(f_515_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_515_2,plain,
    ! [U_1512,U_1511] :
      ( ( c_Nat__Transfer_Otsub(U_1512,U_1511) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1511,U_1512) )
      & ( c_Nat__Transfer_Otsub(U_1512,U_1511) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1512,U_1511)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1511,U_1512) ) ),
    inference(variable_rename,[status(thm)],[f_515_1]) ).

fof(f_515_3,plain,
    ( ! [U_1516,U_1514] :
        ( c_Nat__Transfer_Otsub(U_1516,U_1514) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1514,U_1516) )
    & ! [U_1515,U_1513] :
        ( c_Nat__Transfer_Otsub(U_1515,U_1513) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1515,U_1513)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1513,U_1515) ) ),
    inference(miniscope,[status(thm)],[f_515_2]) ).

fof(f_515_4,plain,
    ( ! [U_1514,U_1516] :
        ( c_Nat__Transfer_Otsub(U_1516,U_1514) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1514,U_1516) )
    & ! [U_1513,U_1515] :
        ( c_Nat__Transfer_Otsub(U_1515,U_1513) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1515,U_1513)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1513,U_1515) ) ),
    inference(definitional_conversion,[status(esa)],[f_515_3]) ).

cnf(f_515_5,plain,
    ( c_Nat__Transfer_Otsub(U_1515,U_1513) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1515,U_1513)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1513,U_1515) ),
    inference(clausify,[status(thm)],[f_515_4]) ).

cnf(f_515_6,plain,
    ( c_Nat__Transfer_Otsub(U_1516,U_1514) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1514,U_1516) ),
    inference(clausify,[status(thm)],[f_515_4]) ).

fof(f_516_1,plain,
    ! [V_X_2,T_a] :
      ( ( ( c_SEQ_OBseq(T_a,V_X_2)
          | ! [B_N] :
            ? [B_n] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),hAPP(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_a,hAPP(V_X_2,B_n)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(B_N)))
          | ~ c_SEQ_OBseq(T_a,V_X_2) ) )
      | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Bseq__iff1a]) ).

fof(f_516_2,plain,
    ! [U_1522,U_1521] :
      ( ( ( c_SEQ_OBseq(U_1521,U_1522)
          | ! [U_1520] :
            ? [U_1519] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1521,hAPP(U_1522,U_1519)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_1520))) )
        & ( ? [U_1518] :
            ! [U_1517] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1521,hAPP(U_1522,U_1517)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_1518)))
          | ~ c_SEQ_OBseq(U_1521,U_1522) ) )
      | ~ class_RealVector_Oreal__normed__vector(U_1521) ),
    inference(variable_rename,[status(thm)],[f_516_1]) ).

fof(f_516_3,plain,
    ! [U_1522,U_1521] :
      ( ( ( c_SEQ_OBseq(U_1521,U_1522)
          | ! [U_1520] :
            ? [U_1519] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1521,hAPP(U_1522,U_1519)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_1520))) )
        & ( ! [U_1517] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1521,hAPP(U_1522,U_1517)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(sK47(U_1522,U_1521))))
          | ~ c_SEQ_OBseq(U_1521,U_1522) ) )
      | ~ class_RealVector_Oreal__normed__vector(U_1521) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_1518,sK47(U_1522,U_1521))],[f_516_2]) ).

fof(f_516_4,plain,
    ! [U_1522,U_1521] :
      ( ( ( c_SEQ_OBseq(U_1521,U_1522)
          | ! [U_1520] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1521,hAPP(U_1522,sK48(U_1522,U_1521,U_1520))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_1520))) )
        & ( ! [U_1517] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1521,hAPP(U_1522,U_1517)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(sK47(U_1522,U_1521))))
          | ~ c_SEQ_OBseq(U_1521,U_1522) ) )
      | ~ class_RealVector_Oreal__normed__vector(U_1521) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_1519,sK48(U_1522,U_1521,U_1520))],[f_516_3]) ).

fof(f_516_5,plain,
    ( ! [U_1517,U_1520,U_1521,U_1522] :
        ( c_SEQ_OBseq(U_1521,U_1522)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1521,hAPP(U_1522,sK48(U_1522,U_1521,U_1520))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_1520)))
        | ~ sP129(U_1517,U_1520,U_1521,U_1522) )
    & ! [U_1517,U_1520,U_1521,U_1522] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1521,hAPP(U_1522,U_1517)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(sK47(U_1522,U_1521))))
        | ~ c_SEQ_OBseq(U_1521,U_1522)
        | ~ sP129(U_1517,U_1520,U_1521,U_1522) )
    & ! [U_1517,U_1520,U_1521,U_1522] :
        ( sP129(U_1517,U_1520,U_1521,U_1522)
        | ~ class_RealVector_Oreal__normed__vector(U_1521) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP129])],[f_516_4]) ).

cnf(f_516_6,plain,
    ( sP129(U_1517,U_1520,U_1521,U_1522)
    | ~ class_RealVector_Oreal__normed__vector(U_1521) ),
    inference(clausify,[status(thm)],[f_516_5]) ).

cnf(f_516_7,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1521,hAPP(U_1522,U_1517)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(sK47(U_1522,U_1521))))
    | ~ c_SEQ_OBseq(U_1521,U_1522)
    | ~ sP129(U_1517,U_1520,U_1521,U_1522) ),
    inference(clausify,[status(thm)],[f_516_5]) ).

cnf(f_516_8,plain,
    ( c_SEQ_OBseq(U_1521,U_1522)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1521,hAPP(U_1522,sK48(U_1522,U_1521,U_1520))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_1520)))
    | ~ sP129(U_1517,U_1520,U_1521,U_1522) ),
    inference(clausify,[status(thm)],[f_516_5]) ).

fof(f_517_1,plain,
    ! [V_X_2,T_a] :
      ( ( ( c_SEQ_OBseq(T_a,V_X_2)
          | ! [B_N] :
            ? [B_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),hAPP(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_a,hAPP(V_X_2,B_n)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(B_N)))
          | ~ c_SEQ_OBseq(T_a,V_X_2) ) )
      | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Bseq__iff]) ).

fof(f_517_2,plain,
    ! [U_1528,U_1527] :
      ( ( ( c_SEQ_OBseq(U_1527,U_1528)
          | ! [U_1526] :
            ? [U_1525] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1527,hAPP(U_1528,U_1525)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_1526))) )
        & ( ? [U_1524] :
            ! [U_1523] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1527,hAPP(U_1528,U_1523)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_1524)))
          | ~ c_SEQ_OBseq(U_1527,U_1528) ) )
      | ~ class_RealVector_Oreal__normed__vector(U_1527) ),
    inference(variable_rename,[status(thm)],[f_517_1]) ).

fof(f_517_3,plain,
    ! [U_1528,U_1527] :
      ( ( ( c_SEQ_OBseq(U_1527,U_1528)
          | ! [U_1526] :
            ? [U_1525] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1527,hAPP(U_1528,U_1525)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_1526))) )
        & ( ! [U_1523] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1527,hAPP(U_1528,U_1523)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(sK49(U_1528,U_1527))))
          | ~ c_SEQ_OBseq(U_1527,U_1528) ) )
      | ~ class_RealVector_Oreal__normed__vector(U_1527) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_1524,sK49(U_1528,U_1527))],[f_517_2]) ).

fof(f_517_4,plain,
    ! [U_1528,U_1527] :
      ( ( ( c_SEQ_OBseq(U_1527,U_1528)
          | ! [U_1526] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1527,hAPP(U_1528,sK50(U_1528,U_1527,U_1526))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_1526))) )
        & ( ! [U_1523] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1527,hAPP(U_1528,U_1523)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(sK49(U_1528,U_1527))))
          | ~ c_SEQ_OBseq(U_1527,U_1528) ) )
      | ~ class_RealVector_Oreal__normed__vector(U_1527) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_1525,sK50(U_1528,U_1527,U_1526))],[f_517_3]) ).

fof(f_517_5,plain,
    ( ! [U_1526,U_1528,U_1527,U_1523] :
        ( c_SEQ_OBseq(U_1527,U_1528)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1527,hAPP(U_1528,sK50(U_1528,U_1527,U_1526))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_1526)))
        | ~ sP130(U_1526,U_1528,U_1527,U_1523) )
    & ! [U_1526,U_1528,U_1527,U_1523] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1527,hAPP(U_1528,U_1523)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(sK49(U_1528,U_1527))))
        | ~ c_SEQ_OBseq(U_1527,U_1528)
        | ~ sP130(U_1526,U_1528,U_1527,U_1523) )
    & ! [U_1526,U_1528,U_1527,U_1523] :
        ( sP130(U_1526,U_1528,U_1527,U_1523)
        | ~ class_RealVector_Oreal__normed__vector(U_1527) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP130])],[f_517_4]) ).

cnf(f_517_6,plain,
    ( sP130(U_1526,U_1528,U_1527,U_1523)
    | ~ class_RealVector_Oreal__normed__vector(U_1527) ),
    inference(clausify,[status(thm)],[f_517_5]) ).

cnf(f_517_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1527,hAPP(U_1528,U_1523)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(sK49(U_1528,U_1527))))
    | ~ c_SEQ_OBseq(U_1527,U_1528)
    | ~ sP130(U_1526,U_1528,U_1527,U_1523) ),
    inference(clausify,[status(thm)],[f_517_5]) ).

cnf(f_517_8,plain,
    ( c_SEQ_OBseq(U_1527,U_1528)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1527,hAPP(U_1528,sK50(U_1528,U_1527,U_1526))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_1526)))
    | ~ sP130(U_1526,U_1528,U_1527,U_1523) ),
    inference(clausify,[status(thm)],[f_517_5]) ).

fof(f_518_1,plain,
    ! [V_X_2,T_a] :
      ( ( ( c_SEQ_OBseq(T_a,V_X_2)
          | ! [B_K] :
              ( ? [B_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,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_K] :
              ( ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,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) )
          | ~ c_SEQ_OBseq(T_a,V_X_2) ) )
      | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Bseq__def]) ).

fof(f_518_2,plain,
    ! [U_1534,U_1533] :
      ( ( ( c_SEQ_OBseq(U_1533,U_1534)
          | ! [U_1532] :
              ( ? [U_1531] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1533,hAPP(U_1534,U_1531)),U_1532)
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1532) ) )
        & ( ? [U_1530] :
              ( ! [U_1529] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1533,hAPP(U_1534,U_1529)),U_1530)
              & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1530) )
          | ~ c_SEQ_OBseq(U_1533,U_1534) ) )
      | ~ class_RealVector_Oreal__normed__vector(U_1533) ),
    inference(variable_rename,[status(thm)],[f_518_1]) ).

fof(f_518_3,plain,
    ! [U_1534,U_1533] :
      ( ( ( c_SEQ_OBseq(U_1533,U_1534)
          | ! [U_1532] :
              ( ? [U_1531] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1533,hAPP(U_1534,U_1531)),U_1532)
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1532) ) )
        & ( ( ! [U_1529] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1533,hAPP(U_1534,U_1529)),sK51(U_1534,U_1533))
            & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK51(U_1534,U_1533)) )
          | ~ c_SEQ_OBseq(U_1533,U_1534) ) )
      | ~ class_RealVector_Oreal__normed__vector(U_1533) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_1530,sK51(U_1534,U_1533))],[f_518_2]) ).

fof(f_518_4,plain,
    ! [U_1534,U_1533] :
      ( ( ( c_SEQ_OBseq(U_1533,U_1534)
          | ! [U_1532] :
              ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1533,hAPP(U_1534,sK52(U_1534,U_1533,U_1532))),U_1532)
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1532) ) )
        & ( ( ! [U_1529] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1533,hAPP(U_1534,U_1529)),sK51(U_1534,U_1533))
            & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK51(U_1534,U_1533)) )
          | ~ c_SEQ_OBseq(U_1533,U_1534) ) )
      | ~ class_RealVector_Oreal__normed__vector(U_1533) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_1531,sK52(U_1534,U_1533,U_1532))],[f_518_3]) ).

fof(f_518_5,plain,
    ( ! [U_1534,U_1533,U_1529] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1533,hAPP(U_1534,U_1529)),sK51(U_1534,U_1533))
        | ~ sP131(U_1534,U_1533,U_1529) )
    & ! [U_1534,U_1533,U_1529] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK51(U_1534,U_1533))
        | ~ sP131(U_1534,U_1533,U_1529) )
    & ! [U_1534,U_1533,U_1532,U_1529] :
        ( c_SEQ_OBseq(U_1533,U_1534)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1533,hAPP(U_1534,sK52(U_1534,U_1533,U_1532))),U_1532)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1532)
        | ~ sP132(U_1534,U_1533,U_1532,U_1529) )
    & ! [U_1534,U_1533,U_1532,U_1529] :
        ( sP131(U_1534,U_1533,U_1529)
        | ~ c_SEQ_OBseq(U_1533,U_1534)
        | ~ sP132(U_1534,U_1533,U_1532,U_1529) )
    & ! [U_1534,U_1533,U_1532,U_1529] :
        ( sP132(U_1534,U_1533,U_1532,U_1529)
        | ~ class_RealVector_Oreal__normed__vector(U_1533) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP131,sP132])],[f_518_4]) ).

cnf(f_518_6,plain,
    ( sP132(U_1534,U_1533,U_1532,U_1529)
    | ~ class_RealVector_Oreal__normed__vector(U_1533) ),
    inference(clausify,[status(thm)],[f_518_5]) ).

cnf(f_518_7,plain,
    ( sP131(U_1534,U_1533,U_1529)
    | ~ c_SEQ_OBseq(U_1533,U_1534)
    | ~ sP132(U_1534,U_1533,U_1532,U_1529) ),
    inference(clausify,[status(thm)],[f_518_5]) ).

cnf(f_518_8,plain,
    ( c_SEQ_OBseq(U_1533,U_1534)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1533,hAPP(U_1534,sK52(U_1534,U_1533,U_1532))),U_1532)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1532)
    | ~ sP132(U_1534,U_1533,U_1532,U_1529) ),
    inference(clausify,[status(thm)],[f_518_5]) ).

cnf(f_518_9,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK51(U_1534,U_1533))
    | ~ sP131(U_1534,U_1533,U_1529) ),
    inference(clausify,[status(thm)],[f_518_5]) ).

cnf(f_518_10,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1533,hAPP(U_1534,U_1529)),sK51(U_1534,U_1533))
    | ~ sP131(U_1534,U_1533,U_1529) ),
    inference(clausify,[status(thm)],[f_518_5]) ).

fof(f_519_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_519_2,plain,
    ! [U_1536,U_1535] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(U_1535,U_1536))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1536)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1535) ),
    inference(variable_rename,[status(thm)],[f_519_1]) ).

fof(f_519_3,plain,
    ! [U_1535,U_1536] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(U_1535,U_1536))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1536)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1535) ),
    inference(definitional_conversion,[status(esa)],[f_519_2]) ).

cnf(f_519_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(U_1535,U_1536))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1536)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1535) ),
    inference(clausify,[status(thm)],[f_519_3]) ).

fof(f_520_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_520_2,plain,
    ! [U_1538,U_1537] :
      ( c_Nat__Transfer_Otsub(U_1538,U_1537) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1538,U_1537)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1537,U_1538) ),
    inference(variable_rename,[status(thm)],[f_520_1]) ).

fof(f_520_3,plain,
    ! [U_1537,U_1538] :
      ( c_Nat__Transfer_Otsub(U_1538,U_1537) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1538,U_1537)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1537,U_1538) ),
    inference(definitional_conversion,[status(esa)],[f_520_2]) ).

cnf(f_520_4,plain,
    ( c_Nat__Transfer_Otsub(U_1538,U_1537) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1538,U_1537)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1537,U_1538) ),
    inference(clausify,[status(thm)],[f_520_3]) ).

fof(f_521_1,plain,
    ! [V_X_2,T_a] :
      ( ? [B_K] :
          ( ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,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) )
      | ~ c_SEQ_OBseq(T_a,V_X_2)
      | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_BseqD]) ).

fof(f_521_2,plain,
    ! [U_1542,U_1541] :
      ( ? [U_1540] :
          ( ! [U_1539] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1541,hAPP(U_1542,U_1539)),U_1540)
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1540) )
      | ~ c_SEQ_OBseq(U_1541,U_1542)
      | ~ class_RealVector_Oreal__normed__vector(U_1541) ),
    inference(variable_rename,[status(thm)],[f_521_1]) ).

fof(f_521_3,plain,
    ! [U_1542,U_1541] :
      ( ( ! [U_1539] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1541,hAPP(U_1542,U_1539)),sK53(U_1542,U_1541))
        & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK53(U_1542,U_1541)) )
      | ~ c_SEQ_OBseq(U_1541,U_1542)
      | ~ class_RealVector_Oreal__normed__vector(U_1541) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_1540,sK53(U_1542,U_1541))],[f_521_2]) ).

fof(f_521_4,plain,
    ( ! [U_1542,U_1539,U_1541] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1541,hAPP(U_1542,U_1539)),sK53(U_1542,U_1541))
        | ~ sP133(U_1542,U_1539,U_1541) )
    & ! [U_1542,U_1539,U_1541] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK53(U_1542,U_1541))
        | ~ sP133(U_1542,U_1539,U_1541) )
    & ! [U_1542,U_1539,U_1541] :
        ( sP133(U_1542,U_1539,U_1541)
        | ~ c_SEQ_OBseq(U_1541,U_1542)
        | ~ class_RealVector_Oreal__normed__vector(U_1541) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP133])],[f_521_3]) ).

cnf(f_521_5,plain,
    ( sP133(U_1542,U_1539,U_1541)
    | ~ c_SEQ_OBseq(U_1541,U_1542)
    | ~ class_RealVector_Oreal__normed__vector(U_1541) ),
    inference(clausify,[status(thm)],[f_521_4]) ).

cnf(f_521_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK53(U_1542,U_1541))
    | ~ sP133(U_1542,U_1539,U_1541) ),
    inference(clausify,[status(thm)],[f_521_4]) ).

cnf(f_521_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1541,hAPP(U_1542,U_1539)),sK53(U_1542,U_1541))
    | ~ sP133(U_1542,U_1539,U_1541) ),
    inference(clausify,[status(thm)],[f_521_4]) ).

fof(f_522_1,plain,
    ! [V_X_2,V_K_2,T_a] :
      ( c_SEQ_OBseq(T_a,V_X_2)
      | ? [B_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),V_K_2)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_K_2)
      | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_BseqI]) ).

fof(f_522_2,plain,
    ! [U_1546,U_1545,U_1544] :
      ( c_SEQ_OBseq(U_1544,U_1546)
      | ? [U_1543] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1544,hAPP(U_1546,U_1543)),U_1545)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1545)
      | ~ class_RealVector_Oreal__normed__vector(U_1544) ),
    inference(variable_rename,[status(thm)],[f_522_1]) ).

fof(f_522_3,plain,
    ! [U_1546,U_1545,U_1544] :
      ( c_SEQ_OBseq(U_1544,U_1546)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1544,hAPP(U_1546,sK54(U_1546,U_1545,U_1544))),U_1545)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1545)
      | ~ class_RealVector_Oreal__normed__vector(U_1544) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_1543,sK54(U_1546,U_1545,U_1544))],[f_522_2]) ).

fof(f_522_4,plain,
    ! [U_1545,U_1544,U_1546] :
      ( c_SEQ_OBseq(U_1544,U_1546)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1544,hAPP(U_1546,sK54(U_1546,U_1545,U_1544))),U_1545)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1545)
      | ~ class_RealVector_Oreal__normed__vector(U_1544) ),
    inference(definitional_conversion,[status(esa)],[f_522_3]) ).

cnf(f_522_5,plain,
    ( c_SEQ_OBseq(U_1544,U_1546)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1544,hAPP(U_1546,sK54(U_1546,U_1545,U_1544))),U_1545)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1545)
    | ~ class_RealVector_Oreal__normed__vector(U_1544) ),
    inference(clausify,[status(thm)],[f_522_4]) ).

fof(f_523_1,plain,
    ! [V_v] :
      ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(V_v))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) )
      & ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__1__add__number__of]) ).

fof(f_523_2,plain,
    ! [U_1547] :
      ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1547)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(U_1547))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1547,c_Int_OPls) )
      & ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1547)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1547,c_Int_OPls) ) ),
    inference(variable_rename,[status(thm)],[f_523_1]) ).

fof(f_523_3,plain,
    ( ! [U_1549] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1549)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(U_1549))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1549,c_Int_OPls) )
    & ! [U_1548] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1548)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1548,c_Int_OPls) ) ),
    inference(miniscope,[status(thm)],[f_523_2]) ).

fof(f_523_4,plain,
    ( ! [U_1549] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1549)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(U_1549))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1549,c_Int_OPls) )
    & ! [U_1548] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1548)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1548,c_Int_OPls) ) ),
    inference(definitional_conversion,[status(esa)],[f_523_3]) ).

cnf(f_523_5,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1548)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1548,c_Int_OPls) ),
    inference(clausify,[status(thm)],[f_523_4]) ).

cnf(f_523_6,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1549)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(U_1549))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1549,c_Int_OPls) ),
    inference(clausify,[status(thm)],[f_523_4]) ).

fof(f_524_1,plain,
    ! [V_v] :
      ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(V_v))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) )
      & ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__number__of__add__1]) ).

fof(f_524_2,plain,
    ! [U_1550] :
      ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1550),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(U_1550))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1550,c_Int_OPls) )
      & ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1550),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1550,c_Int_OPls) ) ),
    inference(variable_rename,[status(thm)],[f_524_1]) ).

fof(f_524_3,plain,
    ( ! [U_1552] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1552),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(U_1552))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1552,c_Int_OPls) )
    & ! [U_1551] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1551),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1551,c_Int_OPls) ) ),
    inference(miniscope,[status(thm)],[f_524_2]) ).

fof(f_524_4,plain,
    ( ! [U_1552] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1552),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(U_1552))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1552,c_Int_OPls) )
    & ! [U_1551] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1551),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1551,c_Int_OPls) ) ),
    inference(definitional_conversion,[status(esa)],[f_524_3]) ).

cnf(f_524_5,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1551),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1551,c_Int_OPls) ),
    inference(clausify,[status(thm)],[f_524_4]) ).

cnf(f_524_6,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1552),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(U_1552))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1552,c_Int_OPls) ),
    inference(clausify,[status(thm)],[f_524_4]) ).

fof(f_525_1,plain,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_Pls__def]) ).

fof(f_525_2,plain,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_525_1]) ).

cnf(f_525_3,plain,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_525_2]) ).

fof(f_526_1,plain,
    ! [V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,V_k) = V_k,
    inference(fof_nnf,[status(thm)],[fact_add__Pls]) ).

fof(f_526_2,plain,
    ! [U_1553] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,U_1553) = U_1553,
    inference(variable_rename,[status(thm)],[f_526_1]) ).

fof(f_526_3,plain,
    ! [U_1553] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,U_1553) = U_1553,
    inference(definitional_conversion,[status(esa)],[f_526_2]) ).

cnf(f_526_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,U_1553) = U_1553,
    inference(clausify,[status(thm)],[f_526_3]) ).

fof(f_527_1,plain,
    ! [V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,c_Int_OPls) = V_k,
    inference(fof_nnf,[status(thm)],[fact_add__Pls__right]) ).

fof(f_527_2,plain,
    ! [U_1554] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1554,c_Int_OPls) = U_1554,
    inference(variable_rename,[status(thm)],[f_527_1]) ).

fof(f_527_3,plain,
    ! [U_1554] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1554,c_Int_OPls) = U_1554,
    inference(definitional_conversion,[status(esa)],[f_527_2]) ).

cnf(f_527_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1554,c_Int_OPls) = U_1554,
    inference(clausify,[status(thm)],[f_527_3]) ).

fof(f_528_1,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I19_J]) ).

fof(f_528_2,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
    inference(definitional_conversion,[status(esa)],[f_528_1]) ).

cnf(f_528_3,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
    inference(clausify,[status(thm)],[f_528_2]) ).

fof(f_529_1,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I2_J]) ).

fof(f_529_2,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
    inference(definitional_conversion,[status(esa)],[f_529_1]) ).

cnf(f_529_3,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
    inference(clausify,[status(thm)],[f_529_2]) ).

fof(f_530_1,plain,
    ! [V_k] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,c_Int_OPls) = V_k,
    inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I1_J]) ).

fof(f_530_2,plain,
    ! [U_1555] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1555,c_Int_OPls) = U_1555,
    inference(variable_rename,[status(thm)],[f_530_1]) ).

fof(f_530_3,plain,
    ! [U_1555] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1555,c_Int_OPls) = U_1555,
    inference(definitional_conversion,[status(esa)],[f_530_2]) ).

cnf(f_530_4,plain,
    c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1555,c_Int_OPls) = U_1555,
    inference(clausify,[status(thm)],[f_530_3]) ).

fof(f_531_1,plain,
    ! [T_a] :
      ( c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_number__of__Pls]) ).

fof(f_531_2,plain,
    ! [U_1556] :
      ( c_Int_Onumber__class_Onumber__of(U_1556,c_Int_OPls) = c_Groups_Ozero__class_Ozero(U_1556)
      | ~ class_Int_Onumber__ring(U_1556) ),
    inference(variable_rename,[status(thm)],[f_531_1]) ).

fof(f_531_3,plain,
    ! [U_1556] :
      ( c_Int_Onumber__class_Onumber__of(U_1556,c_Int_OPls) = c_Groups_Ozero__class_Ozero(U_1556)
      | ~ class_Int_Onumber__ring(U_1556) ),
    inference(definitional_conversion,[status(esa)],[f_531_2]) ).

cnf(f_531_4,plain,
    ( c_Int_Onumber__class_Onumber__of(U_1556,c_Int_OPls) = c_Groups_Ozero__class_Ozero(U_1556)
    | ~ class_Int_Onumber__ring(U_1556) ),
    inference(clausify,[status(thm)],[f_531_3]) ).

fof(f_532_1,plain,
    ! [T_a] :
      ( c_Groups_Ozero__class_Ozero(T_a) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_semiring__norm_I112_J]) ).

fof(f_532_2,plain,
    ! [U_1557] :
      ( c_Groups_Ozero__class_Ozero(U_1557) = c_Int_Onumber__class_Onumber__of(U_1557,c_Int_OPls)
      | ~ class_Int_Onumber__ring(U_1557) ),
    inference(variable_rename,[status(thm)],[f_532_1]) ).

fof(f_532_3,plain,
    ! [U_1557] :
      ( c_Groups_Ozero__class_Ozero(U_1557) = c_Int_Onumber__class_Onumber__of(U_1557,c_Int_OPls)
      | ~ class_Int_Onumber__ring(U_1557) ),
    inference(definitional_conversion,[status(esa)],[f_532_2]) ).

cnf(f_532_4,plain,
    ( c_Groups_Ozero__class_Ozero(U_1557) = c_Int_Onumber__class_Onumber__of(U_1557,c_Int_OPls)
    | ~ class_Int_Onumber__ring(U_1557) ),
    inference(clausify,[status(thm)],[f_532_3]) ).

fof(f_533_1,plain,
    ! [V_a,T_a] :
      ( c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls),V_a) = V_a
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__numeral__0]) ).

fof(f_533_2,plain,
    ! [U_1559,U_1558] :
      ( c_Groups_Oplus__class_Oplus(U_1558,c_Int_Onumber__class_Onumber__of(U_1558,c_Int_OPls),U_1559) = U_1559
      | ~ class_Int_Onumber__ring(U_1558) ),
    inference(variable_rename,[status(thm)],[f_533_1]) ).

fof(f_533_3,plain,
    ! [U_1558,U_1559] :
      ( c_Groups_Oplus__class_Oplus(U_1558,c_Int_Onumber__class_Onumber__of(U_1558,c_Int_OPls),U_1559) = U_1559
      | ~ class_Int_Onumber__ring(U_1558) ),
    inference(definitional_conversion,[status(esa)],[f_533_2]) ).

cnf(f_533_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_1558,c_Int_Onumber__class_Onumber__of(U_1558,c_Int_OPls),U_1559) = U_1559
    | ~ class_Int_Onumber__ring(U_1558) ),
    inference(clausify,[status(thm)],[f_533_3]) ).

fof(f_534_1,plain,
    ! [V_a,T_a] :
      ( c_Groups_Oplus__class_Oplus(T_a,V_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls)) = V_a
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__numeral__0__right]) ).

fof(f_534_2,plain,
    ! [U_1561,U_1560] :
      ( c_Groups_Oplus__class_Oplus(U_1560,U_1561,c_Int_Onumber__class_Onumber__of(U_1560,c_Int_OPls)) = U_1561
      | ~ class_Int_Onumber__ring(U_1560) ),
    inference(variable_rename,[status(thm)],[f_534_1]) ).

fof(f_534_3,plain,
    ! [U_1560,U_1561] :
      ( c_Groups_Oplus__class_Oplus(U_1560,U_1561,c_Int_Onumber__class_Onumber__of(U_1560,c_Int_OPls)) = U_1561
      | ~ class_Int_Onumber__ring(U_1560) ),
    inference(definitional_conversion,[status(esa)],[f_534_2]) ).

cnf(f_534_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_1560,U_1561,c_Int_Onumber__class_Onumber__of(U_1560,c_Int_OPls)) = U_1561
    | ~ class_Int_Onumber__ring(U_1560) ),
    inference(clausify,[status(thm)],[f_534_3]) ).

fof(f_535_1,plain,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_nat__number__of__Pls]) ).

fof(f_535_2,plain,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_535_1]) ).

cnf(f_535_3,plain,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_535_2]) ).

fof(f_536_1,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),
    inference(fof_nnf,[status(thm)],[fact_semiring__norm_I113_J]) ).

fof(f_536_2,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),
    inference(definitional_conversion,[status(esa)],[f_536_1]) ).

cnf(f_536_3,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),
    inference(clausify,[status(thm)],[f_536_2]) ).

fof(f_537_1,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(fof_nnf,[status(thm)],[fact_bin__less__0__simps_I1_J]) ).

fof(f_537_2,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(definitional_conversion,[status(esa)],[f_537_1]) ).

cnf(f_537_3,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_537_2]) ).

fof(f_538_1,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls),
    inference(fof_nnf,[status(thm)],[fact_zero__is__num__zero]) ).

fof(f_538_2,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls),
    inference(definitional_conversion,[status(esa)],[f_538_1]) ).

cnf(f_538_3,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls),
    inference(clausify,[status(thm)],[f_538_2]) ).

fof(f_539_1,plain,
    ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)),
    inference(fof_nnf,[status(thm)],[fact_not__neg__number__of__Pls]) ).

fof(f_539_2,plain,
    ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)),
    inference(definitional_conversion,[status(esa)],[f_539_1]) ).

cnf(f_539_3,plain,
    ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)),
    inference(clausify,[status(thm)],[f_539_2]) ).

fof(f_540_1,plain,
    ! [V_v_2] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_eq__0__number__of]) ).

fof(f_540_2,plain,
    ! [U_1562] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1562)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1562,c_Int_OPls) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1562,c_Int_OPls)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1562) ) ),
    inference(variable_rename,[status(thm)],[f_540_1]) ).

fof(f_540_3,plain,
    ( ! [U_1564] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1564)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1564,c_Int_OPls) )
    & ! [U_1563] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1563,c_Int_OPls)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1563) ) ),
    inference(miniscope,[status(thm)],[f_540_2]) ).

fof(f_540_4,plain,
    ( ! [U_1564] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1564)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1564,c_Int_OPls) )
    & ! [U_1563] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1563,c_Int_OPls)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1563) ) ),
    inference(definitional_conversion,[status(esa)],[f_540_3]) ).

cnf(f_540_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1563,c_Int_OPls)
    | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1563) ),
    inference(clausify,[status(thm)],[f_540_4]) ).

cnf(f_540_6,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1564)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1564,c_Int_OPls) ),
    inference(clausify,[status(thm)],[f_540_4]) ).

fof(f_541_1,plain,
    ! [V_v_2] :
      ( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls)
        | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_eq__number__of__0]) ).

fof(f_541_2,plain,
    ! [U_1565] :
      ( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1565) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1565,c_Int_OPls) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1565,c_Int_OPls)
        | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1565) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_541_1]) ).

fof(f_541_3,plain,
    ( ! [U_1567] :
        ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1567) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1567,c_Int_OPls) )
    & ! [U_1566] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1566,c_Int_OPls)
        | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1566) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_541_2]) ).

fof(f_541_4,plain,
    ( ! [U_1567] :
        ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1567) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1567,c_Int_OPls) )
    & ! [U_1566] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1566,c_Int_OPls)
        | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1566) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_541_3]) ).

cnf(f_541_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1566,c_Int_OPls)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1566) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_541_4]) ).

cnf(f_541_6,plain,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1567) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1567,c_Int_OPls) ),
    inference(clausify,[status(thm)],[f_541_4]) ).

fof(f_542_1,plain,
    ! [V_v_H_2,V_v_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2)
        | ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_H_2)
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2) ) )
      & ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2)
          & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_H_2)
            | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2) ) )
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__nat__number__of]) ).

fof(f_542_2,plain,
    ! [U_1569,U_1568] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1568),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1569))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1568,U_1569)
        | ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1569)
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1568,U_1569) ) )
      & ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1568,U_1569)
          & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1569)
            | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1568,U_1569) ) )
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1568),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1569)) ) ),
    inference(variable_rename,[status(thm)],[f_542_1]) ).

fof(f_542_3,plain,
    ( ! [U_1573,U_1571] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1571),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1573))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1571,U_1573)
        | ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1573)
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1571,U_1573) ) )
    & ! [U_1572,U_1570] :
        ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1570,U_1572)
          & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1572)
            | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1570,U_1572) ) )
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1570),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1572)) ) ),
    inference(miniscope,[status(thm)],[f_542_2]) ).

fof(f_542_4,plain,
    ( ! [U_1571,U_1573] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1573)
        | ~ sP135(U_1571,U_1573) )
    & ! [U_1571,U_1573] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1571,U_1573)
        | ~ sP135(U_1571,U_1573) )
    & ! [U_1570,U_1572] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1570,U_1572)
        | ~ sP134(U_1570,U_1572) )
    & ! [U_1570,U_1572] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1572)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1570,U_1572)
        | ~ sP134(U_1570,U_1572) )
    & ! [U_1571,U_1573] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1571),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1573))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1571,U_1573)
        | sP135(U_1571,U_1573) )
    & ! [U_1570,U_1572] :
        ( sP134(U_1570,U_1572)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1570),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1572)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP134,sP135])],[f_542_3]) ).

cnf(f_542_5,plain,
    ( sP134(U_1570,U_1572)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1570),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1572)) ),
    inference(clausify,[status(thm)],[f_542_4]) ).

cnf(f_542_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1571),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1573))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1571,U_1573)
    | sP135(U_1571,U_1573) ),
    inference(clausify,[status(thm)],[f_542_4]) ).

cnf(f_542_7,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1572)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1570,U_1572)
    | ~ sP134(U_1570,U_1572) ),
    inference(clausify,[status(thm)],[f_542_4]) ).

cnf(f_542_8,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1570,U_1572)
    | ~ sP134(U_1570,U_1572) ),
    inference(clausify,[status(thm)],[f_542_4]) ).

cnf(f_542_9,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1571,U_1573)
    | ~ sP135(U_1571,U_1573) ),
    inference(clausify,[status(thm)],[f_542_4]) ).

cnf(f_542_10,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1573)
    | ~ sP135(U_1571,U_1573) ),
    inference(clausify,[status(thm)],[f_542_4]) ).

fof(f_543_1,plain,
    ! [V_v_H_2,V_v_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2))
        | ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls)
          & ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,V_v_H_2) ) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,V_v_H_2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_le__nat__number__of]) ).

fof(f_543_2,plain,
    ! [U_1575,U_1574] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1574),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1575))
        | ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1574,c_Int_OPls)
          & ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1574,U_1575) ) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1574,c_Int_OPls)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1574,U_1575)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1574),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1575)) ) ),
    inference(variable_rename,[status(thm)],[f_543_1]) ).

fof(f_543_3,plain,
    ( ! [U_1579,U_1577] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1577),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1579))
        | ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1577,c_Int_OPls)
          & ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1577,U_1579) ) )
    & ! [U_1578,U_1576] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1576,c_Int_OPls)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1576,U_1578)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1576),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1578)) ) ),
    inference(miniscope,[status(thm)],[f_543_2]) ).

fof(f_543_4,plain,
    ( ! [U_1577,U_1579] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1577,c_Int_OPls)
        | ~ sP136(U_1577,U_1579) )
    & ! [U_1577,U_1579] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1577,U_1579)
        | ~ sP136(U_1577,U_1579) )
    & ! [U_1577,U_1579] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1577),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1579))
        | sP136(U_1577,U_1579) )
    & ! [U_1576,U_1578] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1576,c_Int_OPls)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1576,U_1578)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1576),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1578)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP136])],[f_543_3]) ).

cnf(f_543_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1576,c_Int_OPls)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1576,U_1578)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1576),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1578)) ),
    inference(clausify,[status(thm)],[f_543_4]) ).

cnf(f_543_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1577),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1579))
    | sP136(U_1577,U_1579) ),
    inference(clausify,[status(thm)],[f_543_4]) ).

cnf(f_543_7,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1577,U_1579)
    | ~ sP136(U_1577,U_1579) ),
    inference(clausify,[status(thm)],[f_543_4]) ).

cnf(f_543_8,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1577,c_Int_OPls)
    | ~ sP136(U_1577,U_1579) ),
    inference(clausify,[status(thm)],[f_543_4]) ).

fof(f_544_1,plain,
    ! [V_x_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Ozero__class_Ozero(T_a))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,c_Int_OPls) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,c_Int_OPls)
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
      | ~ class_Rings_Olinordered__idom(T_a)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__special_I3_J]) ).

fof(f_544_2,plain,
    ! [U_1581,U_1580] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_1580,c_Int_Onumber__class_Onumber__of(U_1580,U_1581),c_Groups_Ozero__class_Ozero(U_1580))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1581,c_Int_OPls) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1581,c_Int_OPls)
          | ~ c_Orderings_Oord__class_Oless__eq(U_1580,c_Int_Onumber__class_Onumber__of(U_1580,U_1581),c_Groups_Ozero__class_Ozero(U_1580)) ) )
      | ~ class_Rings_Olinordered__idom(U_1580)
      | ~ class_Int_Onumber__ring(U_1580) ),
    inference(variable_rename,[status(thm)],[f_544_1]) ).

fof(f_544_3,plain,
    ( ! [U_1580,U_1581] :
        ( c_Orderings_Oord__class_Oless__eq(U_1580,c_Int_Onumber__class_Onumber__of(U_1580,U_1581),c_Groups_Ozero__class_Ozero(U_1580))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1581,c_Int_OPls)
        | ~ sP137(U_1580,U_1581) )
    & ! [U_1580,U_1581] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1581,c_Int_OPls)
        | ~ c_Orderings_Oord__class_Oless__eq(U_1580,c_Int_Onumber__class_Onumber__of(U_1580,U_1581),c_Groups_Ozero__class_Ozero(U_1580))
        | ~ sP137(U_1580,U_1581) )
    & ! [U_1580,U_1581] :
        ( sP137(U_1580,U_1581)
        | ~ class_Rings_Olinordered__idom(U_1580)
        | ~ class_Int_Onumber__ring(U_1580) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP137])],[f_544_2]) ).

cnf(f_544_4,plain,
    ( sP137(U_1580,U_1581)
    | ~ class_Rings_Olinordered__idom(U_1580)
    | ~ class_Int_Onumber__ring(U_1580) ),
    inference(clausify,[status(thm)],[f_544_3]) ).

cnf(f_544_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1581,c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1580,c_Int_Onumber__class_Onumber__of(U_1580,U_1581),c_Groups_Ozero__class_Ozero(U_1580))
    | ~ sP137(U_1580,U_1581) ),
    inference(clausify,[status(thm)],[f_544_3]) ).

cnf(f_544_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1580,c_Int_Onumber__class_Onumber__of(U_1580,U_1581),c_Groups_Ozero__class_Ozero(U_1580))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1581,c_Int_OPls)
    | ~ sP137(U_1580,U_1581) ),
    inference(clausify,[status(thm)],[f_544_3]) ).

fof(f_545_1,plain,
    ! [V_y_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_y_2) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_y_2)
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2)) ) )
      | ~ class_Rings_Olinordered__idom(T_a)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__special_I1_J]) ).

fof(f_545_2,plain,
    ! [U_1583,U_1582] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_1582,c_Groups_Ozero__class_Ozero(U_1582),c_Int_Onumber__class_Onumber__of(U_1582,U_1583))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_1583) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_1583)
          | ~ c_Orderings_Oord__class_Oless__eq(U_1582,c_Groups_Ozero__class_Ozero(U_1582),c_Int_Onumber__class_Onumber__of(U_1582,U_1583)) ) )
      | ~ class_Rings_Olinordered__idom(U_1582)
      | ~ class_Int_Onumber__ring(U_1582) ),
    inference(variable_rename,[status(thm)],[f_545_1]) ).

fof(f_545_3,plain,
    ( ! [U_1583,U_1582] :
        ( c_Orderings_Oord__class_Oless__eq(U_1582,c_Groups_Ozero__class_Ozero(U_1582),c_Int_Onumber__class_Onumber__of(U_1582,U_1583))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_1583)
        | ~ sP138(U_1583,U_1582) )
    & ! [U_1583,U_1582] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_1583)
        | ~ c_Orderings_Oord__class_Oless__eq(U_1582,c_Groups_Ozero__class_Ozero(U_1582),c_Int_Onumber__class_Onumber__of(U_1582,U_1583))
        | ~ sP138(U_1583,U_1582) )
    & ! [U_1583,U_1582] :
        ( sP138(U_1583,U_1582)
        | ~ class_Rings_Olinordered__idom(U_1582)
        | ~ class_Int_Onumber__ring(U_1582) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP138])],[f_545_2]) ).

cnf(f_545_4,plain,
    ( sP138(U_1583,U_1582)
    | ~ class_Rings_Olinordered__idom(U_1582)
    | ~ class_Int_Onumber__ring(U_1582) ),
    inference(clausify,[status(thm)],[f_545_3]) ).

cnf(f_545_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_1583)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1582,c_Groups_Ozero__class_Ozero(U_1582),c_Int_Onumber__class_Onumber__of(U_1582,U_1583))
    | ~ sP138(U_1583,U_1582) ),
    inference(clausify,[status(thm)],[f_545_3]) ).

cnf(f_545_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1582,c_Groups_Ozero__class_Ozero(U_1582),c_Int_Onumber__class_Onumber__of(U_1582,U_1583))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_1583)
    | ~ sP138(U_1583,U_1582) ),
    inference(clausify,[status(thm)],[f_545_3]) ).

fof(f_546_1,plain,
    ! [V_x_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Ozero__class_Ozero(T_a))
          | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,c_Int_OPls) )
        & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,c_Int_OPls)
          | ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
      | ~ class_Rings_Olinordered__idom(T_a)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__special_I3_J]) ).

fof(f_546_2,plain,
    ! [U_1585,U_1584] :
      ( ( ( c_Orderings_Oord__class_Oless(U_1584,c_Int_Onumber__class_Onumber__of(U_1584,U_1585),c_Groups_Ozero__class_Ozero(U_1584))
          | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1585,c_Int_OPls) )
        & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1585,c_Int_OPls)
          | ~ c_Orderings_Oord__class_Oless(U_1584,c_Int_Onumber__class_Onumber__of(U_1584,U_1585),c_Groups_Ozero__class_Ozero(U_1584)) ) )
      | ~ class_Rings_Olinordered__idom(U_1584)
      | ~ class_Int_Onumber__ring(U_1584) ),
    inference(variable_rename,[status(thm)],[f_546_1]) ).

fof(f_546_3,plain,
    ( ! [U_1585,U_1584] :
        ( c_Orderings_Oord__class_Oless(U_1584,c_Int_Onumber__class_Onumber__of(U_1584,U_1585),c_Groups_Ozero__class_Ozero(U_1584))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1585,c_Int_OPls)
        | ~ sP139(U_1585,U_1584) )
    & ! [U_1585,U_1584] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1585,c_Int_OPls)
        | ~ c_Orderings_Oord__class_Oless(U_1584,c_Int_Onumber__class_Onumber__of(U_1584,U_1585),c_Groups_Ozero__class_Ozero(U_1584))
        | ~ sP139(U_1585,U_1584) )
    & ! [U_1585,U_1584] :
        ( sP139(U_1585,U_1584)
        | ~ class_Rings_Olinordered__idom(U_1584)
        | ~ class_Int_Onumber__ring(U_1584) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP139])],[f_546_2]) ).

cnf(f_546_4,plain,
    ( sP139(U_1585,U_1584)
    | ~ class_Rings_Olinordered__idom(U_1584)
    | ~ class_Int_Onumber__ring(U_1584) ),
    inference(clausify,[status(thm)],[f_546_3]) ).

cnf(f_546_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1585,c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless(U_1584,c_Int_Onumber__class_Onumber__of(U_1584,U_1585),c_Groups_Ozero__class_Ozero(U_1584))
    | ~ sP139(U_1585,U_1584) ),
    inference(clausify,[status(thm)],[f_546_3]) ).

cnf(f_546_6,plain,
    ( c_Orderings_Oord__class_Oless(U_1584,c_Int_Onumber__class_Onumber__of(U_1584,U_1585),c_Groups_Ozero__class_Ozero(U_1584))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1585,c_Int_OPls)
    | ~ sP139(U_1585,U_1584) ),
    inference(clausify,[status(thm)],[f_546_3]) ).

fof(f_547_1,plain,
    ! [V_y_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
          | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_y_2) )
        & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_y_2)
          | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2)) ) )
      | ~ class_Rings_Olinordered__idom(T_a)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__special_I1_J]) ).

fof(f_547_2,plain,
    ! [U_1587,U_1586] :
      ( ( ( c_Orderings_Oord__class_Oless(U_1586,c_Groups_Ozero__class_Ozero(U_1586),c_Int_Onumber__class_Onumber__of(U_1586,U_1587))
          | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1587) )
        & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1587)
          | ~ c_Orderings_Oord__class_Oless(U_1586,c_Groups_Ozero__class_Ozero(U_1586),c_Int_Onumber__class_Onumber__of(U_1586,U_1587)) ) )
      | ~ class_Rings_Olinordered__idom(U_1586)
      | ~ class_Int_Onumber__ring(U_1586) ),
    inference(variable_rename,[status(thm)],[f_547_1]) ).

fof(f_547_3,plain,
    ( ! [U_1587,U_1586] :
        ( c_Orderings_Oord__class_Oless(U_1586,c_Groups_Ozero__class_Ozero(U_1586),c_Int_Onumber__class_Onumber__of(U_1586,U_1587))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1587)
        | ~ sP140(U_1587,U_1586) )
    & ! [U_1587,U_1586] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1587)
        | ~ c_Orderings_Oord__class_Oless(U_1586,c_Groups_Ozero__class_Ozero(U_1586),c_Int_Onumber__class_Onumber__of(U_1586,U_1587))
        | ~ sP140(U_1587,U_1586) )
    & ! [U_1587,U_1586] :
        ( sP140(U_1587,U_1586)
        | ~ class_Rings_Olinordered__idom(U_1586)
        | ~ class_Int_Onumber__ring(U_1586) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP140])],[f_547_2]) ).

cnf(f_547_4,plain,
    ( sP140(U_1587,U_1586)
    | ~ class_Rings_Olinordered__idom(U_1586)
    | ~ class_Int_Onumber__ring(U_1586) ),
    inference(clausify,[status(thm)],[f_547_3]) ).

cnf(f_547_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1587)
    | ~ c_Orderings_Oord__class_Oless(U_1586,c_Groups_Ozero__class_Ozero(U_1586),c_Int_Onumber__class_Onumber__of(U_1586,U_1587))
    | ~ sP140(U_1587,U_1586) ),
    inference(clausify,[status(thm)],[f_547_3]) ).

cnf(f_547_6,plain,
    ( c_Orderings_Oord__class_Oless(U_1586,c_Groups_Ozero__class_Ozero(U_1586),c_Int_Onumber__class_Onumber__of(U_1586,U_1587))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1587)
    | ~ sP140(U_1587,U_1586) ),
    inference(clausify,[status(thm)],[f_547_3]) ).

fof(f_548_1,plain,
    ! [V_v_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_2) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_2)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__0__number__of]) ).

fof(f_548_2,plain,
    ! [U_1588] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1588))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1588) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1588)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1588)) ) ),
    inference(variable_rename,[status(thm)],[f_548_1]) ).

fof(f_548_3,plain,
    ( ! [U_1590] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1590))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1590) )
    & ! [U_1589] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1589)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1589)) ) ),
    inference(miniscope,[status(thm)],[f_548_2]) ).

fof(f_548_4,plain,
    ( ! [U_1590] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1590))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1590) )
    & ! [U_1589] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1589)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1589)) ) ),
    inference(definitional_conversion,[status(esa)],[f_548_3]) ).

cnf(f_548_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1589)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1589)) ),
    inference(clausify,[status(thm)],[f_548_4]) ).

cnf(f_548_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1590))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1590) ),
    inference(clausify,[status(thm)],[f_548_4]) ).

fof(f_549_1,plain,
    ! [V_v_H,V_v] :
      ( ( ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_v_H))
            | c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_H,c_Int_OPls) )
          & ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)
            | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_H,c_Int_OPls) ) )
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) )
      & ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) ) ),
    inference(fof_nnf,[status(thm)],[fact_add__nat__number__of]) ).

fof(f_549_2,plain,
    ! [U_1592,U_1591] :
      ( ( ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1591),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1592)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1591,U_1592))
            | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1592,c_Int_OPls) )
          & ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1591),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1592)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1591)
            | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1592,c_Int_OPls) ) )
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1591,c_Int_OPls) )
      & ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1591),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1592)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1592)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1591,c_Int_OPls) ) ),
    inference(variable_rename,[status(thm)],[f_549_1]) ).

fof(f_549_3,plain,
    ( ! [U_1596,U_1594] :
        ( ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1594),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1596)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1594,U_1596))
            | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1596,c_Int_OPls) )
          & ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1594),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1596)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1594)
            | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1596,c_Int_OPls) ) )
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1594,c_Int_OPls) )
    & ! [U_1595,U_1593] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1593),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1595)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1595)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1593,c_Int_OPls) ) ),
    inference(miniscope,[status(thm)],[f_549_2]) ).

fof(f_549_4,plain,
    ( ! [U_1594,U_1596] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1594),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1596)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1594,U_1596))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1596,c_Int_OPls)
        | ~ sP141(U_1594,U_1596) )
    & ! [U_1594,U_1596] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1594),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1596)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1594)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1596,c_Int_OPls)
        | ~ sP141(U_1594,U_1596) )
    & ! [U_1594,U_1596] :
        ( sP141(U_1594,U_1596)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1594,c_Int_OPls) )
    & ! [U_1593,U_1595] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1593),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1595)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1595)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1593,c_Int_OPls) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP141])],[f_549_3]) ).

cnf(f_549_5,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1593),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1595)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1595)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1593,c_Int_OPls) ),
    inference(clausify,[status(thm)],[f_549_4]) ).

cnf(f_549_6,plain,
    ( sP141(U_1594,U_1596)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1594,c_Int_OPls) ),
    inference(clausify,[status(thm)],[f_549_4]) ).

cnf(f_549_7,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1594),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1596)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1594)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1596,c_Int_OPls)
    | ~ sP141(U_1594,U_1596) ),
    inference(clausify,[status(thm)],[f_549_4]) ).

cnf(f_549_8,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1594),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1596)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1594,U_1596))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1596,c_Int_OPls)
    | ~ sP141(U_1594,U_1596) ),
    inference(clausify,[status(thm)],[f_549_4]) ).

fof(f_550_1,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)),
    inference(fof_nnf,[status(thm)],[fact_number__of2]) ).

fof(f_550_2,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)),
    inference(definitional_conversion,[status(esa)],[f_550_1]) ).

cnf(f_550_3,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)),
    inference(clausify,[status(thm)],[f_550_2]) ).

fof(f_551_1,plain,
    ! [V_v] :
      ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Opred(V_v))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v,c_Int_OPls) )
      & ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v,c_Int_OPls) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__number__of__diff__1]) ).

fof(f_551_2,plain,
    ! [U_1597] :
      ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1597),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Opred(U_1597))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1597,c_Int_OPls) )
      & ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1597),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1597,c_Int_OPls) ) ),
    inference(variable_rename,[status(thm)],[f_551_1]) ).

fof(f_551_3,plain,
    ( ! [U_1599] :
        ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1599),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Opred(U_1599))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1599,c_Int_OPls) )
    & ! [U_1598] :
        ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1598),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1598,c_Int_OPls) ) ),
    inference(miniscope,[status(thm)],[f_551_2]) ).

fof(f_551_4,plain,
    ( ! [U_1599] :
        ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1599),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Opred(U_1599))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1599,c_Int_OPls) )
    & ! [U_1598] :
        ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1598),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1598,c_Int_OPls) ) ),
    inference(definitional_conversion,[status(esa)],[f_551_3]) ).

cnf(f_551_5,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1598),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1598,c_Int_OPls) ),
    inference(clausify,[status(thm)],[f_551_4]) ).

cnf(f_551_6,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1599),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Opred(U_1599))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1599,c_Int_OPls) ),
    inference(clausify,[status(thm)],[f_551_4]) ).

fof(f_552_1,plain,
    ! [V_m,V_v] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Opred(V_v)))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__diff__number__of]) ).

fof(f_552_2,plain,
    ! [U_1601,U_1600] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1601),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1600)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1601,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Opred(U_1600)))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1600) ),
    inference(variable_rename,[status(thm)],[f_552_1]) ).

fof(f_552_3,plain,
    ! [U_1600,U_1601] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1601),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1600)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1601,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Opred(U_1600)))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1600) ),
    inference(definitional_conversion,[status(esa)],[f_552_2]) ).

cnf(f_552_4,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1601),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1600)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1601,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Opred(U_1600)))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1600) ),
    inference(clausify,[status(thm)],[f_552_3]) ).

fof(f_553_1,plain,
    c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[fact_expi__zero]) ).

fof(f_553_2,plain,
    c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_553_1]) ).

cnf(f_553_3,plain,
    c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_553_2]) ).

fof(f_554_1,plain,
    ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x,
    inference(fof_nnf,[status(thm)],[fact_succ__pred]) ).

fof(f_554_2,plain,
    ! [U_1602] : c_Int_Osucc(c_Int_Opred(U_1602)) = U_1602,
    inference(variable_rename,[status(thm)],[f_554_1]) ).

fof(f_554_3,plain,
    ! [U_1602] : c_Int_Osucc(c_Int_Opred(U_1602)) = U_1602,
    inference(definitional_conversion,[status(esa)],[f_554_2]) ).

cnf(f_554_4,plain,
    c_Int_Osucc(c_Int_Opred(U_1602)) = U_1602,
    inference(clausify,[status(thm)],[f_554_3]) ).

fof(f_555_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(V_k_2),V_l_2) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(V_k_2),V_l_2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_le__iff__pred__less]) ).

fof(f_555_2,plain,
    ! [U_1604,U_1603] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1603,U_1604)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(U_1603),U_1604) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(U_1603),U_1604)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1603,U_1604) ) ),
    inference(variable_rename,[status(thm)],[f_555_1]) ).

fof(f_555_3,plain,
    ( ! [U_1608,U_1606] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1606,U_1608)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(U_1606),U_1608) )
    & ! [U_1607,U_1605] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(U_1605),U_1607)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1605,U_1607) ) ),
    inference(miniscope,[status(thm)],[f_555_2]) ).

fof(f_555_4,plain,
    ( ! [U_1608,U_1606] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1606,U_1608)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(U_1606),U_1608) )
    & ! [U_1607,U_1605] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(U_1605),U_1607)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1605,U_1607) ) ),
    inference(definitional_conversion,[status(esa)],[f_555_3]) ).

cnf(f_555_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(U_1605),U_1607)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1605,U_1607) ),
    inference(clausify,[status(thm)],[f_555_4]) ).

cnf(f_555_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1606,U_1608)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(U_1606),U_1608) ),
    inference(clausify,[status(thm)],[f_555_4]) ).

fof(f_556_1,plain,
    ! [V_k] : c_Int_Opred(V_k) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(fof_nnf,[status(thm)],[fact_pred__def]) ).

fof(f_556_2,plain,
    ! [U_1609] : c_Int_Opred(U_1609) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1609,c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(variable_rename,[status(thm)],[f_556_1]) ).

fof(f_556_3,plain,
    ! [U_1609] : c_Int_Opred(U_1609) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1609,c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(definitional_conversion,[status(esa)],[f_556_2]) ).

cnf(f_556_4,plain,
    c_Int_Opred(U_1609) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1609,c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_556_3]) ).

fof(f_557_1,plain,
    ! [V_v_2] :
      ( ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_Opred(V_v_2)))
        | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_Opred(V_v_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_neg__number__of__pred__iff__0]) ).

fof(f_557_2,plain,
    ! [U_1610] :
      ( ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_Opred(U_1610)))
        | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1610) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1610) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_Opred(U_1610))) ) ),
    inference(variable_rename,[status(thm)],[f_557_1]) ).

fof(f_557_3,plain,
    ( ! [U_1612] :
        ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_Opred(U_1612)))
        | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1612) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_1611] :
        ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1611) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_Opred(U_1611))) ) ),
    inference(miniscope,[status(thm)],[f_557_2]) ).

fof(f_557_4,plain,
    ( ! [U_1612] :
        ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_Opred(U_1612)))
        | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1612) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_1611] :
        ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1611) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_Opred(U_1611))) ) ),
    inference(definitional_conversion,[status(esa)],[f_557_3]) ).

cnf(f_557_5,plain,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1611) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_Opred(U_1611))) ),
    inference(clausify,[status(thm)],[f_557_4]) ).

cnf(f_557_6,plain,
    ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_Opred(U_1612)))
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1612) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_557_4]) ).

fof(f_558_1,plain,
    ! [V_z,V_x,V_d] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z)),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)),V_z)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d) ),
    inference(fof_nnf,[status(thm)],[fact_decr__lemma]) ).

fof(f_558_2,plain,
    ! [U_1615,U_1614,U_1613] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1614,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1614,U_1615)),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_1613)),U_1615)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1613) ),
    inference(variable_rename,[status(thm)],[f_558_1]) ).

fof(f_558_3,plain,
    ! [U_1613,U_1614,U_1615] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1614,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1614,U_1615)),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_1613)),U_1615)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1613) ),
    inference(definitional_conversion,[status(esa)],[f_558_2]) ).

cnf(f_558_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1614,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1614,U_1615)),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_1613)),U_1615)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1613) ),
    inference(clausify,[status(thm)],[f_558_3]) ).

fof(f_559_1,plain,
    ! [V_x,V_z,V_d] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z)),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d) ),
    inference(fof_nnf,[status(thm)],[fact_incr__lemma]) ).

fof(f_559_2,plain,
    ! [U_1618,U_1617,U_1616] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1617,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1618,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1618,U_1617)),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_1616)))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1616) ),
    inference(variable_rename,[status(thm)],[f_559_1]) ).

fof(f_559_3,plain,
    ! [U_1616,U_1617,U_1618] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1617,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1618,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1618,U_1617)),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_1616)))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1616) ),
    inference(definitional_conversion,[status(esa)],[f_559_2]) ).

cnf(f_559_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1617,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1618,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1618,U_1617)),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_1616)))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1616) ),
    inference(clausify,[status(thm)],[f_559_3]) ).

fof(f_560_1,plain,
    ! [V_v,T_a] :
      ( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Groups_Ozero__class_Ozero(T_a)
          | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v)) )
        & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Int_Onumber__class_Onumber__of(T_a,V_v)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v)) ) )
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__number__of__lemma]) ).

fof(f_560_2,plain,
    ! [U_1620,U_1619] :
      ( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1619),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1620)) = c_Groups_Ozero__class_Ozero(U_1619)
          | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1620)) )
        & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1619),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1620)) = c_Int_Onumber__class_Onumber__of(U_1619,U_1620)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1620)) ) )
      | ~ class_Int_Onumber__ring(U_1619) ),
    inference(variable_rename,[status(thm)],[f_560_1]) ).

fof(f_560_3,plain,
    ( ! [U_1620,U_1619] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1619),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1620)) = c_Groups_Ozero__class_Ozero(U_1619)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1620))
        | ~ sP142(U_1620,U_1619) )
    & ! [U_1620,U_1619] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1619),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1620)) = c_Int_Onumber__class_Onumber__of(U_1619,U_1620)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1620))
        | ~ sP142(U_1620,U_1619) )
    & ! [U_1620,U_1619] :
        ( sP142(U_1620,U_1619)
        | ~ class_Int_Onumber__ring(U_1619) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP142])],[f_560_2]) ).

cnf(f_560_4,plain,
    ( sP142(U_1620,U_1619)
    | ~ class_Int_Onumber__ring(U_1619) ),
    inference(clausify,[status(thm)],[f_560_3]) ).

cnf(f_560_5,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1619),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1620)) = c_Int_Onumber__class_Onumber__of(U_1619,U_1620)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1620))
    | ~ sP142(U_1620,U_1619) ),
    inference(clausify,[status(thm)],[f_560_3]) ).

cnf(f_560_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1619),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1620)) = c_Groups_Ozero__class_Ozero(U_1619)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1620))
    | ~ sP142(U_1620,U_1619) ),
    inference(clausify,[status(thm)],[f_560_3]) ).

fof(f_561_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),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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_Int_Oint,V_i,V_j) ),
    inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2__lemma]) ).

fof(f_561_2,plain,
    ! [U_1623,U_1622,U_1621] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1623)),U_1621),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1623)),U_1622))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1623)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1621,U_1622) ),
    inference(variable_rename,[status(thm)],[f_561_1]) ).

fof(f_561_3,plain,
    ! [U_1623,U_1621,U_1622] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1623)),U_1621),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1623)),U_1622))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1623)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1621,U_1622) ),
    inference(definitional_conversion,[status(esa)],[f_561_2]) ).

cnf(f_561_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1623)),U_1621),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1623)),U_1622))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1623)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1621,U_1622) ),
    inference(clausify,[status(thm)],[f_561_3]) ).

fof(f_562_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_562_2,plain,
    ! [U_1625,U_1624] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1624),U_1625),c_Groups_Ozero__class_Ozero(U_1624)) = c_Groups_Ozero__class_Ozero(U_1624)
      | ~ class_RealVector_Oreal__normed__algebra(U_1624) ),
    inference(variable_rename,[status(thm)],[f_562_1]) ).

fof(f_562_3,plain,
    ! [U_1624,U_1625] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1624),U_1625),c_Groups_Ozero__class_Ozero(U_1624)) = c_Groups_Ozero__class_Ozero(U_1624)
      | ~ class_RealVector_Oreal__normed__algebra(U_1624) ),
    inference(definitional_conversion,[status(esa)],[f_562_2]) ).

cnf(f_562_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1624),U_1625),c_Groups_Ozero__class_Ozero(U_1624)) = c_Groups_Ozero__class_Ozero(U_1624)
    | ~ class_RealVector_Oreal__normed__algebra(U_1624) ),
    inference(clausify,[status(thm)],[f_562_3]) ).

fof(f_563_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_563_2,plain,
    ! [U_1627,U_1626] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1626),U_1627),c_Groups_Ozero__class_Ozero(U_1626)) = c_Groups_Ozero__class_Ozero(U_1626)
      | ~ class_RealVector_Oreal__normed__algebra(U_1626) ),
    inference(variable_rename,[status(thm)],[f_563_1]) ).

fof(f_563_3,plain,
    ! [U_1626,U_1627] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1626),U_1627),c_Groups_Ozero__class_Ozero(U_1626)) = c_Groups_Ozero__class_Ozero(U_1626)
      | ~ class_RealVector_Oreal__normed__algebra(U_1626) ),
    inference(definitional_conversion,[status(esa)],[f_563_2]) ).

cnf(f_563_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1626),U_1627),c_Groups_Ozero__class_Ozero(U_1626)) = c_Groups_Ozero__class_Ozero(U_1626)
    | ~ class_RealVector_Oreal__normed__algebra(U_1626) ),
    inference(clausify,[status(thm)],[f_563_3]) ).

fof(f_564_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_564_2,plain,
    ! [U_1629,U_1628] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1628),c_Groups_Ozero__class_Ozero(U_1628)),U_1629) = c_Groups_Ozero__class_Ozero(U_1628)
      | ~ class_RealVector_Oreal__normed__algebra(U_1628) ),
    inference(variable_rename,[status(thm)],[f_564_1]) ).

fof(f_564_3,plain,
    ! [U_1628,U_1629] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1628),c_Groups_Ozero__class_Ozero(U_1628)),U_1629) = c_Groups_Ozero__class_Ozero(U_1628)
      | ~ class_RealVector_Oreal__normed__algebra(U_1628) ),
    inference(definitional_conversion,[status(esa)],[f_564_2]) ).

cnf(f_564_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1628),c_Groups_Ozero__class_Ozero(U_1628)),U_1629) = c_Groups_Ozero__class_Ozero(U_1628)
    | ~ class_RealVector_Oreal__normed__algebra(U_1628) ),
    inference(clausify,[status(thm)],[f_564_3]) ).

fof(f_565_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_565_2,plain,
    ! [U_1631,U_1630] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1630),c_Groups_Ozero__class_Ozero(U_1630)),U_1631) = c_Groups_Ozero__class_Ozero(U_1630)
      | ~ class_RealVector_Oreal__normed__algebra(U_1630) ),
    inference(variable_rename,[status(thm)],[f_565_1]) ).

fof(f_565_3,plain,
    ! [U_1631,U_1630] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1630),c_Groups_Ozero__class_Ozero(U_1630)),U_1631) = c_Groups_Ozero__class_Ozero(U_1630)
      | ~ class_RealVector_Oreal__normed__algebra(U_1630) ),
    inference(definitional_conversion,[status(esa)],[f_565_2]) ).

cnf(f_565_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1630),c_Groups_Ozero__class_Ozero(U_1630)),U_1631) = c_Groups_Ozero__class_Ozero(U_1630)
    | ~ class_RealVector_Oreal__normed__algebra(U_1630) ),
    inference(clausify,[status(thm)],[f_565_3]) ).

fof(f_566_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_566_2,plain,
    ! [U_1633,U_1632] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1632),c_Groups_Ozero__class_Ozero(U_1632)),U_1633) = c_Groups_Ozero__class_Ozero(U_1632)
      | ~ class_Rings_Ocomm__semiring__1(U_1632) ),
    inference(variable_rename,[status(thm)],[f_566_1]) ).

fof(f_566_3,plain,
    ! [U_1632,U_1633] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1632),c_Groups_Ozero__class_Ozero(U_1632)),U_1633) = c_Groups_Ozero__class_Ozero(U_1632)
      | ~ class_Rings_Ocomm__semiring__1(U_1632) ),
    inference(definitional_conversion,[status(esa)],[f_566_2]) ).

cnf(f_566_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1632),c_Groups_Ozero__class_Ozero(U_1632)),U_1633) = c_Groups_Ozero__class_Ozero(U_1632)
    | ~ class_Rings_Ocomm__semiring__1(U_1632) ),
    inference(clausify,[status(thm)],[f_566_3]) ).

fof(f_567_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_567_2,plain,
    ! [U_1635,U_1634] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1634),U_1635),c_Groups_Ozero__class_Ozero(U_1634)) = c_Groups_Ozero__class_Ozero(U_1634)
      | ~ class_Rings_Ocomm__semiring__1(U_1634) ),
    inference(variable_rename,[status(thm)],[f_567_1]) ).

fof(f_567_3,plain,
    ! [U_1634,U_1635] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1634),U_1635),c_Groups_Ozero__class_Ozero(U_1634)) = c_Groups_Ozero__class_Ozero(U_1634)
      | ~ class_Rings_Ocomm__semiring__1(U_1634) ),
    inference(definitional_conversion,[status(esa)],[f_567_2]) ).

cnf(f_567_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1634),U_1635),c_Groups_Ozero__class_Ozero(U_1634)) = c_Groups_Ozero__class_Ozero(U_1634)
    | ~ class_Rings_Ocomm__semiring__1(U_1634) ),
    inference(clausify,[status(thm)],[f_567_3]) ).

fof(f_568_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_568_2,plain,
    ! [U_1637,U_1636] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1636),c_Groups_Ozero__class_Ozero(U_1636)),U_1637) = c_Groups_Ozero__class_Ozero(U_1636)
      | ~ class_Rings_Omult__zero(U_1636) ),
    inference(variable_rename,[status(thm)],[f_568_1]) ).

fof(f_568_3,plain,
    ! [U_1636,U_1637] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1636),c_Groups_Ozero__class_Ozero(U_1636)),U_1637) = c_Groups_Ozero__class_Ozero(U_1636)
      | ~ class_Rings_Omult__zero(U_1636) ),
    inference(definitional_conversion,[status(esa)],[f_568_2]) ).

cnf(f_568_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1636),c_Groups_Ozero__class_Ozero(U_1636)),U_1637) = c_Groups_Ozero__class_Ozero(U_1636)
    | ~ class_Rings_Omult__zero(U_1636) ),
    inference(clausify,[status(thm)],[f_568_3]) ).

fof(f_569_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_569_2,plain,
    ! [U_1639,U_1638] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1638),U_1639),c_Groups_Ozero__class_Ozero(U_1638)) = c_Groups_Ozero__class_Ozero(U_1638)
      | ~ class_Rings_Omult__zero(U_1638) ),
    inference(variable_rename,[status(thm)],[f_569_1]) ).

fof(f_569_3,plain,
    ! [U_1638,U_1639] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1638),U_1639),c_Groups_Ozero__class_Ozero(U_1638)) = c_Groups_Ozero__class_Ozero(U_1638)
      | ~ class_Rings_Omult__zero(U_1638) ),
    inference(definitional_conversion,[status(esa)],[f_569_2]) ).

cnf(f_569_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1638),U_1639),c_Groups_Ozero__class_Ozero(U_1638)) = c_Groups_Ozero__class_Ozero(U_1638)
    | ~ class_Rings_Omult__zero(U_1638) ),
    inference(clausify,[status(thm)],[f_569_3]) ).

fof(f_570_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
          | ( V_b_2 != c_Groups_Ozero__class_Ozero(T_a)
            & V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) )
        & ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a)
          | V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_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_570_2,plain,
    ! [U_1642,U_1641,U_1640] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1640),U_1641),U_1642) = c_Groups_Ozero__class_Ozero(U_1640)
          | ( U_1642 != c_Groups_Ozero__class_Ozero(U_1640)
            & U_1641 != c_Groups_Ozero__class_Ozero(U_1640) ) )
        & ( U_1642 = c_Groups_Ozero__class_Ozero(U_1640)
          | U_1641 = c_Groups_Ozero__class_Ozero(U_1640)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1640),U_1641),U_1642) != c_Groups_Ozero__class_Ozero(U_1640) ) )
      | ~ class_Rings_Oring__no__zero__divisors(U_1640) ),
    inference(variable_rename,[status(thm)],[f_570_1]) ).

fof(f_570_3,plain,
    ( ! [U_1640,U_1641,U_1642] :
        ( U_1642 != c_Groups_Ozero__class_Ozero(U_1640)
        | ~ sP143(U_1640,U_1641,U_1642) )
    & ! [U_1640,U_1641,U_1642] :
        ( U_1641 != c_Groups_Ozero__class_Ozero(U_1640)
        | ~ sP143(U_1640,U_1641,U_1642) )
    & ! [U_1640,U_1641,U_1642] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1640),U_1641),U_1642) = c_Groups_Ozero__class_Ozero(U_1640)
        | sP143(U_1640,U_1641,U_1642)
        | ~ sP144(U_1640,U_1641,U_1642) )
    & ! [U_1640,U_1641,U_1642] :
        ( U_1642 = c_Groups_Ozero__class_Ozero(U_1640)
        | U_1641 = c_Groups_Ozero__class_Ozero(U_1640)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1640),U_1641),U_1642) != c_Groups_Ozero__class_Ozero(U_1640)
        | ~ sP144(U_1640,U_1641,U_1642) )
    & ! [U_1640,U_1641,U_1642] :
        ( sP144(U_1640,U_1641,U_1642)
        | ~ class_Rings_Oring__no__zero__divisors(U_1640) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP143,sP144])],[f_570_2]) ).

cnf(f_570_4,plain,
    ( sP144(U_1640,U_1641,U_1642)
    | ~ class_Rings_Oring__no__zero__divisors(U_1640) ),
    inference(clausify,[status(thm)],[f_570_3]) ).

cnf(f_570_5,plain,
    ( U_1642 = c_Groups_Ozero__class_Ozero(U_1640)
    | U_1641 = c_Groups_Ozero__class_Ozero(U_1640)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1640),U_1641),U_1642) != c_Groups_Ozero__class_Ozero(U_1640)
    | ~ sP144(U_1640,U_1641,U_1642) ),
    inference(clausify,[status(thm)],[f_570_3]) ).

cnf(f_570_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1640),U_1641),U_1642) = c_Groups_Ozero__class_Ozero(U_1640)
    | sP143(U_1640,U_1641,U_1642)
    | ~ sP144(U_1640,U_1641,U_1642) ),
    inference(clausify,[status(thm)],[f_570_3]) ).

cnf(f_570_7,plain,
    ( U_1641 != c_Groups_Ozero__class_Ozero(U_1640)
    | ~ sP143(U_1640,U_1641,U_1642) ),
    inference(clausify,[status(thm)],[f_570_3]) ).

cnf(f_570_8,plain,
    ( U_1642 != c_Groups_Ozero__class_Ozero(U_1640)
    | ~ sP143(U_1640,U_1641,U_1642) ),
    inference(clausify,[status(thm)],[f_570_3]) ).

fof(f_571_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_571_2,plain,
    ! [U_1645,U_1644,U_1643] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1643),U_1644),U_1645) != c_Groups_Ozero__class_Ozero(U_1643)
      | U_1645 = c_Groups_Ozero__class_Ozero(U_1643)
      | U_1644 = c_Groups_Ozero__class_Ozero(U_1643)
      | ~ class_Rings_Ono__zero__divisors(U_1643) ),
    inference(variable_rename,[status(thm)],[f_571_1]) ).

fof(f_571_3,plain,
    ! [U_1644,U_1643,U_1645] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1643),U_1644),U_1645) != c_Groups_Ozero__class_Ozero(U_1643)
      | U_1645 = c_Groups_Ozero__class_Ozero(U_1643)
      | U_1644 = c_Groups_Ozero__class_Ozero(U_1643)
      | ~ class_Rings_Ono__zero__divisors(U_1643) ),
    inference(definitional_conversion,[status(esa)],[f_571_2]) ).

cnf(f_571_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1643),U_1644),U_1645) != c_Groups_Ozero__class_Ozero(U_1643)
    | U_1645 = c_Groups_Ozero__class_Ozero(U_1643)
    | U_1644 = c_Groups_Ozero__class_Ozero(U_1643)
    | ~ class_Rings_Ono__zero__divisors(U_1643) ),
    inference(clausify,[status(thm)],[f_571_3]) ).

fof(f_572_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_572_2,plain,
    ! [U_1648,U_1647,U_1646] :
      ( U_1648 = c_Groups_Ozero__class_Ozero(U_1646)
      | U_1647 = c_Groups_Ozero__class_Ozero(U_1646)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1646),U_1647),U_1648) != c_Groups_Ozero__class_Ozero(U_1646)
      | ~ class_Rings_Ono__zero__divisors(U_1646) ),
    inference(variable_rename,[status(thm)],[f_572_1]) ).

fof(f_572_3,plain,
    ! [U_1648,U_1646,U_1647] :
      ( U_1648 = c_Groups_Ozero__class_Ozero(U_1646)
      | U_1647 = c_Groups_Ozero__class_Ozero(U_1646)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1646),U_1647),U_1648) != c_Groups_Ozero__class_Ozero(U_1646)
      | ~ class_Rings_Ono__zero__divisors(U_1646) ),
    inference(definitional_conversion,[status(esa)],[f_572_2]) ).

cnf(f_572_4,plain,
    ( U_1648 = c_Groups_Ozero__class_Ozero(U_1646)
    | U_1647 = c_Groups_Ozero__class_Ozero(U_1646)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1646),U_1647),U_1648) != c_Groups_Ozero__class_Ozero(U_1646)
    | ~ class_Rings_Ono__zero__divisors(U_1646) ),
    inference(clausify,[status(thm)],[f_572_3]) ).

fof(f_573_1,plain,
    ! [V_z,V_w,V_v,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w))),V_z)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__number__of__left]) ).

fof(f_573_2,plain,
    ! [U_1652,U_1651,U_1650,U_1649] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1649),c_Int_Onumber__class_Onumber__of(U_1649,U_1650)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1649),c_Int_Onumber__class_Onumber__of(U_1649,U_1651)),U_1652)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1649),c_Int_Onumber__class_Onumber__of(U_1649,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1650),U_1651))),U_1652)
      | ~ class_Int_Onumber__ring(U_1649) ),
    inference(variable_rename,[status(thm)],[f_573_1]) ).

fof(f_573_3,plain,
    ! [U_1649,U_1650,U_1651,U_1652] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1649),c_Int_Onumber__class_Onumber__of(U_1649,U_1650)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1649),c_Int_Onumber__class_Onumber__of(U_1649,U_1651)),U_1652)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1649),c_Int_Onumber__class_Onumber__of(U_1649,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1650),U_1651))),U_1652)
      | ~ class_Int_Onumber__ring(U_1649) ),
    inference(definitional_conversion,[status(esa)],[f_573_2]) ).

cnf(f_573_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1649),c_Int_Onumber__class_Onumber__of(U_1649,U_1650)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1649),c_Int_Onumber__class_Onumber__of(U_1649,U_1651)),U_1652)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1649),c_Int_Onumber__class_Onumber__of(U_1649,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1650),U_1651))),U_1652)
    | ~ class_Int_Onumber__ring(U_1649) ),
    inference(clausify,[status(thm)],[f_573_3]) ).

fof(f_574_1,plain,
    ! [V_w,V_v] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)),
    inference(fof_nnf,[status(thm)],[fact_times__numeral__code_I5_J]) ).

fof(f_574_2,plain,
    ! [U_1654,U_1653] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1653)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1654)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1653),U_1654)),
    inference(variable_rename,[status(thm)],[f_574_1]) ).

fof(f_574_3,plain,
    ! [U_1653,U_1654] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1653)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1654)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1653),U_1654)),
    inference(definitional_conversion,[status(esa)],[f_574_2]) ).

cnf(f_574_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1653)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1654)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1653),U_1654)),
    inference(clausify,[status(thm)],[f_574_3]) ).

fof(f_575_1,plain,
    ! [V_w,V_v,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_v)),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_arith__simps_I32_J]) ).

fof(f_575_2,plain,
    ! [U_1657,U_1656,U_1655] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1655),c_Int_Onumber__class_Onumber__of(U_1655,U_1656)),c_Int_Onumber__class_Onumber__of(U_1655,U_1657)) = c_Int_Onumber__class_Onumber__of(U_1655,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1656),U_1657))
      | ~ class_Int_Onumber__ring(U_1655) ),
    inference(variable_rename,[status(thm)],[f_575_1]) ).

fof(f_575_3,plain,
    ! [U_1655,U_1656,U_1657] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1655),c_Int_Onumber__class_Onumber__of(U_1655,U_1656)),c_Int_Onumber__class_Onumber__of(U_1655,U_1657)) = c_Int_Onumber__class_Onumber__of(U_1655,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1656),U_1657))
      | ~ class_Int_Onumber__ring(U_1655) ),
    inference(definitional_conversion,[status(esa)],[f_575_2]) ).

cnf(f_575_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1655),c_Int_Onumber__class_Onumber__of(U_1655,U_1656)),c_Int_Onumber__class_Onumber__of(U_1655,U_1657)) = c_Int_Onumber__class_Onumber__of(U_1655,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1656),U_1657))
    | ~ class_Int_Onumber__ring(U_1655) ),
    inference(clausify,[status(thm)],[f_575_3]) ).

fof(f_576_1,plain,
    ! [V_w,V_v,T_a] :
      ( c_Int_Onumber__class_Onumber__of(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_v)),c_Int_Onumber__class_Onumber__of(T_a,V_w))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_number__of__mult]) ).

fof(f_576_2,plain,
    ! [U_1660,U_1659,U_1658] :
      ( c_Int_Onumber__class_Onumber__of(U_1658,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1659),U_1660)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1658),c_Int_Onumber__class_Onumber__of(U_1658,U_1659)),c_Int_Onumber__class_Onumber__of(U_1658,U_1660))
      | ~ class_Int_Onumber__ring(U_1658) ),
    inference(variable_rename,[status(thm)],[f_576_1]) ).

fof(f_576_3,plain,
    ! [U_1658,U_1659,U_1660] :
      ( c_Int_Onumber__class_Onumber__of(U_1658,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1659),U_1660)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1658),c_Int_Onumber__class_Onumber__of(U_1658,U_1659)),c_Int_Onumber__class_Onumber__of(U_1658,U_1660))
      | ~ class_Int_Onumber__ring(U_1658) ),
    inference(definitional_conversion,[status(esa)],[f_576_2]) ).

cnf(f_576_4,plain,
    ( c_Int_Onumber__class_Onumber__of(U_1658,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1659),U_1660)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1658),c_Int_Onumber__class_Onumber__of(U_1658,U_1659)),c_Int_Onumber__class_Onumber__of(U_1658,U_1660))
    | ~ class_Int_Onumber__ring(U_1658) ),
    inference(clausify,[status(thm)],[f_576_3]) ).

fof(f_577_1,plain,
    ! [V_n] : ~ c_Nat__Numeral_Oneg(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),
    inference(fof_nnf,[status(thm)],[fact_not__neg__int]) ).

fof(f_577_2,plain,
    ! [U_1661] : ~ c_Nat__Numeral_Oneg(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1661)),
    inference(variable_rename,[status(thm)],[f_577_1]) ).

fof(f_577_3,plain,
    ! [U_1661] : ~ c_Nat__Numeral_Oneg(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1661)),
    inference(definitional_conversion,[status(esa)],[f_577_2]) ).

cnf(f_577_4,plain,
    ~ c_Nat__Numeral_Oneg(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1661)),
    inference(clausify,[status(thm)],[f_577_3]) ).

fof(f_578_1,plain,
    ! [V_m] : c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m),
    inference(fof_nnf,[status(thm)],[fact_abs__int__eq]) ).

fof(f_578_2,plain,
    ! [U_1662] : c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1662)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1662),
    inference(variable_rename,[status(thm)],[f_578_1]) ).

fof(f_578_3,plain,
    ! [U_1662] : c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1662)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1662),
    inference(definitional_conversion,[status(esa)],[f_578_2]) ).

cnf(f_578_4,plain,
    c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1662)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1662),
    inference(clausify,[status(thm)],[f_578_3]) ).

fof(f_579_1,plain,
    ! [V_n,T_a] :
      ( c_Groups_Oabs__class_Oabs(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__of__nat]) ).

fof(f_579_2,plain,
    ! [U_1664,U_1663] :
      ( c_Groups_Oabs__class_Oabs(U_1663,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1663),U_1664)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1663),U_1664)
      | ~ class_Rings_Olinordered__idom(U_1663) ),
    inference(variable_rename,[status(thm)],[f_579_1]) ).

fof(f_579_3,plain,
    ! [U_1663,U_1664] :
      ( c_Groups_Oabs__class_Oabs(U_1663,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1663),U_1664)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1663),U_1664)
      | ~ class_Rings_Olinordered__idom(U_1663) ),
    inference(definitional_conversion,[status(esa)],[f_579_2]) ).

cnf(f_579_4,plain,
    ( c_Groups_Oabs__class_Oabs(U_1663,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1663),U_1664)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1663),U_1664)
    | ~ class_Rings_Olinordered__idom(U_1663) ),
    inference(clausify,[status(thm)],[f_579_3]) ).

fof(f_580_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_580_2,plain,
    ! [U_1668,U_1667,U_1666,U_1665] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1665),U_1666),c_Groups_Oplus__class_Oplus(U_1665,U_1667,U_1668)) = c_Groups_Oplus__class_Oplus(U_1665,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1665),U_1666),U_1667),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1665),U_1666),U_1668))
      | ~ class_RealVector_Oreal__normed__algebra(U_1665) ),
    inference(variable_rename,[status(thm)],[f_580_1]) ).

fof(f_580_3,plain,
    ! [U_1665,U_1666,U_1667,U_1668] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1665),U_1666),c_Groups_Oplus__class_Oplus(U_1665,U_1667,U_1668)) = c_Groups_Oplus__class_Oplus(U_1665,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1665),U_1666),U_1667),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1665),U_1666),U_1668))
      | ~ class_RealVector_Oreal__normed__algebra(U_1665) ),
    inference(definitional_conversion,[status(esa)],[f_580_2]) ).

cnf(f_580_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1665),U_1666),c_Groups_Oplus__class_Oplus(U_1665,U_1667,U_1668)) = c_Groups_Oplus__class_Oplus(U_1665,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1665),U_1666),U_1667),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1665),U_1666),U_1668))
    | ~ class_RealVector_Oreal__normed__algebra(U_1665) ),
    inference(clausify,[status(thm)],[f_580_3]) ).

fof(f_581_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_581_2,plain,
    ! [U_1672,U_1671,U_1670,U_1669] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1669),U_1670),c_Groups_Oplus__class_Oplus(U_1669,U_1671,U_1672)) = c_Groups_Oplus__class_Oplus(U_1669,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1669),U_1670),U_1671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1669),U_1670),U_1672))
      | ~ class_RealVector_Oreal__normed__algebra(U_1669) ),
    inference(variable_rename,[status(thm)],[f_581_1]) ).

fof(f_581_3,plain,
    ! [U_1669,U_1670,U_1671,U_1672] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1669),U_1670),c_Groups_Oplus__class_Oplus(U_1669,U_1671,U_1672)) = c_Groups_Oplus__class_Oplus(U_1669,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1669),U_1670),U_1671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1669),U_1670),U_1672))
      | ~ class_RealVector_Oreal__normed__algebra(U_1669) ),
    inference(definitional_conversion,[status(esa)],[f_581_2]) ).

cnf(f_581_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1669),U_1670),c_Groups_Oplus__class_Oplus(U_1669,U_1671,U_1672)) = c_Groups_Oplus__class_Oplus(U_1669,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1669),U_1670),U_1671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1669),U_1670),U_1672))
    | ~ class_RealVector_Oreal__normed__algebra(U_1669) ),
    inference(clausify,[status(thm)],[f_581_3]) ).

fof(f_582_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_582_2,plain,
    ! [U_1676,U_1675,U_1674,U_1673] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1673),c_Groups_Oplus__class_Oplus(U_1673,U_1674,U_1675)),U_1676) = c_Groups_Oplus__class_Oplus(U_1673,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1673),U_1674),U_1676),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1673),U_1675),U_1676))
      | ~ class_RealVector_Oreal__normed__algebra(U_1673) ),
    inference(variable_rename,[status(thm)],[f_582_1]) ).

fof(f_582_3,plain,
    ! [U_1673,U_1674,U_1675,U_1676] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1673),c_Groups_Oplus__class_Oplus(U_1673,U_1674,U_1675)),U_1676) = c_Groups_Oplus__class_Oplus(U_1673,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1673),U_1674),U_1676),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1673),U_1675),U_1676))
      | ~ class_RealVector_Oreal__normed__algebra(U_1673) ),
    inference(definitional_conversion,[status(esa)],[f_582_2]) ).

cnf(f_582_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1673),c_Groups_Oplus__class_Oplus(U_1673,U_1674,U_1675)),U_1676) = c_Groups_Oplus__class_Oplus(U_1673,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1673),U_1674),U_1676),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1673),U_1675),U_1676))
    | ~ class_RealVector_Oreal__normed__algebra(U_1673) ),
    inference(clausify,[status(thm)],[f_582_3]) ).

fof(f_583_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_583_2,plain,
    ! [U_1680,U_1679,U_1678,U_1677] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1677),c_Groups_Oplus__class_Oplus(U_1677,U_1678,U_1679)),U_1680) = c_Groups_Oplus__class_Oplus(U_1677,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1677),U_1678),U_1680),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1677),U_1679),U_1680))
      | ~ class_RealVector_Oreal__normed__algebra(U_1677) ),
    inference(variable_rename,[status(thm)],[f_583_1]) ).

fof(f_583_3,plain,
    ! [U_1677,U_1678,U_1679,U_1680] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1677),c_Groups_Oplus__class_Oplus(U_1677,U_1678,U_1679)),U_1680) = c_Groups_Oplus__class_Oplus(U_1677,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1677),U_1678),U_1680),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1677),U_1679),U_1680))
      | ~ class_RealVector_Oreal__normed__algebra(U_1677) ),
    inference(definitional_conversion,[status(esa)],[f_583_2]) ).

cnf(f_583_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1677),c_Groups_Oplus__class_Oplus(U_1677,U_1678,U_1679)),U_1680) = c_Groups_Oplus__class_Oplus(U_1677,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1677),U_1678),U_1680),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1677),U_1679),U_1680))
    | ~ class_RealVector_Oreal__normed__algebra(U_1677) ),
    inference(clausify,[status(thm)],[f_583_3]) ).

fof(f_584_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_584_2,plain,
    ! [U_1683,U_1682,U_1681] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1681,U_1682)),U_1683) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1681),U_1683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1682),U_1683)),
    inference(variable_rename,[status(thm)],[f_584_1]) ).

fof(f_584_3,plain,
    ! [U_1681,U_1682,U_1683] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1681,U_1682)),U_1683) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1681),U_1683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1682),U_1683)),
    inference(definitional_conversion,[status(esa)],[f_584_2]) ).

cnf(f_584_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1681,U_1682)),U_1683) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1681),U_1683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1682),U_1683)),
    inference(clausify,[status(thm)],[f_584_3]) ).

fof(f_585_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_585_2,plain,
    ! [U_1686,U_1685,U_1684] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1684),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1685,U_1686)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1684),U_1685),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1684),U_1686)),
    inference(variable_rename,[status(thm)],[f_585_1]) ).

fof(f_585_3,plain,
    ! [U_1684,U_1685,U_1686] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1684),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1685,U_1686)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1684),U_1685),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1684),U_1686)),
    inference(definitional_conversion,[status(esa)],[f_585_2]) ).

cnf(f_585_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1684),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1685,U_1686)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1684),U_1685),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1684),U_1686)),
    inference(clausify,[status(thm)],[f_585_3]) ).

fof(f_586_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_586_2,plain,
    ! [U_1691,U_1690,U_1689,U_1688,U_1687] :
      ( c_Groups_Oplus__class_Oplus(U_1687,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1687),U_1688),U_1689),c_Groups_Oplus__class_Oplus(U_1687,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1687),U_1690),U_1689),U_1691)) = c_Groups_Oplus__class_Oplus(U_1687,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1687),c_Groups_Oplus__class_Oplus(U_1687,U_1688,U_1690)),U_1689),U_1691)
      | ~ class_Rings_Osemiring(U_1687) ),
    inference(variable_rename,[status(thm)],[f_586_1]) ).

fof(f_586_3,plain,
    ! [U_1687,U_1688,U_1689,U_1690,U_1691] :
      ( c_Groups_Oplus__class_Oplus(U_1687,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1687),U_1688),U_1689),c_Groups_Oplus__class_Oplus(U_1687,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1687),U_1690),U_1689),U_1691)) = c_Groups_Oplus__class_Oplus(U_1687,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1687),c_Groups_Oplus__class_Oplus(U_1687,U_1688,U_1690)),U_1689),U_1691)
      | ~ class_Rings_Osemiring(U_1687) ),
    inference(definitional_conversion,[status(esa)],[f_586_2]) ).

cnf(f_586_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_1687,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1687),U_1688),U_1689),c_Groups_Oplus__class_Oplus(U_1687,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1687),U_1690),U_1689),U_1691)) = c_Groups_Oplus__class_Oplus(U_1687,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1687),c_Groups_Oplus__class_Oplus(U_1687,U_1688,U_1690)),U_1689),U_1691)
    | ~ class_Rings_Osemiring(U_1687) ),
    inference(clausify,[status(thm)],[f_586_3]) ).

fof(f_587_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_587_2,plain,
    ! [U_1695,U_1694,U_1693,U_1692] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1692),c_Groups_Oplus__class_Oplus(U_1692,U_1693,U_1694)),U_1695) = c_Groups_Oplus__class_Oplus(U_1692,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1692),U_1693),U_1695),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1692),U_1694),U_1695))
      | ~ class_Rings_Ocomm__semiring(U_1692) ),
    inference(variable_rename,[status(thm)],[f_587_1]) ).

fof(f_587_3,plain,
    ! [U_1692,U_1693,U_1694,U_1695] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1692),c_Groups_Oplus__class_Oplus(U_1692,U_1693,U_1694)),U_1695) = c_Groups_Oplus__class_Oplus(U_1692,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1692),U_1693),U_1695),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1692),U_1694),U_1695))
      | ~ class_Rings_Ocomm__semiring(U_1692) ),
    inference(definitional_conversion,[status(esa)],[f_587_2]) ).

cnf(f_587_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1692),c_Groups_Oplus__class_Oplus(U_1692,U_1693,U_1694)),U_1695) = c_Groups_Oplus__class_Oplus(U_1692,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1692),U_1693),U_1695),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1692),U_1694),U_1695))
    | ~ class_Rings_Ocomm__semiring(U_1692) ),
    inference(clausify,[status(thm)],[f_587_3]) ).

fof(f_588_1,plain,
    ! [V_za_2,V_x_2,V_y_2,V_wa_2,T_a] :
      ( ( ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_wa_2),V_y_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_za_2)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_wa_2),V_za_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2))
          | ( V_y_2 != V_za_2
            & V_wa_2 != V_x_2 ) )
        & ( V_y_2 = V_za_2
          | V_wa_2 = V_x_2
          | c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_wa_2),V_y_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_za_2)) != c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_wa_2),V_za_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_588_2,plain,
    ! [U_1700,U_1699,U_1698,U_1697,U_1696] :
      ( ( ( c_Groups_Oplus__class_Oplus(U_1696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1696),U_1697),U_1698),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1696),U_1699),U_1700)) = c_Groups_Oplus__class_Oplus(U_1696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1696),U_1697),U_1700),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1696),U_1699),U_1698))
          | ( U_1698 != U_1700
            & U_1697 != U_1699 ) )
        & ( U_1698 = U_1700
          | U_1697 = U_1699
          | c_Groups_Oplus__class_Oplus(U_1696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1696),U_1697),U_1698),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1696),U_1699),U_1700)) != c_Groups_Oplus__class_Oplus(U_1696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1696),U_1697),U_1700),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1696),U_1699),U_1698)) ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1696) ),
    inference(variable_rename,[status(thm)],[f_588_1]) ).

fof(f_588_3,plain,
    ( ! [U_1697,U_1698,U_1699,U_1700] :
        ( U_1698 != U_1700
        | ~ sP145(U_1697,U_1698,U_1699,U_1700) )
    & ! [U_1697,U_1698,U_1699,U_1700] :
        ( U_1697 != U_1699
        | ~ sP145(U_1697,U_1698,U_1699,U_1700) )
    & ! [U_1697,U_1698,U_1699,U_1700,U_1696] :
        ( c_Groups_Oplus__class_Oplus(U_1696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1696),U_1697),U_1698),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1696),U_1699),U_1700)) = c_Groups_Oplus__class_Oplus(U_1696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1696),U_1697),U_1700),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1696),U_1699),U_1698))
        | sP145(U_1697,U_1698,U_1699,U_1700)
        | ~ sP146(U_1697,U_1698,U_1699,U_1700,U_1696) )
    & ! [U_1697,U_1698,U_1699,U_1700,U_1696] :
        ( U_1698 = U_1700
        | U_1697 = U_1699
        | c_Groups_Oplus__class_Oplus(U_1696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1696),U_1697),U_1698),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1696),U_1699),U_1700)) != c_Groups_Oplus__class_Oplus(U_1696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1696),U_1697),U_1700),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1696),U_1699),U_1698))
        | ~ sP146(U_1697,U_1698,U_1699,U_1700,U_1696) )
    & ! [U_1697,U_1698,U_1699,U_1700,U_1696] :
        ( sP146(U_1697,U_1698,U_1699,U_1700,U_1696)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1696) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP145,sP146])],[f_588_2]) ).

cnf(f_588_4,plain,
    ( sP146(U_1697,U_1698,U_1699,U_1700,U_1696)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1696) ),
    inference(clausify,[status(thm)],[f_588_3]) ).

cnf(f_588_5,plain,
    ( U_1698 = U_1700
    | U_1697 = U_1699
    | c_Groups_Oplus__class_Oplus(U_1696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1696),U_1697),U_1698),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1696),U_1699),U_1700)) != c_Groups_Oplus__class_Oplus(U_1696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1696),U_1697),U_1700),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1696),U_1699),U_1698))
    | ~ sP146(U_1697,U_1698,U_1699,U_1700,U_1696) ),
    inference(clausify,[status(thm)],[f_588_3]) ).

cnf(f_588_6,plain,
    ( c_Groups_Oplus__class_Oplus(U_1696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1696),U_1697),U_1698),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1696),U_1699),U_1700)) = c_Groups_Oplus__class_Oplus(U_1696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1696),U_1697),U_1700),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1696),U_1699),U_1698))
    | sP145(U_1697,U_1698,U_1699,U_1700)
    | ~ sP146(U_1697,U_1698,U_1699,U_1700,U_1696) ),
    inference(clausify,[status(thm)],[f_588_3]) ).

cnf(f_588_7,plain,
    ( U_1697 != U_1699
    | ~ sP145(U_1697,U_1698,U_1699,U_1700) ),
    inference(clausify,[status(thm)],[f_588_3]) ).

cnf(f_588_8,plain,
    ( U_1698 != U_1700
    | ~ sP145(U_1697,U_1698,U_1699,U_1700) ),
    inference(clausify,[status(thm)],[f_588_3]) ).

fof(f_589_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_589_2,plain,
    ! [U_1704,U_1703,U_1702,U_1701] :
      ( c_Groups_Oplus__class_Oplus(U_1701,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1701),U_1702),U_1703),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1701),U_1704),U_1703)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1701),c_Groups_Oplus__class_Oplus(U_1701,U_1702,U_1704)),U_1703)
      | ~ class_Rings_Ocomm__semiring__1(U_1701) ),
    inference(variable_rename,[status(thm)],[f_589_1]) ).

fof(f_589_3,plain,
    ! [U_1703,U_1704,U_1701,U_1702] :
      ( c_Groups_Oplus__class_Oplus(U_1701,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1701),U_1702),U_1703),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1701),U_1704),U_1703)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1701),c_Groups_Oplus__class_Oplus(U_1701,U_1702,U_1704)),U_1703)
      | ~ class_Rings_Ocomm__semiring__1(U_1701) ),
    inference(definitional_conversion,[status(esa)],[f_589_2]) ).

cnf(f_589_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_1701,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1701),U_1702),U_1703),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1701),U_1704),U_1703)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1701),c_Groups_Oplus__class_Oplus(U_1701,U_1702,U_1704)),U_1703)
    | ~ class_Rings_Ocomm__semiring__1(U_1701) ),
    inference(clausify,[status(thm)],[f_589_3]) ).

fof(f_590_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_590_2,plain,
    ! [U_1708,U_1707,U_1706,U_1705] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1705),c_Groups_Oplus__class_Oplus(U_1705,U_1706,U_1707)),U_1708) = c_Groups_Oplus__class_Oplus(U_1705,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1705),U_1706),U_1708),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1705),U_1707),U_1708))
      | ~ class_Rings_Ocomm__semiring__1(U_1705) ),
    inference(variable_rename,[status(thm)],[f_590_1]) ).

fof(f_590_3,plain,
    ! [U_1705,U_1706,U_1707,U_1708] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1705),c_Groups_Oplus__class_Oplus(U_1705,U_1706,U_1707)),U_1708) = c_Groups_Oplus__class_Oplus(U_1705,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1705),U_1706),U_1708),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1705),U_1707),U_1708))
      | ~ class_Rings_Ocomm__semiring__1(U_1705) ),
    inference(definitional_conversion,[status(esa)],[f_590_2]) ).

cnf(f_590_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1705),c_Groups_Oplus__class_Oplus(U_1705,U_1706,U_1707)),U_1708) = c_Groups_Oplus__class_Oplus(U_1705,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1705),U_1706),U_1708),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1705),U_1707),U_1708))
    | ~ class_Rings_Ocomm__semiring__1(U_1705) ),
    inference(clausify,[status(thm)],[f_590_3]) ).

fof(f_591_1,plain,
    ! [V_da_2,V_c_2,V_b_2,V_a_2,T_a] :
      ( ( ( ( V_c_2 != V_da_2
            & V_a_2 != V_b_2 )
          | c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_da_2)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_da_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)) )
        & ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_da_2)) != c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_da_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2))
          | V_c_2 = V_da_2
          | V_a_2 = V_b_2 ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_crossproduct__noteq]) ).

fof(f_591_2,plain,
    ! [U_1713,U_1712,U_1711,U_1710,U_1709] :
      ( ( ( ( U_1712 != U_1713
            & U_1710 != U_1711 )
          | c_Groups_Oplus__class_Oplus(U_1709,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1709),U_1710),U_1712),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1709),U_1711),U_1713)) = c_Groups_Oplus__class_Oplus(U_1709,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1709),U_1710),U_1713),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1709),U_1711),U_1712)) )
        & ( c_Groups_Oplus__class_Oplus(U_1709,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1709),U_1710),U_1712),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1709),U_1711),U_1713)) != c_Groups_Oplus__class_Oplus(U_1709,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1709),U_1710),U_1713),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1709),U_1711),U_1712))
          | U_1712 = U_1713
          | U_1710 = U_1711 ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1709) ),
    inference(variable_rename,[status(thm)],[f_591_1]) ).

fof(f_591_3,plain,
    ( ! [U_1710,U_1711,U_1712,U_1713] :
        ( U_1712 != U_1713
        | ~ sP147(U_1710,U_1711,U_1712,U_1713) )
    & ! [U_1710,U_1711,U_1712,U_1713] :
        ( U_1710 != U_1711
        | ~ sP147(U_1710,U_1711,U_1712,U_1713) )
    & ! [U_1709,U_1710,U_1711,U_1712,U_1713] :
        ( sP147(U_1710,U_1711,U_1712,U_1713)
        | c_Groups_Oplus__class_Oplus(U_1709,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1709),U_1710),U_1712),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1709),U_1711),U_1713)) = c_Groups_Oplus__class_Oplus(U_1709,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1709),U_1710),U_1713),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1709),U_1711),U_1712))
        | ~ sP148(U_1709,U_1710,U_1711,U_1712,U_1713) )
    & ! [U_1709,U_1710,U_1711,U_1712,U_1713] :
        ( c_Groups_Oplus__class_Oplus(U_1709,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1709),U_1710),U_1712),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1709),U_1711),U_1713)) != c_Groups_Oplus__class_Oplus(U_1709,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1709),U_1710),U_1713),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1709),U_1711),U_1712))
        | U_1712 = U_1713
        | U_1710 = U_1711
        | ~ sP148(U_1709,U_1710,U_1711,U_1712,U_1713) )
    & ! [U_1709,U_1710,U_1711,U_1712,U_1713] :
        ( sP148(U_1709,U_1710,U_1711,U_1712,U_1713)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1709) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP147,sP148])],[f_591_2]) ).

cnf(f_591_4,plain,
    ( sP148(U_1709,U_1710,U_1711,U_1712,U_1713)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1709) ),
    inference(clausify,[status(thm)],[f_591_3]) ).

cnf(f_591_5,plain,
    ( c_Groups_Oplus__class_Oplus(U_1709,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1709),U_1710),U_1712),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1709),U_1711),U_1713)) != c_Groups_Oplus__class_Oplus(U_1709,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1709),U_1710),U_1713),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1709),U_1711),U_1712))
    | U_1712 = U_1713
    | U_1710 = U_1711
    | ~ sP148(U_1709,U_1710,U_1711,U_1712,U_1713) ),
    inference(clausify,[status(thm)],[f_591_3]) ).

cnf(f_591_6,plain,
    ( sP147(U_1710,U_1711,U_1712,U_1713)
    | c_Groups_Oplus__class_Oplus(U_1709,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1709),U_1710),U_1712),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1709),U_1711),U_1713)) = c_Groups_Oplus__class_Oplus(U_1709,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1709),U_1710),U_1713),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1709),U_1711),U_1712))
    | ~ sP148(U_1709,U_1710,U_1711,U_1712,U_1713) ),
    inference(clausify,[status(thm)],[f_591_3]) ).

cnf(f_591_7,plain,
    ( U_1710 != U_1711
    | ~ sP147(U_1710,U_1711,U_1712,U_1713) ),
    inference(clausify,[status(thm)],[f_591_3]) ).

cnf(f_591_8,plain,
    ( U_1712 != U_1713
    | ~ sP147(U_1710,U_1711,U_1712,U_1713) ),
    inference(clausify,[status(thm)],[f_591_3]) ).

fof(f_592_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_592_2,plain,
    ! [U_1717,U_1716,U_1715,U_1714] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1714),U_1715),c_Groups_Oplus__class_Oplus(U_1714,U_1716,U_1717)) = c_Groups_Oplus__class_Oplus(U_1714,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1714),U_1715),U_1716),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1714),U_1715),U_1717))
      | ~ class_Rings_Ocomm__semiring__1(U_1714) ),
    inference(variable_rename,[status(thm)],[f_592_1]) ).

fof(f_592_3,plain,
    ! [U_1715,U_1716,U_1717,U_1714] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1714),U_1715),c_Groups_Oplus__class_Oplus(U_1714,U_1716,U_1717)) = c_Groups_Oplus__class_Oplus(U_1714,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1714),U_1715),U_1716),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1714),U_1715),U_1717))
      | ~ class_Rings_Ocomm__semiring__1(U_1714) ),
    inference(definitional_conversion,[status(esa)],[f_592_2]) ).

cnf(f_592_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1714),U_1715),c_Groups_Oplus__class_Oplus(U_1714,U_1716,U_1717)) = c_Groups_Oplus__class_Oplus(U_1714,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1714),U_1715),U_1716),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1714),U_1715),U_1717))
    | ~ class_Rings_Ocomm__semiring__1(U_1714) ),
    inference(clausify,[status(thm)],[f_592_3]) ).

fof(f_593_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__mult__self]) ).

fof(f_593_2,plain,
    ! [U_1719,U_1718] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1718),c_Groups_Oabs__class_Oabs(U_1718,U_1719)),c_Groups_Oabs__class_Oabs(U_1718,U_1719)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1718),U_1719),U_1719)
      | ~ class_Rings_Olinordered__idom(U_1718) ),
    inference(variable_rename,[status(thm)],[f_593_1]) ).

fof(f_593_3,plain,
    ! [U_1718,U_1719] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1718),c_Groups_Oabs__class_Oabs(U_1718,U_1719)),c_Groups_Oabs__class_Oabs(U_1718,U_1719)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1718),U_1719),U_1719)
      | ~ class_Rings_Olinordered__idom(U_1718) ),
    inference(definitional_conversion,[status(esa)],[f_593_2]) ).

cnf(f_593_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1718),c_Groups_Oabs__class_Oabs(U_1718,U_1719)),c_Groups_Oabs__class_Oabs(U_1718,U_1719)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1718),U_1719),U_1719)
    | ~ class_Rings_Olinordered__idom(U_1718) ),
    inference(clausify,[status(thm)],[f_593_3]) ).

fof(f_594_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Groups_Oabs__class_Oabs(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_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__mult]) ).

fof(f_594_2,plain,
    ! [U_1722,U_1721,U_1720] :
      ( c_Groups_Oabs__class_Oabs(U_1720,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1720),U_1721),U_1722)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1720),c_Groups_Oabs__class_Oabs(U_1720,U_1721)),c_Groups_Oabs__class_Oabs(U_1720,U_1722))
      | ~ class_Rings_Olinordered__idom(U_1720) ),
    inference(variable_rename,[status(thm)],[f_594_1]) ).

fof(f_594_3,plain,
    ! [U_1720,U_1721,U_1722] :
      ( c_Groups_Oabs__class_Oabs(U_1720,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1720),U_1721),U_1722)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1720),c_Groups_Oabs__class_Oabs(U_1720,U_1721)),c_Groups_Oabs__class_Oabs(U_1720,U_1722))
      | ~ class_Rings_Olinordered__idom(U_1720) ),
    inference(definitional_conversion,[status(esa)],[f_594_2]) ).

cnf(f_594_4,plain,
    ( c_Groups_Oabs__class_Oabs(U_1720,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1720),U_1721),U_1722)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1720),c_Groups_Oabs__class_Oabs(U_1720,U_1721)),c_Groups_Oabs__class_Oabs(U_1720,U_1722))
    | ~ class_Rings_Olinordered__idom(U_1720) ),
    inference(clausify,[status(thm)],[f_594_3]) ).

fof(f_595_1,plain,
    c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[fact_real__eq__of__nat]) ).

fof(f_595_2,plain,
    c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_595_1]) ).

cnf(f_595_3,plain,
    c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_595_2]) ).

fof(f_596_1,plain,
    c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[fact_real__of__nat__def]) ).

fof(f_596_2,plain,
    c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_596_1]) ).

cnf(f_596_3,plain,
    c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_596_2]) ).

fof(f_597_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_597_2,plain,
    ! [U_1726,U_1725,U_1724,U_1723] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1723),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1723),U_1724),U_1725)),U_1726) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1723),U_1724),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1723),U_1725),U_1726))
      | ~ class_Groups_Oab__semigroup__mult(U_1723) ),
    inference(variable_rename,[status(thm)],[f_597_1]) ).

fof(f_597_3,plain,
    ! [U_1723,U_1724,U_1725,U_1726] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1723),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1723),U_1724),U_1725)),U_1726) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1723),U_1724),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1723),U_1725),U_1726))
      | ~ class_Groups_Oab__semigroup__mult(U_1723) ),
    inference(definitional_conversion,[status(esa)],[f_597_2]) ).

cnf(f_597_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1723),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1723),U_1724),U_1725)),U_1726) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1723),U_1724),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1723),U_1725),U_1726))
    | ~ class_Groups_Oab__semigroup__mult(U_1723) ),
    inference(clausify,[status(thm)],[f_597_3]) ).

fof(f_598_1,plain,
    ! [V_n_2,V_m_2,T_a] :
      ( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)
          | V_m_2 != V_n_2 )
        & ( V_m_2 = V_n_2
          | hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2) ) )
      | ~ class_Nat_Osemiring__char__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__eq__iff]) ).

fof(f_598_2,plain,
    ! [U_1729,U_1728,U_1727] :
      ( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1727),U_1728) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1727),U_1729)
          | U_1728 != U_1729 )
        & ( U_1728 = U_1729
          | hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1727),U_1728) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1727),U_1729) ) )
      | ~ class_Nat_Osemiring__char__0(U_1727) ),
    inference(variable_rename,[status(thm)],[f_598_1]) ).

fof(f_598_3,plain,
    ( ! [U_1727,U_1728,U_1729] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1727),U_1728) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1727),U_1729)
        | U_1728 != U_1729
        | ~ sP149(U_1727,U_1728,U_1729) )
    & ! [U_1727,U_1728,U_1729] :
        ( U_1728 = U_1729
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1727),U_1728) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1727),U_1729)
        | ~ sP149(U_1727,U_1728,U_1729) )
    & ! [U_1727,U_1728,U_1729] :
        ( sP149(U_1727,U_1728,U_1729)
        | ~ class_Nat_Osemiring__char__0(U_1727) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP149])],[f_598_2]) ).

cnf(f_598_4,plain,
    ( sP149(U_1727,U_1728,U_1729)
    | ~ class_Nat_Osemiring__char__0(U_1727) ),
    inference(clausify,[status(thm)],[f_598_3]) ).

cnf(f_598_5,plain,
    ( U_1728 = U_1729
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1727),U_1728) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1727),U_1729)
    | ~ sP149(U_1727,U_1728,U_1729) ),
    inference(clausify,[status(thm)],[f_598_3]) ).

cnf(f_598_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1727),U_1728) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1727),U_1729)
    | U_1728 != U_1729
    | ~ sP149(U_1727,U_1728,U_1729) ),
    inference(clausify,[status(thm)],[f_598_3]) ).

fof(f_599_1,plain,
    ! [V_n,V_m,T_a] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__mult]) ).

fof(f_599_2,plain,
    ! [U_1732,U_1731,U_1730] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1731),U_1732)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1730),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1730),U_1731)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1730),U_1732))
      | ~ class_Rings_Osemiring__1(U_1730) ),
    inference(variable_rename,[status(thm)],[f_599_1]) ).

fof(f_599_3,plain,
    ! [U_1731,U_1732,U_1730] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1731),U_1732)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1730),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1730),U_1731)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1730),U_1732))
      | ~ class_Rings_Osemiring__1(U_1730) ),
    inference(definitional_conversion,[status(esa)],[f_599_2]) ).

cnf(f_599_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1731),U_1732)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1730),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1730),U_1731)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1730),U_1732))
    | ~ class_Rings_Osemiring__1(U_1730) ),
    inference(clausify,[status(thm)],[f_599_3]) ).

fof(f_600_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_600_2,plain,
    ! [U_1737,U_1736,U_1735,U_1734,U_1733] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1733),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1733),U_1734),U_1735)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1733),U_1736),U_1737)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1733),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1733),U_1734),U_1736)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1733),U_1735),U_1737))
      | ~ class_Rings_Ocomm__semiring__1(U_1733) ),
    inference(variable_rename,[status(thm)],[f_600_1]) ).

fof(f_600_3,plain,
    ! [U_1733,U_1734,U_1735,U_1736,U_1737] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1733),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1733),U_1734),U_1735)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1733),U_1736),U_1737)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1733),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1733),U_1734),U_1736)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1733),U_1735),U_1737))
      | ~ class_Rings_Ocomm__semiring__1(U_1733) ),
    inference(definitional_conversion,[status(esa)],[f_600_2]) ).

cnf(f_600_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1733),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1733),U_1734),U_1735)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1733),U_1736),U_1737)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1733),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1733),U_1734),U_1736)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1733),U_1735),U_1737))
    | ~ class_Rings_Ocomm__semiring__1(U_1733) ),
    inference(clausify,[status(thm)],[f_600_3]) ).

fof(f_601_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_601_2,plain,
    ! [U_1742,U_1741,U_1740,U_1739,U_1738] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1738),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1738),U_1739),U_1740)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1738),U_1741),U_1742)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1738),U_1741),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1738),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1738),U_1739),U_1740)),U_1742))
      | ~ class_Rings_Ocomm__semiring__1(U_1738) ),
    inference(variable_rename,[status(thm)],[f_601_1]) ).

fof(f_601_3,plain,
    ! [U_1738,U_1739,U_1740,U_1741,U_1742] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1738),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1738),U_1739),U_1740)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1738),U_1741),U_1742)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1738),U_1741),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1738),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1738),U_1739),U_1740)),U_1742))
      | ~ class_Rings_Ocomm__semiring__1(U_1738) ),
    inference(definitional_conversion,[status(esa)],[f_601_2]) ).

cnf(f_601_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1738),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1738),U_1739),U_1740)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1738),U_1741),U_1742)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1738),U_1741),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1738),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1738),U_1739),U_1740)),U_1742))
    | ~ class_Rings_Ocomm__semiring__1(U_1738) ),
    inference(clausify,[status(thm)],[f_601_3]) ).

fof(f_602_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_602_2,plain,
    ! [U_1747,U_1746,U_1745,U_1744,U_1743] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1743),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1743),U_1744),U_1745)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1743),U_1746),U_1747)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1743),U_1744),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1743),U_1745),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1743),U_1746),U_1747)))
      | ~ class_Rings_Ocomm__semiring__1(U_1743) ),
    inference(variable_rename,[status(thm)],[f_602_1]) ).

fof(f_602_3,plain,
    ! [U_1743,U_1744,U_1745,U_1746,U_1747] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1743),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1743),U_1744),U_1745)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1743),U_1746),U_1747)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1743),U_1744),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1743),U_1745),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1743),U_1746),U_1747)))
      | ~ class_Rings_Ocomm__semiring__1(U_1743) ),
    inference(definitional_conversion,[status(esa)],[f_602_2]) ).

cnf(f_602_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1743),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1743),U_1744),U_1745)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1743),U_1746),U_1747)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1743),U_1744),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1743),U_1745),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1743),U_1746),U_1747)))
    | ~ class_Rings_Ocomm__semiring__1(U_1743) ),
    inference(clausify,[status(thm)],[f_602_3]) ).

fof(f_603_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_603_2,plain,
    ! [U_1751,U_1750,U_1749,U_1748] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1748),U_1749),U_1750)),U_1751) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1748),U_1749),U_1751)),U_1750)
      | ~ class_Rings_Ocomm__semiring__1(U_1748) ),
    inference(variable_rename,[status(thm)],[f_603_1]) ).

fof(f_603_3,plain,
    ! [U_1748,U_1749,U_1750,U_1751] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1748),U_1749),U_1750)),U_1751) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1748),U_1749),U_1751)),U_1750)
      | ~ class_Rings_Ocomm__semiring__1(U_1748) ),
    inference(definitional_conversion,[status(esa)],[f_603_2]) ).

cnf(f_603_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1748),U_1749),U_1750)),U_1751) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1748),U_1749),U_1751)),U_1750)
    | ~ class_Rings_Ocomm__semiring__1(U_1748) ),
    inference(clausify,[status(thm)],[f_603_3]) ).

fof(f_604_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_604_2,plain,
    ! [U_1755,U_1754,U_1753,U_1752] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1752),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1752),U_1753),U_1754)),U_1755) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1752),U_1753),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1752),U_1754),U_1755))
      | ~ class_Rings_Ocomm__semiring__1(U_1752) ),
    inference(variable_rename,[status(thm)],[f_604_1]) ).

fof(f_604_3,plain,
    ! [U_1752,U_1753,U_1754,U_1755] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1752),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1752),U_1753),U_1754)),U_1755) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1752),U_1753),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1752),U_1754),U_1755))
      | ~ class_Rings_Ocomm__semiring__1(U_1752) ),
    inference(definitional_conversion,[status(esa)],[f_604_2]) ).

cnf(f_604_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1752),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1752),U_1753),U_1754)),U_1755) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1752),U_1753),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1752),U_1754),U_1755))
    | ~ class_Rings_Ocomm__semiring__1(U_1752) ),
    inference(clausify,[status(thm)],[f_604_3]) ).

fof(f_605_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_605_2,plain,
    ! [U_1759,U_1758,U_1757,U_1756] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1756),U_1757),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1756),U_1758),U_1759)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1756),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1756),U_1757),U_1758)),U_1759)
      | ~ class_Rings_Ocomm__semiring__1(U_1756) ),
    inference(variable_rename,[status(thm)],[f_605_1]) ).

fof(f_605_3,plain,
    ! [U_1756,U_1757,U_1758,U_1759] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1756),U_1757),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1756),U_1758),U_1759)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1756),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1756),U_1757),U_1758)),U_1759)
      | ~ class_Rings_Ocomm__semiring__1(U_1756) ),
    inference(definitional_conversion,[status(esa)],[f_605_2]) ).

cnf(f_605_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1756),U_1757),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1756),U_1758),U_1759)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1756),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1756),U_1757),U_1758)),U_1759)
    | ~ class_Rings_Ocomm__semiring__1(U_1756) ),
    inference(clausify,[status(thm)],[f_605_3]) ).

fof(f_606_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_606_2,plain,
    ! [U_1763,U_1762,U_1761,U_1760] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1760),U_1761),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1760),U_1762),U_1763)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1760),U_1762),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1760),U_1761),U_1763))
      | ~ class_Rings_Ocomm__semiring__1(U_1760) ),
    inference(variable_rename,[status(thm)],[f_606_1]) ).

fof(f_606_3,plain,
    ! [U_1760,U_1761,U_1762,U_1763] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1760),U_1761),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1760),U_1762),U_1763)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1760),U_1762),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1760),U_1761),U_1763))
      | ~ class_Rings_Ocomm__semiring__1(U_1760) ),
    inference(definitional_conversion,[status(esa)],[f_606_2]) ).

cnf(f_606_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1760),U_1761),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1760),U_1762),U_1763)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1760),U_1762),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1760),U_1761),U_1763))
    | ~ class_Rings_Ocomm__semiring__1(U_1760) ),
    inference(clausify,[status(thm)],[f_606_3]) ).

fof(f_607_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_607_2,plain,
    ! [U_1766,U_1765,U_1764] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1764),U_1765),U_1766) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1764),U_1766),U_1765)
      | ~ class_Rings_Ocomm__semiring__1(U_1764) ),
    inference(variable_rename,[status(thm)],[f_607_1]) ).

fof(f_607_3,plain,
    ! [U_1764,U_1765,U_1766] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1764),U_1765),U_1766) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1764),U_1766),U_1765)
      | ~ class_Rings_Ocomm__semiring__1(U_1764) ),
    inference(definitional_conversion,[status(esa)],[f_607_2]) ).

cnf(f_607_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1764),U_1765),U_1766) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1764),U_1766),U_1765)
    | ~ class_Rings_Ocomm__semiring__1(U_1764) ),
    inference(clausify,[status(thm)],[f_607_3]) ).

fof(f_608_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_608_2,plain,
    ! [U_1769,U_1768,U_1767] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1767),U_1768)),U_1769) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1767),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1768),U_1769)),
    inference(variable_rename,[status(thm)],[f_608_1]) ).

fof(f_608_3,plain,
    ! [U_1767,U_1768,U_1769] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1767),U_1768)),U_1769) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1767),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1768),U_1769)),
    inference(definitional_conversion,[status(esa)],[f_608_2]) ).

cnf(f_608_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1767),U_1768)),U_1769) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1767),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1768),U_1769)),
    inference(clausify,[status(thm)],[f_608_3]) ).

fof(f_609_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_609_2,plain,
    ! [U_1771,U_1770] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1770),U_1771) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1771),U_1770),
    inference(variable_rename,[status(thm)],[f_609_1]) ).

fof(f_609_3,plain,
    ! [U_1770,U_1771] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1770),U_1771) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1771),U_1770),
    inference(definitional_conversion,[status(esa)],[f_609_2]) ).

cnf(f_609_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1770),U_1771) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1771),U_1770),
    inference(clausify,[status(thm)],[f_609_3]) ).

fof(f_610_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_610_2,plain,
    ! [U_1774,U_1773,U_1772] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1772,U_1773)),U_1774) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1772),U_1774),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1773),U_1774)),
    inference(variable_rename,[status(thm)],[f_610_1]) ).

fof(f_610_3,plain,
    ! [U_1772,U_1773,U_1774] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1772,U_1773)),U_1774) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1772),U_1774),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1773),U_1774)),
    inference(definitional_conversion,[status(esa)],[f_610_2]) ).

cnf(f_610_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1772,U_1773)),U_1774) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1772),U_1774),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1773),U_1774)),
    inference(clausify,[status(thm)],[f_610_3]) ).

fof(f_611_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_611_2,plain,
    ! [U_1777,U_1776,U_1775] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1775),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1776,U_1777)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1775),U_1776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1775),U_1777)),
    inference(variable_rename,[status(thm)],[f_611_1]) ).

fof(f_611_3,plain,
    ! [U_1775,U_1776,U_1777] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1775),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1776,U_1777)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1775),U_1776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1775),U_1777)),
    inference(definitional_conversion,[status(esa)],[f_611_2]) ).

cnf(f_611_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1775),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1776,U_1777)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1775),U_1776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1775),U_1777)),
    inference(clausify,[status(thm)],[f_611_3]) ).

fof(f_612_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_612_2,plain,
    ! [U_1780,U_1779,U_1778] :
      ( c_RealVector_Onorm__class_Onorm(U_1778,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1778),U_1779),U_1780)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1778,U_1779)),c_RealVector_Onorm__class_Onorm(U_1778,U_1780))
      | ~ class_RealVector_Oreal__normed__div__algebra(U_1778) ),
    inference(variable_rename,[status(thm)],[f_612_1]) ).

fof(f_612_3,plain,
    ! [U_1778,U_1779,U_1780] :
      ( c_RealVector_Onorm__class_Onorm(U_1778,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1778),U_1779),U_1780)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1778,U_1779)),c_RealVector_Onorm__class_Onorm(U_1778,U_1780))
      | ~ class_RealVector_Oreal__normed__div__algebra(U_1778) ),
    inference(definitional_conversion,[status(esa)],[f_612_2]) ).

cnf(f_612_4,plain,
    ( c_RealVector_Onorm__class_Onorm(U_1778,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1778),U_1779),U_1780)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1778,U_1779)),c_RealVector_Onorm__class_Onorm(U_1778,U_1780))
    | ~ class_RealVector_Oreal__normed__div__algebra(U_1778) ),
    inference(clausify,[status(thm)],[f_612_3]) ).

fof(f_613_1,plain,
    ! [V_n,T_a] :
      ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),V_n)
      | ~ class_RealVector_Oreal__normed__algebra__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_norm__of__nat]) ).

fof(f_613_2,plain,
    ! [U_1782,U_1781] :
      ( c_RealVector_Onorm__class_Onorm(U_1781,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1781),U_1782)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),U_1782)
      | ~ class_RealVector_Oreal__normed__algebra__1(U_1781) ),
    inference(variable_rename,[status(thm)],[f_613_1]) ).

fof(f_613_3,plain,
    ! [U_1781,U_1782] :
      ( c_RealVector_Onorm__class_Onorm(U_1781,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1781),U_1782)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),U_1782)
      | ~ class_RealVector_Oreal__normed__algebra__1(U_1781) ),
    inference(definitional_conversion,[status(esa)],[f_613_2]) ).

cnf(f_613_4,plain,
    ( c_RealVector_Onorm__class_Onorm(U_1781,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1781),U_1782)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),U_1782)
    | ~ class_RealVector_Oreal__normed__algebra__1(U_1781) ),
    inference(clausify,[status(thm)],[f_613_3]) ).

fof(f_614_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_614_2,plain,
    ! [U_1785,U_1784,U_1783] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1783,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1783),U_1784),U_1785)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1783,U_1784)),c_RealVector_Onorm__class_Onorm(U_1783,U_1785)))
      | ~ class_RealVector_Oreal__normed__algebra(U_1783) ),
    inference(variable_rename,[status(thm)],[f_614_1]) ).

fof(f_614_3,plain,
    ! [U_1783,U_1784,U_1785] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1783,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1783),U_1784),U_1785)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1783,U_1784)),c_RealVector_Onorm__class_Onorm(U_1783,U_1785)))
      | ~ class_RealVector_Oreal__normed__algebra(U_1783) ),
    inference(definitional_conversion,[status(esa)],[f_614_2]) ).

cnf(f_614_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1783,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1783),U_1784),U_1785)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1783,U_1784)),c_RealVector_Onorm__class_Onorm(U_1783,U_1785)))
    | ~ class_RealVector_Oreal__normed__algebra(U_1783) ),
    inference(clausify,[status(thm)],[f_614_3]) ).

fof(f_615_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_615_2,plain,
    ! [U_1789,U_1788,U_1787,U_1786] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1786),c_Groups_Ominus__class_Ominus(U_1786,U_1787,U_1788)),U_1789) = c_Groups_Ominus__class_Ominus(U_1786,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1786),U_1787),U_1789),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1786),U_1788),U_1789))
      | ~ class_RealVector_Oreal__normed__algebra(U_1786) ),
    inference(variable_rename,[status(thm)],[f_615_1]) ).

fof(f_615_3,plain,
    ! [U_1786,U_1787,U_1788,U_1789] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1786),c_Groups_Ominus__class_Ominus(U_1786,U_1787,U_1788)),U_1789) = c_Groups_Ominus__class_Ominus(U_1786,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1786),U_1787),U_1789),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1786),U_1788),U_1789))
      | ~ class_RealVector_Oreal__normed__algebra(U_1786) ),
    inference(definitional_conversion,[status(esa)],[f_615_2]) ).

cnf(f_615_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1786),c_Groups_Ominus__class_Ominus(U_1786,U_1787,U_1788)),U_1789) = c_Groups_Ominus__class_Ominus(U_1786,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1786),U_1787),U_1789),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1786),U_1788),U_1789))
    | ~ class_RealVector_Oreal__normed__algebra(U_1786) ),
    inference(clausify,[status(thm)],[f_615_3]) ).

fof(f_616_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_616_2,plain,
    ! [U_1793,U_1792,U_1791,U_1790] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1790),c_Groups_Ominus__class_Ominus(U_1790,U_1791,U_1792)),U_1793) = c_Groups_Ominus__class_Ominus(U_1790,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1790),U_1791),U_1793),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1790),U_1792),U_1793))
      | ~ class_RealVector_Oreal__normed__algebra(U_1790) ),
    inference(variable_rename,[status(thm)],[f_616_1]) ).

fof(f_616_3,plain,
    ! [U_1790,U_1791,U_1792,U_1793] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1790),c_Groups_Ominus__class_Ominus(U_1790,U_1791,U_1792)),U_1793) = c_Groups_Ominus__class_Ominus(U_1790,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1790),U_1791),U_1793),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1790),U_1792),U_1793))
      | ~ class_RealVector_Oreal__normed__algebra(U_1790) ),
    inference(definitional_conversion,[status(esa)],[f_616_2]) ).

cnf(f_616_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1790),c_Groups_Ominus__class_Ominus(U_1790,U_1791,U_1792)),U_1793) = c_Groups_Ominus__class_Ominus(U_1790,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1790),U_1791),U_1793),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1790),U_1792),U_1793))
    | ~ class_RealVector_Oreal__normed__algebra(U_1790) ),
    inference(clausify,[status(thm)],[f_616_3]) ).

fof(f_617_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_617_2,plain,
    ! [U_1797,U_1796,U_1795,U_1794] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1794),U_1795),c_Groups_Ominus__class_Ominus(U_1794,U_1796,U_1797)) = c_Groups_Ominus__class_Ominus(U_1794,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1794),U_1795),U_1796),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1794),U_1795),U_1797))
      | ~ class_RealVector_Oreal__normed__algebra(U_1794) ),
    inference(variable_rename,[status(thm)],[f_617_1]) ).

fof(f_617_3,plain,
    ! [U_1794,U_1795,U_1796,U_1797] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1794),U_1795),c_Groups_Ominus__class_Ominus(U_1794,U_1796,U_1797)) = c_Groups_Ominus__class_Ominus(U_1794,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1794),U_1795),U_1796),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1794),U_1795),U_1797))
      | ~ class_RealVector_Oreal__normed__algebra(U_1794) ),
    inference(definitional_conversion,[status(esa)],[f_617_2]) ).

cnf(f_617_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1794),U_1795),c_Groups_Ominus__class_Ominus(U_1794,U_1796,U_1797)) = c_Groups_Ominus__class_Ominus(U_1794,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1794),U_1795),U_1796),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1794),U_1795),U_1797))
    | ~ class_RealVector_Oreal__normed__algebra(U_1794) ),
    inference(clausify,[status(thm)],[f_617_3]) ).

fof(f_618_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_618_2,plain,
    ! [U_1801,U_1800,U_1799,U_1798] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1798),U_1799),c_Groups_Ominus__class_Ominus(U_1798,U_1800,U_1801)) = c_Groups_Ominus__class_Ominus(U_1798,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1798),U_1799),U_1800),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1798),U_1799),U_1801))
      | ~ class_RealVector_Oreal__normed__algebra(U_1798) ),
    inference(variable_rename,[status(thm)],[f_618_1]) ).

fof(f_618_3,plain,
    ! [U_1798,U_1799,U_1800,U_1801] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1798),U_1799),c_Groups_Ominus__class_Ominus(U_1798,U_1800,U_1801)) = c_Groups_Ominus__class_Ominus(U_1798,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1798),U_1799),U_1800),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1798),U_1799),U_1801))
      | ~ class_RealVector_Oreal__normed__algebra(U_1798) ),
    inference(definitional_conversion,[status(esa)],[f_618_2]) ).

cnf(f_618_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1798),U_1799),c_Groups_Ominus__class_Ominus(U_1798,U_1800,U_1801)) = c_Groups_Ominus__class_Ominus(U_1798,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1798),U_1799),U_1800),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1798),U_1799),U_1801))
    | ~ class_RealVector_Oreal__normed__algebra(U_1798) ),
    inference(clausify,[status(thm)],[f_618_3]) ).

fof(f_619_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_619_2,plain,
    ! [U_1806,U_1805,U_1804,U_1803,U_1802] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1802,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1802),U_1803),U_1805)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1804),U_1806))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1802,U_1805),U_1806)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1802,U_1803),U_1804)
      | ~ class_RealVector_Oreal__normed__algebra(U_1802) ),
    inference(variable_rename,[status(thm)],[f_619_1]) ).

fof(f_619_3,plain,
    ! [U_1802,U_1803,U_1804,U_1805,U_1806] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1802,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1802),U_1803),U_1805)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1804),U_1806))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1802,U_1805),U_1806)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1802,U_1803),U_1804)
      | ~ class_RealVector_Oreal__normed__algebra(U_1802) ),
    inference(definitional_conversion,[status(esa)],[f_619_2]) ).

cnf(f_619_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1802,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1802),U_1803),U_1805)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1804),U_1806))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1802,U_1805),U_1806)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1802,U_1803),U_1804)
    | ~ class_RealVector_Oreal__normed__algebra(U_1802) ),
    inference(clausify,[status(thm)],[f_619_3]) ).

fof(f_620_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_620_2,plain,
    ! [U_1807] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1807),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_1807,
    inference(variable_rename,[status(thm)],[f_620_1]) ).

fof(f_620_3,plain,
    ! [U_1807] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1807),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_1807,
    inference(definitional_conversion,[status(esa)],[f_620_2]) ).

cnf(f_620_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1807),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_1807,
    inference(clausify,[status(thm)],[f_620_3]) ).

fof(f_621_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_621_2,plain,
    ! [U_1808] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1808) = U_1808,
    inference(variable_rename,[status(thm)],[f_621_1]) ).

fof(f_621_3,plain,
    ! [U_1808] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1808) = U_1808,
    inference(definitional_conversion,[status(esa)],[f_621_2]) ).

cnf(f_621_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1808) = U_1808,
    inference(clausify,[status(thm)],[f_621_3]) ).

fof(f_622_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_622_2,plain,
    ! [U_1810,U_1809] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1809),c_Groups_Oone__class_Oone(U_1809)),U_1810) = U_1810
      | ~ class_Groups_Omonoid__mult(U_1809) ),
    inference(variable_rename,[status(thm)],[f_622_1]) ).

fof(f_622_3,plain,
    ! [U_1809,U_1810] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1809),c_Groups_Oone__class_Oone(U_1809)),U_1810) = U_1810
      | ~ class_Groups_Omonoid__mult(U_1809) ),
    inference(definitional_conversion,[status(esa)],[f_622_2]) ).

cnf(f_622_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1809),c_Groups_Oone__class_Oone(U_1809)),U_1810) = U_1810
    | ~ class_Groups_Omonoid__mult(U_1809) ),
    inference(clausify,[status(thm)],[f_622_3]) ).

fof(f_623_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_623_2,plain,
    ! [U_1812,U_1811] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1811),c_Groups_Oone__class_Oone(U_1811)),U_1812) = U_1812
      | ~ class_Groups_Ocomm__monoid__mult(U_1811) ),
    inference(variable_rename,[status(thm)],[f_623_1]) ).

fof(f_623_3,plain,
    ! [U_1811,U_1812] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1811),c_Groups_Oone__class_Oone(U_1811)),U_1812) = U_1812
      | ~ class_Groups_Ocomm__monoid__mult(U_1811) ),
    inference(definitional_conversion,[status(esa)],[f_623_2]) ).

cnf(f_623_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1811),c_Groups_Oone__class_Oone(U_1811)),U_1812) = U_1812
    | ~ class_Groups_Ocomm__monoid__mult(U_1811) ),
    inference(clausify,[status(thm)],[f_623_3]) ).

fof(f_624_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_624_2,plain,
    ! [U_1814,U_1813] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1813),U_1814),c_Groups_Oone__class_Oone(U_1813)) = U_1814
      | ~ class_Groups_Omonoid__mult(U_1813) ),
    inference(variable_rename,[status(thm)],[f_624_1]) ).

fof(f_624_3,plain,
    ! [U_1813,U_1814] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1813),U_1814),c_Groups_Oone__class_Oone(U_1813)) = U_1814
      | ~ class_Groups_Omonoid__mult(U_1813) ),
    inference(definitional_conversion,[status(esa)],[f_624_2]) ).

cnf(f_624_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1813),U_1814),c_Groups_Oone__class_Oone(U_1813)) = U_1814
    | ~ class_Groups_Omonoid__mult(U_1813) ),
    inference(clausify,[status(thm)],[f_624_3]) ).

fof(f_625_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_625_2,plain,
    ! [U_1816,U_1815] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1815),U_1816),c_Groups_Oone__class_Oone(U_1815)) = U_1816
      | ~ class_Groups_Ocomm__monoid__mult(U_1815) ),
    inference(variable_rename,[status(thm)],[f_625_1]) ).

fof(f_625_3,plain,
    ! [U_1815,U_1816] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1815),U_1816),c_Groups_Oone__class_Oone(U_1815)) = U_1816
      | ~ class_Groups_Ocomm__monoid__mult(U_1815) ),
    inference(definitional_conversion,[status(esa)],[f_625_2]) ).

cnf(f_625_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1815),U_1816),c_Groups_Oone__class_Oone(U_1815)) = U_1816
    | ~ class_Groups_Ocomm__monoid__mult(U_1815) ),
    inference(clausify,[status(thm)],[f_625_3]) ).

fof(f_626_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_626_2,plain,
    ! [U_1818,U_1817] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1817),U_1818),c_Groups_Oone__class_Oone(U_1817)) = U_1818
      | ~ class_Rings_Ocomm__semiring__1(U_1817) ),
    inference(variable_rename,[status(thm)],[f_626_1]) ).

fof(f_626_3,plain,
    ! [U_1817,U_1818] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1817),U_1818),c_Groups_Oone__class_Oone(U_1817)) = U_1818
      | ~ class_Rings_Ocomm__semiring__1(U_1817) ),
    inference(definitional_conversion,[status(esa)],[f_626_2]) ).

cnf(f_626_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1817),U_1818),c_Groups_Oone__class_Oone(U_1817)) = U_1818
    | ~ class_Rings_Ocomm__semiring__1(U_1817) ),
    inference(clausify,[status(thm)],[f_626_3]) ).

fof(f_627_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_627_2,plain,
    ! [U_1820,U_1819] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1819),c_Groups_Oone__class_Oone(U_1819)),U_1820) = U_1820
      | ~ class_Rings_Ocomm__semiring__1(U_1819) ),
    inference(variable_rename,[status(thm)],[f_627_1]) ).

fof(f_627_3,plain,
    ! [U_1819,U_1820] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1819),c_Groups_Oone__class_Oone(U_1819)),U_1820) = U_1820
      | ~ class_Rings_Ocomm__semiring__1(U_1819) ),
    inference(definitional_conversion,[status(esa)],[f_627_2]) ).

cnf(f_627_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1819),c_Groups_Oone__class_Oone(U_1819)),U_1820) = U_1820
    | ~ class_Rings_Ocomm__semiring__1(U_1819) ),
    inference(clausify,[status(thm)],[f_627_3]) ).

fof(f_628_1,plain,
    ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls,
    inference(fof_nnf,[status(thm)],[fact_mult__Pls]) ).

fof(f_628_2,plain,
    ! [U_1821] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),U_1821) = c_Int_OPls,
    inference(variable_rename,[status(thm)],[f_628_1]) ).

fof(f_628_3,plain,
    ! [U_1821] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),U_1821) = c_Int_OPls,
    inference(definitional_conversion,[status(esa)],[f_628_2]) ).

cnf(f_628_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),U_1821) = c_Int_OPls,
    inference(clausify,[status(thm)],[f_628_3]) ).

fof(f_629_1,plain,
    ! [V_n,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__0__le__iff]) ).

fof(f_629_2,plain,
    ! [U_1823,U_1822] :
      ( c_Orderings_Oord__class_Oless__eq(U_1822,c_Groups_Ozero__class_Ozero(U_1822),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1822),U_1823))
      | ~ class_Rings_Olinordered__semidom(U_1822) ),
    inference(variable_rename,[status(thm)],[f_629_1]) ).

fof(f_629_3,plain,
    ! [U_1822,U_1823] :
      ( c_Orderings_Oord__class_Oless__eq(U_1822,c_Groups_Ozero__class_Ozero(U_1822),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1822),U_1823))
      | ~ class_Rings_Olinordered__semidom(U_1822) ),
    inference(definitional_conversion,[status(esa)],[f_629_2]) ).

cnf(f_629_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1822,c_Groups_Ozero__class_Ozero(U_1822),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1822),U_1823))
    | ~ class_Rings_Olinordered__semidom(U_1822) ),
    inference(clausify,[status(thm)],[f_629_3]) ).

fof(f_630_1,plain,
    ! [V_m,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__le__imp__of__nat]) ).

fof(f_630_2,plain,
    ! [U_1825,U_1824] :
      ( c_Orderings_Oord__class_Oless__eq(U_1824,c_Groups_Ozero__class_Ozero(U_1824),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1824),U_1825))
      | ~ class_Rings_Olinordered__semidom(U_1824) ),
    inference(variable_rename,[status(thm)],[f_630_1]) ).

fof(f_630_3,plain,
    ! [U_1824,U_1825] :
      ( c_Orderings_Oord__class_Oless__eq(U_1824,c_Groups_Ozero__class_Ozero(U_1824),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1824),U_1825))
      | ~ class_Rings_Olinordered__semidom(U_1824) ),
    inference(definitional_conversion,[status(esa)],[f_630_2]) ).

cnf(f_630_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1824,c_Groups_Ozero__class_Ozero(U_1824),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1824),U_1825))
    | ~ class_Rings_Olinordered__semidom(U_1824) ),
    inference(clausify,[status(thm)],[f_630_3]) ).

fof(f_631_1,plain,
    ! [V_m,T_a] :
      ( ~ c_Orderings_Oord__class_Oless(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m),c_Groups_Ozero__class_Ozero(T_a))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__less__0__iff]) ).

fof(f_631_2,plain,
    ! [U_1827,U_1826] :
      ( ~ c_Orderings_Oord__class_Oless(U_1826,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1826),U_1827),c_Groups_Ozero__class_Ozero(U_1826))
      | ~ class_Rings_Olinordered__semidom(U_1826) ),
    inference(variable_rename,[status(thm)],[f_631_1]) ).

fof(f_631_3,plain,
    ! [U_1826,U_1827] :
      ( ~ c_Orderings_Oord__class_Oless(U_1826,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1826),U_1827),c_Groups_Ozero__class_Ozero(U_1826))
      | ~ class_Rings_Olinordered__semidom(U_1826) ),
    inference(definitional_conversion,[status(esa)],[f_631_2]) ).

cnf(f_631_4,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_1826,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1826),U_1827),c_Groups_Ozero__class_Ozero(U_1826))
    | ~ class_Rings_Olinordered__semidom(U_1826) ),
    inference(clausify,[status(thm)],[f_631_3]) ).

fof(f_632_1,plain,
    ! [T_a] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__0]) ).

fof(f_632_2,plain,
    ! [U_1828] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1828),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(U_1828)
      | ~ class_Rings_Osemiring__1(U_1828) ),
    inference(variable_rename,[status(thm)],[f_632_1]) ).

fof(f_632_3,plain,
    ! [U_1828] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1828),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(U_1828)
      | ~ class_Rings_Osemiring__1(U_1828) ),
    inference(definitional_conversion,[status(esa)],[f_632_2]) ).

cnf(f_632_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1828),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(U_1828)
    | ~ class_Rings_Osemiring__1(U_1828) ),
    inference(clausify,[status(thm)],[f_632_3]) ).

fof(f_633_1,plain,
    ! [V_n,V_m,T_a] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
      | ~ c_Orderings_Oord__class_Oless(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__less__imp__less]) ).

fof(f_633_2,plain,
    ! [U_1831,U_1830,U_1829] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1830,U_1831)
      | ~ c_Orderings_Oord__class_Oless(U_1829,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1829),U_1830),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1829),U_1831))
      | ~ class_Rings_Olinordered__semidom(U_1829) ),
    inference(variable_rename,[status(thm)],[f_633_1]) ).

fof(f_633_3,plain,
    ! [U_1829,U_1830,U_1831] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1830,U_1831)
      | ~ c_Orderings_Oord__class_Oless(U_1829,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1829),U_1830),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1829),U_1831))
      | ~ class_Rings_Olinordered__semidom(U_1829) ),
    inference(definitional_conversion,[status(esa)],[f_633_2]) ).

cnf(f_633_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1830,U_1831)
    | ~ c_Orderings_Oord__class_Oless(U_1829,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1829),U_1830),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1829),U_1831))
    | ~ class_Rings_Olinordered__semidom(U_1829) ),
    inference(clausify,[status(thm)],[f_633_3]) ).

fof(f_634_1,plain,
    ! [V_n,V_m,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__imp__of__nat__less]) ).

fof(f_634_2,plain,
    ! [U_1834,U_1833,U_1832] :
      ( c_Orderings_Oord__class_Oless(U_1832,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1832),U_1833),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1832),U_1834))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1833,U_1834)
      | ~ class_Rings_Olinordered__semidom(U_1832) ),
    inference(variable_rename,[status(thm)],[f_634_1]) ).

fof(f_634_3,plain,
    ! [U_1832,U_1833,U_1834] :
      ( c_Orderings_Oord__class_Oless(U_1832,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1832),U_1833),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1832),U_1834))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1833,U_1834)
      | ~ class_Rings_Olinordered__semidom(U_1832) ),
    inference(definitional_conversion,[status(esa)],[f_634_2]) ).

cnf(f_634_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1832,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1832),U_1833),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1832),U_1834))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1833,U_1834)
    | ~ class_Rings_Olinordered__semidom(U_1832) ),
    inference(clausify,[status(thm)],[f_634_3]) ).

fof(f_635_1,plain,
    ! [V_n_2,V_m_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),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(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)) ) )
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__less__iff]) ).

fof(f_635_2,plain,
    ! [U_1837,U_1836,U_1835] :
      ( ( ( c_Orderings_Oord__class_Oless(U_1835,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1835),U_1836),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1835),U_1837))
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1836,U_1837) )
        & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1836,U_1837)
          | ~ c_Orderings_Oord__class_Oless(U_1835,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1835),U_1836),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1835),U_1837)) ) )
      | ~ class_Rings_Olinordered__semidom(U_1835) ),
    inference(variable_rename,[status(thm)],[f_635_1]) ).

fof(f_635_3,plain,
    ( ! [U_1835,U_1836,U_1837] :
        ( c_Orderings_Oord__class_Oless(U_1835,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1835),U_1836),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1835),U_1837))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1836,U_1837)
        | ~ sP150(U_1835,U_1836,U_1837) )
    & ! [U_1835,U_1836,U_1837] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1836,U_1837)
        | ~ c_Orderings_Oord__class_Oless(U_1835,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1835),U_1836),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1835),U_1837))
        | ~ sP150(U_1835,U_1836,U_1837) )
    & ! [U_1835,U_1836,U_1837] :
        ( sP150(U_1835,U_1836,U_1837)
        | ~ class_Rings_Olinordered__semidom(U_1835) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP150])],[f_635_2]) ).

cnf(f_635_4,plain,
    ( sP150(U_1835,U_1836,U_1837)
    | ~ class_Rings_Olinordered__semidom(U_1835) ),
    inference(clausify,[status(thm)],[f_635_3]) ).

cnf(f_635_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1836,U_1837)
    | ~ c_Orderings_Oord__class_Oless(U_1835,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1835),U_1836),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1835),U_1837))
    | ~ sP150(U_1835,U_1836,U_1837) ),
    inference(clausify,[status(thm)],[f_635_3]) ).

cnf(f_635_6,plain,
    ( c_Orderings_Oord__class_Oless(U_1835,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1835),U_1836),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1835),U_1837))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1836,U_1837)
    | ~ sP150(U_1835,U_1836,U_1837) ),
    inference(clausify,[status(thm)],[f_635_3]) ).

fof(f_636_1,plain,
    ! [V_n_2,V_m_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),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(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)) ) )
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__le__iff]) ).

fof(f_636_2,plain,
    ! [U_1840,U_1839,U_1838] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_1838,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1838),U_1839),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1838),U_1840))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1839,U_1840) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1839,U_1840)
          | ~ c_Orderings_Oord__class_Oless__eq(U_1838,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1838),U_1839),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1838),U_1840)) ) )
      | ~ class_Rings_Olinordered__semidom(U_1838) ),
    inference(variable_rename,[status(thm)],[f_636_1]) ).

fof(f_636_3,plain,
    ( ! [U_1839,U_1840,U_1838] :
        ( c_Orderings_Oord__class_Oless__eq(U_1838,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1838),U_1839),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1838),U_1840))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1839,U_1840)
        | ~ sP151(U_1839,U_1840,U_1838) )
    & ! [U_1839,U_1840,U_1838] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1839,U_1840)
        | ~ c_Orderings_Oord__class_Oless__eq(U_1838,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1838),U_1839),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1838),U_1840))
        | ~ sP151(U_1839,U_1840,U_1838) )
    & ! [U_1839,U_1840,U_1838] :
        ( sP151(U_1839,U_1840,U_1838)
        | ~ class_Rings_Olinordered__semidom(U_1838) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP151])],[f_636_2]) ).

cnf(f_636_4,plain,
    ( sP151(U_1839,U_1840,U_1838)
    | ~ class_Rings_Olinordered__semidom(U_1838) ),
    inference(clausify,[status(thm)],[f_636_3]) ).

cnf(f_636_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1839,U_1840)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1838,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1838),U_1839),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1838),U_1840))
    | ~ sP151(U_1839,U_1840,U_1838) ),
    inference(clausify,[status(thm)],[f_636_3]) ).

cnf(f_636_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1838,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1838),U_1839),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1838),U_1840))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1839,U_1840)
    | ~ sP151(U_1839,U_1840,U_1838) ),
    inference(clausify,[status(thm)],[f_636_3]) ).

fof(f_637_1,plain,
    ! [V_n,V_m,T_a] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__add]) ).

fof(f_637_2,plain,
    ! [U_1843,U_1842,U_1841] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1841),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1842,U_1843)) = c_Groups_Oplus__class_Oplus(U_1841,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1841),U_1842),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1841),U_1843))
      | ~ class_Rings_Osemiring__1(U_1841) ),
    inference(variable_rename,[status(thm)],[f_637_1]) ).

fof(f_637_3,plain,
    ! [U_1843,U_1842,U_1841] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1841),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1842,U_1843)) = c_Groups_Oplus__class_Oplus(U_1841,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1841),U_1842),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1841),U_1843))
      | ~ class_Rings_Osemiring__1(U_1841) ),
    inference(definitional_conversion,[status(esa)],[f_637_2]) ).

cnf(f_637_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1841),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1842,U_1843)) = c_Groups_Oplus__class_Oplus(U_1841,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1841),U_1842),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1841),U_1843))
    | ~ class_Rings_Osemiring__1(U_1841) ),
    inference(clausify,[status(thm)],[f_637_3]) ).

fof(f_638_1,plain,
    ! [T_a] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a)
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__1]) ).

fof(f_638_2,plain,
    ! [U_1844] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1844),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_1844)
      | ~ class_Rings_Osemiring__1(U_1844) ),
    inference(variable_rename,[status(thm)],[f_638_1]) ).

fof(f_638_3,plain,
    ! [U_1844] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1844),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_1844)
      | ~ class_Rings_Osemiring__1(U_1844) ),
    inference(definitional_conversion,[status(esa)],[f_638_2]) ).

cnf(f_638_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1844),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_1844)
    | ~ class_Rings_Osemiring__1(U_1844) ),
    inference(clausify,[status(thm)],[f_638_3]) ).

fof(f_639_1,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__numerals_I1_J]) ).

fof(f_639_2,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_639_1]) ).

cnf(f_639_3,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_639_2]) ).

fof(f_640_1,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_int__0]) ).

fof(f_640_2,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_640_1]) ).

cnf(f_640_3,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_640_2]) ).

fof(f_641_1,plain,
    ! [V_n_2] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(fof_nnf,[status(thm)],[fact_int__eq__0__conv]) ).

fof(f_641_2,plain,
    ! [U_1845] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1845) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_1845 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_1845 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1845) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_641_1]) ).

fof(f_641_3,plain,
    ( ! [U_1847] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1847) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_1847 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_1846] :
        ( U_1846 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1846) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_641_2]) ).

fof(f_641_4,plain,
    ( ! [U_1847] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1847) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_1847 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_1846] :
        ( U_1846 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1846) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa)],[f_641_3]) ).

cnf(f_641_5,plain,
    ( U_1846 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1846) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_641_4]) ).

cnf(f_641_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1847) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_1847 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_641_4]) ).

fof(f_642_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_642_2,plain,
    ! [U_1849,U_1848] :
      ( c_Orderings_Oord__class_Oless__eq(U_1848,c_Groups_Ozero__class_Ozero(U_1848),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1848),U_1849),U_1849))
      | ~ class_Rings_Olinordered__ring(U_1848) ),
    inference(variable_rename,[status(thm)],[f_642_1]) ).

fof(f_642_3,plain,
    ! [U_1848,U_1849] :
      ( c_Orderings_Oord__class_Oless__eq(U_1848,c_Groups_Ozero__class_Ozero(U_1848),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1848),U_1849),U_1849))
      | ~ class_Rings_Olinordered__ring(U_1848) ),
    inference(definitional_conversion,[status(esa)],[f_642_2]) ).

cnf(f_642_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1848,c_Groups_Ozero__class_Ozero(U_1848),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1848),U_1849),U_1849))
    | ~ class_Rings_Olinordered__ring(U_1848) ),
    inference(clausify,[status(thm)],[f_642_3]) ).

fof(f_643_1,plain,
    ! [V_b_2,V_a_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_a_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_a_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_a_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_a_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_a_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_a_2),V_b_2)) ) )
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__le__mult__iff]) ).

fof(f_643_2,plain,
    ! [U_1852,U_1851,U_1850] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_1850,c_Groups_Ozero__class_Ozero(U_1850),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1850),U_1851),U_1852))
          | ( ( ~ c_Orderings_Oord__class_Oless__eq(U_1850,U_1852,c_Groups_Ozero__class_Ozero(U_1850))
              | ~ c_Orderings_Oord__class_Oless__eq(U_1850,U_1851,c_Groups_Ozero__class_Ozero(U_1850)) )
            & ( ~ c_Orderings_Oord__class_Oless__eq(U_1850,c_Groups_Ozero__class_Ozero(U_1850),U_1852)
              | ~ c_Orderings_Oord__class_Oless__eq(U_1850,c_Groups_Ozero__class_Ozero(U_1850),U_1851) ) ) )
        & ( ( c_Orderings_Oord__class_Oless__eq(U_1850,U_1852,c_Groups_Ozero__class_Ozero(U_1850))
            & c_Orderings_Oord__class_Oless__eq(U_1850,U_1851,c_Groups_Ozero__class_Ozero(U_1850)) )
          | ( c_Orderings_Oord__class_Oless__eq(U_1850,c_Groups_Ozero__class_Ozero(U_1850),U_1852)
            & c_Orderings_Oord__class_Oless__eq(U_1850,c_Groups_Ozero__class_Ozero(U_1850),U_1851) )
          | ~ c_Orderings_Oord__class_Oless__eq(U_1850,c_Groups_Ozero__class_Ozero(U_1850),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1850),U_1851),U_1852)) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_1850) ),
    inference(variable_rename,[status(thm)],[f_643_1]) ).

fof(f_643_3,plain,
    ( ! [U_1851,U_1852,U_1850] :
        ( ~ c_Orderings_Oord__class_Oless__eq(U_1850,U_1852,c_Groups_Ozero__class_Ozero(U_1850))
        | ~ c_Orderings_Oord__class_Oless__eq(U_1850,U_1851,c_Groups_Ozero__class_Ozero(U_1850))
        | ~ sP154(U_1851,U_1852,U_1850) )
    & ! [U_1851,U_1852,U_1850] :
        ( ~ c_Orderings_Oord__class_Oless__eq(U_1850,c_Groups_Ozero__class_Ozero(U_1850),U_1852)
        | ~ c_Orderings_Oord__class_Oless__eq(U_1850,c_Groups_Ozero__class_Ozero(U_1850),U_1851)
        | ~ sP154(U_1851,U_1852,U_1850) )
    & ! [U_1851,U_1852,U_1850] :
        ( c_Orderings_Oord__class_Oless__eq(U_1850,U_1852,c_Groups_Ozero__class_Ozero(U_1850))
        | ~ sP153(U_1851,U_1852,U_1850) )
    & ! [U_1851,U_1852,U_1850] :
        ( c_Orderings_Oord__class_Oless__eq(U_1850,U_1851,c_Groups_Ozero__class_Ozero(U_1850))
        | ~ sP153(U_1851,U_1852,U_1850) )
    & ! [U_1851,U_1852,U_1850] :
        ( c_Orderings_Oord__class_Oless__eq(U_1850,c_Groups_Ozero__class_Ozero(U_1850),U_1852)
        | ~ sP152(U_1851,U_1852,U_1850) )
    & ! [U_1851,U_1852,U_1850] :
        ( c_Orderings_Oord__class_Oless__eq(U_1850,c_Groups_Ozero__class_Ozero(U_1850),U_1851)
        | ~ sP152(U_1851,U_1852,U_1850) )
    & ! [U_1851,U_1852,U_1850] :
        ( c_Orderings_Oord__class_Oless__eq(U_1850,c_Groups_Ozero__class_Ozero(U_1850),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1850),U_1851),U_1852))
        | sP154(U_1851,U_1852,U_1850)
        | ~ sP155(U_1851,U_1852,U_1850) )
    & ! [U_1851,U_1852,U_1850] :
        ( sP153(U_1851,U_1852,U_1850)
        | sP152(U_1851,U_1852,U_1850)
        | ~ c_Orderings_Oord__class_Oless__eq(U_1850,c_Groups_Ozero__class_Ozero(U_1850),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1850),U_1851),U_1852))
        | ~ sP155(U_1851,U_1852,U_1850) )
    & ! [U_1851,U_1852,U_1850] :
        ( sP155(U_1851,U_1852,U_1850)
        | ~ class_Rings_Olinordered__ring__strict(U_1850) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP152,sP153,sP154,sP155])],[f_643_2]) ).

cnf(f_643_4,plain,
    ( sP155(U_1851,U_1852,U_1850)
    | ~ class_Rings_Olinordered__ring__strict(U_1850) ),
    inference(clausify,[status(thm)],[f_643_3]) ).

cnf(f_643_5,plain,
    ( sP153(U_1851,U_1852,U_1850)
    | sP152(U_1851,U_1852,U_1850)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1850,c_Groups_Ozero__class_Ozero(U_1850),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1850),U_1851),U_1852))
    | ~ sP155(U_1851,U_1852,U_1850) ),
    inference(clausify,[status(thm)],[f_643_3]) ).

cnf(f_643_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1850,c_Groups_Ozero__class_Ozero(U_1850),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1850),U_1851),U_1852))
    | sP154(U_1851,U_1852,U_1850)
    | ~ sP155(U_1851,U_1852,U_1850) ),
    inference(clausify,[status(thm)],[f_643_3]) ).

cnf(f_643_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1850,c_Groups_Ozero__class_Ozero(U_1850),U_1851)
    | ~ sP152(U_1851,U_1852,U_1850) ),
    inference(clausify,[status(thm)],[f_643_3]) ).

cnf(f_643_8,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1850,c_Groups_Ozero__class_Ozero(U_1850),U_1852)
    | ~ sP152(U_1851,U_1852,U_1850) ),
    inference(clausify,[status(thm)],[f_643_3]) ).

cnf(f_643_9,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1850,U_1851,c_Groups_Ozero__class_Ozero(U_1850))
    | ~ sP153(U_1851,U_1852,U_1850) ),
    inference(clausify,[status(thm)],[f_643_3]) ).

cnf(f_643_10,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1850,U_1852,c_Groups_Ozero__class_Ozero(U_1850))
    | ~ sP153(U_1851,U_1852,U_1850) ),
    inference(clausify,[status(thm)],[f_643_3]) ).

cnf(f_643_11,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(U_1850,c_Groups_Ozero__class_Ozero(U_1850),U_1852)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1850,c_Groups_Ozero__class_Ozero(U_1850),U_1851)
    | ~ sP154(U_1851,U_1852,U_1850) ),
    inference(clausify,[status(thm)],[f_643_3]) ).

cnf(f_643_12,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(U_1850,U_1852,c_Groups_Ozero__class_Ozero(U_1850))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1850,U_1851,c_Groups_Ozero__class_Ozero(U_1850))
    | ~ sP154(U_1851,U_1852,U_1850) ),
    inference(clausify,[status(thm)],[f_643_3]) ).

fof(f_644_1,plain,
    ! [V_b_2,V_a_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_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_a_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_a_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_a_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_a_2) )
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_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_644_2,plain,
    ! [U_1855,U_1854,U_1853] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_1853,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1853),U_1854),U_1855),c_Groups_Ozero__class_Ozero(U_1853))
          | ( ( ~ c_Orderings_Oord__class_Oless__eq(U_1853,c_Groups_Ozero__class_Ozero(U_1853),U_1855)
              | ~ c_Orderings_Oord__class_Oless__eq(U_1853,U_1854,c_Groups_Ozero__class_Ozero(U_1853)) )
            & ( ~ c_Orderings_Oord__class_Oless__eq(U_1853,U_1855,c_Groups_Ozero__class_Ozero(U_1853))
              | ~ c_Orderings_Oord__class_Oless__eq(U_1853,c_Groups_Ozero__class_Ozero(U_1853),U_1854) ) ) )
        & ( ( c_Orderings_Oord__class_Oless__eq(U_1853,c_Groups_Ozero__class_Ozero(U_1853),U_1855)
            & c_Orderings_Oord__class_Oless__eq(U_1853,U_1854,c_Groups_Ozero__class_Ozero(U_1853)) )
          | ( c_Orderings_Oord__class_Oless__eq(U_1853,U_1855,c_Groups_Ozero__class_Ozero(U_1853))
            & c_Orderings_Oord__class_Oless__eq(U_1853,c_Groups_Ozero__class_Ozero(U_1853),U_1854) )
          | ~ c_Orderings_Oord__class_Oless__eq(U_1853,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1853),U_1854),U_1855),c_Groups_Ozero__class_Ozero(U_1853)) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_1853) ),
    inference(variable_rename,[status(thm)],[f_644_1]) ).

fof(f_644_3,plain,
    ( ! [U_1855,U_1854,U_1853] :
        ( ~ c_Orderings_Oord__class_Oless__eq(U_1853,c_Groups_Ozero__class_Ozero(U_1853),U_1855)
        | ~ c_Orderings_Oord__class_Oless__eq(U_1853,U_1854,c_Groups_Ozero__class_Ozero(U_1853))
        | ~ sP158(U_1855,U_1854,U_1853) )
    & ! [U_1855,U_1854,U_1853] :
        ( ~ c_Orderings_Oord__class_Oless__eq(U_1853,U_1855,c_Groups_Ozero__class_Ozero(U_1853))
        | ~ c_Orderings_Oord__class_Oless__eq(U_1853,c_Groups_Ozero__class_Ozero(U_1853),U_1854)
        | ~ sP158(U_1855,U_1854,U_1853) )
    & ! [U_1855,U_1854,U_1853] :
        ( c_Orderings_Oord__class_Oless__eq(U_1853,c_Groups_Ozero__class_Ozero(U_1853),U_1855)
        | ~ sP157(U_1855,U_1854,U_1853) )
    & ! [U_1855,U_1854,U_1853] :
        ( c_Orderings_Oord__class_Oless__eq(U_1853,U_1854,c_Groups_Ozero__class_Ozero(U_1853))
        | ~ sP157(U_1855,U_1854,U_1853) )
    & ! [U_1855,U_1854,U_1853] :
        ( c_Orderings_Oord__class_Oless__eq(U_1853,U_1855,c_Groups_Ozero__class_Ozero(U_1853))
        | ~ sP156(U_1855,U_1854,U_1853) )
    & ! [U_1855,U_1854,U_1853] :
        ( c_Orderings_Oord__class_Oless__eq(U_1853,c_Groups_Ozero__class_Ozero(U_1853),U_1854)
        | ~ sP156(U_1855,U_1854,U_1853) )
    & ! [U_1855,U_1854,U_1853] :
        ( c_Orderings_Oord__class_Oless__eq(U_1853,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1853),U_1854),U_1855),c_Groups_Ozero__class_Ozero(U_1853))
        | sP158(U_1855,U_1854,U_1853)
        | ~ sP159(U_1855,U_1854,U_1853) )
    & ! [U_1855,U_1854,U_1853] :
        ( sP157(U_1855,U_1854,U_1853)
        | sP156(U_1855,U_1854,U_1853)
        | ~ c_Orderings_Oord__class_Oless__eq(U_1853,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1853),U_1854),U_1855),c_Groups_Ozero__class_Ozero(U_1853))
        | ~ sP159(U_1855,U_1854,U_1853) )
    & ! [U_1855,U_1854,U_1853] :
        ( sP159(U_1855,U_1854,U_1853)
        | ~ class_Rings_Olinordered__ring__strict(U_1853) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP156,sP157,sP158,sP159])],[f_644_2]) ).

cnf(f_644_4,plain,
    ( sP159(U_1855,U_1854,U_1853)
    | ~ class_Rings_Olinordered__ring__strict(U_1853) ),
    inference(clausify,[status(thm)],[f_644_3]) ).

cnf(f_644_5,plain,
    ( sP157(U_1855,U_1854,U_1853)
    | sP156(U_1855,U_1854,U_1853)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1853,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1853),U_1854),U_1855),c_Groups_Ozero__class_Ozero(U_1853))
    | ~ sP159(U_1855,U_1854,U_1853) ),
    inference(clausify,[status(thm)],[f_644_3]) ).

cnf(f_644_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1853,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1853),U_1854),U_1855),c_Groups_Ozero__class_Ozero(U_1853))
    | sP158(U_1855,U_1854,U_1853)
    | ~ sP159(U_1855,U_1854,U_1853) ),
    inference(clausify,[status(thm)],[f_644_3]) ).

cnf(f_644_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1853,c_Groups_Ozero__class_Ozero(U_1853),U_1854)
    | ~ sP156(U_1855,U_1854,U_1853) ),
    inference(clausify,[status(thm)],[f_644_3]) ).

cnf(f_644_8,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1853,U_1855,c_Groups_Ozero__class_Ozero(U_1853))
    | ~ sP156(U_1855,U_1854,U_1853) ),
    inference(clausify,[status(thm)],[f_644_3]) ).

cnf(f_644_9,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1853,U_1854,c_Groups_Ozero__class_Ozero(U_1853))
    | ~ sP157(U_1855,U_1854,U_1853) ),
    inference(clausify,[status(thm)],[f_644_3]) ).

cnf(f_644_10,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1853,c_Groups_Ozero__class_Ozero(U_1853),U_1855)
    | ~ sP157(U_1855,U_1854,U_1853) ),
    inference(clausify,[status(thm)],[f_644_3]) ).

cnf(f_644_11,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(U_1853,U_1855,c_Groups_Ozero__class_Ozero(U_1853))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1853,c_Groups_Ozero__class_Ozero(U_1853),U_1854)
    | ~ sP158(U_1855,U_1854,U_1853) ),
    inference(clausify,[status(thm)],[f_644_3]) ).

cnf(f_644_12,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(U_1853,c_Groups_Ozero__class_Ozero(U_1853),U_1855)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1853,U_1854,c_Groups_Ozero__class_Ozero(U_1853))
    | ~ sP158(U_1855,U_1854,U_1853) ),
    inference(clausify,[status(thm)],[f_644_3]) ).

fof(f_645_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_645_2,plain,
    ! [U_1858,U_1857,U_1856] :
      ( c_Orderings_Oord__class_Oless__eq(U_1856,c_Groups_Ozero__class_Ozero(U_1856),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1856),U_1857),U_1858))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1856,c_Groups_Ozero__class_Ozero(U_1856),U_1858)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1856,c_Groups_Ozero__class_Ozero(U_1856),U_1857)
      | ~ class_Rings_Oordered__cancel__semiring(U_1856) ),
    inference(variable_rename,[status(thm)],[f_645_1]) ).

fof(f_645_3,plain,
    ! [U_1858,U_1856,U_1857] :
      ( c_Orderings_Oord__class_Oless__eq(U_1856,c_Groups_Ozero__class_Ozero(U_1856),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1856),U_1857),U_1858))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1856,c_Groups_Ozero__class_Ozero(U_1856),U_1858)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1856,c_Groups_Ozero__class_Ozero(U_1856),U_1857)
      | ~ class_Rings_Oordered__cancel__semiring(U_1856) ),
    inference(definitional_conversion,[status(esa)],[f_645_2]) ).

cnf(f_645_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1856,c_Groups_Ozero__class_Ozero(U_1856),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1856),U_1857),U_1858))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1856,c_Groups_Ozero__class_Ozero(U_1856),U_1858)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1856,c_Groups_Ozero__class_Ozero(U_1856),U_1857)
    | ~ class_Rings_Oordered__cancel__semiring(U_1856) ),
    inference(clausify,[status(thm)],[f_645_3]) ).

fof(f_646_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_646_2,plain,
    ! [U_1861,U_1860,U_1859] :
      ( c_Orderings_Oord__class_Oless__eq(U_1859,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1859),U_1860),U_1861),c_Groups_Ozero__class_Ozero(U_1859))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1859,U_1861,c_Groups_Ozero__class_Ozero(U_1859))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1859,c_Groups_Ozero__class_Ozero(U_1859),U_1860)
      | ~ class_Rings_Oordered__cancel__semiring(U_1859) ),
    inference(variable_rename,[status(thm)],[f_646_1]) ).

fof(f_646_3,plain,
    ! [U_1859,U_1860,U_1861] :
      ( c_Orderings_Oord__class_Oless__eq(U_1859,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1859),U_1860),U_1861),c_Groups_Ozero__class_Ozero(U_1859))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1859,U_1861,c_Groups_Ozero__class_Ozero(U_1859))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1859,c_Groups_Ozero__class_Ozero(U_1859),U_1860)
      | ~ class_Rings_Oordered__cancel__semiring(U_1859) ),
    inference(definitional_conversion,[status(esa)],[f_646_2]) ).

cnf(f_646_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1859,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1859),U_1860),U_1861),c_Groups_Ozero__class_Ozero(U_1859))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1859,U_1861,c_Groups_Ozero__class_Ozero(U_1859))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1859,c_Groups_Ozero__class_Ozero(U_1859),U_1860)
    | ~ class_Rings_Oordered__cancel__semiring(U_1859) ),
    inference(clausify,[status(thm)],[f_646_3]) ).

fof(f_647_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_647_2,plain,
    ! [U_1864,U_1863,U_1862] :
      ( c_Orderings_Oord__class_Oless__eq(U_1862,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1862),U_1864),U_1863),c_Groups_Ozero__class_Ozero(U_1862))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1862,U_1864,c_Groups_Ozero__class_Ozero(U_1862))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1862,c_Groups_Ozero__class_Ozero(U_1862),U_1863)
      | ~ class_Rings_Oordered__cancel__semiring(U_1862) ),
    inference(variable_rename,[status(thm)],[f_647_1]) ).

fof(f_647_3,plain,
    ! [U_1862,U_1863,U_1864] :
      ( c_Orderings_Oord__class_Oless__eq(U_1862,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1862),U_1864),U_1863),c_Groups_Ozero__class_Ozero(U_1862))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1862,U_1864,c_Groups_Ozero__class_Ozero(U_1862))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1862,c_Groups_Ozero__class_Ozero(U_1862),U_1863)
      | ~ class_Rings_Oordered__cancel__semiring(U_1862) ),
    inference(definitional_conversion,[status(esa)],[f_647_2]) ).

cnf(f_647_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1862,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1862),U_1864),U_1863),c_Groups_Ozero__class_Ozero(U_1862))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1862,U_1864,c_Groups_Ozero__class_Ozero(U_1862))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1862,c_Groups_Ozero__class_Ozero(U_1862),U_1863)
    | ~ class_Rings_Oordered__cancel__semiring(U_1862) ),
    inference(clausify,[status(thm)],[f_647_3]) ).

fof(f_648_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_648_2,plain,
    ! [U_1867,U_1866,U_1865] :
      ( c_Orderings_Oord__class_Oless__eq(U_1865,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1865),U_1866),U_1867),c_Groups_Ozero__class_Ozero(U_1865))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1865,c_Groups_Ozero__class_Ozero(U_1865),U_1867)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1865,U_1866,c_Groups_Ozero__class_Ozero(U_1865))
      | ~ class_Rings_Oordered__cancel__semiring(U_1865) ),
    inference(variable_rename,[status(thm)],[f_648_1]) ).

fof(f_648_3,plain,
    ! [U_1865,U_1866,U_1867] :
      ( c_Orderings_Oord__class_Oless__eq(U_1865,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1865),U_1866),U_1867),c_Groups_Ozero__class_Ozero(U_1865))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1865,c_Groups_Ozero__class_Ozero(U_1865),U_1867)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1865,U_1866,c_Groups_Ozero__class_Ozero(U_1865))
      | ~ class_Rings_Oordered__cancel__semiring(U_1865) ),
    inference(definitional_conversion,[status(esa)],[f_648_2]) ).

cnf(f_648_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1865,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1865),U_1866),U_1867),c_Groups_Ozero__class_Ozero(U_1865))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1865,c_Groups_Ozero__class_Ozero(U_1865),U_1867)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1865,U_1866,c_Groups_Ozero__class_Ozero(U_1865))
    | ~ class_Rings_Oordered__cancel__semiring(U_1865) ),
    inference(clausify,[status(thm)],[f_648_3]) ).

fof(f_649_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_649_2,plain,
    ! [U_1870,U_1869,U_1868] :
      ( c_Orderings_Oord__class_Oless__eq(U_1868,c_Groups_Ozero__class_Ozero(U_1868),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1868),U_1869),U_1870))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1868,U_1870,c_Groups_Ozero__class_Ozero(U_1868))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1868,U_1869,c_Groups_Ozero__class_Ozero(U_1868))
      | ~ class_Rings_Oordered__ring(U_1868) ),
    inference(variable_rename,[status(thm)],[f_649_1]) ).

fof(f_649_3,plain,
    ! [U_1870,U_1869,U_1868] :
      ( c_Orderings_Oord__class_Oless__eq(U_1868,c_Groups_Ozero__class_Ozero(U_1868),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1868),U_1869),U_1870))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1868,U_1870,c_Groups_Ozero__class_Ozero(U_1868))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1868,U_1869,c_Groups_Ozero__class_Ozero(U_1868))
      | ~ class_Rings_Oordered__ring(U_1868) ),
    inference(definitional_conversion,[status(esa)],[f_649_2]) ).

cnf(f_649_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1868,c_Groups_Ozero__class_Ozero(U_1868),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1868),U_1869),U_1870))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1868,U_1870,c_Groups_Ozero__class_Ozero(U_1868))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1868,U_1869,c_Groups_Ozero__class_Ozero(U_1868))
    | ~ class_Rings_Oordered__ring(U_1868) ),
    inference(clausify,[status(thm)],[f_649_3]) ).

fof(f_650_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_650_2,plain,
    ! [U_1874,U_1873,U_1872,U_1871] :
      ( c_Orderings_Oord__class_Oless__eq(U_1871,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1871),U_1872),U_1874),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1871),U_1873),U_1874))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1871,c_Groups_Ozero__class_Ozero(U_1871),U_1874)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1871,U_1872,U_1873)
      | ~ class_Rings_Oordered__semiring(U_1871) ),
    inference(variable_rename,[status(thm)],[f_650_1]) ).

fof(f_650_3,plain,
    ! [U_1871,U_1872,U_1873,U_1874] :
      ( c_Orderings_Oord__class_Oless__eq(U_1871,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1871),U_1872),U_1874),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1871),U_1873),U_1874))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1871,c_Groups_Ozero__class_Ozero(U_1871),U_1874)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1871,U_1872,U_1873)
      | ~ class_Rings_Oordered__semiring(U_1871) ),
    inference(definitional_conversion,[status(esa)],[f_650_2]) ).

cnf(f_650_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1871,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1871),U_1872),U_1874),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1871),U_1873),U_1874))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1871,c_Groups_Ozero__class_Ozero(U_1871),U_1874)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1871,U_1872,U_1873)
    | ~ class_Rings_Oordered__semiring(U_1871) ),
    inference(clausify,[status(thm)],[f_650_3]) ).

fof(f_651_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_651_2,plain,
    ! [U_1878,U_1877,U_1876,U_1875] :
      ( c_Orderings_Oord__class_Oless__eq(U_1875,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1875),U_1878),U_1876),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1875),U_1878),U_1877))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1875,c_Groups_Ozero__class_Ozero(U_1875),U_1878)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1875,U_1876,U_1877)
      | ~ class_Rings_Oordered__semiring(U_1875) ),
    inference(variable_rename,[status(thm)],[f_651_1]) ).

fof(f_651_3,plain,
    ! [U_1875,U_1876,U_1877,U_1878] :
      ( c_Orderings_Oord__class_Oless__eq(U_1875,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1875),U_1878),U_1876),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1875),U_1878),U_1877))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1875,c_Groups_Ozero__class_Ozero(U_1875),U_1878)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1875,U_1876,U_1877)
      | ~ class_Rings_Oordered__semiring(U_1875) ),
    inference(definitional_conversion,[status(esa)],[f_651_2]) ).

cnf(f_651_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1875,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1875),U_1878),U_1876),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1875),U_1878),U_1877))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1875,c_Groups_Ozero__class_Ozero(U_1875),U_1878)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1875,U_1876,U_1877)
    | ~ class_Rings_Oordered__semiring(U_1875) ),
    inference(clausify,[status(thm)],[f_651_3]) ).

fof(f_652_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_652_2,plain,
    ! [U_1882,U_1881,U_1880,U_1879] :
      ( c_Orderings_Oord__class_Oless__eq(U_1879,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1879),U_1882),U_1880),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1879),U_1882),U_1881))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1879,c_Groups_Ozero__class_Ozero(U_1879),U_1882)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1879,U_1880,U_1881)
      | ~ class_Rings_Oordered__comm__semiring(U_1879) ),
    inference(variable_rename,[status(thm)],[f_652_1]) ).

fof(f_652_3,plain,
    ! [U_1879,U_1880,U_1881,U_1882] :
      ( c_Orderings_Oord__class_Oless__eq(U_1879,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1879),U_1882),U_1880),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1879),U_1882),U_1881))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1879,c_Groups_Ozero__class_Ozero(U_1879),U_1882)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1879,U_1880,U_1881)
      | ~ class_Rings_Oordered__comm__semiring(U_1879) ),
    inference(definitional_conversion,[status(esa)],[f_652_2]) ).

cnf(f_652_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1879,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1879),U_1882),U_1880),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1879),U_1882),U_1881))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1879,c_Groups_Ozero__class_Ozero(U_1879),U_1882)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1879,U_1880,U_1881)
    | ~ class_Rings_Oordered__comm__semiring(U_1879) ),
    inference(clausify,[status(thm)],[f_652_3]) ).

fof(f_653_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_653_2,plain,
    ! [U_1886,U_1885,U_1884,U_1883] :
      ( c_Orderings_Oord__class_Oless__eq(U_1883,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1883),U_1885),U_1886),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1883),U_1884),U_1886))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1883,U_1886,c_Groups_Ozero__class_Ozero(U_1883))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1883,U_1884,U_1885)
      | ~ class_Rings_Oordered__ring(U_1883) ),
    inference(variable_rename,[status(thm)],[f_653_1]) ).

fof(f_653_3,plain,
    ! [U_1883,U_1884,U_1885,U_1886] :
      ( c_Orderings_Oord__class_Oless__eq(U_1883,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1883),U_1885),U_1886),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1883),U_1884),U_1886))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1883,U_1886,c_Groups_Ozero__class_Ozero(U_1883))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1883,U_1884,U_1885)
      | ~ class_Rings_Oordered__ring(U_1883) ),
    inference(definitional_conversion,[status(esa)],[f_653_2]) ).

cnf(f_653_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1883,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1883),U_1885),U_1886),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1883),U_1884),U_1886))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1883,U_1886,c_Groups_Ozero__class_Ozero(U_1883))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1883,U_1884,U_1885)
    | ~ class_Rings_Oordered__ring(U_1883) ),
    inference(clausify,[status(thm)],[f_653_3]) ).

fof(f_654_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_654_2,plain,
    ! [U_1890,U_1889,U_1888,U_1887] :
      ( c_Orderings_Oord__class_Oless__eq(U_1887,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1887),U_1890),U_1889),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1887),U_1890),U_1888))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1887,U_1890,c_Groups_Ozero__class_Ozero(U_1887))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1887,U_1888,U_1889)
      | ~ class_Rings_Oordered__ring(U_1887) ),
    inference(variable_rename,[status(thm)],[f_654_1]) ).

fof(f_654_3,plain,
    ! [U_1887,U_1888,U_1889,U_1890] :
      ( c_Orderings_Oord__class_Oless__eq(U_1887,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1887),U_1890),U_1889),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1887),U_1890),U_1888))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1887,U_1890,c_Groups_Ozero__class_Ozero(U_1887))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1887,U_1888,U_1889)
      | ~ class_Rings_Oordered__ring(U_1887) ),
    inference(definitional_conversion,[status(esa)],[f_654_2]) ).

cnf(f_654_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1887,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1887),U_1890),U_1889),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1887),U_1890),U_1888))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1887,U_1890,c_Groups_Ozero__class_Ozero(U_1887))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1887,U_1888,U_1889)
    | ~ class_Rings_Oordered__ring(U_1887) ),
    inference(clausify,[status(thm)],[f_654_3]) ).

fof(f_655_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_655_2,plain,
    ! [U_1895,U_1894,U_1893,U_1892,U_1891] :
      ( c_Orderings_Oord__class_Oless__eq(U_1891,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1891),U_1892),U_1894),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1891),U_1893),U_1895))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1891,c_Groups_Ozero__class_Ozero(U_1891),U_1894)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1891,c_Groups_Ozero__class_Ozero(U_1891),U_1892)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1891,U_1894,U_1895)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1891,U_1892,U_1893)
      | ~ class_Rings_Oordered__semiring(U_1891) ),
    inference(variable_rename,[status(thm)],[f_655_1]) ).

fof(f_655_3,plain,
    ! [U_1891,U_1892,U_1893,U_1894,U_1895] :
      ( c_Orderings_Oord__class_Oless__eq(U_1891,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1891),U_1892),U_1894),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1891),U_1893),U_1895))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1891,c_Groups_Ozero__class_Ozero(U_1891),U_1894)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1891,c_Groups_Ozero__class_Ozero(U_1891),U_1892)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1891,U_1894,U_1895)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1891,U_1892,U_1893)
      | ~ class_Rings_Oordered__semiring(U_1891) ),
    inference(definitional_conversion,[status(esa)],[f_655_2]) ).

cnf(f_655_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1891,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1891),U_1892),U_1894),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1891),U_1893),U_1895))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1891,c_Groups_Ozero__class_Ozero(U_1891),U_1894)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1891,c_Groups_Ozero__class_Ozero(U_1891),U_1892)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1891,U_1894,U_1895)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1891,U_1892,U_1893)
    | ~ class_Rings_Oordered__semiring(U_1891) ),
    inference(clausify,[status(thm)],[f_655_3]) ).

fof(f_656_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_656_2,plain,
    ! [U_1900,U_1899,U_1898,U_1897,U_1896] :
      ( c_Orderings_Oord__class_Oless__eq(U_1896,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1896),U_1897),U_1899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1896),U_1898),U_1900))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1896,c_Groups_Ozero__class_Ozero(U_1896),U_1899)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1896,c_Groups_Ozero__class_Ozero(U_1896),U_1898)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1896,U_1899,U_1900)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1896,U_1897,U_1898)
      | ~ class_Rings_Oordered__semiring(U_1896) ),
    inference(variable_rename,[status(thm)],[f_656_1]) ).

fof(f_656_3,plain,
    ! [U_1899,U_1897,U_1898,U_1896,U_1900] :
      ( c_Orderings_Oord__class_Oless__eq(U_1896,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1896),U_1897),U_1899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1896),U_1898),U_1900))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1896,c_Groups_Ozero__class_Ozero(U_1896),U_1899)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1896,c_Groups_Ozero__class_Ozero(U_1896),U_1898)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1896,U_1899,U_1900)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1896,U_1897,U_1898)
      | ~ class_Rings_Oordered__semiring(U_1896) ),
    inference(definitional_conversion,[status(esa)],[f_656_2]) ).

cnf(f_656_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1896,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1896),U_1897),U_1899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1896),U_1898),U_1900))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1896,c_Groups_Ozero__class_Ozero(U_1896),U_1899)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1896,c_Groups_Ozero__class_Ozero(U_1896),U_1898)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1896,U_1899,U_1900)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1896,U_1897,U_1898)
    | ~ class_Rings_Oordered__semiring(U_1896) ),
    inference(clausify,[status(thm)],[f_656_3]) ).

fof(f_657_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_657_2,plain,
    ! [U_1903,U_1902,U_1901] :
      ( c_Orderings_Oord__class_Oless__eq(U_1901,c_Groups_Ozero__class_Ozero(U_1901),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1901),U_1902),U_1903))
      | ( ( ~ c_Orderings_Oord__class_Oless__eq(U_1901,U_1903,c_Groups_Ozero__class_Ozero(U_1901))
          | ~ c_Orderings_Oord__class_Oless__eq(U_1901,U_1902,c_Groups_Ozero__class_Ozero(U_1901)) )
        & ( ~ c_Orderings_Oord__class_Oless__eq(U_1901,c_Groups_Ozero__class_Ozero(U_1901),U_1903)
          | ~ c_Orderings_Oord__class_Oless__eq(U_1901,c_Groups_Ozero__class_Ozero(U_1901),U_1902) ) )
      | ~ class_Rings_Oordered__ring(U_1901) ),
    inference(variable_rename,[status(thm)],[f_657_1]) ).

fof(f_657_3,plain,
    ( ! [U_1901,U_1902,U_1903] :
        ( ~ c_Orderings_Oord__class_Oless__eq(U_1901,U_1903,c_Groups_Ozero__class_Ozero(U_1901))
        | ~ c_Orderings_Oord__class_Oless__eq(U_1901,U_1902,c_Groups_Ozero__class_Ozero(U_1901))
        | ~ sP160(U_1901,U_1902,U_1903) )
    & ! [U_1901,U_1902,U_1903] :
        ( ~ c_Orderings_Oord__class_Oless__eq(U_1901,c_Groups_Ozero__class_Ozero(U_1901),U_1903)
        | ~ c_Orderings_Oord__class_Oless__eq(U_1901,c_Groups_Ozero__class_Ozero(U_1901),U_1902)
        | ~ sP160(U_1901,U_1902,U_1903) )
    & ! [U_1901,U_1902,U_1903] :
        ( c_Orderings_Oord__class_Oless__eq(U_1901,c_Groups_Ozero__class_Ozero(U_1901),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1901),U_1902),U_1903))
        | sP160(U_1901,U_1902,U_1903)
        | ~ class_Rings_Oordered__ring(U_1901) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP160])],[f_657_2]) ).

cnf(f_657_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1901,c_Groups_Ozero__class_Ozero(U_1901),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1901),U_1902),U_1903))
    | sP160(U_1901,U_1902,U_1903)
    | ~ class_Rings_Oordered__ring(U_1901) ),
    inference(clausify,[status(thm)],[f_657_3]) ).

cnf(f_657_5,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(U_1901,c_Groups_Ozero__class_Ozero(U_1901),U_1903)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1901,c_Groups_Ozero__class_Ozero(U_1901),U_1902)
    | ~ sP160(U_1901,U_1902,U_1903) ),
    inference(clausify,[status(thm)],[f_657_3]) ).

cnf(f_657_6,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(U_1901,U_1903,c_Groups_Ozero__class_Ozero(U_1901))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1901,U_1902,c_Groups_Ozero__class_Ozero(U_1901))
    | ~ sP160(U_1901,U_1902,U_1903) ),
    inference(clausify,[status(thm)],[f_657_3]) ).

fof(f_658_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_658_2,plain,
    ! [U_1906,U_1905,U_1904] :
      ( c_Orderings_Oord__class_Oless__eq(U_1904,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1904),U_1905),U_1906),c_Groups_Ozero__class_Ozero(U_1904))
      | ( ( ~ c_Orderings_Oord__class_Oless__eq(U_1904,c_Groups_Ozero__class_Ozero(U_1904),U_1906)
          | ~ c_Orderings_Oord__class_Oless__eq(U_1904,U_1905,c_Groups_Ozero__class_Ozero(U_1904)) )
        & ( ~ c_Orderings_Oord__class_Oless__eq(U_1904,U_1906,c_Groups_Ozero__class_Ozero(U_1904))
          | ~ c_Orderings_Oord__class_Oless__eq(U_1904,c_Groups_Ozero__class_Ozero(U_1904),U_1905) ) )
      | ~ class_Rings_Oordered__cancel__semiring(U_1904) ),
    inference(variable_rename,[status(thm)],[f_658_1]) ).

fof(f_658_3,plain,
    ( ! [U_1904,U_1905,U_1906] :
        ( ~ c_Orderings_Oord__class_Oless__eq(U_1904,c_Groups_Ozero__class_Ozero(U_1904),U_1906)
        | ~ c_Orderings_Oord__class_Oless__eq(U_1904,U_1905,c_Groups_Ozero__class_Ozero(U_1904))
        | ~ sP161(U_1904,U_1905,U_1906) )
    & ! [U_1904,U_1905,U_1906] :
        ( ~ c_Orderings_Oord__class_Oless__eq(U_1904,U_1906,c_Groups_Ozero__class_Ozero(U_1904))
        | ~ c_Orderings_Oord__class_Oless__eq(U_1904,c_Groups_Ozero__class_Ozero(U_1904),U_1905)
        | ~ sP161(U_1904,U_1905,U_1906) )
    & ! [U_1904,U_1905,U_1906] :
        ( c_Orderings_Oord__class_Oless__eq(U_1904,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1904),U_1905),U_1906),c_Groups_Ozero__class_Ozero(U_1904))
        | sP161(U_1904,U_1905,U_1906)
        | ~ class_Rings_Oordered__cancel__semiring(U_1904) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP161])],[f_658_2]) ).

cnf(f_658_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1904,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1904),U_1905),U_1906),c_Groups_Ozero__class_Ozero(U_1904))
    | sP161(U_1904,U_1905,U_1906)
    | ~ class_Rings_Oordered__cancel__semiring(U_1904) ),
    inference(clausify,[status(thm)],[f_658_3]) ).

cnf(f_658_5,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(U_1904,U_1906,c_Groups_Ozero__class_Ozero(U_1904))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1904,c_Groups_Ozero__class_Ozero(U_1904),U_1905)
    | ~ sP161(U_1904,U_1905,U_1906) ),
    inference(clausify,[status(thm)],[f_658_3]) ).

cnf(f_658_6,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(U_1904,c_Groups_Ozero__class_Ozero(U_1904),U_1906)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1904,U_1905,c_Groups_Ozero__class_Ozero(U_1904))
    | ~ sP161(U_1904,U_1905,U_1906) ),
    inference(clausify,[status(thm)],[f_658_3]) ).

fof(f_659_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_659_2,plain,
    ! [U_1908,U_1907] :
      ( ~ c_Orderings_Oord__class_Oless(U_1907,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1907),U_1908),U_1908),c_Groups_Ozero__class_Ozero(U_1907))
      | ~ class_Rings_Olinordered__ring(U_1907) ),
    inference(variable_rename,[status(thm)],[f_659_1]) ).

fof(f_659_3,plain,
    ! [U_1908,U_1907] :
      ( ~ c_Orderings_Oord__class_Oless(U_1907,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1907),U_1908),U_1908),c_Groups_Ozero__class_Ozero(U_1907))
      | ~ class_Rings_Olinordered__ring(U_1907) ),
    inference(definitional_conversion,[status(esa)],[f_659_2]) ).

cnf(f_659_4,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_1907,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1907),U_1908),U_1908),c_Groups_Ozero__class_Ozero(U_1907))
    | ~ class_Rings_Olinordered__ring(U_1907) ),
    inference(clausify,[status(thm)],[f_659_3]) ).

fof(f_660_1,plain,
    ! [V_b_2,V_c_2,V_a_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2))
          | ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)
              | ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) )
            & ( ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
              | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) ) ) )
        & ( ( c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)
            & c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) )
          | ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
            & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) )
          | ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)) ) )
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__right__disj]) ).

fof(f_660_2,plain,
    ! [U_1912,U_1911,U_1910,U_1909] :
      ( ( ( c_Orderings_Oord__class_Oless(U_1909,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1909),U_1910),U_1911),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1909),U_1912),U_1911))
          | ( ( ~ c_Orderings_Oord__class_Oless(U_1909,U_1912,U_1910)
              | ~ c_Orderings_Oord__class_Oless(U_1909,U_1911,c_Groups_Ozero__class_Ozero(U_1909)) )
            & ( ~ c_Orderings_Oord__class_Oless(U_1909,U_1910,U_1912)
              | ~ c_Orderings_Oord__class_Oless(U_1909,c_Groups_Ozero__class_Ozero(U_1909),U_1911) ) ) )
        & ( ( c_Orderings_Oord__class_Oless(U_1909,U_1912,U_1910)
            & c_Orderings_Oord__class_Oless(U_1909,U_1911,c_Groups_Ozero__class_Ozero(U_1909)) )
          | ( c_Orderings_Oord__class_Oless(U_1909,U_1910,U_1912)
            & c_Orderings_Oord__class_Oless(U_1909,c_Groups_Ozero__class_Ozero(U_1909),U_1911) )
          | ~ c_Orderings_Oord__class_Oless(U_1909,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1909),U_1910),U_1911),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1909),U_1912),U_1911)) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_1909) ),
    inference(variable_rename,[status(thm)],[f_660_1]) ).

fof(f_660_3,plain,
    ( ! [U_1909,U_1910,U_1911,U_1912] :
        ( ~ c_Orderings_Oord__class_Oless(U_1909,U_1912,U_1910)
        | ~ c_Orderings_Oord__class_Oless(U_1909,U_1911,c_Groups_Ozero__class_Ozero(U_1909))
        | ~ sP164(U_1909,U_1910,U_1911,U_1912) )
    & ! [U_1909,U_1910,U_1911,U_1912] :
        ( ~ c_Orderings_Oord__class_Oless(U_1909,U_1910,U_1912)
        | ~ c_Orderings_Oord__class_Oless(U_1909,c_Groups_Ozero__class_Ozero(U_1909),U_1911)
        | ~ sP164(U_1909,U_1910,U_1911,U_1912) )
    & ! [U_1909,U_1910,U_1911,U_1912] :
        ( c_Orderings_Oord__class_Oless(U_1909,U_1912,U_1910)
        | ~ sP163(U_1909,U_1910,U_1911,U_1912) )
    & ! [U_1909,U_1910,U_1911,U_1912] :
        ( c_Orderings_Oord__class_Oless(U_1909,U_1911,c_Groups_Ozero__class_Ozero(U_1909))
        | ~ sP163(U_1909,U_1910,U_1911,U_1912) )
    & ! [U_1909,U_1910,U_1911,U_1912] :
        ( c_Orderings_Oord__class_Oless(U_1909,U_1910,U_1912)
        | ~ sP162(U_1909,U_1910,U_1911,U_1912) )
    & ! [U_1909,U_1910,U_1911,U_1912] :
        ( c_Orderings_Oord__class_Oless(U_1909,c_Groups_Ozero__class_Ozero(U_1909),U_1911)
        | ~ sP162(U_1909,U_1910,U_1911,U_1912) )
    & ! [U_1909,U_1910,U_1911,U_1912] :
        ( c_Orderings_Oord__class_Oless(U_1909,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1909),U_1910),U_1911),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1909),U_1912),U_1911))
        | sP164(U_1909,U_1910,U_1911,U_1912)
        | ~ sP165(U_1909,U_1910,U_1911,U_1912) )
    & ! [U_1909,U_1910,U_1911,U_1912] :
        ( sP163(U_1909,U_1910,U_1911,U_1912)
        | sP162(U_1909,U_1910,U_1911,U_1912)
        | ~ c_Orderings_Oord__class_Oless(U_1909,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1909),U_1910),U_1911),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1909),U_1912),U_1911))
        | ~ sP165(U_1909,U_1910,U_1911,U_1912) )
    & ! [U_1909,U_1910,U_1911,U_1912] :
        ( sP165(U_1909,U_1910,U_1911,U_1912)
        | ~ class_Rings_Olinordered__ring__strict(U_1909) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP162,sP163,sP164,sP165])],[f_660_2]) ).

cnf(f_660_4,plain,
    ( sP165(U_1909,U_1910,U_1911,U_1912)
    | ~ class_Rings_Olinordered__ring__strict(U_1909) ),
    inference(clausify,[status(thm)],[f_660_3]) ).

cnf(f_660_5,plain,
    ( sP163(U_1909,U_1910,U_1911,U_1912)
    | sP162(U_1909,U_1910,U_1911,U_1912)
    | ~ c_Orderings_Oord__class_Oless(U_1909,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1909),U_1910),U_1911),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1909),U_1912),U_1911))
    | ~ sP165(U_1909,U_1910,U_1911,U_1912) ),
    inference(clausify,[status(thm)],[f_660_3]) ).

cnf(f_660_6,plain,
    ( c_Orderings_Oord__class_Oless(U_1909,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1909),U_1910),U_1911),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1909),U_1912),U_1911))
    | sP164(U_1909,U_1910,U_1911,U_1912)
    | ~ sP165(U_1909,U_1910,U_1911,U_1912) ),
    inference(clausify,[status(thm)],[f_660_3]) ).

cnf(f_660_7,plain,
    ( c_Orderings_Oord__class_Oless(U_1909,c_Groups_Ozero__class_Ozero(U_1909),U_1911)
    | ~ sP162(U_1909,U_1910,U_1911,U_1912) ),
    inference(clausify,[status(thm)],[f_660_3]) ).

cnf(f_660_8,plain,
    ( c_Orderings_Oord__class_Oless(U_1909,U_1910,U_1912)
    | ~ sP162(U_1909,U_1910,U_1911,U_1912) ),
    inference(clausify,[status(thm)],[f_660_3]) ).

cnf(f_660_9,plain,
    ( c_Orderings_Oord__class_Oless(U_1909,U_1911,c_Groups_Ozero__class_Ozero(U_1909))
    | ~ sP163(U_1909,U_1910,U_1911,U_1912) ),
    inference(clausify,[status(thm)],[f_660_3]) ).

cnf(f_660_10,plain,
    ( c_Orderings_Oord__class_Oless(U_1909,U_1912,U_1910)
    | ~ sP163(U_1909,U_1910,U_1911,U_1912) ),
    inference(clausify,[status(thm)],[f_660_3]) ).

cnf(f_660_11,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_1909,U_1910,U_1912)
    | ~ c_Orderings_Oord__class_Oless(U_1909,c_Groups_Ozero__class_Ozero(U_1909),U_1911)
    | ~ sP164(U_1909,U_1910,U_1911,U_1912) ),
    inference(clausify,[status(thm)],[f_660_3]) ).

cnf(f_660_12,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_1909,U_1912,U_1910)
    | ~ c_Orderings_Oord__class_Oless(U_1909,U_1911,c_Groups_Ozero__class_Ozero(U_1909))
    | ~ sP164(U_1909,U_1910,U_1911,U_1912) ),
    inference(clausify,[status(thm)],[f_660_3]) ).

fof(f_661_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
          | ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)
              | ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) )
            & ( ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
              | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) ) ) )
        & ( ( c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)
            & c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) )
          | ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
            & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) )
          | ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)) ) )
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__disj]) ).

fof(f_661_2,plain,
    ! [U_1916,U_1915,U_1914,U_1913] :
      ( ( ( c_Orderings_Oord__class_Oless(U_1913,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1913),U_1914),U_1915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1913),U_1914),U_1916))
          | ( ( ~ c_Orderings_Oord__class_Oless(U_1913,U_1916,U_1915)
              | ~ c_Orderings_Oord__class_Oless(U_1913,U_1914,c_Groups_Ozero__class_Ozero(U_1913)) )
            & ( ~ c_Orderings_Oord__class_Oless(U_1913,U_1915,U_1916)
              | ~ c_Orderings_Oord__class_Oless(U_1913,c_Groups_Ozero__class_Ozero(U_1913),U_1914) ) ) )
        & ( ( c_Orderings_Oord__class_Oless(U_1913,U_1916,U_1915)
            & c_Orderings_Oord__class_Oless(U_1913,U_1914,c_Groups_Ozero__class_Ozero(U_1913)) )
          | ( c_Orderings_Oord__class_Oless(U_1913,U_1915,U_1916)
            & c_Orderings_Oord__class_Oless(U_1913,c_Groups_Ozero__class_Ozero(U_1913),U_1914) )
          | ~ c_Orderings_Oord__class_Oless(U_1913,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1913),U_1914),U_1915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1913),U_1914),U_1916)) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_1913) ),
    inference(variable_rename,[status(thm)],[f_661_1]) ).

fof(f_661_3,plain,
    ( ! [U_1916,U_1914,U_1913,U_1915] :
        ( ~ c_Orderings_Oord__class_Oless(U_1913,U_1916,U_1915)
        | ~ c_Orderings_Oord__class_Oless(U_1913,U_1914,c_Groups_Ozero__class_Ozero(U_1913))
        | ~ sP168(U_1916,U_1914,U_1913,U_1915) )
    & ! [U_1916,U_1914,U_1913,U_1915] :
        ( ~ c_Orderings_Oord__class_Oless(U_1913,U_1915,U_1916)
        | ~ c_Orderings_Oord__class_Oless(U_1913,c_Groups_Ozero__class_Ozero(U_1913),U_1914)
        | ~ sP168(U_1916,U_1914,U_1913,U_1915) )
    & ! [U_1916,U_1914,U_1913,U_1915] :
        ( c_Orderings_Oord__class_Oless(U_1913,U_1916,U_1915)
        | ~ sP167(U_1916,U_1914,U_1913,U_1915) )
    & ! [U_1916,U_1914,U_1913,U_1915] :
        ( c_Orderings_Oord__class_Oless(U_1913,U_1914,c_Groups_Ozero__class_Ozero(U_1913))
        | ~ sP167(U_1916,U_1914,U_1913,U_1915) )
    & ! [U_1916,U_1914,U_1913,U_1915] :
        ( c_Orderings_Oord__class_Oless(U_1913,U_1915,U_1916)
        | ~ sP166(U_1916,U_1914,U_1913,U_1915) )
    & ! [U_1916,U_1914,U_1913,U_1915] :
        ( c_Orderings_Oord__class_Oless(U_1913,c_Groups_Ozero__class_Ozero(U_1913),U_1914)
        | ~ sP166(U_1916,U_1914,U_1913,U_1915) )
    & ! [U_1916,U_1914,U_1913,U_1915] :
        ( c_Orderings_Oord__class_Oless(U_1913,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1913),U_1914),U_1915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1913),U_1914),U_1916))
        | sP168(U_1916,U_1914,U_1913,U_1915)
        | ~ sP169(U_1916,U_1914,U_1913,U_1915) )
    & ! [U_1916,U_1914,U_1913,U_1915] :
        ( sP167(U_1916,U_1914,U_1913,U_1915)
        | sP166(U_1916,U_1914,U_1913,U_1915)
        | ~ c_Orderings_Oord__class_Oless(U_1913,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1913),U_1914),U_1915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1913),U_1914),U_1916))
        | ~ sP169(U_1916,U_1914,U_1913,U_1915) )
    & ! [U_1916,U_1914,U_1913,U_1915] :
        ( sP169(U_1916,U_1914,U_1913,U_1915)
        | ~ class_Rings_Olinordered__ring__strict(U_1913) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP166,sP167,sP168,sP169])],[f_661_2]) ).

cnf(f_661_4,plain,
    ( sP169(U_1916,U_1914,U_1913,U_1915)
    | ~ class_Rings_Olinordered__ring__strict(U_1913) ),
    inference(clausify,[status(thm)],[f_661_3]) ).

cnf(f_661_5,plain,
    ( sP167(U_1916,U_1914,U_1913,U_1915)
    | sP166(U_1916,U_1914,U_1913,U_1915)
    | ~ c_Orderings_Oord__class_Oless(U_1913,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1913),U_1914),U_1915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1913),U_1914),U_1916))
    | ~ sP169(U_1916,U_1914,U_1913,U_1915) ),
    inference(clausify,[status(thm)],[f_661_3]) ).

cnf(f_661_6,plain,
    ( c_Orderings_Oord__class_Oless(U_1913,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1913),U_1914),U_1915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1913),U_1914),U_1916))
    | sP168(U_1916,U_1914,U_1913,U_1915)
    | ~ sP169(U_1916,U_1914,U_1913,U_1915) ),
    inference(clausify,[status(thm)],[f_661_3]) ).

cnf(f_661_7,plain,
    ( c_Orderings_Oord__class_Oless(U_1913,c_Groups_Ozero__class_Ozero(U_1913),U_1914)
    | ~ sP166(U_1916,U_1914,U_1913,U_1915) ),
    inference(clausify,[status(thm)],[f_661_3]) ).

cnf(f_661_8,plain,
    ( c_Orderings_Oord__class_Oless(U_1913,U_1915,U_1916)
    | ~ sP166(U_1916,U_1914,U_1913,U_1915) ),
    inference(clausify,[status(thm)],[f_661_3]) ).

cnf(f_661_9,plain,
    ( c_Orderings_Oord__class_Oless(U_1913,U_1914,c_Groups_Ozero__class_Ozero(U_1913))
    | ~ sP167(U_1916,U_1914,U_1913,U_1915) ),
    inference(clausify,[status(thm)],[f_661_3]) ).

cnf(f_661_10,plain,
    ( c_Orderings_Oord__class_Oless(U_1913,U_1916,U_1915)
    | ~ sP167(U_1916,U_1914,U_1913,U_1915) ),
    inference(clausify,[status(thm)],[f_661_3]) ).

cnf(f_661_11,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_1913,U_1915,U_1916)
    | ~ c_Orderings_Oord__class_Oless(U_1913,c_Groups_Ozero__class_Ozero(U_1913),U_1914)
    | ~ sP168(U_1916,U_1914,U_1913,U_1915) ),
    inference(clausify,[status(thm)],[f_661_3]) ).

cnf(f_661_12,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_1913,U_1916,U_1915)
    | ~ c_Orderings_Oord__class_Oless(U_1913,U_1914,c_Groups_Ozero__class_Ozero(U_1913))
    | ~ sP168(U_1916,U_1914,U_1913,U_1915) ),
    inference(clausify,[status(thm)],[f_661_3]) ).

fof(f_662_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
          | ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) )
        & ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
          | ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)) ) )
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__pos]) ).

fof(f_662_2,plain,
    ! [U_1920,U_1919,U_1918,U_1917] :
      ( ( ( c_Orderings_Oord__class_Oless(U_1917,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1917),U_1918),U_1919),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1917),U_1918),U_1920))
          | ~ c_Orderings_Oord__class_Oless(U_1917,U_1919,U_1920) )
        & ( c_Orderings_Oord__class_Oless(U_1917,U_1919,U_1920)
          | ~ c_Orderings_Oord__class_Oless(U_1917,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1917),U_1918),U_1919),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1917),U_1918),U_1920)) ) )
      | ~ c_Orderings_Oord__class_Oless(U_1917,c_Groups_Ozero__class_Ozero(U_1917),U_1918)
      | ~ class_Rings_Olinordered__ring__strict(U_1917) ),
    inference(variable_rename,[status(thm)],[f_662_1]) ).

fof(f_662_3,plain,
    ( ! [U_1919,U_1918,U_1917,U_1920] :
        ( c_Orderings_Oord__class_Oless(U_1917,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1917),U_1918),U_1919),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1917),U_1918),U_1920))
        | ~ c_Orderings_Oord__class_Oless(U_1917,U_1919,U_1920)
        | ~ sP170(U_1919,U_1918,U_1917,U_1920) )
    & ! [U_1919,U_1918,U_1917,U_1920] :
        ( c_Orderings_Oord__class_Oless(U_1917,U_1919,U_1920)
        | ~ c_Orderings_Oord__class_Oless(U_1917,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1917),U_1918),U_1919),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1917),U_1918),U_1920))
        | ~ sP170(U_1919,U_1918,U_1917,U_1920) )
    & ! [U_1919,U_1918,U_1917,U_1920] :
        ( sP170(U_1919,U_1918,U_1917,U_1920)
        | ~ c_Orderings_Oord__class_Oless(U_1917,c_Groups_Ozero__class_Ozero(U_1917),U_1918)
        | ~ class_Rings_Olinordered__ring__strict(U_1917) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP170])],[f_662_2]) ).

cnf(f_662_4,plain,
    ( sP170(U_1919,U_1918,U_1917,U_1920)
    | ~ c_Orderings_Oord__class_Oless(U_1917,c_Groups_Ozero__class_Ozero(U_1917),U_1918)
    | ~ class_Rings_Olinordered__ring__strict(U_1917) ),
    inference(clausify,[status(thm)],[f_662_3]) ).

cnf(f_662_5,plain,
    ( c_Orderings_Oord__class_Oless(U_1917,U_1919,U_1920)
    | ~ c_Orderings_Oord__class_Oless(U_1917,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1917),U_1918),U_1919),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1917),U_1918),U_1920))
    | ~ sP170(U_1919,U_1918,U_1917,U_1920) ),
    inference(clausify,[status(thm)],[f_662_3]) ).

cnf(f_662_6,plain,
    ( c_Orderings_Oord__class_Oless(U_1917,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1917),U_1918),U_1919),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1917),U_1918),U_1920))
    | ~ c_Orderings_Oord__class_Oless(U_1917,U_1919,U_1920)
    | ~ sP170(U_1919,U_1918,U_1917,U_1920) ),
    inference(clausify,[status(thm)],[f_662_3]) ).

fof(f_663_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_663_2,plain,
    ! [U_1923,U_1922,U_1921] :
      ( c_Orderings_Oord__class_Oless(U_1921,c_Groups_Ozero__class_Ozero(U_1921),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1921),U_1922),U_1923))
      | ~ c_Orderings_Oord__class_Oless(U_1921,c_Groups_Ozero__class_Ozero(U_1921),U_1923)
      | ~ c_Orderings_Oord__class_Oless(U_1921,c_Groups_Ozero__class_Ozero(U_1921),U_1922)
      | ~ class_Rings_Olinordered__semiring__strict(U_1921) ),
    inference(variable_rename,[status(thm)],[f_663_1]) ).

fof(f_663_3,plain,
    ! [U_1923,U_1921,U_1922] :
      ( c_Orderings_Oord__class_Oless(U_1921,c_Groups_Ozero__class_Ozero(U_1921),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1921),U_1922),U_1923))
      | ~ c_Orderings_Oord__class_Oless(U_1921,c_Groups_Ozero__class_Ozero(U_1921),U_1923)
      | ~ c_Orderings_Oord__class_Oless(U_1921,c_Groups_Ozero__class_Ozero(U_1921),U_1922)
      | ~ class_Rings_Olinordered__semiring__strict(U_1921) ),
    inference(definitional_conversion,[status(esa)],[f_663_2]) ).

cnf(f_663_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1921,c_Groups_Ozero__class_Ozero(U_1921),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1921),U_1922),U_1923))
    | ~ c_Orderings_Oord__class_Oless(U_1921,c_Groups_Ozero__class_Ozero(U_1921),U_1923)
    | ~ c_Orderings_Oord__class_Oless(U_1921,c_Groups_Ozero__class_Ozero(U_1921),U_1922)
    | ~ class_Rings_Olinordered__semiring__strict(U_1921) ),
    inference(clausify,[status(thm)],[f_663_3]) ).

fof(f_664_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_664_2,plain,
    ! [U_1926,U_1925,U_1924] :
      ( c_Orderings_Oord__class_Oless(U_1924,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1924),U_1925),U_1926),c_Groups_Ozero__class_Ozero(U_1924))
      | ~ c_Orderings_Oord__class_Oless(U_1924,U_1926,c_Groups_Ozero__class_Ozero(U_1924))
      | ~ c_Orderings_Oord__class_Oless(U_1924,c_Groups_Ozero__class_Ozero(U_1924),U_1925)
      | ~ class_Rings_Olinordered__semiring__strict(U_1924) ),
    inference(variable_rename,[status(thm)],[f_664_1]) ).

fof(f_664_3,plain,
    ! [U_1925,U_1924,U_1926] :
      ( c_Orderings_Oord__class_Oless(U_1924,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1924),U_1925),U_1926),c_Groups_Ozero__class_Ozero(U_1924))
      | ~ c_Orderings_Oord__class_Oless(U_1924,U_1926,c_Groups_Ozero__class_Ozero(U_1924))
      | ~ c_Orderings_Oord__class_Oless(U_1924,c_Groups_Ozero__class_Ozero(U_1924),U_1925)
      | ~ class_Rings_Olinordered__semiring__strict(U_1924) ),
    inference(definitional_conversion,[status(esa)],[f_664_2]) ).

cnf(f_664_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1924,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1924),U_1925),U_1926),c_Groups_Ozero__class_Ozero(U_1924))
    | ~ c_Orderings_Oord__class_Oless(U_1924,U_1926,c_Groups_Ozero__class_Ozero(U_1924))
    | ~ c_Orderings_Oord__class_Oless(U_1924,c_Groups_Ozero__class_Ozero(U_1924),U_1925)
    | ~ class_Rings_Olinordered__semiring__strict(U_1924) ),
    inference(clausify,[status(thm)],[f_664_3]) ).

fof(f_665_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_665_2,plain,
    ! [U_1929,U_1928,U_1927] :
      ( c_Orderings_Oord__class_Oless(U_1927,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1927),U_1929),U_1928),c_Groups_Ozero__class_Ozero(U_1927))
      | ~ c_Orderings_Oord__class_Oless(U_1927,U_1929,c_Groups_Ozero__class_Ozero(U_1927))
      | ~ c_Orderings_Oord__class_Oless(U_1927,c_Groups_Ozero__class_Ozero(U_1927),U_1928)
      | ~ class_Rings_Olinordered__semiring__strict(U_1927) ),
    inference(variable_rename,[status(thm)],[f_665_1]) ).

fof(f_665_3,plain,
    ! [U_1927,U_1928,U_1929] :
      ( c_Orderings_Oord__class_Oless(U_1927,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1927),U_1929),U_1928),c_Groups_Ozero__class_Ozero(U_1927))
      | ~ c_Orderings_Oord__class_Oless(U_1927,U_1929,c_Groups_Ozero__class_Ozero(U_1927))
      | ~ c_Orderings_Oord__class_Oless(U_1927,c_Groups_Ozero__class_Ozero(U_1927),U_1928)
      | ~ class_Rings_Olinordered__semiring__strict(U_1927) ),
    inference(definitional_conversion,[status(esa)],[f_665_2]) ).

cnf(f_665_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1927,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1927),U_1929),U_1928),c_Groups_Ozero__class_Ozero(U_1927))
    | ~ c_Orderings_Oord__class_Oless(U_1927,U_1929,c_Groups_Ozero__class_Ozero(U_1927))
    | ~ c_Orderings_Oord__class_Oless(U_1927,c_Groups_Ozero__class_Ozero(U_1927),U_1928)
    | ~ class_Rings_Olinordered__semiring__strict(U_1927) ),
    inference(clausify,[status(thm)],[f_665_3]) ).

fof(f_666_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_666_2,plain,
    ! [U_1932,U_1931,U_1930] :
      ( c_Orderings_Oord__class_Oless(U_1930,c_Groups_Ozero__class_Ozero(U_1930),U_1932)
      | ~ c_Orderings_Oord__class_Oless(U_1930,c_Groups_Ozero__class_Ozero(U_1930),U_1931)
      | ~ c_Orderings_Oord__class_Oless(U_1930,c_Groups_Ozero__class_Ozero(U_1930),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1930),U_1931),U_1932))
      | ~ class_Rings_Olinordered__semiring__strict(U_1930) ),
    inference(variable_rename,[status(thm)],[f_666_1]) ).

fof(f_666_3,plain,
    ! [U_1930,U_1931,U_1932] :
      ( c_Orderings_Oord__class_Oless(U_1930,c_Groups_Ozero__class_Ozero(U_1930),U_1932)
      | ~ c_Orderings_Oord__class_Oless(U_1930,c_Groups_Ozero__class_Ozero(U_1930),U_1931)
      | ~ c_Orderings_Oord__class_Oless(U_1930,c_Groups_Ozero__class_Ozero(U_1930),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1930),U_1931),U_1932))
      | ~ class_Rings_Olinordered__semiring__strict(U_1930) ),
    inference(definitional_conversion,[status(esa)],[f_666_2]) ).

cnf(f_666_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1930,c_Groups_Ozero__class_Ozero(U_1930),U_1932)
    | ~ c_Orderings_Oord__class_Oless(U_1930,c_Groups_Ozero__class_Ozero(U_1930),U_1931)
    | ~ c_Orderings_Oord__class_Oless(U_1930,c_Groups_Ozero__class_Ozero(U_1930),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1930),U_1931),U_1932))
    | ~ class_Rings_Olinordered__semiring__strict(U_1930) ),
    inference(clausify,[status(thm)],[f_666_3]) ).

fof(f_667_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_667_2,plain,
    ! [U_1935,U_1934,U_1933] :
      ( c_Orderings_Oord__class_Oless(U_1933,c_Groups_Ozero__class_Ozero(U_1933),U_1934)
      | ~ c_Orderings_Oord__class_Oless(U_1933,c_Groups_Ozero__class_Ozero(U_1933),U_1935)
      | ~ c_Orderings_Oord__class_Oless(U_1933,c_Groups_Ozero__class_Ozero(U_1933),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1933),U_1934),U_1935))
      | ~ class_Rings_Olinordered__semiring__strict(U_1933) ),
    inference(variable_rename,[status(thm)],[f_667_1]) ).

fof(f_667_3,plain,
    ! [U_1933,U_1934,U_1935] :
      ( c_Orderings_Oord__class_Oless(U_1933,c_Groups_Ozero__class_Ozero(U_1933),U_1934)
      | ~ c_Orderings_Oord__class_Oless(U_1933,c_Groups_Ozero__class_Ozero(U_1933),U_1935)
      | ~ c_Orderings_Oord__class_Oless(U_1933,c_Groups_Ozero__class_Ozero(U_1933),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1933),U_1934),U_1935))
      | ~ class_Rings_Olinordered__semiring__strict(U_1933) ),
    inference(definitional_conversion,[status(esa)],[f_667_2]) ).

cnf(f_667_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1933,c_Groups_Ozero__class_Ozero(U_1933),U_1934)
    | ~ c_Orderings_Oord__class_Oless(U_1933,c_Groups_Ozero__class_Ozero(U_1933),U_1935)
    | ~ c_Orderings_Oord__class_Oless(U_1933,c_Groups_Ozero__class_Ozero(U_1933),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1933),U_1934),U_1935))
    | ~ class_Rings_Olinordered__semiring__strict(U_1933) ),
    inference(clausify,[status(thm)],[f_667_3]) ).

fof(f_668_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
          | ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2) )
        & ( c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)
          | ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)) ) )
      | ~ c_Orderings_Oord__class_Oless(T_a,V_c_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_668_2,plain,
    ! [U_1939,U_1938,U_1937,U_1936] :
      ( ( ( c_Orderings_Oord__class_Oless(U_1936,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1936),U_1937),U_1938),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1936),U_1937),U_1939))
          | ~ c_Orderings_Oord__class_Oless(U_1936,U_1939,U_1938) )
        & ( c_Orderings_Oord__class_Oless(U_1936,U_1939,U_1938)
          | ~ c_Orderings_Oord__class_Oless(U_1936,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1936),U_1937),U_1938),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1936),U_1937),U_1939)) ) )
      | ~ c_Orderings_Oord__class_Oless(U_1936,U_1937,c_Groups_Ozero__class_Ozero(U_1936))
      | ~ class_Rings_Olinordered__ring__strict(U_1936) ),
    inference(variable_rename,[status(thm)],[f_668_1]) ).

fof(f_668_3,plain,
    ( ! [U_1936,U_1937,U_1938,U_1939] :
        ( c_Orderings_Oord__class_Oless(U_1936,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1936),U_1937),U_1938),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1936),U_1937),U_1939))
        | ~ c_Orderings_Oord__class_Oless(U_1936,U_1939,U_1938)
        | ~ sP171(U_1936,U_1937,U_1938,U_1939) )
    & ! [U_1936,U_1937,U_1938,U_1939] :
        ( c_Orderings_Oord__class_Oless(U_1936,U_1939,U_1938)
        | ~ c_Orderings_Oord__class_Oless(U_1936,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1936),U_1937),U_1938),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1936),U_1937),U_1939))
        | ~ sP171(U_1936,U_1937,U_1938,U_1939) )
    & ! [U_1936,U_1937,U_1938,U_1939] :
        ( sP171(U_1936,U_1937,U_1938,U_1939)
        | ~ c_Orderings_Oord__class_Oless(U_1936,U_1937,c_Groups_Ozero__class_Ozero(U_1936))
        | ~ class_Rings_Olinordered__ring__strict(U_1936) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP171])],[f_668_2]) ).

cnf(f_668_4,plain,
    ( sP171(U_1936,U_1937,U_1938,U_1939)
    | ~ c_Orderings_Oord__class_Oless(U_1936,U_1937,c_Groups_Ozero__class_Ozero(U_1936))
    | ~ class_Rings_Olinordered__ring__strict(U_1936) ),
    inference(clausify,[status(thm)],[f_668_3]) ).

cnf(f_668_5,plain,
    ( c_Orderings_Oord__class_Oless(U_1936,U_1939,U_1938)
    | ~ c_Orderings_Oord__class_Oless(U_1936,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1936),U_1937),U_1938),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1936),U_1937),U_1939))
    | ~ sP171(U_1936,U_1937,U_1938,U_1939) ),
    inference(clausify,[status(thm)],[f_668_3]) ).

cnf(f_668_6,plain,
    ( c_Orderings_Oord__class_Oless(U_1936,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1936),U_1937),U_1938),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1936),U_1937),U_1939))
    | ~ c_Orderings_Oord__class_Oless(U_1936,U_1939,U_1938)
    | ~ sP171(U_1936,U_1937,U_1938,U_1939) ),
    inference(clausify,[status(thm)],[f_668_3]) ).

fof(f_669_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_669_2,plain,
    ! [U_1942,U_1941,U_1940] :
      ( c_Orderings_Oord__class_Oless(U_1940,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1940),U_1941),U_1942),c_Groups_Ozero__class_Ozero(U_1940))
      | ~ c_Orderings_Oord__class_Oless(U_1940,c_Groups_Ozero__class_Ozero(U_1940),U_1942)
      | ~ c_Orderings_Oord__class_Oless(U_1940,U_1941,c_Groups_Ozero__class_Ozero(U_1940))
      | ~ class_Rings_Olinordered__semiring__strict(U_1940) ),
    inference(variable_rename,[status(thm)],[f_669_1]) ).

fof(f_669_3,plain,
    ! [U_1942,U_1940,U_1941] :
      ( c_Orderings_Oord__class_Oless(U_1940,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1940),U_1941),U_1942),c_Groups_Ozero__class_Ozero(U_1940))
      | ~ c_Orderings_Oord__class_Oless(U_1940,c_Groups_Ozero__class_Ozero(U_1940),U_1942)
      | ~ c_Orderings_Oord__class_Oless(U_1940,U_1941,c_Groups_Ozero__class_Ozero(U_1940))
      | ~ class_Rings_Olinordered__semiring__strict(U_1940) ),
    inference(definitional_conversion,[status(esa)],[f_669_2]) ).

cnf(f_669_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1940,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1940),U_1941),U_1942),c_Groups_Ozero__class_Ozero(U_1940))
    | ~ c_Orderings_Oord__class_Oless(U_1940,c_Groups_Ozero__class_Ozero(U_1940),U_1942)
    | ~ c_Orderings_Oord__class_Oless(U_1940,U_1941,c_Groups_Ozero__class_Ozero(U_1940))
    | ~ class_Rings_Olinordered__semiring__strict(U_1940) ),
    inference(clausify,[status(thm)],[f_669_3]) ).

fof(f_670_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_670_2,plain,
    ! [U_1945,U_1944,U_1943] :
      ( c_Orderings_Oord__class_Oless(U_1943,c_Groups_Ozero__class_Ozero(U_1943),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1943),U_1944),U_1945))
      | ~ c_Orderings_Oord__class_Oless(U_1943,U_1945,c_Groups_Ozero__class_Ozero(U_1943))
      | ~ c_Orderings_Oord__class_Oless(U_1943,U_1944,c_Groups_Ozero__class_Ozero(U_1943))
      | ~ class_Rings_Olinordered__ring__strict(U_1943) ),
    inference(variable_rename,[status(thm)],[f_670_1]) ).

fof(f_670_3,plain,
    ! [U_1943,U_1944,U_1945] :
      ( c_Orderings_Oord__class_Oless(U_1943,c_Groups_Ozero__class_Ozero(U_1943),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1943),U_1944),U_1945))
      | ~ c_Orderings_Oord__class_Oless(U_1943,U_1945,c_Groups_Ozero__class_Ozero(U_1943))
      | ~ c_Orderings_Oord__class_Oless(U_1943,U_1944,c_Groups_Ozero__class_Ozero(U_1943))
      | ~ class_Rings_Olinordered__ring__strict(U_1943) ),
    inference(definitional_conversion,[status(esa)],[f_670_2]) ).

cnf(f_670_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1943,c_Groups_Ozero__class_Ozero(U_1943),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1943),U_1944),U_1945))
    | ~ c_Orderings_Oord__class_Oless(U_1943,U_1945,c_Groups_Ozero__class_Ozero(U_1943))
    | ~ c_Orderings_Oord__class_Oless(U_1943,U_1944,c_Groups_Ozero__class_Ozero(U_1943))
    | ~ class_Rings_Olinordered__ring__strict(U_1943) ),
    inference(clausify,[status(thm)],[f_670_3]) ).

fof(f_671_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_671_2,plain,
    ! [U_1949,U_1948,U_1947,U_1946] :
      ( c_Orderings_Oord__class_Oless(U_1946,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1946),U_1947),U_1949),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1946),U_1948),U_1949))
      | ~ c_Orderings_Oord__class_Oless(U_1946,c_Groups_Ozero__class_Ozero(U_1946),U_1949)
      | ~ c_Orderings_Oord__class_Oless(U_1946,U_1947,U_1948)
      | ~ class_Rings_Olinordered__semiring__strict(U_1946) ),
    inference(variable_rename,[status(thm)],[f_671_1]) ).

fof(f_671_3,plain,
    ! [U_1947,U_1949,U_1948,U_1946] :
      ( c_Orderings_Oord__class_Oless(U_1946,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1946),U_1947),U_1949),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1946),U_1948),U_1949))
      | ~ c_Orderings_Oord__class_Oless(U_1946,c_Groups_Ozero__class_Ozero(U_1946),U_1949)
      | ~ c_Orderings_Oord__class_Oless(U_1946,U_1947,U_1948)
      | ~ class_Rings_Olinordered__semiring__strict(U_1946) ),
    inference(definitional_conversion,[status(esa)],[f_671_2]) ).

cnf(f_671_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1946,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1946),U_1947),U_1949),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1946),U_1948),U_1949))
    | ~ c_Orderings_Oord__class_Oless(U_1946,c_Groups_Ozero__class_Ozero(U_1946),U_1949)
    | ~ c_Orderings_Oord__class_Oless(U_1946,U_1947,U_1948)
    | ~ class_Rings_Olinordered__semiring__strict(U_1946) ),
    inference(clausify,[status(thm)],[f_671_3]) ).

fof(f_672_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_672_2,plain,
    ! [U_1953,U_1952,U_1951,U_1950] :
      ( c_Orderings_Oord__class_Oless(U_1950,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1950),U_1953),U_1951),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1950),U_1953),U_1952))
      | ~ c_Orderings_Oord__class_Oless(U_1950,c_Groups_Ozero__class_Ozero(U_1950),U_1953)
      | ~ c_Orderings_Oord__class_Oless(U_1950,U_1951,U_1952)
      | ~ class_Rings_Olinordered__semiring__strict(U_1950) ),
    inference(variable_rename,[status(thm)],[f_672_1]) ).

fof(f_672_3,plain,
    ! [U_1950,U_1951,U_1952,U_1953] :
      ( c_Orderings_Oord__class_Oless(U_1950,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1950),U_1953),U_1951),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1950),U_1953),U_1952))
      | ~ c_Orderings_Oord__class_Oless(U_1950,c_Groups_Ozero__class_Ozero(U_1950),U_1953)
      | ~ c_Orderings_Oord__class_Oless(U_1950,U_1951,U_1952)
      | ~ class_Rings_Olinordered__semiring__strict(U_1950) ),
    inference(definitional_conversion,[status(esa)],[f_672_2]) ).

cnf(f_672_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1950,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1950),U_1953),U_1951),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1950),U_1953),U_1952))
    | ~ c_Orderings_Oord__class_Oless(U_1950,c_Groups_Ozero__class_Ozero(U_1950),U_1953)
    | ~ c_Orderings_Oord__class_Oless(U_1950,U_1951,U_1952)
    | ~ class_Rings_Olinordered__semiring__strict(U_1950) ),
    inference(clausify,[status(thm)],[f_672_3]) ).

fof(f_673_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_673_2,plain,
    ! [U_1957,U_1956,U_1955,U_1954] :
      ( c_Orderings_Oord__class_Oless(U_1954,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1954),U_1957),U_1955),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1954),U_1957),U_1956))
      | ~ c_Orderings_Oord__class_Oless(U_1954,c_Groups_Ozero__class_Ozero(U_1954),U_1957)
      | ~ c_Orderings_Oord__class_Oless(U_1954,U_1955,U_1956)
      | ~ class_Rings_Olinordered__comm__semiring__strict(U_1954) ),
    inference(variable_rename,[status(thm)],[f_673_1]) ).

fof(f_673_3,plain,
    ! [U_1954,U_1955,U_1956,U_1957] :
      ( c_Orderings_Oord__class_Oless(U_1954,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1954),U_1957),U_1955),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1954),U_1957),U_1956))
      | ~ c_Orderings_Oord__class_Oless(U_1954,c_Groups_Ozero__class_Ozero(U_1954),U_1957)
      | ~ c_Orderings_Oord__class_Oless(U_1954,U_1955,U_1956)
      | ~ class_Rings_Olinordered__comm__semiring__strict(U_1954) ),
    inference(definitional_conversion,[status(esa)],[f_673_2]) ).

cnf(f_673_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1954,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1954),U_1957),U_1955),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1954),U_1957),U_1956))
    | ~ c_Orderings_Oord__class_Oless(U_1954,c_Groups_Ozero__class_Ozero(U_1954),U_1957)
    | ~ c_Orderings_Oord__class_Oless(U_1954,U_1955,U_1956)
    | ~ class_Rings_Olinordered__comm__semiring__strict(U_1954) ),
    inference(clausify,[status(thm)],[f_673_3]) ).

fof(f_674_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_674_2,plain,
    ! [U_1961,U_1960,U_1959,U_1958] :
      ( c_Orderings_Oord__class_Oless(U_1958,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1958),U_1960),U_1961),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1958),U_1959),U_1961))
      | ~ c_Orderings_Oord__class_Oless(U_1958,U_1961,c_Groups_Ozero__class_Ozero(U_1958))
      | ~ c_Orderings_Oord__class_Oless(U_1958,U_1959,U_1960)
      | ~ class_Rings_Olinordered__ring__strict(U_1958) ),
    inference(variable_rename,[status(thm)],[f_674_1]) ).

fof(f_674_3,plain,
    ! [U_1958,U_1959,U_1960,U_1961] :
      ( c_Orderings_Oord__class_Oless(U_1958,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1958),U_1960),U_1961),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1958),U_1959),U_1961))
      | ~ c_Orderings_Oord__class_Oless(U_1958,U_1961,c_Groups_Ozero__class_Ozero(U_1958))
      | ~ c_Orderings_Oord__class_Oless(U_1958,U_1959,U_1960)
      | ~ class_Rings_Olinordered__ring__strict(U_1958) ),
    inference(definitional_conversion,[status(esa)],[f_674_2]) ).

cnf(f_674_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1958,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1958),U_1960),U_1961),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1958),U_1959),U_1961))
    | ~ c_Orderings_Oord__class_Oless(U_1958,U_1961,c_Groups_Ozero__class_Ozero(U_1958))
    | ~ c_Orderings_Oord__class_Oless(U_1958,U_1959,U_1960)
    | ~ class_Rings_Olinordered__ring__strict(U_1958) ),
    inference(clausify,[status(thm)],[f_674_3]) ).

fof(f_675_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_675_2,plain,
    ! [U_1965,U_1964,U_1963,U_1962] :
      ( c_Orderings_Oord__class_Oless(U_1962,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1962),U_1965),U_1964),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1962),U_1965),U_1963))
      | ~ c_Orderings_Oord__class_Oless(U_1962,U_1965,c_Groups_Ozero__class_Ozero(U_1962))
      | ~ c_Orderings_Oord__class_Oless(U_1962,U_1963,U_1964)
      | ~ class_Rings_Olinordered__ring__strict(U_1962) ),
    inference(variable_rename,[status(thm)],[f_675_1]) ).

fof(f_675_3,plain,
    ! [U_1962,U_1964,U_1965,U_1963] :
      ( c_Orderings_Oord__class_Oless(U_1962,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1962),U_1965),U_1964),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1962),U_1965),U_1963))
      | ~ c_Orderings_Oord__class_Oless(U_1962,U_1965,c_Groups_Ozero__class_Ozero(U_1962))
      | ~ c_Orderings_Oord__class_Oless(U_1962,U_1963,U_1964)
      | ~ class_Rings_Olinordered__ring__strict(U_1962) ),
    inference(definitional_conversion,[status(esa)],[f_675_2]) ).

cnf(f_675_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1962,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1962),U_1965),U_1964),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1962),U_1965),U_1963))
    | ~ c_Orderings_Oord__class_Oless(U_1962,U_1965,c_Groups_Ozero__class_Ozero(U_1962))
    | ~ c_Orderings_Oord__class_Oless(U_1962,U_1963,U_1964)
    | ~ class_Rings_Olinordered__ring__strict(U_1962) ),
    inference(clausify,[status(thm)],[f_675_3]) ).

fof(f_676_1,plain,
    ! [V_P_2] :
      ( ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B_x) )
        | ? [B_x] : ~ hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) )
      & ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x)))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B_x) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__quantifiers_I1_J]) ).

fof(f_676_2,plain,
    ! [U_1970] :
      ( ( ! [U_1969] :
            ( hBOOL(hAPP(U_1970,U_1969))
            | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1969) )
        | ? [U_1968] : ~ hBOOL(hAPP(U_1970,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1968))) )
      & ( ! [U_1967] : hBOOL(hAPP(U_1970,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1967)))
        | ? [U_1966] :
            ( ~ hBOOL(hAPP(U_1970,U_1966))
            & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1966) ) ) ),
    inference(variable_rename,[status(thm)],[f_676_1]) ).

fof(f_676_3,plain,
    ( ! [U_1972] :
        ( ! [U_1969] :
            ( hBOOL(hAPP(U_1972,U_1969))
            | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1969) )
        | ? [U_1968] : ~ hBOOL(hAPP(U_1972,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1968))) )
    & ! [U_1971] :
        ( ! [U_1967] : hBOOL(hAPP(U_1971,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1967)))
        | ? [U_1966] :
            ( ~ hBOOL(hAPP(U_1971,U_1966))
            & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1966) ) ) ),
    inference(miniscope,[status(thm)],[f_676_2]) ).

fof(f_676_4,plain,
    ( ! [U_1972] :
        ( ! [U_1969] :
            ( hBOOL(hAPP(U_1972,U_1969))
            | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1969) )
        | ? [U_1968] : ~ hBOOL(hAPP(U_1972,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1968))) )
    & ! [U_1971] :
        ( ! [U_1967] : hBOOL(hAPP(U_1971,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1967)))
        | ( ~ hBOOL(hAPP(U_1971,sK55(U_1971)))
          & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK55(U_1971)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_1966,sK55(U_1971))],[f_676_3]) ).

fof(f_676_5,plain,
    ( ! [U_1972] :
        ( ! [U_1969] :
            ( hBOOL(hAPP(U_1972,U_1969))
            | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1969) )
        | ~ hBOOL(hAPP(U_1972,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK56(U_1972)))) )
    & ! [U_1971] :
        ( ! [U_1967] : hBOOL(hAPP(U_1971,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1967)))
        | ( ~ hBOOL(hAPP(U_1971,sK55(U_1971)))
          & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK55(U_1971)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_1968,sK56(U_1972))],[f_676_4]) ).

fof(f_676_6,plain,
    ( ! [U_1971] :
        ( ~ hBOOL(hAPP(U_1971,sK55(U_1971)))
        | ~ sP172(U_1971) )
    & ! [U_1971] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK55(U_1971))
        | ~ sP172(U_1971) )
    & ! [U_1969,U_1972] :
        ( hBOOL(hAPP(U_1972,U_1969))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1969)
        | ~ hBOOL(hAPP(U_1972,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK56(U_1972)))) )
    & ! [U_1967,U_1971] :
        ( hBOOL(hAPP(U_1971,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1967)))
        | sP172(U_1971) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP172])],[f_676_5]) ).

cnf(f_676_7,plain,
    ( hBOOL(hAPP(U_1971,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1967)))
    | sP172(U_1971) ),
    inference(clausify,[status(thm)],[f_676_6]) ).

cnf(f_676_8,plain,
    ( hBOOL(hAPP(U_1972,U_1969))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1969)
    | ~ hBOOL(hAPP(U_1972,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK56(U_1972)))) ),
    inference(clausify,[status(thm)],[f_676_6]) ).

cnf(f_676_9,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK55(U_1971))
    | ~ sP172(U_1971) ),
    inference(clausify,[status(thm)],[f_676_6]) ).

cnf(f_676_10,plain,
    ( ~ hBOOL(hAPP(U_1971,sK55(U_1971)))
    | ~ sP172(U_1971) ),
    inference(clausify,[status(thm)],[f_676_6]) ).

fof(f_677_1,plain,
    ! [V_P_2] :
      ( ( ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B_x) )
        | ! [B_x] : ~ hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) )
      & ( ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x)))
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B_x) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__quantifiers_I2_J]) ).

fof(f_677_2,plain,
    ! [U_1977] :
      ( ( ? [U_1976] :
            ( hBOOL(hAPP(U_1977,U_1976))
            & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1976) )
        | ! [U_1975] : ~ hBOOL(hAPP(U_1977,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1975))) )
      & ( ? [U_1974] : hBOOL(hAPP(U_1977,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1974)))
        | ! [U_1973] :
            ( ~ hBOOL(hAPP(U_1977,U_1973))
            | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1973) ) ) ),
    inference(variable_rename,[status(thm)],[f_677_1]) ).

fof(f_677_3,plain,
    ( ! [U_1979] :
        ( ? [U_1976] :
            ( hBOOL(hAPP(U_1979,U_1976))
            & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1976) )
        | ! [U_1975] : ~ hBOOL(hAPP(U_1979,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1975))) )
    & ! [U_1978] :
        ( ? [U_1974] : hBOOL(hAPP(U_1978,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1974)))
        | ! [U_1973] :
            ( ~ hBOOL(hAPP(U_1978,U_1973))
            | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1973) ) ) ),
    inference(miniscope,[status(thm)],[f_677_2]) ).

fof(f_677_4,plain,
    ( ! [U_1979] :
        ( ? [U_1976] :
            ( hBOOL(hAPP(U_1979,U_1976))
            & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1976) )
        | ! [U_1975] : ~ hBOOL(hAPP(U_1979,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1975))) )
    & ! [U_1978] :
        ( hBOOL(hAPP(U_1978,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK57(U_1978))))
        | ! [U_1973] :
            ( ~ hBOOL(hAPP(U_1978,U_1973))
            | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1973) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_1974,sK57(U_1978))],[f_677_3]) ).

fof(f_677_5,plain,
    ( ! [U_1979] :
        ( ( hBOOL(hAPP(U_1979,sK58(U_1979)))
          & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK58(U_1979)) )
        | ! [U_1975] : ~ hBOOL(hAPP(U_1979,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1975))) )
    & ! [U_1978] :
        ( hBOOL(hAPP(U_1978,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK57(U_1978))))
        | ! [U_1973] :
            ( ~ hBOOL(hAPP(U_1978,U_1973))
            | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1973) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_1976,sK58(U_1979))],[f_677_4]) ).

fof(f_677_6,plain,
    ( ! [U_1979] :
        ( hBOOL(hAPP(U_1979,sK58(U_1979)))
        | ~ sP173(U_1979) )
    & ! [U_1979] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK58(U_1979))
        | ~ sP173(U_1979) )
    & ! [U_1975,U_1979] :
        ( sP173(U_1979)
        | ~ hBOOL(hAPP(U_1979,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1975))) )
    & ! [U_1973,U_1978] :
        ( hBOOL(hAPP(U_1978,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK57(U_1978))))
        | ~ hBOOL(hAPP(U_1978,U_1973))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1973) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP173])],[f_677_5]) ).

cnf(f_677_7,plain,
    ( hBOOL(hAPP(U_1978,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK57(U_1978))))
    | ~ hBOOL(hAPP(U_1978,U_1973))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1973) ),
    inference(clausify,[status(thm)],[f_677_6]) ).

cnf(f_677_8,plain,
    ( sP173(U_1979)
    | ~ hBOOL(hAPP(U_1979,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1975))) ),
    inference(clausify,[status(thm)],[f_677_6]) ).

cnf(f_677_9,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK58(U_1979))
    | ~ sP173(U_1979) ),
    inference(clausify,[status(thm)],[f_677_6]) ).

cnf(f_677_10,plain,
    ( hBOOL(hAPP(U_1979,sK58(U_1979)))
    | ~ sP173(U_1979) ),
    inference(clausify,[status(thm)],[f_677_6]) ).

fof(f_678_1,plain,
    ! [V_z] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J]) ).

fof(f_678_2,plain,
    ! [U_1980] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1980)),
    inference(variable_rename,[status(thm)],[f_678_1]) ).

fof(f_678_3,plain,
    ! [U_1980] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1980)),
    inference(definitional_conversion,[status(esa)],[f_678_2]) ).

cnf(f_678_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1980)),
    inference(clausify,[status(thm)],[f_678_3]) ).

fof(f_679_1,plain,
    ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),
    inference(fof_nnf,[status(thm)],[fact_zero__zle__int]) ).

fof(f_679_2,plain,
    ! [U_1981] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1981)),
    inference(variable_rename,[status(thm)],[f_679_1]) ).

fof(f_679_3,plain,
    ! [U_1981] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1981)),
    inference(definitional_conversion,[status(esa)],[f_679_2]) ).

cnf(f_679_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1981)),
    inference(clausify,[status(thm)],[f_679_3]) ).

fof(f_680_1,plain,
    ! [V_k] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(fof_nnf,[status(thm)],[fact_int__less__0__conv]) ).

fof(f_680_2,plain,
    ! [U_1982] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1982),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(variable_rename,[status(thm)],[f_680_1]) ).

fof(f_680_3,plain,
    ! [U_1982] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1982),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(definitional_conversion,[status(esa)],[f_680_2]) ).

cnf(f_680_4,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1982),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_680_3]) ).

fof(f_681_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_681_2,plain,
    ! [U_1985,U_1984,U_1983] :
      ( ( ( c_Groups_Oplus__class_Oplus(U_1983,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1983),U_1984),U_1984),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1983),U_1985),U_1985)) = c_Groups_Ozero__class_Ozero(U_1983)
          | U_1985 != c_Groups_Ozero__class_Ozero(U_1983)
          | U_1984 != c_Groups_Ozero__class_Ozero(U_1983) )
        & ( ( U_1985 = c_Groups_Ozero__class_Ozero(U_1983)
            & U_1984 = c_Groups_Ozero__class_Ozero(U_1983) )
          | c_Groups_Oplus__class_Oplus(U_1983,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1983),U_1984),U_1984),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1983),U_1985),U_1985)) != c_Groups_Ozero__class_Ozero(U_1983) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_1983) ),
    inference(variable_rename,[status(thm)],[f_681_1]) ).

fof(f_681_3,plain,
    ( ! [U_1983,U_1984,U_1985] :
        ( U_1985 = c_Groups_Ozero__class_Ozero(U_1983)
        | ~ sP174(U_1983,U_1984,U_1985) )
    & ! [U_1983,U_1984,U_1985] :
        ( U_1984 = c_Groups_Ozero__class_Ozero(U_1983)
        | ~ sP174(U_1983,U_1984,U_1985) )
    & ! [U_1983,U_1984,U_1985] :
        ( c_Groups_Oplus__class_Oplus(U_1983,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1983),U_1984),U_1984),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1983),U_1985),U_1985)) = c_Groups_Ozero__class_Ozero(U_1983)
        | U_1985 != c_Groups_Ozero__class_Ozero(U_1983)
        | U_1984 != c_Groups_Ozero__class_Ozero(U_1983)
        | ~ sP175(U_1983,U_1984,U_1985) )
    & ! [U_1983,U_1984,U_1985] :
        ( sP174(U_1983,U_1984,U_1985)
        | c_Groups_Oplus__class_Oplus(U_1983,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1983),U_1984),U_1984),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1983),U_1985),U_1985)) != c_Groups_Ozero__class_Ozero(U_1983)
        | ~ sP175(U_1983,U_1984,U_1985) )
    & ! [U_1983,U_1984,U_1985] :
        ( sP175(U_1983,U_1984,U_1985)
        | ~ class_Rings_Olinordered__ring__strict(U_1983) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP174,sP175])],[f_681_2]) ).

cnf(f_681_4,plain,
    ( sP175(U_1983,U_1984,U_1985)
    | ~ class_Rings_Olinordered__ring__strict(U_1983) ),
    inference(clausify,[status(thm)],[f_681_3]) ).

cnf(f_681_5,plain,
    ( sP174(U_1983,U_1984,U_1985)
    | c_Groups_Oplus__class_Oplus(U_1983,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1983),U_1984),U_1984),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1983),U_1985),U_1985)) != c_Groups_Ozero__class_Ozero(U_1983)
    | ~ sP175(U_1983,U_1984,U_1985) ),
    inference(clausify,[status(thm)],[f_681_3]) ).

cnf(f_681_6,plain,
    ( c_Groups_Oplus__class_Oplus(U_1983,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1983),U_1984),U_1984),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1983),U_1985),U_1985)) = c_Groups_Ozero__class_Ozero(U_1983)
    | U_1985 != c_Groups_Ozero__class_Ozero(U_1983)
    | U_1984 != c_Groups_Ozero__class_Ozero(U_1983)
    | ~ sP175(U_1983,U_1984,U_1985) ),
    inference(clausify,[status(thm)],[f_681_3]) ).

cnf(f_681_7,plain,
    ( U_1984 = c_Groups_Ozero__class_Ozero(U_1983)
    | ~ sP174(U_1983,U_1984,U_1985) ),
    inference(clausify,[status(thm)],[f_681_3]) ).

cnf(f_681_8,plain,
    ( U_1985 = c_Groups_Ozero__class_Ozero(U_1983)
    | ~ sP174(U_1983,U_1984,U_1985) ),
    inference(clausify,[status(thm)],[f_681_3]) ).

fof(f_682_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_682_2,plain,
    ! [U_1991,U_1990,U_1989,U_1988,U_1987,U_1986] :
      ( c_Groups_Oplus__class_Oplus(U_1986,U_1988,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1986),U_1987),U_1990)) != c_Groups_Oplus__class_Oplus(U_1986,U_1989,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1986),U_1987),U_1991))
      | U_1990 = U_1991
      | U_1988 != U_1989
      | U_1987 = c_Groups_Ozero__class_Ozero(U_1986)
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1986) ),
    inference(variable_rename,[status(thm)],[f_682_1]) ).

fof(f_682_3,plain,
    ! [U_1990,U_1988,U_1991,U_1987,U_1986,U_1989] :
      ( c_Groups_Oplus__class_Oplus(U_1986,U_1988,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1986),U_1987),U_1990)) != c_Groups_Oplus__class_Oplus(U_1986,U_1989,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1986),U_1987),U_1991))
      | U_1990 = U_1991
      | U_1988 != U_1989
      | U_1987 = c_Groups_Ozero__class_Ozero(U_1986)
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1986) ),
    inference(definitional_conversion,[status(esa)],[f_682_2]) ).

cnf(f_682_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_1986,U_1988,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1986),U_1987),U_1990)) != c_Groups_Oplus__class_Oplus(U_1986,U_1989,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1986),U_1987),U_1991))
    | U_1990 = U_1991
    | U_1988 != U_1989
    | U_1987 = c_Groups_Ozero__class_Ozero(U_1986)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1986) ),
    inference(clausify,[status(thm)],[f_682_3]) ).

fof(f_683_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__relations_I2_J]) ).

fof(f_683_2,plain,
    ! [U_1993,U_1992] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1992),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1993))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1992,U_1993) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1992,U_1993)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1992),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1993)) ) ),
    inference(variable_rename,[status(thm)],[f_683_1]) ).

fof(f_683_3,plain,
    ( ! [U_1997,U_1995] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1995),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1997))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1995,U_1997) )
    & ! [U_1996,U_1994] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1994,U_1996)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1994),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1996)) ) ),
    inference(miniscope,[status(thm)],[f_683_2]) ).

fof(f_683_4,plain,
    ( ! [U_1995,U_1997] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1995),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1997))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1995,U_1997) )
    & ! [U_1994,U_1996] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1994,U_1996)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1994),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1996)) ) ),
    inference(definitional_conversion,[status(esa)],[f_683_3]) ).

cnf(f_683_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1994,U_1996)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1994),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1996)) ),
    inference(clausify,[status(thm)],[f_683_4]) ).

cnf(f_683_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1995),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1997))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1995,U_1997) ),
    inference(clausify,[status(thm)],[f_683_4]) ).

fof(f_684_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_zless__int]) ).

fof(f_684_2,plain,
    ! [U_1999,U_1998] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1998),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1999))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1998,U_1999) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1998,U_1999)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1998),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1999)) ) ),
    inference(variable_rename,[status(thm)],[f_684_1]) ).

fof(f_684_3,plain,
    ( ! [U_2003,U_2001] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2001),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2003))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2001,U_2003) )
    & ! [U_2002,U_2000] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2000,U_2002)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2000),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2002)) ) ),
    inference(miniscope,[status(thm)],[f_684_2]) ).

fof(f_684_4,plain,
    ( ! [U_2001,U_2003] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2001),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2003))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2001,U_2003) )
    & ! [U_2000,U_2002] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2000,U_2002)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2000),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2002)) ) ),
    inference(definitional_conversion,[status(esa)],[f_684_3]) ).

cnf(f_684_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2000,U_2002)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2000),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2002)) ),
    inference(clausify,[status(thm)],[f_684_4]) ).

cnf(f_684_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2001),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2003))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2001,U_2003) ),
    inference(clausify,[status(thm)],[f_684_4]) ).

fof(f_685_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__relations_I3_J]) ).

fof(f_685_2,plain,
    ! [U_2005,U_2004] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2004),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2005))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2004,U_2005) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2004,U_2005)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2004),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2005)) ) ),
    inference(variable_rename,[status(thm)],[f_685_1]) ).

fof(f_685_3,plain,
    ( ! [U_2009,U_2007] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2007),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2009))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2007,U_2009) )
    & ! [U_2008,U_2006] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2006,U_2008)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2006),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2008)) ) ),
    inference(miniscope,[status(thm)],[f_685_2]) ).

fof(f_685_4,plain,
    ( ! [U_2007,U_2009] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2007),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2009))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2007,U_2009) )
    & ! [U_2008,U_2006] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2006,U_2008)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2006),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2008)) ) ),
    inference(definitional_conversion,[status(esa)],[f_685_3]) ).

cnf(f_685_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2006,U_2008)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2006),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2008)) ),
    inference(clausify,[status(thm)],[f_685_4]) ).

cnf(f_685_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2007),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2009))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2007,U_2009) ),
    inference(clausify,[status(thm)],[f_685_4]) ).

fof(f_686_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_zle__int]) ).

fof(f_686_2,plain,
    ! [U_2011,U_2010] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2010),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2011))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2010,U_2011) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2010,U_2011)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2010),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2011)) ) ),
    inference(variable_rename,[status(thm)],[f_686_1]) ).

fof(f_686_3,plain,
    ( ! [U_2015,U_2013] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2013),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2015))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2013,U_2015) )
    & ! [U_2014,U_2012] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2012,U_2014)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2012),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2014)) ) ),
    inference(miniscope,[status(thm)],[f_686_2]) ).

fof(f_686_4,plain,
    ( ! [U_2015,U_2013] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2013),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2015))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2013,U_2015) )
    & ! [U_2014,U_2012] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2012,U_2014)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2012),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2014)) ) ),
    inference(definitional_conversion,[status(esa)],[f_686_3]) ).

cnf(f_686_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2012,U_2014)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2012),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2014)) ),
    inference(clausify,[status(thm)],[f_686_4]) ).

cnf(f_686_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2013),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2015))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2013,U_2015) ),
    inference(clausify,[status(thm)],[f_686_4]) ).

fof(f_687_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_687_2,plain,
    ! [U_2018,U_2017,U_2016] :
      ( c_Orderings_Oord__class_Oless(U_2016,c_Groups_Oone__class_Oone(U_2016),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2016),U_2017),U_2018))
      | ~ c_Orderings_Oord__class_Oless(U_2016,c_Groups_Oone__class_Oone(U_2016),U_2018)
      | ~ c_Orderings_Oord__class_Oless(U_2016,c_Groups_Oone__class_Oone(U_2016),U_2017)
      | ~ class_Rings_Olinordered__semidom(U_2016) ),
    inference(variable_rename,[status(thm)],[f_687_1]) ).

fof(f_687_3,plain,
    ! [U_2018,U_2017,U_2016] :
      ( c_Orderings_Oord__class_Oless(U_2016,c_Groups_Oone__class_Oone(U_2016),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2016),U_2017),U_2018))
      | ~ c_Orderings_Oord__class_Oless(U_2016,c_Groups_Oone__class_Oone(U_2016),U_2018)
      | ~ c_Orderings_Oord__class_Oless(U_2016,c_Groups_Oone__class_Oone(U_2016),U_2017)
      | ~ class_Rings_Olinordered__semidom(U_2016) ),
    inference(definitional_conversion,[status(esa)],[f_687_2]) ).

cnf(f_687_4,plain,
    ( c_Orderings_Oord__class_Oless(U_2016,c_Groups_Oone__class_Oone(U_2016),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2016),U_2017),U_2018))
    | ~ c_Orderings_Oord__class_Oless(U_2016,c_Groups_Oone__class_Oone(U_2016),U_2018)
    | ~ c_Orderings_Oord__class_Oless(U_2016,c_Groups_Oone__class_Oone(U_2016),U_2017)
    | ~ class_Rings_Olinordered__semidom(U_2016) ),
    inference(clausify,[status(thm)],[f_687_3]) ).

fof(f_688_1,plain,
    ! [V_v,V_b,V_a,T_b] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Groups_Oplus__class_Oplus(T_b,V_a,V_b)),c_Int_Onumber__class_Onumber__of(T_b,V_v)) = c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),c_Int_Onumber__class_Onumber__of(T_b,V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)))
      | ~ class_Rings_Osemiring(T_b)
      | ~ class_Int_Onumber(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_left__distrib__number__of]) ).

fof(f_688_2,plain,
    ! [U_2022,U_2021,U_2020,U_2019] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2019),c_Groups_Oplus__class_Oplus(U_2019,U_2020,U_2021)),c_Int_Onumber__class_Onumber__of(U_2019,U_2022)) = c_Groups_Oplus__class_Oplus(U_2019,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2019),U_2020),c_Int_Onumber__class_Onumber__of(U_2019,U_2022)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2019),U_2021),c_Int_Onumber__class_Onumber__of(U_2019,U_2022)))
      | ~ class_Rings_Osemiring(U_2019)
      | ~ class_Int_Onumber(U_2019) ),
    inference(variable_rename,[status(thm)],[f_688_1]) ).

fof(f_688_3,plain,
    ! [U_2019,U_2020,U_2021,U_2022] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2019),c_Groups_Oplus__class_Oplus(U_2019,U_2020,U_2021)),c_Int_Onumber__class_Onumber__of(U_2019,U_2022)) = c_Groups_Oplus__class_Oplus(U_2019,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2019),U_2020),c_Int_Onumber__class_Onumber__of(U_2019,U_2022)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2019),U_2021),c_Int_Onumber__class_Onumber__of(U_2019,U_2022)))
      | ~ class_Rings_Osemiring(U_2019)
      | ~ class_Int_Onumber(U_2019) ),
    inference(definitional_conversion,[status(esa)],[f_688_2]) ).

cnf(f_688_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2019),c_Groups_Oplus__class_Oplus(U_2019,U_2020,U_2021)),c_Int_Onumber__class_Onumber__of(U_2019,U_2022)) = c_Groups_Oplus__class_Oplus(U_2019,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2019),U_2020),c_Int_Onumber__class_Onumber__of(U_2019,U_2022)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2019),U_2021),c_Int_Onumber__class_Onumber__of(U_2019,U_2022)))
    | ~ class_Rings_Osemiring(U_2019)
    | ~ class_Int_Onumber(U_2019) ),
    inference(clausify,[status(thm)],[f_688_3]) ).

fof(f_689_1,plain,
    ! [V_c,V_b,V_v,T_b] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)),c_Groups_Oplus__class_Oplus(T_b,V_b,V_c)) = c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)),V_c))
      | ~ class_Rings_Osemiring(T_b)
      | ~ class_Int_Onumber(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_right__distrib__number__of]) ).

fof(f_689_2,plain,
    ! [U_2026,U_2025,U_2024,U_2023] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2023),c_Int_Onumber__class_Onumber__of(U_2023,U_2024)),c_Groups_Oplus__class_Oplus(U_2023,U_2025,U_2026)) = c_Groups_Oplus__class_Oplus(U_2023,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2023),c_Int_Onumber__class_Onumber__of(U_2023,U_2024)),U_2025),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2023),c_Int_Onumber__class_Onumber__of(U_2023,U_2024)),U_2026))
      | ~ class_Rings_Osemiring(U_2023)
      | ~ class_Int_Onumber(U_2023) ),
    inference(variable_rename,[status(thm)],[f_689_1]) ).

fof(f_689_3,plain,
    ! [U_2024,U_2023,U_2025,U_2026] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2023),c_Int_Onumber__class_Onumber__of(U_2023,U_2024)),c_Groups_Oplus__class_Oplus(U_2023,U_2025,U_2026)) = c_Groups_Oplus__class_Oplus(U_2023,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2023),c_Int_Onumber__class_Onumber__of(U_2023,U_2024)),U_2025),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2023),c_Int_Onumber__class_Onumber__of(U_2023,U_2024)),U_2026))
      | ~ class_Rings_Osemiring(U_2023)
      | ~ class_Int_Onumber(U_2023) ),
    inference(definitional_conversion,[status(esa)],[f_689_2]) ).

cnf(f_689_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2023),c_Int_Onumber__class_Onumber__of(U_2023,U_2024)),c_Groups_Oplus__class_Oplus(U_2023,U_2025,U_2026)) = c_Groups_Oplus__class_Oplus(U_2023,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2023),c_Int_Onumber__class_Onumber__of(U_2023,U_2024)),U_2025),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2023),c_Int_Onumber__class_Onumber__of(U_2023,U_2024)),U_2026))
    | ~ class_Rings_Osemiring(U_2023)
    | ~ class_Int_Onumber(U_2023) ),
    inference(clausify,[status(thm)],[f_689_3]) ).

fof(f_690_1,plain,
    ! [V_za_2,V_wa_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_wa_2,V_za_2)
        | ! [B_n] : V_za_2 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_wa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)) )
      & ( ? [B_n] : V_za_2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_wa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_wa_2,V_za_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_zle__iff__zadd]) ).

fof(f_690_2,plain,
    ! [U_2030,U_2029] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2029,U_2030)
        | ! [U_2028] : U_2030 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2029,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2028)) )
      & ( ? [U_2027] : U_2030 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2029,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2027))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2029,U_2030) ) ),
    inference(variable_rename,[status(thm)],[f_690_1]) ).

fof(f_690_3,plain,
    ( ! [U_2034,U_2032] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2032,U_2034)
        | ! [U_2028] : U_2034 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2032,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2028)) )
    & ! [U_2033,U_2031] :
        ( ? [U_2027] : U_2033 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2031,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2027))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2031,U_2033) ) ),
    inference(miniscope,[status(thm)],[f_690_2]) ).

fof(f_690_4,plain,
    ( ! [U_2034,U_2032] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2032,U_2034)
        | ! [U_2028] : U_2034 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2032,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2028)) )
    & ! [U_2033,U_2031] :
        ( U_2033 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2031,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK59(U_2033,U_2031)))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2031,U_2033) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_2027,sK59(U_2033,U_2031))],[f_690_3]) ).

fof(f_690_5,plain,
    ( ! [U_2032,U_2034,U_2028] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2032,U_2034)
        | U_2034 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2032,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2028)) )
    & ! [U_2031,U_2033] :
        ( U_2033 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2031,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK59(U_2033,U_2031)))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2031,U_2033) ) ),
    inference(definitional_conversion,[status(esa)],[f_690_4]) ).

cnf(f_690_6,plain,
    ( U_2033 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2031,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK59(U_2033,U_2031)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2031,U_2033) ),
    inference(clausify,[status(thm)],[f_690_5]) ).

cnf(f_690_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2032,U_2034)
    | U_2034 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2032,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2028)) ),
    inference(clausify,[status(thm)],[f_690_5]) ).

fof(f_691_1,plain,
    ! [V_y,V_x] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_y)),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J]) ).

fof(f_691_2,plain,
    ! [U_2036,U_2035] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2035),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2036)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2035,U_2036)),
    inference(variable_rename,[status(thm)],[f_691_1]) ).

fof(f_691_3,plain,
    ! [U_2036,U_2035] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2035),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2036)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2035,U_2036)),
    inference(definitional_conversion,[status(esa)],[f_691_2]) ).

cnf(f_691_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2035),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2036)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2035,U_2036)),
    inference(clausify,[status(thm)],[f_691_3]) ).

fof(f_692_1,plain,
    ! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),
    inference(fof_nnf,[status(thm)],[fact_zadd__int]) ).

fof(f_692_2,plain,
    ! [U_2038,U_2037] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2037),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2038)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2037,U_2038)),
    inference(variable_rename,[status(thm)],[f_692_1]) ).

fof(f_692_3,plain,
    ! [U_2037,U_2038] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2037),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2038)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2037,U_2038)),
    inference(definitional_conversion,[status(esa)],[f_692_2]) ).

cnf(f_692_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2037),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2038)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2037,U_2038)),
    inference(clausify,[status(thm)],[f_692_3]) ).

fof(f_693_1,plain,
    ! [V_z,V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n),V_z)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),V_z),
    inference(fof_nnf,[status(thm)],[fact_zadd__int__left]) ).

fof(f_693_2,plain,
    ! [U_2041,U_2040,U_2039] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2039),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2040),U_2041)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2039,U_2040)),U_2041),
    inference(variable_rename,[status(thm)],[f_693_1]) ).

fof(f_693_3,plain,
    ! [U_2039,U_2040,U_2041] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2039),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2040),U_2041)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2039,U_2040)),U_2041),
    inference(definitional_conversion,[status(esa)],[f_693_2]) ).

cnf(f_693_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2039),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2040),U_2041)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2039,U_2040)),U_2041),
    inference(clausify,[status(thm)],[f_693_3]) ).

fof(f_694_1,plain,
    ! [V_da_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
      ( ( ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_da_2)
          | V_c_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_a_2)),V_e_2),V_da_2) )
        & ( V_c_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_a_2)),V_e_2),V_da_2)
          | c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2) != c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_da_2) ) )
      | ~ class_Rings_Oring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_eq__add__iff2]) ).

fof(f_694_2,plain,
    ! [U_2047,U_2046,U_2045,U_2044,U_2043,U_2042] :
      ( ( ( c_Groups_Oplus__class_Oplus(U_2042,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2042),U_2043),U_2044),U_2045) = c_Groups_Oplus__class_Oplus(U_2042,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2042),U_2046),U_2044),U_2047)
          | U_2045 != c_Groups_Oplus__class_Oplus(U_2042,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2042),c_Groups_Ominus__class_Ominus(U_2042,U_2046,U_2043)),U_2044),U_2047) )
        & ( U_2045 = c_Groups_Oplus__class_Oplus(U_2042,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2042),c_Groups_Ominus__class_Ominus(U_2042,U_2046,U_2043)),U_2044),U_2047)
          | c_Groups_Oplus__class_Oplus(U_2042,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2042),U_2043),U_2044),U_2045) != c_Groups_Oplus__class_Oplus(U_2042,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2042),U_2046),U_2044),U_2047) ) )
      | ~ class_Rings_Oring(U_2042) ),
    inference(variable_rename,[status(thm)],[f_694_1]) ).

fof(f_694_3,plain,
    ( ! [U_2042,U_2043,U_2044,U_2045,U_2046,U_2047] :
        ( c_Groups_Oplus__class_Oplus(U_2042,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2042),U_2043),U_2044),U_2045) = c_Groups_Oplus__class_Oplus(U_2042,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2042),U_2046),U_2044),U_2047)
        | U_2045 != c_Groups_Oplus__class_Oplus(U_2042,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2042),c_Groups_Ominus__class_Ominus(U_2042,U_2046,U_2043)),U_2044),U_2047)
        | ~ sP176(U_2042,U_2043,U_2044,U_2045,U_2046,U_2047) )
    & ! [U_2042,U_2043,U_2044,U_2045,U_2046,U_2047] :
        ( U_2045 = c_Groups_Oplus__class_Oplus(U_2042,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2042),c_Groups_Ominus__class_Ominus(U_2042,U_2046,U_2043)),U_2044),U_2047)
        | c_Groups_Oplus__class_Oplus(U_2042,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2042),U_2043),U_2044),U_2045) != c_Groups_Oplus__class_Oplus(U_2042,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2042),U_2046),U_2044),U_2047)
        | ~ sP176(U_2042,U_2043,U_2044,U_2045,U_2046,U_2047) )
    & ! [U_2042,U_2043,U_2044,U_2045,U_2046,U_2047] :
        ( sP176(U_2042,U_2043,U_2044,U_2045,U_2046,U_2047)
        | ~ class_Rings_Oring(U_2042) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP176])],[f_694_2]) ).

cnf(f_694_4,plain,
    ( sP176(U_2042,U_2043,U_2044,U_2045,U_2046,U_2047)
    | ~ class_Rings_Oring(U_2042) ),
    inference(clausify,[status(thm)],[f_694_3]) ).

cnf(f_694_5,plain,
    ( U_2045 = c_Groups_Oplus__class_Oplus(U_2042,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2042),c_Groups_Ominus__class_Ominus(U_2042,U_2046,U_2043)),U_2044),U_2047)
    | c_Groups_Oplus__class_Oplus(U_2042,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2042),U_2043),U_2044),U_2045) != c_Groups_Oplus__class_Oplus(U_2042,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2042),U_2046),U_2044),U_2047)
    | ~ sP176(U_2042,U_2043,U_2044,U_2045,U_2046,U_2047) ),
    inference(clausify,[status(thm)],[f_694_3]) ).

cnf(f_694_6,plain,
    ( c_Groups_Oplus__class_Oplus(U_2042,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2042),U_2043),U_2044),U_2045) = c_Groups_Oplus__class_Oplus(U_2042,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2042),U_2046),U_2044),U_2047)
    | U_2045 != c_Groups_Oplus__class_Oplus(U_2042,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2042),c_Groups_Ominus__class_Ominus(U_2042,U_2046,U_2043)),U_2044),U_2047)
    | ~ sP176(U_2042,U_2043,U_2044,U_2045,U_2046,U_2047) ),
    inference(clausify,[status(thm)],[f_694_3]) ).

fof(f_695_1,plain,
    ! [V_da_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
      ( ( ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_da_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_a_2,V_b_2)),V_e_2),V_c_2) != V_da_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_a_2,V_b_2)),V_e_2),V_c_2) = V_da_2
          | c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2) != c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_da_2) ) )
      | ~ class_Rings_Oring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_eq__add__iff1]) ).

fof(f_695_2,plain,
    ! [U_2053,U_2052,U_2051,U_2050,U_2049,U_2048] :
      ( ( ( c_Groups_Oplus__class_Oplus(U_2048,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2048),U_2049),U_2050),U_2051) = c_Groups_Oplus__class_Oplus(U_2048,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2048),U_2052),U_2050),U_2053)
          | c_Groups_Oplus__class_Oplus(U_2048,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2048),c_Groups_Ominus__class_Ominus(U_2048,U_2049,U_2052)),U_2050),U_2051) != U_2053 )
        & ( c_Groups_Oplus__class_Oplus(U_2048,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2048),c_Groups_Ominus__class_Ominus(U_2048,U_2049,U_2052)),U_2050),U_2051) = U_2053
          | c_Groups_Oplus__class_Oplus(U_2048,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2048),U_2049),U_2050),U_2051) != c_Groups_Oplus__class_Oplus(U_2048,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2048),U_2052),U_2050),U_2053) ) )
      | ~ class_Rings_Oring(U_2048) ),
    inference(variable_rename,[status(thm)],[f_695_1]) ).

fof(f_695_3,plain,
    ( ! [U_2050,U_2048,U_2049,U_2051,U_2052,U_2053] :
        ( c_Groups_Oplus__class_Oplus(U_2048,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2048),U_2049),U_2050),U_2051) = c_Groups_Oplus__class_Oplus(U_2048,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2048),U_2052),U_2050),U_2053)
        | c_Groups_Oplus__class_Oplus(U_2048,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2048),c_Groups_Ominus__class_Ominus(U_2048,U_2049,U_2052)),U_2050),U_2051) != U_2053
        | ~ sP177(U_2050,U_2048,U_2049,U_2051,U_2052,U_2053) )
    & ! [U_2050,U_2048,U_2049,U_2051,U_2052,U_2053] :
        ( c_Groups_Oplus__class_Oplus(U_2048,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2048),c_Groups_Ominus__class_Ominus(U_2048,U_2049,U_2052)),U_2050),U_2051) = U_2053
        | c_Groups_Oplus__class_Oplus(U_2048,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2048),U_2049),U_2050),U_2051) != c_Groups_Oplus__class_Oplus(U_2048,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2048),U_2052),U_2050),U_2053)
        | ~ sP177(U_2050,U_2048,U_2049,U_2051,U_2052,U_2053) )
    & ! [U_2050,U_2048,U_2049,U_2051,U_2052,U_2053] :
        ( sP177(U_2050,U_2048,U_2049,U_2051,U_2052,U_2053)
        | ~ class_Rings_Oring(U_2048) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP177])],[f_695_2]) ).

cnf(f_695_4,plain,
    ( sP177(U_2050,U_2048,U_2049,U_2051,U_2052,U_2053)
    | ~ class_Rings_Oring(U_2048) ),
    inference(clausify,[status(thm)],[f_695_3]) ).

cnf(f_695_5,plain,
    ( c_Groups_Oplus__class_Oplus(U_2048,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2048),c_Groups_Ominus__class_Ominus(U_2048,U_2049,U_2052)),U_2050),U_2051) = U_2053
    | c_Groups_Oplus__class_Oplus(U_2048,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2048),U_2049),U_2050),U_2051) != c_Groups_Oplus__class_Oplus(U_2048,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2048),U_2052),U_2050),U_2053)
    | ~ sP177(U_2050,U_2048,U_2049,U_2051,U_2052,U_2053) ),
    inference(clausify,[status(thm)],[f_695_3]) ).

cnf(f_695_6,plain,
    ( c_Groups_Oplus__class_Oplus(U_2048,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2048),U_2049),U_2050),U_2051) = c_Groups_Oplus__class_Oplus(U_2048,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2048),U_2052),U_2050),U_2053)
    | c_Groups_Oplus__class_Oplus(U_2048,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2048),c_Groups_Ominus__class_Ominus(U_2048,U_2049,U_2052)),U_2050),U_2051) != U_2053
    | ~ sP177(U_2050,U_2048,U_2049,U_2051,U_2052,U_2053) ),
    inference(clausify,[status(thm)],[f_695_3]) ).

fof(f_696_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_696_2,plain,
    ! [U_2058,U_2057,U_2056,U_2055,U_2054] :
      ( c_Groups_Ominus__class_Ominus(U_2054,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2054),U_2055),U_2056),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2054),U_2057),U_2058)) = c_Groups_Oplus__class_Oplus(U_2054,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2054),U_2055),c_Groups_Ominus__class_Ominus(U_2054,U_2056,U_2058)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2054),c_Groups_Ominus__class_Ominus(U_2054,U_2055,U_2057)),U_2058))
      | ~ class_Rings_Oring(U_2054) ),
    inference(variable_rename,[status(thm)],[f_696_1]) ).

fof(f_696_3,plain,
    ! [U_2056,U_2057,U_2054,U_2055,U_2058] :
      ( c_Groups_Ominus__class_Ominus(U_2054,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2054),U_2055),U_2056),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2054),U_2057),U_2058)) = c_Groups_Oplus__class_Oplus(U_2054,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2054),U_2055),c_Groups_Ominus__class_Ominus(U_2054,U_2056,U_2058)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2054),c_Groups_Ominus__class_Ominus(U_2054,U_2055,U_2057)),U_2058))
      | ~ class_Rings_Oring(U_2054) ),
    inference(definitional_conversion,[status(esa)],[f_696_2]) ).

cnf(f_696_4,plain,
    ( c_Groups_Ominus__class_Ominus(U_2054,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2054),U_2055),U_2056),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2054),U_2057),U_2058)) = c_Groups_Oplus__class_Oplus(U_2054,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2054),U_2055),c_Groups_Ominus__class_Ominus(U_2054,U_2056,U_2058)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2054),c_Groups_Ominus__class_Ominus(U_2054,U_2055,U_2057)),U_2058))
    | ~ class_Rings_Oring(U_2054) ),
    inference(clausify,[status(thm)],[f_696_3]) ).

fof(f_697_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_697_2,plain,
    ! [U_2063,U_2062,U_2061,U_2060,U_2059] :
      ( c_Groups_Ominus__class_Ominus(U_2059,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2059),U_2060),U_2061),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2059),U_2062),U_2063)) = c_Groups_Oplus__class_Oplus(U_2059,c_Groups_Oplus__class_Oplus(U_2059,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2059),c_Groups_Ominus__class_Ominus(U_2059,U_2060,U_2062)),c_Groups_Ominus__class_Ominus(U_2059,U_2061,U_2063)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2059),c_Groups_Ominus__class_Ominus(U_2059,U_2060,U_2062)),U_2063)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2059),U_2062),c_Groups_Ominus__class_Ominus(U_2059,U_2061,U_2063)))
      | ~ class_RealVector_Oreal__normed__algebra(U_2059) ),
    inference(variable_rename,[status(thm)],[f_697_1]) ).

fof(f_697_3,plain,
    ! [U_2059,U_2060,U_2061,U_2062,U_2063] :
      ( c_Groups_Ominus__class_Ominus(U_2059,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2059),U_2060),U_2061),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2059),U_2062),U_2063)) = c_Groups_Oplus__class_Oplus(U_2059,c_Groups_Oplus__class_Oplus(U_2059,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2059),c_Groups_Ominus__class_Ominus(U_2059,U_2060,U_2062)),c_Groups_Ominus__class_Ominus(U_2059,U_2061,U_2063)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2059),c_Groups_Ominus__class_Ominus(U_2059,U_2060,U_2062)),U_2063)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2059),U_2062),c_Groups_Ominus__class_Ominus(U_2059,U_2061,U_2063)))
      | ~ class_RealVector_Oreal__normed__algebra(U_2059) ),
    inference(definitional_conversion,[status(esa)],[f_697_2]) ).

cnf(f_697_4,plain,
    ( c_Groups_Ominus__class_Ominus(U_2059,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2059),U_2060),U_2061),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2059),U_2062),U_2063)) = c_Groups_Oplus__class_Oplus(U_2059,c_Groups_Oplus__class_Oplus(U_2059,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2059),c_Groups_Ominus__class_Ominus(U_2059,U_2060,U_2062)),c_Groups_Ominus__class_Ominus(U_2059,U_2061,U_2063)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2059),c_Groups_Ominus__class_Ominus(U_2059,U_2060,U_2062)),U_2063)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2059),U_2062),c_Groups_Ominus__class_Ominus(U_2059,U_2061,U_2063)))
    | ~ class_RealVector_Oreal__normed__algebra(U_2059) ),
    inference(clausify,[status(thm)],[f_697_3]) ).

fof(f_698_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_698_2,plain,
    ! [U_2065,U_2064] :
      ( c_Groups_Oplus__class_Oplus(U_2064,U_2065,U_2065) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2064),c_Groups_Oplus__class_Oplus(U_2064,c_Groups_Oone__class_Oone(U_2064),c_Groups_Oone__class_Oone(U_2064))),U_2065)
      | ~ class_Rings_Ocomm__semiring__1(U_2064) ),
    inference(variable_rename,[status(thm)],[f_698_1]) ).

fof(f_698_3,plain,
    ! [U_2064,U_2065] :
      ( c_Groups_Oplus__class_Oplus(U_2064,U_2065,U_2065) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2064),c_Groups_Oplus__class_Oplus(U_2064,c_Groups_Oone__class_Oone(U_2064),c_Groups_Oone__class_Oone(U_2064))),U_2065)
      | ~ class_Rings_Ocomm__semiring__1(U_2064) ),
    inference(definitional_conversion,[status(esa)],[f_698_2]) ).

cnf(f_698_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_2064,U_2065,U_2065) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2064),c_Groups_Oplus__class_Oplus(U_2064,c_Groups_Oone__class_Oone(U_2064),c_Groups_Oone__class_Oone(U_2064))),U_2065)
    | ~ class_Rings_Ocomm__semiring__1(U_2064) ),
    inference(clausify,[status(thm)],[f_698_3]) ).

fof(f_699_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_699_2,plain,
    ! [U_2068,U_2067,U_2066] :
      ( c_Groups_Oplus__class_Oplus(U_2066,U_2067,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2066),U_2068),U_2067)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2066),c_Groups_Oplus__class_Oplus(U_2066,U_2068,c_Groups_Oone__class_Oone(U_2066))),U_2067)
      | ~ class_Rings_Ocomm__semiring__1(U_2066) ),
    inference(variable_rename,[status(thm)],[f_699_1]) ).

fof(f_699_3,plain,
    ! [U_2066,U_2067,U_2068] :
      ( c_Groups_Oplus__class_Oplus(U_2066,U_2067,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2066),U_2068),U_2067)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2066),c_Groups_Oplus__class_Oplus(U_2066,U_2068,c_Groups_Oone__class_Oone(U_2066))),U_2067)
      | ~ class_Rings_Ocomm__semiring__1(U_2066) ),
    inference(definitional_conversion,[status(esa)],[f_699_2]) ).

cnf(f_699_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_2066,U_2067,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2066),U_2068),U_2067)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2066),c_Groups_Oplus__class_Oplus(U_2066,U_2068,c_Groups_Oone__class_Oone(U_2066))),U_2067)
    | ~ class_Rings_Ocomm__semiring__1(U_2066) ),
    inference(clausify,[status(thm)],[f_699_3]) ).

fof(f_700_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_700_2,plain,
    ! [U_2071,U_2070,U_2069] :
      ( c_Groups_Oplus__class_Oplus(U_2069,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2069),U_2070),U_2071),U_2071) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2069),c_Groups_Oplus__class_Oplus(U_2069,U_2070,c_Groups_Oone__class_Oone(U_2069))),U_2071)
      | ~ class_Rings_Ocomm__semiring__1(U_2069) ),
    inference(variable_rename,[status(thm)],[f_700_1]) ).

fof(f_700_3,plain,
    ! [U_2069,U_2070,U_2071] :
      ( c_Groups_Oplus__class_Oplus(U_2069,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2069),U_2070),U_2071),U_2071) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2069),c_Groups_Oplus__class_Oplus(U_2069,U_2070,c_Groups_Oone__class_Oone(U_2069))),U_2071)
      | ~ class_Rings_Ocomm__semiring__1(U_2069) ),
    inference(definitional_conversion,[status(esa)],[f_700_2]) ).

cnf(f_700_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_2069,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2069),U_2070),U_2071),U_2071) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2069),c_Groups_Oplus__class_Oplus(U_2069,U_2070,c_Groups_Oone__class_Oone(U_2069))),U_2071)
    | ~ class_Rings_Ocomm__semiring__1(U_2069) ),
    inference(clausify,[status(thm)],[f_700_3]) ).

fof(f_701_1,plain,
    ! [V_c,V_b,V_v,T_b] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)),c_Groups_Ominus__class_Ominus(T_b,V_b,V_c)) = c_Groups_Ominus__class_Ominus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)),V_c))
      | ~ class_Rings_Oring(T_b)
      | ~ class_Int_Onumber(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_right__diff__distrib__number__of]) ).

fof(f_701_2,plain,
    ! [U_2075,U_2074,U_2073,U_2072] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2072),c_Int_Onumber__class_Onumber__of(U_2072,U_2073)),c_Groups_Ominus__class_Ominus(U_2072,U_2074,U_2075)) = c_Groups_Ominus__class_Ominus(U_2072,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2072),c_Int_Onumber__class_Onumber__of(U_2072,U_2073)),U_2074),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2072),c_Int_Onumber__class_Onumber__of(U_2072,U_2073)),U_2075))
      | ~ class_Rings_Oring(U_2072)
      | ~ class_Int_Onumber(U_2072) ),
    inference(variable_rename,[status(thm)],[f_701_1]) ).

fof(f_701_3,plain,
    ! [U_2072,U_2073,U_2074,U_2075] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2072),c_Int_Onumber__class_Onumber__of(U_2072,U_2073)),c_Groups_Ominus__class_Ominus(U_2072,U_2074,U_2075)) = c_Groups_Ominus__class_Ominus(U_2072,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2072),c_Int_Onumber__class_Onumber__of(U_2072,U_2073)),U_2074),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2072),c_Int_Onumber__class_Onumber__of(U_2072,U_2073)),U_2075))
      | ~ class_Rings_Oring(U_2072)
      | ~ class_Int_Onumber(U_2072) ),
    inference(definitional_conversion,[status(esa)],[f_701_2]) ).

cnf(f_701_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2072),c_Int_Onumber__class_Onumber__of(U_2072,U_2073)),c_Groups_Ominus__class_Ominus(U_2072,U_2074,U_2075)) = c_Groups_Ominus__class_Ominus(U_2072,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2072),c_Int_Onumber__class_Onumber__of(U_2072,U_2073)),U_2074),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2072),c_Int_Onumber__class_Onumber__of(U_2072,U_2073)),U_2075))
    | ~ class_Rings_Oring(U_2072)
    | ~ class_Int_Onumber(U_2072) ),
    inference(clausify,[status(thm)],[f_701_3]) ).

fof(f_702_1,plain,
    ! [V_v,V_b,V_a,T_b] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Groups_Ominus__class_Ominus(T_b,V_a,V_b)),c_Int_Onumber__class_Onumber__of(T_b,V_v)) = c_Groups_Ominus__class_Ominus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),c_Int_Onumber__class_Onumber__of(T_b,V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)))
      | ~ class_Rings_Oring(T_b)
      | ~ class_Int_Onumber(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_left__diff__distrib__number__of]) ).

fof(f_702_2,plain,
    ! [U_2079,U_2078,U_2077,U_2076] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2076),c_Groups_Ominus__class_Ominus(U_2076,U_2077,U_2078)),c_Int_Onumber__class_Onumber__of(U_2076,U_2079)) = c_Groups_Ominus__class_Ominus(U_2076,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2076),U_2077),c_Int_Onumber__class_Onumber__of(U_2076,U_2079)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2076),U_2078),c_Int_Onumber__class_Onumber__of(U_2076,U_2079)))
      | ~ class_Rings_Oring(U_2076)
      | ~ class_Int_Onumber(U_2076) ),
    inference(variable_rename,[status(thm)],[f_702_1]) ).

fof(f_702_3,plain,
    ! [U_2077,U_2076,U_2078,U_2079] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2076),c_Groups_Ominus__class_Ominus(U_2076,U_2077,U_2078)),c_Int_Onumber__class_Onumber__of(U_2076,U_2079)) = c_Groups_Ominus__class_Ominus(U_2076,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2076),U_2077),c_Int_Onumber__class_Onumber__of(U_2076,U_2079)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2076),U_2078),c_Int_Onumber__class_Onumber__of(U_2076,U_2079)))
      | ~ class_Rings_Oring(U_2076)
      | ~ class_Int_Onumber(U_2076) ),
    inference(definitional_conversion,[status(esa)],[f_702_2]) ).

cnf(f_702_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2076),c_Groups_Ominus__class_Ominus(U_2076,U_2077,U_2078)),c_Int_Onumber__class_Onumber__of(U_2076,U_2079)) = c_Groups_Ominus__class_Ominus(U_2076,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2076),U_2077),c_Int_Onumber__class_Onumber__of(U_2076,U_2079)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2076),U_2078),c_Int_Onumber__class_Onumber__of(U_2076,U_2079)))
    | ~ class_Rings_Oring(U_2076)
    | ~ class_Int_Onumber(U_2076) ),
    inference(clausify,[status(thm)],[f_702_3]) ).

fof(f_703_1,plain,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__numerals_I2_J]) ).

fof(f_703_2,plain,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_703_1]) ).

cnf(f_703_3,plain,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_703_2]) ).

fof(f_704_1,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_int__1]) ).

fof(f_704_2,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_704_1]) ).

cnf(f_704_3,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_704_2]) ).

fof(f_705_1,plain,
    ! [V_d,V_b,V_c,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d))
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_b),V_d)
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_c)
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__mult__less]) ).

fof(f_705_2,plain,
    ! [U_2084,U_2083,U_2082,U_2081,U_2080] :
      ( c_Orderings_Oord__class_Oless(U_2080,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2080),c_Groups_Oabs__class_Oabs(U_2080,U_2081)),c_Groups_Oabs__class_Oabs(U_2080,U_2083)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2080),U_2082),U_2084))
      | ~ c_Orderings_Oord__class_Oless(U_2080,c_Groups_Oabs__class_Oabs(U_2080,U_2083),U_2084)
      | ~ c_Orderings_Oord__class_Oless(U_2080,c_Groups_Oabs__class_Oabs(U_2080,U_2081),U_2082)
      | ~ class_Rings_Olinordered__idom(U_2080) ),
    inference(variable_rename,[status(thm)],[f_705_1]) ).

fof(f_705_3,plain,
    ! [U_2081,U_2080,U_2082,U_2083,U_2084] :
      ( c_Orderings_Oord__class_Oless(U_2080,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2080),c_Groups_Oabs__class_Oabs(U_2080,U_2081)),c_Groups_Oabs__class_Oabs(U_2080,U_2083)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2080),U_2082),U_2084))
      | ~ c_Orderings_Oord__class_Oless(U_2080,c_Groups_Oabs__class_Oabs(U_2080,U_2083),U_2084)
      | ~ c_Orderings_Oord__class_Oless(U_2080,c_Groups_Oabs__class_Oabs(U_2080,U_2081),U_2082)
      | ~ class_Rings_Olinordered__idom(U_2080) ),
    inference(definitional_conversion,[status(esa)],[f_705_2]) ).

cnf(f_705_4,plain,
    ( c_Orderings_Oord__class_Oless(U_2080,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2080),c_Groups_Oabs__class_Oabs(U_2080,U_2081)),c_Groups_Oabs__class_Oabs(U_2080,U_2083)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2080),U_2082),U_2084))
    | ~ c_Orderings_Oord__class_Oless(U_2080,c_Groups_Oabs__class_Oabs(U_2080,U_2083),U_2084)
    | ~ c_Orderings_Oord__class_Oless(U_2080,c_Groups_Oabs__class_Oabs(U_2080,U_2081),U_2082)
    | ~ class_Rings_Olinordered__idom(U_2080) ),
    inference(clausify,[status(thm)],[f_705_3]) ).

fof(f_706_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_706_2,plain,
    ! [U_2086,U_2085] :
      ( 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_2085),U_2086))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2086)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2085) ),
    inference(variable_rename,[status(thm)],[f_706_1]) ).

fof(f_706_3,plain,
    ! [U_2086,U_2085] :
      ( 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_2085),U_2086))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2086)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2085) ),
    inference(definitional_conversion,[status(esa)],[f_706_2]) ).

cnf(f_706_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_2085),U_2086))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2086)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2085) ),
    inference(clausify,[status(thm)],[f_706_3]) ).

fof(f_707_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_707_2,plain,
    ! [U_2089,U_2088,U_2087] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2089),U_2087),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2089),U_2088))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2089)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2087,U_2088) ),
    inference(variable_rename,[status(thm)],[f_707_1]) ).

fof(f_707_3,plain,
    ! [U_2087,U_2088,U_2089] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2089),U_2087),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2089),U_2088))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2089)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2087,U_2088) ),
    inference(definitional_conversion,[status(esa)],[f_707_2]) ).

cnf(f_707_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2089),U_2087),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2089),U_2088))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2089)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2087,U_2088) ),
    inference(clausify,[status(thm)],[f_707_3]) ).

fof(f_708_1,plain,
    ! [V_n,V_m] :
      ( c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(fof_nnf,[status(thm)],[fact_abs__zmult__eq__1]) ).

fof(f_708_2,plain,
    ! [U_2091,U_2090] :
      ( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2090) = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2090),U_2091)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_708_1]) ).

fof(f_708_3,plain,
    ! [U_2091,U_2090] :
      ( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2090) = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2090),U_2091)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(definitional_conversion,[status(esa)],[f_708_2]) ).

cnf(f_708_4,plain,
    ( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2090) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2090),U_2091)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_708_3]) ).

fof(f_709_1,plain,
    ! [V_y,V_x] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_x,V_y)),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J]) ).

fof(f_709_2,plain,
    ! [U_2093,U_2092] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2092),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2093)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2092,U_2093)),
    inference(variable_rename,[status(thm)],[f_709_1]) ).

fof(f_709_3,plain,
    ! [U_2092,U_2093] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2092),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2093)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2092,U_2093)),
    inference(definitional_conversion,[status(esa)],[f_709_2]) ).

cnf(f_709_4,plain,
    c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2092),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2093)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2092,U_2093)),
    inference(clausify,[status(thm)],[f_709_3]) ).

fof(f_710_1,plain,
    ! [V_m,T_a] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Nat_OSuc(V_m)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m))
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__Suc]) ).

fof(f_710_2,plain,
    ! [U_2095,U_2094] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2094),c_Nat_OSuc(U_2095)) = c_Groups_Oplus__class_Oplus(U_2094,c_Groups_Oone__class_Oone(U_2094),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2094),U_2095))
      | ~ class_Rings_Osemiring__1(U_2094) ),
    inference(variable_rename,[status(thm)],[f_710_1]) ).

fof(f_710_3,plain,
    ! [U_2094,U_2095] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2094),c_Nat_OSuc(U_2095)) = c_Groups_Oplus__class_Oplus(U_2094,c_Groups_Oone__class_Oone(U_2094),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2094),U_2095))
      | ~ class_Rings_Osemiring__1(U_2094) ),
    inference(definitional_conversion,[status(esa)],[f_710_2]) ).

cnf(f_710_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2094),c_Nat_OSuc(U_2095)) = c_Groups_Oplus__class_Oplus(U_2094,c_Groups_Oone__class_Oone(U_2094),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2094),U_2095))
    | ~ class_Rings_Osemiring__1(U_2094) ),
    inference(clausify,[status(thm)],[f_710_3]) ).

fof(f_711_1,plain,
    ! [V_m,V_n,T_a] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Ominus__class_Ominus(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__diff]) ).

fof(f_711_2,plain,
    ! [U_2098,U_2097,U_2096] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2096),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2098,U_2097)) = c_Groups_Ominus__class_Ominus(U_2096,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2096),U_2098),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2096),U_2097))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2097,U_2098)
      | ~ class_Rings_Oring__1(U_2096) ),
    inference(variable_rename,[status(thm)],[f_711_1]) ).

fof(f_711_3,plain,
    ! [U_2096,U_2097,U_2098] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2096),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2098,U_2097)) = c_Groups_Ominus__class_Ominus(U_2096,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2096),U_2098),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2096),U_2097))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2097,U_2098)
      | ~ class_Rings_Oring__1(U_2096) ),
    inference(definitional_conversion,[status(esa)],[f_711_2]) ).

cnf(f_711_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2096),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2098,U_2097)) = c_Groups_Ominus__class_Ominus(U_2096,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2096),U_2098),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2096),U_2097))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2097,U_2098)
    | ~ class_Rings_Oring__1(U_2096) ),
    inference(clausify,[status(thm)],[f_711_3]) ).

fof(f_712_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) )
        & ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)) ) )
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__pos]) ).

fof(f_712_2,plain,
    ! [U_2102,U_2101,U_2100,U_2099] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_2099,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2099),U_2100),U_2101),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2099),U_2100),U_2102))
          | ~ c_Orderings_Oord__class_Oless__eq(U_2099,U_2101,U_2102) )
        & ( c_Orderings_Oord__class_Oless__eq(U_2099,U_2101,U_2102)
          | ~ c_Orderings_Oord__class_Oless__eq(U_2099,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2099),U_2100),U_2101),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2099),U_2100),U_2102)) ) )
      | ~ c_Orderings_Oord__class_Oless(U_2099,c_Groups_Ozero__class_Ozero(U_2099),U_2100)
      | ~ class_Rings_Olinordered__ring__strict(U_2099) ),
    inference(variable_rename,[status(thm)],[f_712_1]) ).

fof(f_712_3,plain,
    ( ! [U_2099,U_2100,U_2101,U_2102] :
        ( c_Orderings_Oord__class_Oless__eq(U_2099,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2099),U_2100),U_2101),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2099),U_2100),U_2102))
        | ~ c_Orderings_Oord__class_Oless__eq(U_2099,U_2101,U_2102)
        | ~ sP178(U_2099,U_2100,U_2101,U_2102) )
    & ! [U_2099,U_2100,U_2101,U_2102] :
        ( c_Orderings_Oord__class_Oless__eq(U_2099,U_2101,U_2102)
        | ~ c_Orderings_Oord__class_Oless__eq(U_2099,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2099),U_2100),U_2101),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2099),U_2100),U_2102))
        | ~ sP178(U_2099,U_2100,U_2101,U_2102) )
    & ! [U_2099,U_2100,U_2101,U_2102] :
        ( sP178(U_2099,U_2100,U_2101,U_2102)
        | ~ c_Orderings_Oord__class_Oless(U_2099,c_Groups_Ozero__class_Ozero(U_2099),U_2100)
        | ~ class_Rings_Olinordered__ring__strict(U_2099) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP178])],[f_712_2]) ).

cnf(f_712_4,plain,
    ( sP178(U_2099,U_2100,U_2101,U_2102)
    | ~ c_Orderings_Oord__class_Oless(U_2099,c_Groups_Ozero__class_Ozero(U_2099),U_2100)
    | ~ class_Rings_Olinordered__ring__strict(U_2099) ),
    inference(clausify,[status(thm)],[f_712_3]) ).

cnf(f_712_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2099,U_2101,U_2102)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2099,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2099),U_2100),U_2101),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2099),U_2100),U_2102))
    | ~ sP178(U_2099,U_2100,U_2101,U_2102) ),
    inference(clausify,[status(thm)],[f_712_3]) ).

cnf(f_712_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2099,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2099),U_2100),U_2101),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2099),U_2100),U_2102))
    | ~ c_Orderings_Oord__class_Oless__eq(U_2099,U_2101,U_2102)
    | ~ sP178(U_2099,U_2100,U_2101,U_2102) ),
    inference(clausify,[status(thm)],[f_712_3]) ).

fof(f_713_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_a_2) )
        & ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_a_2)
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)) ) )
      | ~ c_Orderings_Oord__class_Oless(T_a,V_c_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_713_2,plain,
    ! [U_2106,U_2105,U_2104,U_2103] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_2103,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2103),U_2104),U_2105),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2103),U_2104),U_2106))
          | ~ c_Orderings_Oord__class_Oless__eq(U_2103,U_2106,U_2105) )
        & ( c_Orderings_Oord__class_Oless__eq(U_2103,U_2106,U_2105)
          | ~ c_Orderings_Oord__class_Oless__eq(U_2103,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2103),U_2104),U_2105),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2103),U_2104),U_2106)) ) )
      | ~ c_Orderings_Oord__class_Oless(U_2103,U_2104,c_Groups_Ozero__class_Ozero(U_2103))
      | ~ class_Rings_Olinordered__ring__strict(U_2103) ),
    inference(variable_rename,[status(thm)],[f_713_1]) ).

fof(f_713_3,plain,
    ( ! [U_2104,U_2103,U_2106,U_2105] :
        ( c_Orderings_Oord__class_Oless__eq(U_2103,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2103),U_2104),U_2105),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2103),U_2104),U_2106))
        | ~ c_Orderings_Oord__class_Oless__eq(U_2103,U_2106,U_2105)
        | ~ sP179(U_2104,U_2103,U_2106,U_2105) )
    & ! [U_2104,U_2103,U_2106,U_2105] :
        ( c_Orderings_Oord__class_Oless__eq(U_2103,U_2106,U_2105)
        | ~ c_Orderings_Oord__class_Oless__eq(U_2103,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2103),U_2104),U_2105),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2103),U_2104),U_2106))
        | ~ sP179(U_2104,U_2103,U_2106,U_2105) )
    & ! [U_2104,U_2103,U_2106,U_2105] :
        ( sP179(U_2104,U_2103,U_2106,U_2105)
        | ~ c_Orderings_Oord__class_Oless(U_2103,U_2104,c_Groups_Ozero__class_Ozero(U_2103))
        | ~ class_Rings_Olinordered__ring__strict(U_2103) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP179])],[f_713_2]) ).

cnf(f_713_4,plain,
    ( sP179(U_2104,U_2103,U_2106,U_2105)
    | ~ c_Orderings_Oord__class_Oless(U_2103,U_2104,c_Groups_Ozero__class_Ozero(U_2103))
    | ~ class_Rings_Olinordered__ring__strict(U_2103) ),
    inference(clausify,[status(thm)],[f_713_3]) ).

cnf(f_713_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2103,U_2106,U_2105)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2103,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2103),U_2104),U_2105),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2103),U_2104),U_2106))
    | ~ sP179(U_2104,U_2103,U_2106,U_2105) ),
    inference(clausify,[status(thm)],[f_713_3]) ).

cnf(f_713_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2103,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2103),U_2104),U_2105),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2103),U_2104),U_2106))
    | ~ c_Orderings_Oord__class_Oless__eq(U_2103,U_2106,U_2105)
    | ~ sP179(U_2104,U_2103,U_2106,U_2105) ),
    inference(clausify,[status(thm)],[f_713_3]) ).

fof(f_714_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_714_2,plain,
    ! [U_2111,U_2110,U_2109,U_2108,U_2107] :
      ( c_Orderings_Oord__class_Oless(U_2107,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2107),U_2108),U_2110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2107),U_2109),U_2111))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2107,c_Groups_Ozero__class_Ozero(U_2107),U_2110)
      | ~ c_Orderings_Oord__class_Oless(U_2107,c_Groups_Ozero__class_Ozero(U_2107),U_2109)
      | ~ c_Orderings_Oord__class_Oless(U_2107,U_2110,U_2111)
      | ~ c_Orderings_Oord__class_Oless(U_2107,U_2108,U_2109)
      | ~ class_Rings_Olinordered__semiring__strict(U_2107) ),
    inference(variable_rename,[status(thm)],[f_714_1]) ).

fof(f_714_3,plain,
    ! [U_2107,U_2108,U_2109,U_2110,U_2111] :
      ( c_Orderings_Oord__class_Oless(U_2107,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2107),U_2108),U_2110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2107),U_2109),U_2111))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2107,c_Groups_Ozero__class_Ozero(U_2107),U_2110)
      | ~ c_Orderings_Oord__class_Oless(U_2107,c_Groups_Ozero__class_Ozero(U_2107),U_2109)
      | ~ c_Orderings_Oord__class_Oless(U_2107,U_2110,U_2111)
      | ~ c_Orderings_Oord__class_Oless(U_2107,U_2108,U_2109)
      | ~ class_Rings_Olinordered__semiring__strict(U_2107) ),
    inference(definitional_conversion,[status(esa)],[f_714_2]) ).

cnf(f_714_4,plain,
    ( c_Orderings_Oord__class_Oless(U_2107,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2107),U_2108),U_2110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2107),U_2109),U_2111))
    | ~ c_Orderings_Oord__class_Oless__eq(U_2107,c_Groups_Ozero__class_Ozero(U_2107),U_2110)
    | ~ c_Orderings_Oord__class_Oless(U_2107,c_Groups_Ozero__class_Ozero(U_2107),U_2109)
    | ~ c_Orderings_Oord__class_Oless(U_2107,U_2110,U_2111)
    | ~ c_Orderings_Oord__class_Oless(U_2107,U_2108,U_2109)
    | ~ class_Rings_Olinordered__semiring__strict(U_2107) ),
    inference(clausify,[status(thm)],[f_714_3]) ).

fof(f_715_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_715_2,plain,
    ! [U_2116,U_2115,U_2114,U_2113,U_2112] :
      ( c_Orderings_Oord__class_Oless(U_2112,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2112),U_2113),U_2115),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2112),U_2114),U_2116))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2112,c_Groups_Ozero__class_Ozero(U_2112),U_2115)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2112,c_Groups_Ozero__class_Ozero(U_2112),U_2113)
      | ~ c_Orderings_Oord__class_Oless(U_2112,U_2115,U_2116)
      | ~ c_Orderings_Oord__class_Oless(U_2112,U_2113,U_2114)
      | ~ class_Rings_Olinordered__semiring__strict(U_2112) ),
    inference(variable_rename,[status(thm)],[f_715_1]) ).

fof(f_715_3,plain,
    ! [U_2114,U_2113,U_2116,U_2115,U_2112] :
      ( c_Orderings_Oord__class_Oless(U_2112,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2112),U_2113),U_2115),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2112),U_2114),U_2116))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2112,c_Groups_Ozero__class_Ozero(U_2112),U_2115)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2112,c_Groups_Ozero__class_Ozero(U_2112),U_2113)
      | ~ c_Orderings_Oord__class_Oless(U_2112,U_2115,U_2116)
      | ~ c_Orderings_Oord__class_Oless(U_2112,U_2113,U_2114)
      | ~ class_Rings_Olinordered__semiring__strict(U_2112) ),
    inference(definitional_conversion,[status(esa)],[f_715_2]) ).

cnf(f_715_4,plain,
    ( c_Orderings_Oord__class_Oless(U_2112,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2112),U_2113),U_2115),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2112),U_2114),U_2116))
    | ~ c_Orderings_Oord__class_Oless__eq(U_2112,c_Groups_Ozero__class_Ozero(U_2112),U_2115)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2112,c_Groups_Ozero__class_Ozero(U_2112),U_2113)
    | ~ c_Orderings_Oord__class_Oless(U_2112,U_2115,U_2116)
    | ~ c_Orderings_Oord__class_Oless(U_2112,U_2113,U_2114)
    | ~ class_Rings_Olinordered__semiring__strict(U_2112) ),
    inference(clausify,[status(thm)],[f_715_3]) ).

fof(f_716_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_716_2,plain,
    ! [U_2121,U_2120,U_2119,U_2118,U_2117] :
      ( c_Orderings_Oord__class_Oless(U_2117,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2117),U_2118),U_2120),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2117),U_2119),U_2121))
      | ~ c_Orderings_Oord__class_Oless(U_2117,c_Groups_Ozero__class_Ozero(U_2117),U_2120)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2117,c_Groups_Ozero__class_Ozero(U_2117),U_2118)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2117,U_2120,U_2121)
      | ~ c_Orderings_Oord__class_Oless(U_2117,U_2118,U_2119)
      | ~ class_Rings_Olinordered__semiring__strict(U_2117) ),
    inference(variable_rename,[status(thm)],[f_716_1]) ).

fof(f_716_3,plain,
    ! [U_2117,U_2119,U_2118,U_2121,U_2120] :
      ( c_Orderings_Oord__class_Oless(U_2117,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2117),U_2118),U_2120),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2117),U_2119),U_2121))
      | ~ c_Orderings_Oord__class_Oless(U_2117,c_Groups_Ozero__class_Ozero(U_2117),U_2120)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2117,c_Groups_Ozero__class_Ozero(U_2117),U_2118)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2117,U_2120,U_2121)
      | ~ c_Orderings_Oord__class_Oless(U_2117,U_2118,U_2119)
      | ~ class_Rings_Olinordered__semiring__strict(U_2117) ),
    inference(definitional_conversion,[status(esa)],[f_716_2]) ).

cnf(f_716_4,plain,
    ( c_Orderings_Oord__class_Oless(U_2117,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2117),U_2118),U_2120),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2117),U_2119),U_2121))
    | ~ c_Orderings_Oord__class_Oless(U_2117,c_Groups_Ozero__class_Ozero(U_2117),U_2120)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2117,c_Groups_Ozero__class_Ozero(U_2117),U_2118)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2117,U_2120,U_2121)
    | ~ c_Orderings_Oord__class_Oless(U_2117,U_2118,U_2119)
    | ~ class_Rings_Olinordered__semiring__strict(U_2117) ),
    inference(clausify,[status(thm)],[f_716_3]) ).

fof(f_717_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_717_2,plain,
    ! [U_2126,U_2125,U_2124,U_2123,U_2122] :
      ( c_Orderings_Oord__class_Oless(U_2122,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2122),U_2123),U_2125),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2122),U_2124),U_2126))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2122,c_Groups_Ozero__class_Ozero(U_2122),U_2125)
      | ~ c_Orderings_Oord__class_Oless(U_2122,c_Groups_Ozero__class_Ozero(U_2122),U_2123)
      | ~ c_Orderings_Oord__class_Oless(U_2122,U_2125,U_2126)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2122,U_2123,U_2124)
      | ~ class_Rings_Olinordered__semiring__strict(U_2122) ),
    inference(variable_rename,[status(thm)],[f_717_1]) ).

fof(f_717_3,plain,
    ! [U_2124,U_2126,U_2122,U_2125,U_2123] :
      ( c_Orderings_Oord__class_Oless(U_2122,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2122),U_2123),U_2125),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2122),U_2124),U_2126))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2122,c_Groups_Ozero__class_Ozero(U_2122),U_2125)
      | ~ c_Orderings_Oord__class_Oless(U_2122,c_Groups_Ozero__class_Ozero(U_2122),U_2123)
      | ~ c_Orderings_Oord__class_Oless(U_2122,U_2125,U_2126)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2122,U_2123,U_2124)
      | ~ class_Rings_Olinordered__semiring__strict(U_2122) ),
    inference(definitional_conversion,[status(esa)],[f_717_2]) ).

cnf(f_717_4,plain,
    ( c_Orderings_Oord__class_Oless(U_2122,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2122),U_2123),U_2125),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2122),U_2124),U_2126))
    | ~ c_Orderings_Oord__class_Oless__eq(U_2122,c_Groups_Ozero__class_Ozero(U_2122),U_2125)
    | ~ c_Orderings_Oord__class_Oless(U_2122,c_Groups_Ozero__class_Ozero(U_2122),U_2123)
    | ~ c_Orderings_Oord__class_Oless(U_2122,U_2125,U_2126)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2122,U_2123,U_2124)
    | ~ class_Rings_Olinordered__semiring__strict(U_2122) ),
    inference(clausify,[status(thm)],[f_717_3]) ).

fof(f_718_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_718_2,plain,
    ! [U_2130,U_2129,U_2128,U_2127] :
      ( c_Orderings_Oord__class_Oless(U_2127,U_2128,U_2130)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2127,c_Groups_Ozero__class_Ozero(U_2127),U_2129)
      | ~ c_Orderings_Oord__class_Oless(U_2127,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2127),U_2128),U_2129),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2127),U_2130),U_2129))
      | ~ class_Rings_Olinordered__semiring(U_2127) ),
    inference(variable_rename,[status(thm)],[f_718_1]) ).

fof(f_718_3,plain,
    ! [U_2129,U_2130,U_2128,U_2127] :
      ( c_Orderings_Oord__class_Oless(U_2127,U_2128,U_2130)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2127,c_Groups_Ozero__class_Ozero(U_2127),U_2129)
      | ~ c_Orderings_Oord__class_Oless(U_2127,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2127),U_2128),U_2129),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2127),U_2130),U_2129))
      | ~ class_Rings_Olinordered__semiring(U_2127) ),
    inference(definitional_conversion,[status(esa)],[f_718_2]) ).

cnf(f_718_4,plain,
    ( c_Orderings_Oord__class_Oless(U_2127,U_2128,U_2130)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2127,c_Groups_Ozero__class_Ozero(U_2127),U_2129)
    | ~ c_Orderings_Oord__class_Oless(U_2127,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2127),U_2128),U_2129),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2127),U_2130),U_2129))
    | ~ class_Rings_Olinordered__semiring(U_2127) ),
    inference(clausify,[status(thm)],[f_718_3]) ).

fof(f_719_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_719_2,plain,
    ! [U_2134,U_2133,U_2132,U_2131] :
      ( c_Orderings_Oord__class_Oless(U_2131,U_2132,U_2134)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2131,c_Groups_Ozero__class_Ozero(U_2131),U_2133)
      | ~ c_Orderings_Oord__class_Oless(U_2131,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2131),U_2132),U_2133),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2131),U_2134),U_2133))
      | ~ class_Rings_Olinordered__semiring__strict(U_2131) ),
    inference(variable_rename,[status(thm)],[f_719_1]) ).

fof(f_719_3,plain,
    ! [U_2131,U_2132,U_2133,U_2134] :
      ( c_Orderings_Oord__class_Oless(U_2131,U_2132,U_2134)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2131,c_Groups_Ozero__class_Ozero(U_2131),U_2133)
      | ~ c_Orderings_Oord__class_Oless(U_2131,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2131),U_2132),U_2133),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2131),U_2134),U_2133))
      | ~ class_Rings_Olinordered__semiring__strict(U_2131) ),
    inference(definitional_conversion,[status(esa)],[f_719_2]) ).

cnf(f_719_4,plain,
    ( c_Orderings_Oord__class_Oless(U_2131,U_2132,U_2134)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2131,c_Groups_Ozero__class_Ozero(U_2131),U_2133)
    | ~ c_Orderings_Oord__class_Oless(U_2131,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2131),U_2132),U_2133),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2131),U_2134),U_2133))
    | ~ class_Rings_Olinordered__semiring__strict(U_2131) ),
    inference(clausify,[status(thm)],[f_719_3]) ).

fof(f_720_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_720_2,plain,
    ! [U_2138,U_2137,U_2136,U_2135] :
      ( c_Orderings_Oord__class_Oless(U_2135,U_2137,U_2138)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2135,c_Groups_Ozero__class_Ozero(U_2135),U_2136)
      | ~ c_Orderings_Oord__class_Oless(U_2135,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2135),U_2136),U_2137),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2135),U_2136),U_2138))
      | ~ class_Rings_Olinordered__semiring(U_2135) ),
    inference(variable_rename,[status(thm)],[f_720_1]) ).

fof(f_720_3,plain,
    ! [U_2135,U_2136,U_2137,U_2138] :
      ( c_Orderings_Oord__class_Oless(U_2135,U_2137,U_2138)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2135,c_Groups_Ozero__class_Ozero(U_2135),U_2136)
      | ~ c_Orderings_Oord__class_Oless(U_2135,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2135),U_2136),U_2137),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2135),U_2136),U_2138))
      | ~ class_Rings_Olinordered__semiring(U_2135) ),
    inference(definitional_conversion,[status(esa)],[f_720_2]) ).

cnf(f_720_4,plain,
    ( c_Orderings_Oord__class_Oless(U_2135,U_2137,U_2138)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2135,c_Groups_Ozero__class_Ozero(U_2135),U_2136)
    | ~ c_Orderings_Oord__class_Oless(U_2135,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2135),U_2136),U_2137),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2135),U_2136),U_2138))
    | ~ class_Rings_Olinordered__semiring(U_2135) ),
    inference(clausify,[status(thm)],[f_720_3]) ).

fof(f_721_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_721_2,plain,
    ! [U_2142,U_2141,U_2140,U_2139] :
      ( c_Orderings_Oord__class_Oless(U_2139,U_2141,U_2142)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2139,c_Groups_Ozero__class_Ozero(U_2139),U_2140)
      | ~ c_Orderings_Oord__class_Oless(U_2139,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2139),U_2140),U_2141),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2139),U_2140),U_2142))
      | ~ class_Rings_Olinordered__semiring__strict(U_2139) ),
    inference(variable_rename,[status(thm)],[f_721_1]) ).

fof(f_721_3,plain,
    ! [U_2139,U_2140,U_2141,U_2142] :
      ( c_Orderings_Oord__class_Oless(U_2139,U_2141,U_2142)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2139,c_Groups_Ozero__class_Ozero(U_2139),U_2140)
      | ~ c_Orderings_Oord__class_Oless(U_2139,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2139),U_2140),U_2141),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2139),U_2140),U_2142))
      | ~ class_Rings_Olinordered__semiring__strict(U_2139) ),
    inference(definitional_conversion,[status(esa)],[f_721_2]) ).

cnf(f_721_4,plain,
    ( c_Orderings_Oord__class_Oless(U_2139,U_2141,U_2142)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2139,c_Groups_Ozero__class_Ozero(U_2139),U_2140)
    | ~ c_Orderings_Oord__class_Oless(U_2139,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2139),U_2140),U_2141),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2139),U_2140),U_2142))
    | ~ class_Rings_Olinordered__semiring__strict(U_2139) ),
    inference(clausify,[status(thm)],[f_721_3]) ).

fof(f_722_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_722_2,plain,
    ! [U_2146,U_2145,U_2144,U_2143] :
      ( c_Orderings_Oord__class_Oless__eq(U_2143,U_2144,U_2146)
      | ~ c_Orderings_Oord__class_Oless(U_2143,c_Groups_Ozero__class_Ozero(U_2143),U_2145)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2143,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2143),U_2144),U_2145),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2143),U_2146),U_2145))
      | ~ class_Rings_Olinordered__semiring__strict(U_2143) ),
    inference(variable_rename,[status(thm)],[f_722_1]) ).

fof(f_722_3,plain,
    ! [U_2143,U_2144,U_2145,U_2146] :
      ( c_Orderings_Oord__class_Oless__eq(U_2143,U_2144,U_2146)
      | ~ c_Orderings_Oord__class_Oless(U_2143,c_Groups_Ozero__class_Ozero(U_2143),U_2145)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2143,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2143),U_2144),U_2145),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2143),U_2146),U_2145))
      | ~ class_Rings_Olinordered__semiring__strict(U_2143) ),
    inference(definitional_conversion,[status(esa)],[f_722_2]) ).

cnf(f_722_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2143,U_2144,U_2146)
    | ~ c_Orderings_Oord__class_Oless(U_2143,c_Groups_Ozero__class_Ozero(U_2143),U_2145)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2143,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2143),U_2144),U_2145),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2143),U_2146),U_2145))
    | ~ class_Rings_Olinordered__semiring__strict(U_2143) ),
    inference(clausify,[status(thm)],[f_722_3]) ).

fof(f_723_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_723_2,plain,
    ! [U_2150,U_2149,U_2148,U_2147] :
      ( c_Orderings_Oord__class_Oless__eq(U_2147,U_2149,U_2150)
      | ~ c_Orderings_Oord__class_Oless(U_2147,c_Groups_Ozero__class_Ozero(U_2147),U_2148)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2147,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2147),U_2148),U_2149),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2147),U_2148),U_2150))
      | ~ class_Rings_Olinordered__semiring__strict(U_2147) ),
    inference(variable_rename,[status(thm)],[f_723_1]) ).

fof(f_723_3,plain,
    ! [U_2147,U_2148,U_2149,U_2150] :
      ( c_Orderings_Oord__class_Oless__eq(U_2147,U_2149,U_2150)
      | ~ c_Orderings_Oord__class_Oless(U_2147,c_Groups_Ozero__class_Ozero(U_2147),U_2148)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2147,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2147),U_2148),U_2149),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2147),U_2148),U_2150))
      | ~ class_Rings_Olinordered__semiring__strict(U_2147) ),
    inference(definitional_conversion,[status(esa)],[f_723_2]) ).

cnf(f_723_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2147,U_2149,U_2150)
    | ~ c_Orderings_Oord__class_Oless(U_2147,c_Groups_Ozero__class_Ozero(U_2147),U_2148)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2147,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2147),U_2148),U_2149),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2147),U_2148),U_2150))
    | ~ class_Rings_Olinordered__semiring__strict(U_2147) ),
    inference(clausify,[status(thm)],[f_723_3]) ).

fof(f_724_1,plain,
    ! [V_n_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | 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_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    inference(fof_nnf,[status(thm)],[fact_int__le__0__conv]) ).

fof(f_724_2,plain,
    ! [U_2151] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2151),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | U_2151 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_2151 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2151),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    inference(variable_rename,[status(thm)],[f_724_1]) ).

fof(f_724_3,plain,
    ( ! [U_2153] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2153),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | U_2153 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_2152] :
        ( U_2152 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2152),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    inference(miniscope,[status(thm)],[f_724_2]) ).

fof(f_724_4,plain,
    ( ! [U_2153] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2153),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | U_2153 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_2152] :
        ( U_2152 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2152),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    inference(definitional_conversion,[status(esa)],[f_724_3]) ).

cnf(f_724_5,plain,
    ( U_2152 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2152),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(clausify,[status(thm)],[f_724_4]) ).

cnf(f_724_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2153),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | U_2153 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_724_4]) ).

fof(f_725_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_725_2,plain,
    ! [U_2156,U_2155,U_2154] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_2154,c_Groups_Oplus__class_Oplus(U_2154,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2154),U_2155),U_2155),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2154),U_2156),U_2156)),c_Groups_Ozero__class_Ozero(U_2154))
          | U_2156 != c_Groups_Ozero__class_Ozero(U_2154)
          | U_2155 != c_Groups_Ozero__class_Ozero(U_2154) )
        & ( ( U_2156 = c_Groups_Ozero__class_Ozero(U_2154)
            & U_2155 = c_Groups_Ozero__class_Ozero(U_2154) )
          | ~ c_Orderings_Oord__class_Oless__eq(U_2154,c_Groups_Oplus__class_Oplus(U_2154,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2154),U_2155),U_2155),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2154),U_2156),U_2156)),c_Groups_Ozero__class_Ozero(U_2154)) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_2154) ),
    inference(variable_rename,[status(thm)],[f_725_1]) ).

fof(f_725_3,plain,
    ( ! [U_2154,U_2155,U_2156] :
        ( U_2156 = c_Groups_Ozero__class_Ozero(U_2154)
        | ~ sP180(U_2154,U_2155,U_2156) )
    & ! [U_2154,U_2155,U_2156] :
        ( U_2155 = c_Groups_Ozero__class_Ozero(U_2154)
        | ~ sP180(U_2154,U_2155,U_2156) )
    & ! [U_2154,U_2155,U_2156] :
        ( c_Orderings_Oord__class_Oless__eq(U_2154,c_Groups_Oplus__class_Oplus(U_2154,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2154),U_2155),U_2155),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2154),U_2156),U_2156)),c_Groups_Ozero__class_Ozero(U_2154))
        | U_2156 != c_Groups_Ozero__class_Ozero(U_2154)
        | U_2155 != c_Groups_Ozero__class_Ozero(U_2154)
        | ~ sP181(U_2154,U_2155,U_2156) )
    & ! [U_2154,U_2155,U_2156] :
        ( sP180(U_2154,U_2155,U_2156)
        | ~ c_Orderings_Oord__class_Oless__eq(U_2154,c_Groups_Oplus__class_Oplus(U_2154,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2154),U_2155),U_2155),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2154),U_2156),U_2156)),c_Groups_Ozero__class_Ozero(U_2154))
        | ~ sP181(U_2154,U_2155,U_2156) )
    & ! [U_2154,U_2155,U_2156] :
        ( sP181(U_2154,U_2155,U_2156)
        | ~ class_Rings_Olinordered__ring__strict(U_2154) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP180,sP181])],[f_725_2]) ).

cnf(f_725_4,plain,
    ( sP181(U_2154,U_2155,U_2156)
    | ~ class_Rings_Olinordered__ring__strict(U_2154) ),
    inference(clausify,[status(thm)],[f_725_3]) ).

cnf(f_725_5,plain,
    ( sP180(U_2154,U_2155,U_2156)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2154,c_Groups_Oplus__class_Oplus(U_2154,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2154),U_2155),U_2155),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2154),U_2156),U_2156)),c_Groups_Ozero__class_Ozero(U_2154))
    | ~ sP181(U_2154,U_2155,U_2156) ),
    inference(clausify,[status(thm)],[f_725_3]) ).

cnf(f_725_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2154,c_Groups_Oplus__class_Oplus(U_2154,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2154),U_2155),U_2155),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2154),U_2156),U_2156)),c_Groups_Ozero__class_Ozero(U_2154))
    | U_2156 != c_Groups_Ozero__class_Ozero(U_2154)
    | U_2155 != c_Groups_Ozero__class_Ozero(U_2154)
    | ~ sP181(U_2154,U_2155,U_2156) ),
    inference(clausify,[status(thm)],[f_725_3]) ).

cnf(f_725_7,plain,
    ( U_2155 = c_Groups_Ozero__class_Ozero(U_2154)
    | ~ sP180(U_2154,U_2155,U_2156) ),
    inference(clausify,[status(thm)],[f_725_3]) ).

cnf(f_725_8,plain,
    ( U_2156 = c_Groups_Ozero__class_Ozero(U_2154)
    | ~ sP180(U_2154,U_2155,U_2156) ),
    inference(clausify,[status(thm)],[f_725_3]) ).

fof(f_726_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_726_2,plain,
    ! [U_2159,U_2158,U_2157] :
      ( c_Orderings_Oord__class_Oless__eq(U_2157,c_Groups_Ozero__class_Ozero(U_2157),c_Groups_Oplus__class_Oplus(U_2157,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2157),U_2158),U_2158),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2157),U_2159),U_2159)))
      | ~ class_Rings_Olinordered__ring(U_2157) ),
    inference(variable_rename,[status(thm)],[f_726_1]) ).

fof(f_726_3,plain,
    ! [U_2158,U_2159,U_2157] :
      ( c_Orderings_Oord__class_Oless__eq(U_2157,c_Groups_Ozero__class_Ozero(U_2157),c_Groups_Oplus__class_Oplus(U_2157,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2157),U_2158),U_2158),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2157),U_2159),U_2159)))
      | ~ class_Rings_Olinordered__ring(U_2157) ),
    inference(definitional_conversion,[status(esa)],[f_726_2]) ).

cnf(f_726_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2157,c_Groups_Ozero__class_Ozero(U_2157),c_Groups_Oplus__class_Oplus(U_2157,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2157),U_2158),U_2158),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2157),U_2159),U_2159)))
    | ~ class_Rings_Olinordered__ring(U_2157) ),
    inference(clausify,[status(thm)],[f_726_3]) ).

fof(f_727_1,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_int__Suc0__eq__1]) ).

fof(f_727_2,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_727_1]) ).

cnf(f_727_3,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_727_2]) ).

fof(f_728_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_728_2,plain,
    ! [U_2162,U_2161,U_2160] :
      ( ~ c_Orderings_Oord__class_Oless(U_2160,c_Groups_Oplus__class_Oplus(U_2160,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2160),U_2161),U_2161),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2160),U_2162),U_2162)),c_Groups_Ozero__class_Ozero(U_2160))
      | ~ class_Rings_Olinordered__ring(U_2160) ),
    inference(variable_rename,[status(thm)],[f_728_1]) ).

fof(f_728_3,plain,
    ! [U_2162,U_2161,U_2160] :
      ( ~ c_Orderings_Oord__class_Oless(U_2160,c_Groups_Oplus__class_Oplus(U_2160,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2160),U_2161),U_2161),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2160),U_2162),U_2162)),c_Groups_Ozero__class_Ozero(U_2160))
      | ~ class_Rings_Olinordered__ring(U_2160) ),
    inference(definitional_conversion,[status(esa)],[f_728_2]) ).

cnf(f_728_4,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_2160,c_Groups_Oplus__class_Oplus(U_2160,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2160),U_2161),U_2161),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2160),U_2162),U_2162)),c_Groups_Ozero__class_Ozero(U_2160))
    | ~ class_Rings_Olinordered__ring(U_2160) ),
    inference(clausify,[status(thm)],[f_728_3]) ).

fof(f_729_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_729_2,plain,
    ! [U_2165,U_2164,U_2163] :
      ( ( ( c_Orderings_Oord__class_Oless(U_2163,c_Groups_Ozero__class_Ozero(U_2163),c_Groups_Oplus__class_Oplus(U_2163,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2163),U_2164),U_2164),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2163),U_2165),U_2165)))
          | ( U_2165 = c_Groups_Ozero__class_Ozero(U_2163)
            & U_2164 = c_Groups_Ozero__class_Ozero(U_2163) ) )
        & ( U_2165 != c_Groups_Ozero__class_Ozero(U_2163)
          | U_2164 != c_Groups_Ozero__class_Ozero(U_2163)
          | ~ c_Orderings_Oord__class_Oless(U_2163,c_Groups_Ozero__class_Ozero(U_2163),c_Groups_Oplus__class_Oplus(U_2163,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2163),U_2164),U_2164),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2163),U_2165),U_2165))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_2163) ),
    inference(variable_rename,[status(thm)],[f_729_1]) ).

fof(f_729_3,plain,
    ( ! [U_2163,U_2164,U_2165] :
        ( U_2165 = c_Groups_Ozero__class_Ozero(U_2163)
        | ~ sP182(U_2163,U_2164,U_2165) )
    & ! [U_2163,U_2164,U_2165] :
        ( U_2164 = c_Groups_Ozero__class_Ozero(U_2163)
        | ~ sP182(U_2163,U_2164,U_2165) )
    & ! [U_2163,U_2164,U_2165] :
        ( c_Orderings_Oord__class_Oless(U_2163,c_Groups_Ozero__class_Ozero(U_2163),c_Groups_Oplus__class_Oplus(U_2163,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2163),U_2164),U_2164),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2163),U_2165),U_2165)))
        | sP182(U_2163,U_2164,U_2165)
        | ~ sP183(U_2163,U_2164,U_2165) )
    & ! [U_2163,U_2164,U_2165] :
        ( U_2165 != c_Groups_Ozero__class_Ozero(U_2163)
        | U_2164 != c_Groups_Ozero__class_Ozero(U_2163)
        | ~ c_Orderings_Oord__class_Oless(U_2163,c_Groups_Ozero__class_Ozero(U_2163),c_Groups_Oplus__class_Oplus(U_2163,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2163),U_2164),U_2164),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2163),U_2165),U_2165)))
        | ~ sP183(U_2163,U_2164,U_2165) )
    & ! [U_2163,U_2164,U_2165] :
        ( sP183(U_2163,U_2164,U_2165)
        | ~ class_Rings_Olinordered__ring__strict(U_2163) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP182,sP183])],[f_729_2]) ).

cnf(f_729_4,plain,
    ( sP183(U_2163,U_2164,U_2165)
    | ~ class_Rings_Olinordered__ring__strict(U_2163) ),
    inference(clausify,[status(thm)],[f_729_3]) ).

cnf(f_729_5,plain,
    ( U_2165 != c_Groups_Ozero__class_Ozero(U_2163)
    | U_2164 != c_Groups_Ozero__class_Ozero(U_2163)
    | ~ c_Orderings_Oord__class_Oless(U_2163,c_Groups_Ozero__class_Ozero(U_2163),c_Groups_Oplus__class_Oplus(U_2163,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2163),U_2164),U_2164),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2163),U_2165),U_2165)))
    | ~ sP183(U_2163,U_2164,U_2165) ),
    inference(clausify,[status(thm)],[f_729_3]) ).

cnf(f_729_6,plain,
    ( c_Orderings_Oord__class_Oless(U_2163,c_Groups_Ozero__class_Ozero(U_2163),c_Groups_Oplus__class_Oplus(U_2163,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2163),U_2164),U_2164),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2163),U_2165),U_2165)))
    | sP182(U_2163,U_2164,U_2165)
    | ~ sP183(U_2163,U_2164,U_2165) ),
    inference(clausify,[status(thm)],[f_729_3]) ).

cnf(f_729_7,plain,
    ( U_2164 = c_Groups_Ozero__class_Ozero(U_2163)
    | ~ sP182(U_2163,U_2164,U_2165) ),
    inference(clausify,[status(thm)],[f_729_3]) ).

cnf(f_729_8,plain,
    ( U_2165 = c_Groups_Ozero__class_Ozero(U_2163)
    | ~ sP182(U_2163,U_2164,U_2165) ),
    inference(clausify,[status(thm)],[f_729_3]) ).

fof(f_730_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_730_2,plain,
    ! [U_2168,U_2167,U_2166] :
      ( c_Orderings_Oord__class_Oless__eq(U_2166,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2166),U_2167),U_2168),U_2167)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2166,U_2168,c_Groups_Oone__class_Oone(U_2166))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2166,c_Groups_Ozero__class_Ozero(U_2166),U_2168)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2166,c_Groups_Ozero__class_Ozero(U_2166),U_2167)
      | ~ class_Rings_Olinordered__idom(U_2166) ),
    inference(variable_rename,[status(thm)],[f_730_1]) ).

fof(f_730_3,plain,
    ! [U_2167,U_2166,U_2168] :
      ( c_Orderings_Oord__class_Oless__eq(U_2166,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2166),U_2167),U_2168),U_2167)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2166,U_2168,c_Groups_Oone__class_Oone(U_2166))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2166,c_Groups_Ozero__class_Ozero(U_2166),U_2168)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2166,c_Groups_Ozero__class_Ozero(U_2166),U_2167)
      | ~ class_Rings_Olinordered__idom(U_2166) ),
    inference(definitional_conversion,[status(esa)],[f_730_2]) ).

cnf(f_730_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2166,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2166),U_2167),U_2168),U_2167)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2166,U_2168,c_Groups_Oone__class_Oone(U_2166))
    | ~ c_Orderings_Oord__class_Oless__eq(U_2166,c_Groups_Ozero__class_Ozero(U_2166),U_2168)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2166,c_Groups_Ozero__class_Ozero(U_2166),U_2167)
    | ~ class_Rings_Olinordered__idom(U_2166) ),
    inference(clausify,[status(thm)],[f_730_3]) ).

fof(f_731_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_731_2,plain,
    ! [U_2171,U_2170,U_2169] :
      ( c_Orderings_Oord__class_Oless__eq(U_2169,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2169),U_2171),U_2170),U_2170)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2169,U_2171,c_Groups_Oone__class_Oone(U_2169))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2169,c_Groups_Ozero__class_Ozero(U_2169),U_2171)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2169,c_Groups_Ozero__class_Ozero(U_2169),U_2170)
      | ~ class_Rings_Olinordered__idom(U_2169) ),
    inference(variable_rename,[status(thm)],[f_731_1]) ).

fof(f_731_3,plain,
    ! [U_2169,U_2170,U_2171] :
      ( c_Orderings_Oord__class_Oless__eq(U_2169,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2169),U_2171),U_2170),U_2170)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2169,U_2171,c_Groups_Oone__class_Oone(U_2169))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2169,c_Groups_Ozero__class_Ozero(U_2169),U_2171)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2169,c_Groups_Ozero__class_Ozero(U_2169),U_2170)
      | ~ class_Rings_Olinordered__idom(U_2169) ),
    inference(definitional_conversion,[status(esa)],[f_731_2]) ).

cnf(f_731_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2169,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2169),U_2171),U_2170),U_2170)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2169,U_2171,c_Groups_Oone__class_Oone(U_2169))
    | ~ c_Orderings_Oord__class_Oless__eq(U_2169,c_Groups_Ozero__class_Ozero(U_2169),U_2171)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2169,c_Groups_Ozero__class_Ozero(U_2169),U_2170)
    | ~ class_Rings_Olinordered__idom(U_2169) ),
    inference(clausify,[status(thm)],[f_731_3]) ).

fof(f_732_1,plain,
    ! [V_da_2,V_b_2,V_c_2,V_e_2,V_a_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_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_da_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_a_2,V_b_2)),V_e_2),V_c_2),V_da_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_a_2,V_b_2)),V_e_2),V_c_2),V_da_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_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_da_2)) ) )
      | ~ class_Rings_Oordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__add__iff1]) ).

fof(f_732_2,plain,
    ! [U_2177,U_2176,U_2175,U_2174,U_2173,U_2172] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_2172,c_Groups_Oplus__class_Oplus(U_2172,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2172),U_2173),U_2174),U_2175),c_Groups_Oplus__class_Oplus(U_2172,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2172),U_2176),U_2174),U_2177))
          | ~ c_Orderings_Oord__class_Oless__eq(U_2172,c_Groups_Oplus__class_Oplus(U_2172,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2172),c_Groups_Ominus__class_Ominus(U_2172,U_2173,U_2176)),U_2174),U_2175),U_2177) )
        & ( c_Orderings_Oord__class_Oless__eq(U_2172,c_Groups_Oplus__class_Oplus(U_2172,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2172),c_Groups_Ominus__class_Ominus(U_2172,U_2173,U_2176)),U_2174),U_2175),U_2177)
          | ~ c_Orderings_Oord__class_Oless__eq(U_2172,c_Groups_Oplus__class_Oplus(U_2172,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2172),U_2173),U_2174),U_2175),c_Groups_Oplus__class_Oplus(U_2172,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2172),U_2176),U_2174),U_2177)) ) )
      | ~ class_Rings_Oordered__ring(U_2172) ),
    inference(variable_rename,[status(thm)],[f_732_1]) ).

fof(f_732_3,plain,
    ( ! [U_2173,U_2176,U_2174,U_2175,U_2172,U_2177] :
        ( c_Orderings_Oord__class_Oless__eq(U_2172,c_Groups_Oplus__class_Oplus(U_2172,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2172),U_2173),U_2174),U_2175),c_Groups_Oplus__class_Oplus(U_2172,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2172),U_2176),U_2174),U_2177))
        | ~ c_Orderings_Oord__class_Oless__eq(U_2172,c_Groups_Oplus__class_Oplus(U_2172,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2172),c_Groups_Ominus__class_Ominus(U_2172,U_2173,U_2176)),U_2174),U_2175),U_2177)
        | ~ sP184(U_2173,U_2176,U_2174,U_2175,U_2172,U_2177) )
    & ! [U_2173,U_2176,U_2174,U_2175,U_2172,U_2177] :
        ( c_Orderings_Oord__class_Oless__eq(U_2172,c_Groups_Oplus__class_Oplus(U_2172,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2172),c_Groups_Ominus__class_Ominus(U_2172,U_2173,U_2176)),U_2174),U_2175),U_2177)
        | ~ c_Orderings_Oord__class_Oless__eq(U_2172,c_Groups_Oplus__class_Oplus(U_2172,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2172),U_2173),U_2174),U_2175),c_Groups_Oplus__class_Oplus(U_2172,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2172),U_2176),U_2174),U_2177))
        | ~ sP184(U_2173,U_2176,U_2174,U_2175,U_2172,U_2177) )
    & ! [U_2173,U_2176,U_2174,U_2175,U_2172,U_2177] :
        ( sP184(U_2173,U_2176,U_2174,U_2175,U_2172,U_2177)
        | ~ class_Rings_Oordered__ring(U_2172) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP184])],[f_732_2]) ).

cnf(f_732_4,plain,
    ( sP184(U_2173,U_2176,U_2174,U_2175,U_2172,U_2177)
    | ~ class_Rings_Oordered__ring(U_2172) ),
    inference(clausify,[status(thm)],[f_732_3]) ).

cnf(f_732_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2172,c_Groups_Oplus__class_Oplus(U_2172,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2172),c_Groups_Ominus__class_Ominus(U_2172,U_2173,U_2176)),U_2174),U_2175),U_2177)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2172,c_Groups_Oplus__class_Oplus(U_2172,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2172),U_2173),U_2174),U_2175),c_Groups_Oplus__class_Oplus(U_2172,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2172),U_2176),U_2174),U_2177))
    | ~ sP184(U_2173,U_2176,U_2174,U_2175,U_2172,U_2177) ),
    inference(clausify,[status(thm)],[f_732_3]) ).

cnf(f_732_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2172,c_Groups_Oplus__class_Oplus(U_2172,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2172),U_2173),U_2174),U_2175),c_Groups_Oplus__class_Oplus(U_2172,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2172),U_2176),U_2174),U_2177))
    | ~ c_Orderings_Oord__class_Oless__eq(U_2172,c_Groups_Oplus__class_Oplus(U_2172,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2172),c_Groups_Ominus__class_Ominus(U_2172,U_2173,U_2176)),U_2174),U_2175),U_2177)
    | ~ sP184(U_2173,U_2176,U_2174,U_2175,U_2172,U_2177) ),
    inference(clausify,[status(thm)],[f_732_3]) ).

fof(f_733_1,plain,
    ! [V_da_2,V_b_2,V_c_2,V_e_2,V_a_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_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_da_2))
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c_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_a_2)),V_e_2),V_da_2)) )
        & ( c_Orderings_Oord__class_Oless__eq(T_a,V_c_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_a_2)),V_e_2),V_da_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_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_da_2)) ) )
      | ~ class_Rings_Oordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__add__iff2]) ).

fof(f_733_2,plain,
    ! [U_2183,U_2182,U_2181,U_2180,U_2179,U_2178] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_2178,c_Groups_Oplus__class_Oplus(U_2178,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),U_2179),U_2180),U_2181),c_Groups_Oplus__class_Oplus(U_2178,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),U_2182),U_2180),U_2183))
          | ~ c_Orderings_Oord__class_Oless__eq(U_2178,U_2181,c_Groups_Oplus__class_Oplus(U_2178,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),c_Groups_Ominus__class_Ominus(U_2178,U_2182,U_2179)),U_2180),U_2183)) )
        & ( c_Orderings_Oord__class_Oless__eq(U_2178,U_2181,c_Groups_Oplus__class_Oplus(U_2178,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),c_Groups_Ominus__class_Ominus(U_2178,U_2182,U_2179)),U_2180),U_2183))
          | ~ c_Orderings_Oord__class_Oless__eq(U_2178,c_Groups_Oplus__class_Oplus(U_2178,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),U_2179),U_2180),U_2181),c_Groups_Oplus__class_Oplus(U_2178,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),U_2182),U_2180),U_2183)) ) )
      | ~ class_Rings_Oordered__ring(U_2178) ),
    inference(variable_rename,[status(thm)],[f_733_1]) ).

fof(f_733_3,plain,
    ( ! [U_2180,U_2182,U_2178,U_2181,U_2183,U_2179] :
        ( c_Orderings_Oord__class_Oless__eq(U_2178,c_Groups_Oplus__class_Oplus(U_2178,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),U_2179),U_2180),U_2181),c_Groups_Oplus__class_Oplus(U_2178,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),U_2182),U_2180),U_2183))
        | ~ c_Orderings_Oord__class_Oless__eq(U_2178,U_2181,c_Groups_Oplus__class_Oplus(U_2178,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),c_Groups_Ominus__class_Ominus(U_2178,U_2182,U_2179)),U_2180),U_2183))
        | ~ sP185(U_2180,U_2182,U_2178,U_2181,U_2183,U_2179) )
    & ! [U_2180,U_2182,U_2178,U_2181,U_2183,U_2179] :
        ( c_Orderings_Oord__class_Oless__eq(U_2178,U_2181,c_Groups_Oplus__class_Oplus(U_2178,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),c_Groups_Ominus__class_Ominus(U_2178,U_2182,U_2179)),U_2180),U_2183))
        | ~ c_Orderings_Oord__class_Oless__eq(U_2178,c_Groups_Oplus__class_Oplus(U_2178,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),U_2179),U_2180),U_2181),c_Groups_Oplus__class_Oplus(U_2178,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),U_2182),U_2180),U_2183))
        | ~ sP185(U_2180,U_2182,U_2178,U_2181,U_2183,U_2179) )
    & ! [U_2180,U_2182,U_2178,U_2181,U_2183,U_2179] :
        ( sP185(U_2180,U_2182,U_2178,U_2181,U_2183,U_2179)
        | ~ class_Rings_Oordered__ring(U_2178) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP185])],[f_733_2]) ).

cnf(f_733_4,plain,
    ( sP185(U_2180,U_2182,U_2178,U_2181,U_2183,U_2179)
    | ~ class_Rings_Oordered__ring(U_2178) ),
    inference(clausify,[status(thm)],[f_733_3]) ).

cnf(f_733_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2178,U_2181,c_Groups_Oplus__class_Oplus(U_2178,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),c_Groups_Ominus__class_Ominus(U_2178,U_2182,U_2179)),U_2180),U_2183))
    | ~ c_Orderings_Oord__class_Oless__eq(U_2178,c_Groups_Oplus__class_Oplus(U_2178,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),U_2179),U_2180),U_2181),c_Groups_Oplus__class_Oplus(U_2178,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),U_2182),U_2180),U_2183))
    | ~ sP185(U_2180,U_2182,U_2178,U_2181,U_2183,U_2179) ),
    inference(clausify,[status(thm)],[f_733_3]) ).

cnf(f_733_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2178,c_Groups_Oplus__class_Oplus(U_2178,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),U_2179),U_2180),U_2181),c_Groups_Oplus__class_Oplus(U_2178,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),U_2182),U_2180),U_2183))
    | ~ c_Orderings_Oord__class_Oless__eq(U_2178,U_2181,c_Groups_Oplus__class_Oplus(U_2178,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2178),c_Groups_Ominus__class_Ominus(U_2178,U_2182,U_2179)),U_2180),U_2183))
    | ~ sP185(U_2180,U_2182,U_2178,U_2181,U_2183,U_2179) ),
    inference(clausify,[status(thm)],[f_733_3]) ).

fof(f_734_1,plain,
    ! [V_da_2,V_b_2,V_c_2,V_e_2,V_a_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_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_da_2))
          | ~ c_Orderings_Oord__class_Oless(T_a,V_c_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_a_2)),V_e_2),V_da_2)) )
        & ( c_Orderings_Oord__class_Oless(T_a,V_c_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_a_2)),V_e_2),V_da_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_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_da_2)) ) )
      | ~ class_Rings_Oordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__add__iff2]) ).

fof(f_734_2,plain,
    ! [U_2189,U_2188,U_2187,U_2186,U_2185,U_2184] :
      ( ( ( c_Orderings_Oord__class_Oless(U_2184,c_Groups_Oplus__class_Oplus(U_2184,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2184),U_2185),U_2186),U_2187),c_Groups_Oplus__class_Oplus(U_2184,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2184),U_2188),U_2186),U_2189))
          | ~ c_Orderings_Oord__class_Oless(U_2184,U_2187,c_Groups_Oplus__class_Oplus(U_2184,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2184),c_Groups_Ominus__class_Ominus(U_2184,U_2188,U_2185)),U_2186),U_2189)) )
        & ( c_Orderings_Oord__class_Oless(U_2184,U_2187,c_Groups_Oplus__class_Oplus(U_2184,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2184),c_Groups_Ominus__class_Ominus(U_2184,U_2188,U_2185)),U_2186),U_2189))
          | ~ c_Orderings_Oord__class_Oless(U_2184,c_Groups_Oplus__class_Oplus(U_2184,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2184),U_2185),U_2186),U_2187),c_Groups_Oplus__class_Oplus(U_2184,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2184),U_2188),U_2186),U_2189)) ) )
      | ~ class_Rings_Oordered__ring(U_2184) ),
    inference(variable_rename,[status(thm)],[f_734_1]) ).

fof(f_734_3,plain,
    ( ! [U_2187,U_2184,U_2188,U_2186,U_2185,U_2189] :
        ( c_Orderings_Oord__class_Oless(U_2184,c_Groups_Oplus__class_Oplus(U_2184,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2184),U_2185),U_2186),U_2187),c_Groups_Oplus__class_Oplus(U_2184,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2184),U_2188),U_2186),U_2189))
        | ~ c_Orderings_Oord__class_Oless(U_2184,U_2187,c_Groups_Oplus__class_Oplus(U_2184,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2184),c_Groups_Ominus__class_Ominus(U_2184,U_2188,U_2185)),U_2186),U_2189))
        | ~ sP186(U_2187,U_2184,U_2188,U_2186,U_2185,U_2189) )
    & ! [U_2187,U_2184,U_2188,U_2186,U_2185,U_2189] :
        ( c_Orderings_Oord__class_Oless(U_2184,U_2187,c_Groups_Oplus__class_Oplus(U_2184,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2184),c_Groups_Ominus__class_Ominus(U_2184,U_2188,U_2185)),U_2186),U_2189))
        | ~ c_Orderings_Oord__class_Oless(U_2184,c_Groups_Oplus__class_Oplus(U_2184,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2184),U_2185),U_2186),U_2187),c_Groups_Oplus__class_Oplus(U_2184,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2184),U_2188),U_2186),U_2189))
        | ~ sP186(U_2187,U_2184,U_2188,U_2186,U_2185,U_2189) )
    & ! [U_2187,U_2184,U_2188,U_2186,U_2185,U_2189] :
        ( sP186(U_2187,U_2184,U_2188,U_2186,U_2185,U_2189)
        | ~ class_Rings_Oordered__ring(U_2184) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP186])],[f_734_2]) ).

cnf(f_734_4,plain,
    ( sP186(U_2187,U_2184,U_2188,U_2186,U_2185,U_2189)
    | ~ class_Rings_Oordered__ring(U_2184) ),
    inference(clausify,[status(thm)],[f_734_3]) ).

cnf(f_734_5,plain,
    ( c_Orderings_Oord__class_Oless(U_2184,U_2187,c_Groups_Oplus__class_Oplus(U_2184,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2184),c_Groups_Ominus__class_Ominus(U_2184,U_2188,U_2185)),U_2186),U_2189))
    | ~ c_Orderings_Oord__class_Oless(U_2184,c_Groups_Oplus__class_Oplus(U_2184,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2184),U_2185),U_2186),U_2187),c_Groups_Oplus__class_Oplus(U_2184,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2184),U_2188),U_2186),U_2189))
    | ~ sP186(U_2187,U_2184,U_2188,U_2186,U_2185,U_2189) ),
    inference(clausify,[status(thm)],[f_734_3]) ).

cnf(f_734_6,plain,
    ( c_Orderings_Oord__class_Oless(U_2184,c_Groups_Oplus__class_Oplus(U_2184,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2184),U_2185),U_2186),U_2187),c_Groups_Oplus__class_Oplus(U_2184,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2184),U_2188),U_2186),U_2189))
    | ~ c_Orderings_Oord__class_Oless(U_2184,U_2187,c_Groups_Oplus__class_Oplus(U_2184,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2184),c_Groups_Ominus__class_Ominus(U_2184,U_2188,U_2185)),U_2186),U_2189))
    | ~ sP186(U_2187,U_2184,U_2188,U_2186,U_2185,U_2189) ),
    inference(clausify,[status(thm)],[f_734_3]) ).

fof(f_735_1,plain,
    ! [V_da_2,V_b_2,V_c_2,V_e_2,V_a_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_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_da_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_a_2,V_b_2)),V_e_2),V_c_2),V_da_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_a_2,V_b_2)),V_e_2),V_c_2),V_da_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_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_da_2)) ) )
      | ~ class_Rings_Oordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__add__iff1]) ).

fof(f_735_2,plain,
    ! [U_2195,U_2194,U_2193,U_2192,U_2191,U_2190] :
      ( ( ( c_Orderings_Oord__class_Oless(U_2190,c_Groups_Oplus__class_Oplus(U_2190,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2190),U_2191),U_2192),U_2193),c_Groups_Oplus__class_Oplus(U_2190,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2190),U_2194),U_2192),U_2195))
          | ~ c_Orderings_Oord__class_Oless(U_2190,c_Groups_Oplus__class_Oplus(U_2190,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2190),c_Groups_Ominus__class_Ominus(U_2190,U_2191,U_2194)),U_2192),U_2193),U_2195) )
        & ( c_Orderings_Oord__class_Oless(U_2190,c_Groups_Oplus__class_Oplus(U_2190,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2190),c_Groups_Ominus__class_Ominus(U_2190,U_2191,U_2194)),U_2192),U_2193),U_2195)
          | ~ c_Orderings_Oord__class_Oless(U_2190,c_Groups_Oplus__class_Oplus(U_2190,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2190),U_2191),U_2192),U_2193),c_Groups_Oplus__class_Oplus(U_2190,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2190),U_2194),U_2192),U_2195)) ) )
      | ~ class_Rings_Oordered__ring(U_2190) ),
    inference(variable_rename,[status(thm)],[f_735_1]) ).

fof(f_735_3,plain,
    ( ! [U_2190,U_2191,U_2192,U_2193,U_2194,U_2195] :
        ( c_Orderings_Oord__class_Oless(U_2190,c_Groups_Oplus__class_Oplus(U_2190,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2190),U_2191),U_2192),U_2193),c_Groups_Oplus__class_Oplus(U_2190,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2190),U_2194),U_2192),U_2195))
        | ~ c_Orderings_Oord__class_Oless(U_2190,c_Groups_Oplus__class_Oplus(U_2190,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2190),c_Groups_Ominus__class_Ominus(U_2190,U_2191,U_2194)),U_2192),U_2193),U_2195)
        | ~ sP187(U_2190,U_2191,U_2192,U_2193,U_2194,U_2195) )
    & ! [U_2190,U_2191,U_2192,U_2193,U_2194,U_2195] :
        ( c_Orderings_Oord__class_Oless(U_2190,c_Groups_Oplus__class_Oplus(U_2190,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2190),c_Groups_Ominus__class_Ominus(U_2190,U_2191,U_2194)),U_2192),U_2193),U_2195)
        | ~ c_Orderings_Oord__class_Oless(U_2190,c_Groups_Oplus__class_Oplus(U_2190,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2190),U_2191),U_2192),U_2193),c_Groups_Oplus__class_Oplus(U_2190,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2190),U_2194),U_2192),U_2195))
        | ~ sP187(U_2190,U_2191,U_2192,U_2193,U_2194,U_2195) )
    & ! [U_2190,U_2191,U_2192,U_2193,U_2194,U_2195] :
        ( sP187(U_2190,U_2191,U_2192,U_2193,U_2194,U_2195)
        | ~ class_Rings_Oordered__ring(U_2190) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP187])],[f_735_2]) ).

cnf(f_735_4,plain,
    ( sP187(U_2190,U_2191,U_2192,U_2193,U_2194,U_2195)
    | ~ class_Rings_Oordered__ring(U_2190) ),
    inference(clausify,[status(thm)],[f_735_3]) ).

cnf(f_735_5,plain,
    ( c_Orderings_Oord__class_Oless(U_2190,c_Groups_Oplus__class_Oplus(U_2190,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2190),c_Groups_Ominus__class_Ominus(U_2190,U_2191,U_2194)),U_2192),U_2193),U_2195)
    | ~ c_Orderings_Oord__class_Oless(U_2190,c_Groups_Oplus__class_Oplus(U_2190,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2190),U_2191),U_2192),U_2193),c_Groups_Oplus__class_Oplus(U_2190,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2190),U_2194),U_2192),U_2195))
    | ~ sP187(U_2190,U_2191,U_2192,U_2193,U_2194,U_2195) ),
    inference(clausify,[status(thm)],[f_735_3]) ).

cnf(f_735_6,plain,
    ( c_Orderings_Oord__class_Oless(U_2190,c_Groups_Oplus__class_Oplus(U_2190,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2190),U_2191),U_2192),U_2193),c_Groups_Oplus__class_Oplus(U_2190,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2190),U_2194),U_2192),U_2195))
    | ~ c_Orderings_Oord__class_Oless(U_2190,c_Groups_Oplus__class_Oplus(U_2190,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2190),c_Groups_Ominus__class_Ominus(U_2190,U_2191,U_2194)),U_2192),U_2193),U_2195)
    | ~ sP187(U_2190,U_2191,U_2192,U_2193,U_2194,U_2195) ),
    inference(clausify,[status(thm)],[f_735_3]) ).

fof(f_736_1,plain,
    ! [V_za_2,V_wa_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2)
        | ! [B_n] : V_za_2 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_wa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(B_n))) )
      & ( ? [B_n] : V_za_2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_wa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(B_n)))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_zless__iff__Suc__zadd]) ).

fof(f_736_2,plain,
    ! [U_2199,U_2198] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2198,U_2199)
        | ! [U_2197] : U_2199 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2198,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(U_2197))) )
      & ( ? [U_2196] : U_2199 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2198,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(U_2196)))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2198,U_2199) ) ),
    inference(variable_rename,[status(thm)],[f_736_1]) ).

fof(f_736_3,plain,
    ( ! [U_2203,U_2201] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2201,U_2203)
        | ! [U_2197] : U_2203 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2201,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(U_2197))) )
    & ! [U_2202,U_2200] :
        ( ? [U_2196] : U_2202 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2200,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(U_2196)))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2200,U_2202) ) ),
    inference(miniscope,[status(thm)],[f_736_2]) ).

fof(f_736_4,plain,
    ( ! [U_2203,U_2201] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2201,U_2203)
        | ! [U_2197] : U_2203 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2201,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(U_2197))) )
    & ! [U_2202,U_2200] :
        ( U_2202 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2200,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(sK60(U_2202,U_2200))))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2200,U_2202) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_2196,sK60(U_2202,U_2200))],[f_736_3]) ).

fof(f_736_5,plain,
    ( ! [U_2203,U_2197,U_2201] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2201,U_2203)
        | U_2203 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2201,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(U_2197))) )
    & ! [U_2200,U_2202] :
        ( U_2202 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2200,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(sK60(U_2202,U_2200))))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2200,U_2202) ) ),
    inference(definitional_conversion,[status(esa)],[f_736_4]) ).

cnf(f_736_6,plain,
    ( U_2202 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2200,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(sK60(U_2202,U_2200))))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2200,U_2202) ),
    inference(clausify,[status(thm)],[f_736_5]) ).

cnf(f_736_7,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2201,U_2203)
    | U_2203 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2201,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(U_2197))) ),
    inference(clausify,[status(thm)],[f_736_5]) ).

fof(f_737_1,plain,
    ! [V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(V_m)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),
    inference(fof_nnf,[status(thm)],[fact_int__Suc]) ).

fof(f_737_2,plain,
    ! [U_2204] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(U_2204)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2204)),
    inference(variable_rename,[status(thm)],[f_737_1]) ).

fof(f_737_3,plain,
    ! [U_2204] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(U_2204)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2204)),
    inference(definitional_conversion,[status(esa)],[f_737_2]) ).

cnf(f_737_4,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(U_2204)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2204)),
    inference(clausify,[status(thm)],[f_737_3]) ).

fof(f_738_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_738_2,plain,
    ! [U_2206,U_2205] :
      ( c_Groups_Ominus__class_Ominus(U_2205,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2205),U_2206),U_2206),c_Groups_Oone__class_Oone(U_2205)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2205),c_Groups_Oplus__class_Oplus(U_2205,U_2206,c_Groups_Oone__class_Oone(U_2205))),c_Groups_Ominus__class_Ominus(U_2205,U_2206,c_Groups_Oone__class_Oone(U_2205)))
      | ~ class_Rings_Oring__1(U_2205) ),
    inference(variable_rename,[status(thm)],[f_738_1]) ).

fof(f_738_3,plain,
    ! [U_2205,U_2206] :
      ( c_Groups_Ominus__class_Ominus(U_2205,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2205),U_2206),U_2206),c_Groups_Oone__class_Oone(U_2205)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2205),c_Groups_Oplus__class_Oplus(U_2205,U_2206,c_Groups_Oone__class_Oone(U_2205))),c_Groups_Ominus__class_Ominus(U_2205,U_2206,c_Groups_Oone__class_Oone(U_2205)))
      | ~ class_Rings_Oring__1(U_2205) ),
    inference(definitional_conversion,[status(esa)],[f_738_2]) ).

cnf(f_738_4,plain,
    ( c_Groups_Ominus__class_Ominus(U_2205,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2205),U_2206),U_2206),c_Groups_Oone__class_Oone(U_2205)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2205),c_Groups_Oplus__class_Oplus(U_2205,U_2206,c_Groups_Oone__class_Oone(U_2205))),c_Groups_Ominus__class_Ominus(U_2205,U_2206,c_Groups_Oone__class_Oone(U_2205)))
    | ~ class_Rings_Oring__1(U_2205) ),
    inference(clausify,[status(thm)],[f_738_3]) ).

fof(f_739_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Groups_Oabs__class_Oabs(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_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_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,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,c_Groups_Ozero__class_Ozero(T_a),V_a) )
      | ~ class_Rings_Oordered__ring__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__eq__mult]) ).

fof(f_739_2,plain,
    ! [U_2209,U_2208,U_2207] :
      ( c_Groups_Oabs__class_Oabs(U_2207,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2207),U_2208),U_2209)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2207),c_Groups_Oabs__class_Oabs(U_2207,U_2208)),c_Groups_Oabs__class_Oabs(U_2207,U_2209))
      | ( ~ c_Orderings_Oord__class_Oless__eq(U_2207,U_2209,c_Groups_Ozero__class_Ozero(U_2207))
        & ~ c_Orderings_Oord__class_Oless__eq(U_2207,c_Groups_Ozero__class_Ozero(U_2207),U_2209) )
      | ( ~ c_Orderings_Oord__class_Oless__eq(U_2207,U_2208,c_Groups_Ozero__class_Ozero(U_2207))
        & ~ c_Orderings_Oord__class_Oless__eq(U_2207,c_Groups_Ozero__class_Ozero(U_2207),U_2208) )
      | ~ class_Rings_Oordered__ring__abs(U_2207) ),
    inference(variable_rename,[status(thm)],[f_739_1]) ).

fof(f_739_3,plain,
    ( ! [U_2207,U_2209] :
        ( ~ c_Orderings_Oord__class_Oless__eq(U_2207,U_2209,c_Groups_Ozero__class_Ozero(U_2207))
        | ~ sP189(U_2207,U_2209) )
    & ! [U_2207,U_2209] :
        ( ~ c_Orderings_Oord__class_Oless__eq(U_2207,c_Groups_Ozero__class_Ozero(U_2207),U_2209)
        | ~ sP189(U_2207,U_2209) )
    & ! [U_2208,U_2207] :
        ( ~ c_Orderings_Oord__class_Oless__eq(U_2207,U_2208,c_Groups_Ozero__class_Ozero(U_2207))
        | ~ sP188(U_2208,U_2207) )
    & ! [U_2208,U_2207] :
        ( ~ c_Orderings_Oord__class_Oless__eq(U_2207,c_Groups_Ozero__class_Ozero(U_2207),U_2208)
        | ~ sP188(U_2208,U_2207) )
    & ! [U_2208,U_2207,U_2209] :
        ( c_Groups_Oabs__class_Oabs(U_2207,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2207),U_2208),U_2209)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2207),c_Groups_Oabs__class_Oabs(U_2207,U_2208)),c_Groups_Oabs__class_Oabs(U_2207,U_2209))
        | sP189(U_2207,U_2209)
        | sP188(U_2208,U_2207)
        | ~ class_Rings_Oordered__ring__abs(U_2207) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP188,sP189])],[f_739_2]) ).

cnf(f_739_4,plain,
    ( c_Groups_Oabs__class_Oabs(U_2207,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2207),U_2208),U_2209)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2207),c_Groups_Oabs__class_Oabs(U_2207,U_2208)),c_Groups_Oabs__class_Oabs(U_2207,U_2209))
    | sP189(U_2207,U_2209)
    | sP188(U_2208,U_2207)
    | ~ class_Rings_Oordered__ring__abs(U_2207) ),
    inference(clausify,[status(thm)],[f_739_3]) ).

cnf(f_739_5,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(U_2207,c_Groups_Ozero__class_Ozero(U_2207),U_2208)
    | ~ sP188(U_2208,U_2207) ),
    inference(clausify,[status(thm)],[f_739_3]) ).

cnf(f_739_6,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(U_2207,U_2208,c_Groups_Ozero__class_Ozero(U_2207))
    | ~ sP188(U_2208,U_2207) ),
    inference(clausify,[status(thm)],[f_739_3]) ).

cnf(f_739_7,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(U_2207,c_Groups_Ozero__class_Ozero(U_2207),U_2209)
    | ~ sP189(U_2207,U_2209) ),
    inference(clausify,[status(thm)],[f_739_3]) ).

cnf(f_739_8,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(U_2207,U_2209,c_Groups_Ozero__class_Ozero(U_2207))
    | ~ sP189(U_2207,U_2209) ),
    inference(clausify,[status(thm)],[f_739_3]) ).

fof(f_740_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_y)),V_x) = c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x))
      | ~ 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_abs__mult__pos]) ).

fof(f_740_2,plain,
    ! [U_2212,U_2211,U_2210] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2210),c_Groups_Oabs__class_Oabs(U_2210,U_2212)),U_2211) = c_Groups_Oabs__class_Oabs(U_2210,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2210),U_2212),U_2211))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2210,c_Groups_Ozero__class_Ozero(U_2210),U_2211)
      | ~ class_Rings_Olinordered__idom(U_2210) ),
    inference(variable_rename,[status(thm)],[f_740_1]) ).

fof(f_740_3,plain,
    ! [U_2212,U_2210,U_2211] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2210),c_Groups_Oabs__class_Oabs(U_2210,U_2212)),U_2211) = c_Groups_Oabs__class_Oabs(U_2210,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2210),U_2212),U_2211))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2210,c_Groups_Ozero__class_Ozero(U_2210),U_2211)
      | ~ class_Rings_Olinordered__idom(U_2210) ),
    inference(definitional_conversion,[status(esa)],[f_740_2]) ).

cnf(f_740_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2210),c_Groups_Oabs__class_Oabs(U_2210,U_2212)),U_2211) = c_Groups_Oabs__class_Oabs(U_2210,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2210),U_2212),U_2211))
    | ~ c_Orderings_Oord__class_Oless__eq(U_2210,c_Groups_Ozero__class_Ozero(U_2210),U_2211)
    | ~ class_Rings_Olinordered__idom(U_2210) ),
    inference(clausify,[status(thm)],[f_740_3]) ).

fof(f_741_1,plain,
    ! [V_m,V_n] :
      ( c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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_zdiff__int]) ).

fof(f_741_2,plain,
    ! [U_2214,U_2213] :
      ( c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2214),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2213)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2214,U_2213))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2213,U_2214) ),
    inference(variable_rename,[status(thm)],[f_741_1]) ).

fof(f_741_3,plain,
    ! [U_2213,U_2214] :
      ( c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2214),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2213)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2214,U_2213))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2213,U_2214) ),
    inference(definitional_conversion,[status(esa)],[f_741_2]) ).

cnf(f_741_4,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2214),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2213)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2214,U_2213))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2213,U_2214) ),
    inference(clausify,[status(thm)],[f_741_3]) ).

fof(f_742_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_742_2,plain,
    ! [U_2216,U_2215] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2215),U_2216) = c_Groups_Oone__class_Oone(tc_Int_Oint)
          | U_2216 != c_Groups_Oone__class_Oone(tc_Int_Oint)
          | U_2215 != c_Groups_Oone__class_Oone(tc_Int_Oint) )
        & ( ( U_2216 = c_Groups_Oone__class_Oone(tc_Int_Oint)
            & U_2215 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2215),U_2216) != 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_2215) ),
    inference(variable_rename,[status(thm)],[f_742_1]) ).

fof(f_742_3,plain,
    ( ! [U_2215,U_2216] :
        ( U_2216 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ sP190(U_2215,U_2216) )
    & ! [U_2215,U_2216] :
        ( U_2215 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ sP190(U_2215,U_2216) )
    & ! [U_2215,U_2216] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2215),U_2216) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | U_2216 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | U_2215 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ sP191(U_2215,U_2216) )
    & ! [U_2215,U_2216] :
        ( sP190(U_2215,U_2216)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2215),U_2216) != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ sP191(U_2215,U_2216) )
    & ! [U_2215,U_2216] :
        ( sP191(U_2215,U_2216)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2215) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP190,sP191])],[f_742_2]) ).

cnf(f_742_4,plain,
    ( sP191(U_2215,U_2216)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2215) ),
    inference(clausify,[status(thm)],[f_742_3]) ).

cnf(f_742_5,plain,
    ( sP190(U_2215,U_2216)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2215),U_2216) != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ sP191(U_2215,U_2216) ),
    inference(clausify,[status(thm)],[f_742_3]) ).

cnf(f_742_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2215),U_2216) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | U_2216 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | U_2215 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ sP191(U_2215,U_2216) ),
    inference(clausify,[status(thm)],[f_742_3]) ).

cnf(f_742_7,plain,
    ( U_2215 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ sP190(U_2215,U_2216) ),
    inference(clausify,[status(thm)],[f_742_3]) ).

cnf(f_742_8,plain,
    ( U_2216 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ sP190(U_2215,U_2216) ),
    inference(clausify,[status(thm)],[f_742_3]) ).

fof(f_743_1,plain,
    ! [V_n_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),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(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)) ) )
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__0__less__iff]) ).

fof(f_743_2,plain,
    ! [U_2218,U_2217] :
      ( ( ( c_Orderings_Oord__class_Oless(U_2217,c_Groups_Ozero__class_Ozero(U_2217),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2217),U_2218))
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2218) )
        & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2218)
          | ~ c_Orderings_Oord__class_Oless(U_2217,c_Groups_Ozero__class_Ozero(U_2217),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2217),U_2218)) ) )
      | ~ class_Rings_Olinordered__semidom(U_2217) ),
    inference(variable_rename,[status(thm)],[f_743_1]) ).

fof(f_743_3,plain,
    ( ! [U_2217,U_2218] :
        ( c_Orderings_Oord__class_Oless(U_2217,c_Groups_Ozero__class_Ozero(U_2217),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2217),U_2218))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2218)
        | ~ sP192(U_2217,U_2218) )
    & ! [U_2217,U_2218] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2218)
        | ~ c_Orderings_Oord__class_Oless(U_2217,c_Groups_Ozero__class_Ozero(U_2217),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2217),U_2218))
        | ~ sP192(U_2217,U_2218) )
    & ! [U_2217,U_2218] :
        ( sP192(U_2217,U_2218)
        | ~ class_Rings_Olinordered__semidom(U_2217) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP192])],[f_743_2]) ).

cnf(f_743_4,plain,
    ( sP192(U_2217,U_2218)
    | ~ class_Rings_Olinordered__semidom(U_2217) ),
    inference(clausify,[status(thm)],[f_743_3]) ).

cnf(f_743_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2218)
    | ~ c_Orderings_Oord__class_Oless(U_2217,c_Groups_Ozero__class_Ozero(U_2217),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2217),U_2218))
    | ~ sP192(U_2217,U_2218) ),
    inference(clausify,[status(thm)],[f_743_3]) ).

cnf(f_743_6,plain,
    ( c_Orderings_Oord__class_Oless(U_2217,c_Groups_Ozero__class_Ozero(U_2217),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2217),U_2218))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2218)
    | ~ sP192(U_2217,U_2218) ),
    inference(clausify,[status(thm)],[f_743_3]) ).

fof(f_744_1,plain,
    ! [V_n_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__int__conv]) ).

fof(f_744_2,plain,
    ! [U_2219] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2219))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2219) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2219)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2219)) ) ),
    inference(variable_rename,[status(thm)],[f_744_1]) ).

fof(f_744_3,plain,
    ( ! [U_2221] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2221))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2221) )
    & ! [U_2220] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2220)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2220)) ) ),
    inference(miniscope,[status(thm)],[f_744_2]) ).

fof(f_744_4,plain,
    ( ! [U_2221] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2221))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2221) )
    & ! [U_2220] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2220)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2220)) ) ),
    inference(definitional_conversion,[status(esa)],[f_744_3]) ).

cnf(f_744_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2220)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2220)) ),
    inference(clausify,[status(thm)],[f_744_4]) ).

cnf(f_744_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2221))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2221) ),
    inference(clausify,[status(thm)],[f_744_4]) ).

fof(f_745_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_745_2,plain,
    ! [U_2227,U_2226,U_2225,U_2224,U_2223,U_2222] :
      ( c_Orderings_Oord__class_Oless__eq(U_2222,c_Groups_Oplus__class_Oplus(U_2222,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2222),U_2226),U_2223),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2222),U_2227),U_2225)),U_2224)
      | c_Groups_Oplus__class_Oplus(U_2222,U_2226,U_2227) != c_Groups_Oone__class_Oone(U_2222)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2222,c_Groups_Ozero__class_Ozero(U_2222),U_2227)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2222,c_Groups_Ozero__class_Ozero(U_2222),U_2226)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2222,U_2225,U_2224)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2222,U_2223,U_2224)
      | ~ class_Rings_Olinordered__semiring__1(U_2222) ),
    inference(variable_rename,[status(thm)],[f_745_1]) ).

fof(f_745_3,plain,
    ! [U_2223,U_2222,U_2224,U_2225,U_2226,U_2227] :
      ( c_Orderings_Oord__class_Oless__eq(U_2222,c_Groups_Oplus__class_Oplus(U_2222,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2222),U_2226),U_2223),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2222),U_2227),U_2225)),U_2224)
      | c_Groups_Oplus__class_Oplus(U_2222,U_2226,U_2227) != c_Groups_Oone__class_Oone(U_2222)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2222,c_Groups_Ozero__class_Ozero(U_2222),U_2227)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2222,c_Groups_Ozero__class_Ozero(U_2222),U_2226)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2222,U_2225,U_2224)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2222,U_2223,U_2224)
      | ~ class_Rings_Olinordered__semiring__1(U_2222) ),
    inference(definitional_conversion,[status(esa)],[f_745_2]) ).

cnf(f_745_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2222,c_Groups_Oplus__class_Oplus(U_2222,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2222),U_2226),U_2223),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2222),U_2227),U_2225)),U_2224)
    | c_Groups_Oplus__class_Oplus(U_2222,U_2226,U_2227) != c_Groups_Oone__class_Oone(U_2222)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2222,c_Groups_Ozero__class_Ozero(U_2222),U_2227)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2222,c_Groups_Ozero__class_Ozero(U_2222),U_2226)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2222,U_2225,U_2224)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2222,U_2223,U_2224)
    | ~ class_Rings_Olinordered__semiring__1(U_2222) ),
    inference(clausify,[status(thm)],[f_745_3]) ).

fof(f_746_1,plain,
    ! [V_v] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v)
        | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v)) )
      & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v)) ) ),
    inference(fof_nnf,[status(thm)],[fact_int__nat__number__of]) ).

fof(f_746_2,plain,
    ! [U_2228] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2228)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2228)
        | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2228)) )
      & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2228)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2228)) ) ),
    inference(variable_rename,[status(thm)],[f_746_1]) ).

fof(f_746_3,plain,
    ( ! [U_2230] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2230)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2230)
        | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2230)) )
    & ! [U_2229] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2229)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2229)) ) ),
    inference(miniscope,[status(thm)],[f_746_2]) ).

fof(f_746_4,plain,
    ( ! [U_2230] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2230)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2230)
        | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2230)) )
    & ! [U_2229] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2229)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2229)) ) ),
    inference(definitional_conversion,[status(esa)],[f_746_3]) ).

cnf(f_746_5,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2229)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2229)) ),
    inference(clausify,[status(thm)],[f_746_4]) ).

cnf(f_746_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2230)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2230)
    | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2230)) ),
    inference(clausify,[status(thm)],[f_746_4]) ).

fof(f_747_1,plain,
    ! [V_v,T_a] :
      ( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Int_Onumber__class_Onumber__of(T_a,V_v)
          | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v)) )
        & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Groups_Ozero__class_Ozero(T_a)
          | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v)) ) )
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__number__of__eq]) ).

fof(f_747_2,plain,
    ! [U_2232,U_2231] :
      ( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2231),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2232)) = c_Int_Onumber__class_Onumber__of(U_2231,U_2232)
          | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2232)) )
        & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2231),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2232)) = c_Groups_Ozero__class_Ozero(U_2231)
          | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2232)) ) )
      | ~ class_Int_Onumber__ring(U_2231) ),
    inference(variable_rename,[status(thm)],[f_747_1]) ).

fof(f_747_3,plain,
    ( ! [U_2231,U_2232] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2231),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2232)) = c_Int_Onumber__class_Onumber__of(U_2231,U_2232)
        | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2232))
        | ~ sP193(U_2231,U_2232) )
    & ! [U_2231,U_2232] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2231),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2232)) = c_Groups_Ozero__class_Ozero(U_2231)
        | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2232))
        | ~ sP193(U_2231,U_2232) )
    & ! [U_2231,U_2232] :
        ( sP193(U_2231,U_2232)
        | ~ class_Int_Onumber__ring(U_2231) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP193])],[f_747_2]) ).

cnf(f_747_4,plain,
    ( sP193(U_2231,U_2232)
    | ~ class_Int_Onumber__ring(U_2231) ),
    inference(clausify,[status(thm)],[f_747_3]) ).

cnf(f_747_5,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2231),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2232)) = c_Groups_Ozero__class_Ozero(U_2231)
    | ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2232))
    | ~ sP193(U_2231,U_2232) ),
    inference(clausify,[status(thm)],[f_747_3]) ).

cnf(f_747_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2231),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2232)) = c_Int_Onumber__class_Onumber__of(U_2231,U_2232)
    | c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2232))
    | ~ sP193(U_2231,U_2232) ),
    inference(clausify,[status(thm)],[f_747_3]) ).

fof(f_748_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_748_2,plain,
    ! [U_2238,U_2237,U_2236,U_2235,U_2234,U_2233] :
      ( c_Orderings_Oord__class_Oless(U_2233,c_Groups_Oplus__class_Oplus(U_2233,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2233),U_2237),U_2234),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2233),U_2238),U_2236)),U_2235)
      | c_Groups_Oplus__class_Oplus(U_2233,U_2237,U_2238) != c_Groups_Oone__class_Oone(U_2233)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2233,c_Groups_Ozero__class_Ozero(U_2233),U_2238)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2233,c_Groups_Ozero__class_Ozero(U_2233),U_2237)
      | ~ c_Orderings_Oord__class_Oless(U_2233,U_2236,U_2235)
      | ~ c_Orderings_Oord__class_Oless(U_2233,U_2234,U_2235)
      | ~ class_Rings_Olinordered__semiring__1__strict(U_2233) ),
    inference(variable_rename,[status(thm)],[f_748_1]) ).

fof(f_748_3,plain,
    ! [U_2234,U_2235,U_2236,U_2233,U_2237,U_2238] :
      ( c_Orderings_Oord__class_Oless(U_2233,c_Groups_Oplus__class_Oplus(U_2233,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2233),U_2237),U_2234),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2233),U_2238),U_2236)),U_2235)
      | c_Groups_Oplus__class_Oplus(U_2233,U_2237,U_2238) != c_Groups_Oone__class_Oone(U_2233)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2233,c_Groups_Ozero__class_Ozero(U_2233),U_2238)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2233,c_Groups_Ozero__class_Ozero(U_2233),U_2237)
      | ~ c_Orderings_Oord__class_Oless(U_2233,U_2236,U_2235)
      | ~ c_Orderings_Oord__class_Oless(U_2233,U_2234,U_2235)
      | ~ class_Rings_Olinordered__semiring__1__strict(U_2233) ),
    inference(definitional_conversion,[status(esa)],[f_748_2]) ).

cnf(f_748_4,plain,
    ( c_Orderings_Oord__class_Oless(U_2233,c_Groups_Oplus__class_Oplus(U_2233,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2233),U_2237),U_2234),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2233),U_2238),U_2236)),U_2235)
    | c_Groups_Oplus__class_Oplus(U_2233,U_2237,U_2238) != c_Groups_Oone__class_Oone(U_2233)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2233,c_Groups_Ozero__class_Ozero(U_2233),U_2238)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2233,c_Groups_Ozero__class_Ozero(U_2233),U_2237)
    | ~ c_Orderings_Oord__class_Oless(U_2233,U_2236,U_2235)
    | ~ c_Orderings_Oord__class_Oless(U_2233,U_2234,U_2235)
    | ~ class_Rings_Olinordered__semiring__1__strict(U_2233) ),
    inference(clausify,[status(thm)],[f_748_3]) ).

fof(f_749_1,plain,
    ! [V_y_2,V_x_2,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_x_2,V_y_2))))
        | ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2) )
        | ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))))
          & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_y_2,V_x_2) ) )
      & ( ( ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2) )
          & ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))))
            | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_y_2,V_x_2) ) )
        | ~ hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_x_2,V_y_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zdiff__int__split]) ).

fof(f_749_2,plain,
    ! [U_2241,U_2240,U_2239] :
      ( ( hBOOL(hAPP(U_2239,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2240,U_2241))))
        | ( ~ hBOOL(hAPP(U_2239,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2240,U_2241) )
        | ( ~ hBOOL(hAPP(U_2239,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2240),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2241))))
          & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2241,U_2240) ) )
      & ( ( ( hBOOL(hAPP(U_2239,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2240,U_2241) )
          & ( hBOOL(hAPP(U_2239,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2240),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2241))))
            | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2241,U_2240) ) )
        | ~ hBOOL(hAPP(U_2239,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2240,U_2241)))) ) ),
    inference(variable_rename,[status(thm)],[f_749_1]) ).

fof(f_749_3,plain,
    ( ! [U_2247,U_2245,U_2243] :
        ( hBOOL(hAPP(U_2243,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2245,U_2247))))
        | ( ~ hBOOL(hAPP(U_2243,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2245,U_2247) )
        | ( ~ hBOOL(hAPP(U_2243,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2245),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2247))))
          & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2247,U_2245) ) )
    & ! [U_2246,U_2244,U_2242] :
        ( ( ( hBOOL(hAPP(U_2242,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2244,U_2246) )
          & ( hBOOL(hAPP(U_2242,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2244),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2246))))
            | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2246,U_2244) ) )
        | ~ hBOOL(hAPP(U_2242,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2244,U_2246)))) ) ),
    inference(miniscope,[status(thm)],[f_749_2]) ).

fof(f_749_4,plain,
    ( ! [U_2243,U_2245,U_2247] :
        ( ~ hBOOL(hAPP(U_2243,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP196(U_2243,U_2245,U_2247) )
    & ! [U_2243,U_2245,U_2247] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2245,U_2247)
        | ~ sP196(U_2243,U_2245,U_2247) )
    & ! [U_2243,U_2245,U_2247] :
        ( ~ hBOOL(hAPP(U_2243,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2245),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2247))))
        | ~ sP195(U_2243,U_2245,U_2247) )
    & ! [U_2243,U_2245,U_2247] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2247,U_2245)
        | ~ sP195(U_2243,U_2245,U_2247) )
    & ! [U_2244,U_2246,U_2242] :
        ( hBOOL(hAPP(U_2242,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2244,U_2246)
        | ~ sP194(U_2244,U_2246,U_2242) )
    & ! [U_2244,U_2246,U_2242] :
        ( hBOOL(hAPP(U_2242,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2244),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2246))))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2246,U_2244)
        | ~ sP194(U_2244,U_2246,U_2242) )
    & ! [U_2243,U_2245,U_2247] :
        ( hBOOL(hAPP(U_2243,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2245,U_2247))))
        | sP196(U_2243,U_2245,U_2247)
        | sP195(U_2243,U_2245,U_2247) )
    & ! [U_2244,U_2246,U_2242] :
        ( sP194(U_2244,U_2246,U_2242)
        | ~ hBOOL(hAPP(U_2242,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2244,U_2246)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP194,sP195,sP196])],[f_749_3]) ).

cnf(f_749_5,plain,
    ( sP194(U_2244,U_2246,U_2242)
    | ~ hBOOL(hAPP(U_2242,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2244,U_2246)))) ),
    inference(clausify,[status(thm)],[f_749_4]) ).

cnf(f_749_6,plain,
    ( hBOOL(hAPP(U_2243,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2245,U_2247))))
    | sP196(U_2243,U_2245,U_2247)
    | sP195(U_2243,U_2245,U_2247) ),
    inference(clausify,[status(thm)],[f_749_4]) ).

cnf(f_749_7,plain,
    ( hBOOL(hAPP(U_2242,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2244),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2246))))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2246,U_2244)
    | ~ sP194(U_2244,U_2246,U_2242) ),
    inference(clausify,[status(thm)],[f_749_4]) ).

cnf(f_749_8,plain,
    ( hBOOL(hAPP(U_2242,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2244,U_2246)
    | ~ sP194(U_2244,U_2246,U_2242) ),
    inference(clausify,[status(thm)],[f_749_4]) ).

cnf(f_749_9,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2247,U_2245)
    | ~ sP195(U_2243,U_2245,U_2247) ),
    inference(clausify,[status(thm)],[f_749_4]) ).

cnf(f_749_10,plain,
    ( ~ hBOOL(hAPP(U_2243,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2245),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2247))))
    | ~ sP195(U_2243,U_2245,U_2247) ),
    inference(clausify,[status(thm)],[f_749_4]) ).

cnf(f_749_11,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2245,U_2247)
    | ~ sP196(U_2243,U_2245,U_2247) ),
    inference(clausify,[status(thm)],[f_749_4]) ).

cnf(f_749_12,plain,
    ( ~ hBOOL(hAPP(U_2243,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP196(U_2243,U_2245,U_2247) ),
    inference(clausify,[status(thm)],[f_749_4]) ).

fof(f_750_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_750_2,plain,
    ! [U_2250,U_2249,U_2248] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2250,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_2249)
      | U_2248 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2249,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2248),U_2250))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2248) ),
    inference(variable_rename,[status(thm)],[f_750_1]) ).

fof(f_750_3,plain,
    ! [U_2249,U_2250,U_2248] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2250,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_2249)
      | U_2248 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2249,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2248),U_2250))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2248) ),
    inference(definitional_conversion,[status(esa)],[f_750_2]) ).

cnf(f_750_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2250,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_2249)
    | U_2248 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2249,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2248),U_2250))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2248) ),
    inference(clausify,[status(thm)],[f_750_3]) ).

fof(f_751_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_751_2,plain,
    ! [U_2253,U_2252,U_2251] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2253)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2252,U_2251)
      | U_2251 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2252,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2251),U_2253))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2251) ),
    inference(variable_rename,[status(thm)],[f_751_1]) ).

fof(f_751_3,plain,
    ! [U_2251,U_2253,U_2252] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2253)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2252,U_2251)
      | U_2251 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2252,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2251),U_2253))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2251) ),
    inference(definitional_conversion,[status(esa)],[f_751_2]) ).

cnf(f_751_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2253)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2252,U_2251)
    | U_2251 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2252,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2251),U_2253))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2251) ),
    inference(clausify,[status(thm)],[f_751_3]) ).

fof(f_752_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_752_2,plain,
    ! [U_2259,U_2258,U_2257,U_2256,U_2255,U_2254] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2258,U_2255)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2257,U_2254)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2257)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2259)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2256,U_2254)
      | ~ 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_2257),U_2258),U_2259),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_2254),U_2255),U_2256) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2257),U_2258),U_2259) ),
    inference(variable_rename,[status(thm)],[f_752_1]) ).

fof(f_752_3,plain,
    ! [U_2259,U_2254,U_2257,U_2258,U_2255,U_2256] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2258,U_2255)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2257,U_2254)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2257)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2259)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2256,U_2254)
      | ~ 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_2257),U_2258),U_2259),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_2254),U_2255),U_2256) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2257),U_2258),U_2259) ),
    inference(definitional_conversion,[status(esa)],[f_752_2]) ).

cnf(f_752_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2258,U_2255)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2257,U_2254)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2257)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2259)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2256,U_2254)
    | ~ 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_2257),U_2258),U_2259),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_2254),U_2255),U_2256) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2257),U_2258),U_2259) ),
    inference(clausify,[status(thm)],[f_752_3]) ).

fof(f_753_1,plain,
    ! [V_b_2,V_a_2,V_c_2] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a_2),V_c_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_c_2)
          | V_a_2 != V_b_2 )
        & ( V_a_2 = V_b_2
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a_2),V_c_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_c_2) ) )
      | V_c_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(fof_nnf,[status(thm)],[fact_real__mult__right__cancel]) ).

fof(f_753_2,plain,
    ! [U_2262,U_2261,U_2260] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2261),U_2260) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2262),U_2260)
          | U_2261 != U_2262 )
        & ( U_2261 = U_2262
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2261),U_2260) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2262),U_2260) ) )
      | U_2260 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(variable_rename,[status(thm)],[f_753_1]) ).

fof(f_753_3,plain,
    ( ! [U_2260,U_2261,U_2262] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2261),U_2260) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2262),U_2260)
        | U_2261 != U_2262
        | ~ sP197(U_2260,U_2261,U_2262) )
    & ! [U_2260,U_2261,U_2262] :
        ( U_2261 = U_2262
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2261),U_2260) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2262),U_2260)
        | ~ sP197(U_2260,U_2261,U_2262) )
    & ! [U_2260,U_2261,U_2262] :
        ( sP197(U_2260,U_2261,U_2262)
        | U_2260 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP197])],[f_753_2]) ).

cnf(f_753_4,plain,
    ( sP197(U_2260,U_2261,U_2262)
    | U_2260 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(clausify,[status(thm)],[f_753_3]) ).

cnf(f_753_5,plain,
    ( U_2261 = U_2262
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2261),U_2260) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2262),U_2260)
    | ~ sP197(U_2260,U_2261,U_2262) ),
    inference(clausify,[status(thm)],[f_753_3]) ).

cnf(f_753_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2261),U_2260) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2262),U_2260)
    | U_2261 != U_2262
    | ~ sP197(U_2260,U_2261,U_2262) ),
    inference(clausify,[status(thm)],[f_753_3]) ).

fof(f_754_1,plain,
    ! [V_b_2,V_a_2,V_c_2] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_b_2)
          | V_a_2 != V_b_2 )
        & ( V_a_2 = V_b_2
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_a_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_b_2) ) )
      | V_c_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(fof_nnf,[status(thm)],[fact_real__mult__left__cancel]) ).

fof(f_754_2,plain,
    ! [U_2265,U_2264,U_2263] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2263),U_2264) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2263),U_2265)
          | U_2264 != U_2265 )
        & ( U_2264 = U_2265
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2263),U_2264) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2263),U_2265) ) )
      | U_2263 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(variable_rename,[status(thm)],[f_754_1]) ).

fof(f_754_3,plain,
    ( ! [U_2265,U_2263,U_2264] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2263),U_2264) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2263),U_2265)
        | U_2264 != U_2265
        | ~ sP198(U_2265,U_2263,U_2264) )
    & ! [U_2265,U_2263,U_2264] :
        ( U_2264 = U_2265
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2263),U_2264) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2263),U_2265)
        | ~ sP198(U_2265,U_2263,U_2264) )
    & ! [U_2265,U_2263,U_2264] :
        ( sP198(U_2265,U_2263,U_2264)
        | U_2263 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP198])],[f_754_2]) ).

cnf(f_754_4,plain,
    ( sP198(U_2265,U_2263,U_2264)
    | U_2263 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(clausify,[status(thm)],[f_754_3]) ).

cnf(f_754_5,plain,
    ( U_2264 = U_2265
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2263),U_2264) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2263),U_2265)
    | ~ sP198(U_2265,U_2263,U_2264) ),
    inference(clausify,[status(thm)],[f_754_3]) ).

cnf(f_754_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2263),U_2264) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2263),U_2265)
    | U_2264 != U_2265
    | ~ sP198(U_2265,U_2263,U_2264) ),
    inference(clausify,[status(thm)],[f_754_3]) ).

fof(f_755_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_755_2,plain,
    ! [U_2266] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2266) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_755_1]) ).

fof(f_755_3,plain,
    ! [U_2266] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2266) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_755_2]) ).

cnf(f_755_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2266) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_755_3]) ).

fof(f_756_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_756_2,plain,
    ! [U_2267] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2267),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_756_1]) ).

fof(f_756_3,plain,
    ! [U_2267] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2267),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_756_2]) ).

cnf(f_756_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2267),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_756_3]) ).

fof(f_757_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_757_2,plain,
    ! [U_2269,U_2268] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2268),U_2269) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( U_2269 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_2268 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( U_2269 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2268 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2268),U_2269) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_757_1]) ).

fof(f_757_3,plain,
    ( ! [U_2273,U_2271] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2271),U_2273) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( U_2273 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_2271 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_2272,U_2270] :
        ( U_2272 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2270 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2270),U_2272) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_757_2]) ).

fof(f_757_4,plain,
    ( ! [U_2273,U_2271] :
        ( U_2273 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP199(U_2273,U_2271) )
    & ! [U_2273,U_2271] :
        ( U_2271 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP199(U_2273,U_2271) )
    & ! [U_2273,U_2271] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2271),U_2273) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | sP199(U_2273,U_2271) )
    & ! [U_2272,U_2270] :
        ( U_2272 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2270 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2270),U_2272) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP199])],[f_757_3]) ).

cnf(f_757_5,plain,
    ( U_2272 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_2270 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2270),U_2272) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_757_4]) ).

cnf(f_757_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2271),U_2273) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | sP199(U_2273,U_2271) ),
    inference(clausify,[status(thm)],[f_757_4]) ).

cnf(f_757_7,plain,
    ( U_2271 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP199(U_2273,U_2271) ),
    inference(clausify,[status(thm)],[f_757_4]) ).

cnf(f_757_8,plain,
    ( U_2273 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP199(U_2273,U_2271) ),
    inference(clausify,[status(thm)],[f_757_4]) ).

fof(f_758_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_758_2,plain,
    ! [U_2276,U_2275,U_2274] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2274),U_2275) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2274),U_2276)
        | ( U_2274 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_2275 != U_2276 ) )
      & ( U_2274 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2275 = U_2276
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2274),U_2275) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2274),U_2276) ) ),
    inference(variable_rename,[status(thm)],[f_758_1]) ).

fof(f_758_3,plain,
    ( ! [U_2282,U_2280,U_2278] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2278),U_2280) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2278),U_2282)
        | ( U_2278 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_2280 != U_2282 ) )
    & ! [U_2281,U_2279,U_2277] :
        ( U_2277 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2279 = U_2281
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2277),U_2279) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2277),U_2281) ) ),
    inference(miniscope,[status(thm)],[f_758_2]) ).

fof(f_758_4,plain,
    ( ! [U_2280,U_2282,U_2278] :
        ( U_2278 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP200(U_2280,U_2282,U_2278) )
    & ! [U_2280,U_2282,U_2278] :
        ( U_2280 != U_2282
        | ~ sP200(U_2280,U_2282,U_2278) )
    & ! [U_2280,U_2282,U_2278] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2278),U_2280) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2278),U_2282)
        | sP200(U_2280,U_2282,U_2278) )
    & ! [U_2279,U_2277,U_2281] :
        ( U_2277 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2279 = U_2281
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2277),U_2279) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2277),U_2281) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP200])],[f_758_3]) ).

cnf(f_758_5,plain,
    ( U_2277 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_2279 = U_2281
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2277),U_2279) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2277),U_2281) ),
    inference(clausify,[status(thm)],[f_758_4]) ).

cnf(f_758_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2278),U_2280) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2278),U_2282)
    | sP200(U_2280,U_2282,U_2278) ),
    inference(clausify,[status(thm)],[f_758_4]) ).

cnf(f_758_7,plain,
    ( U_2280 != U_2282
    | ~ sP200(U_2280,U_2282,U_2278) ),
    inference(clausify,[status(thm)],[f_758_4]) ).

cnf(f_758_8,plain,
    ( U_2278 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP200(U_2280,U_2282,U_2278) ),
    inference(clausify,[status(thm)],[f_758_4]) ).

fof(f_759_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_759_2,plain,
    ! [U_2285,U_2284,U_2283] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2283),U_2284) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2285),U_2284)
        | ( U_2284 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_2283 != U_2285 ) )
      & ( U_2284 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2283 = U_2285
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2283),U_2284) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2285),U_2284) ) ),
    inference(variable_rename,[status(thm)],[f_759_1]) ).

fof(f_759_3,plain,
    ( ! [U_2291,U_2289,U_2287] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2287),U_2289) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2291),U_2289)
        | ( U_2289 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_2287 != U_2291 ) )
    & ! [U_2290,U_2288,U_2286] :
        ( U_2288 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2286 = U_2290
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2286),U_2288) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2290),U_2288) ) ),
    inference(miniscope,[status(thm)],[f_759_2]) ).

fof(f_759_4,plain,
    ( ! [U_2291,U_2289,U_2287] :
        ( U_2289 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP201(U_2291,U_2289,U_2287) )
    & ! [U_2291,U_2289,U_2287] :
        ( U_2287 != U_2291
        | ~ sP201(U_2291,U_2289,U_2287) )
    & ! [U_2291,U_2289,U_2287] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2287),U_2289) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2291),U_2289)
        | sP201(U_2291,U_2289,U_2287) )
    & ! [U_2288,U_2286,U_2290] :
        ( U_2288 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2286 = U_2290
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2286),U_2288) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2290),U_2288) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP201])],[f_759_3]) ).

cnf(f_759_5,plain,
    ( U_2288 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_2286 = U_2290
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2286),U_2288) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2290),U_2288) ),
    inference(clausify,[status(thm)],[f_759_4]) ).

cnf(f_759_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2287),U_2289) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2291),U_2289)
    | sP201(U_2291,U_2289,U_2287) ),
    inference(clausify,[status(thm)],[f_759_4]) ).

cnf(f_759_7,plain,
    ( U_2287 != U_2291
    | ~ sP201(U_2291,U_2289,U_2287) ),
    inference(clausify,[status(thm)],[f_759_4]) ).

cnf(f_759_8,plain,
    ( U_2289 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP201(U_2291,U_2289,U_2287) ),
    inference(clausify,[status(thm)],[f_759_4]) ).

fof(f_760_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_760_2,plain,
    ! [U_2294,U_2293,U_2292] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2292,U_2293)),U_2294) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2292),U_2294),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2293),U_2294)),
    inference(variable_rename,[status(thm)],[f_760_1]) ).

fof(f_760_3,plain,
    ! [U_2292,U_2293,U_2294] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2292,U_2293)),U_2294) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2292),U_2294),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2293),U_2294)),
    inference(definitional_conversion,[status(esa)],[f_760_2]) ).

cnf(f_760_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2292,U_2293)),U_2294) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2292),U_2294),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2293),U_2294)),
    inference(clausify,[status(thm)],[f_760_3]) ).

fof(f_761_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_761_2,plain,
    ! [U_2297,U_2296,U_2295] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2295),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2296,U_2297)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2295),U_2296),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2295),U_2297)),
    inference(variable_rename,[status(thm)],[f_761_1]) ).

fof(f_761_3,plain,
    ! [U_2295,U_2296,U_2297] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2295),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2296,U_2297)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2295),U_2296),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2295),U_2297)),
    inference(definitional_conversion,[status(esa)],[f_761_2]) ).

cnf(f_761_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2295),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2296,U_2297)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2295),U_2296),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2295),U_2297)),
    inference(clausify,[status(thm)],[f_761_3]) ).

fof(f_762_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_762_2,plain,
    ! [U_2300,U_2299,U_2298] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2298,U_2299)),U_2300) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2298),U_2300),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2299),U_2300)),
    inference(variable_rename,[status(thm)],[f_762_1]) ).

fof(f_762_3,plain,
    ! [U_2298,U_2299,U_2300] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2298,U_2299)),U_2300) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2298),U_2300),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2299),U_2300)),
    inference(definitional_conversion,[status(esa)],[f_762_2]) ).

cnf(f_762_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2298,U_2299)),U_2300) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2298),U_2300),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2299),U_2300)),
    inference(clausify,[status(thm)],[f_762_3]) ).

fof(f_763_1,plain,
    ! [V_n,V_m] : hAPP(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),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)),
    inference(fof_nnf,[status(thm)],[fact_real__of__nat__mult]) ).

fof(f_763_2,plain,
    ! [U_2302,U_2301] : hAPP(c_RealDef_Oreal(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2301),U_2302)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_2301)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_2302)),
    inference(variable_rename,[status(thm)],[f_763_1]) ).

fof(f_763_3,plain,
    ! [U_2301,U_2302] : hAPP(c_RealDef_Oreal(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2301),U_2302)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_2301)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_2302)),
    inference(definitional_conversion,[status(esa)],[f_763_2]) ).

cnf(f_763_4,plain,
    hAPP(c_RealDef_Oreal(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2301),U_2302)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_2301)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_2302)),
    inference(clausify,[status(thm)],[f_763_3]) ).

fof(f_764_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_764_2,plain,
    ! [U_2305,U_2304,U_2303] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2303),U_2304)),U_2305) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2303),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2304),U_2305)),
    inference(variable_rename,[status(thm)],[f_764_1]) ).

fof(f_764_3,plain,
    ! [U_2303,U_2304,U_2305] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2303),U_2304)),U_2305) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2303),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2304),U_2305)),
    inference(definitional_conversion,[status(esa)],[f_764_2]) ).

cnf(f_764_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2303),U_2304)),U_2305) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2303),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2304),U_2305)),
    inference(clausify,[status(thm)],[f_764_3]) ).

fof(f_765_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_765_2,plain,
    ! [U_2307,U_2306] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2306),U_2307) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2307),U_2306),
    inference(variable_rename,[status(thm)],[f_765_1]) ).

fof(f_765_3,plain,
    ! [U_2306,U_2307] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2306),U_2307) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2307),U_2306),
    inference(definitional_conversion,[status(esa)],[f_765_2]) ).

cnf(f_765_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2306),U_2307) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2307),U_2306),
    inference(clausify,[status(thm)],[f_765_3]) ).

fof(f_766_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_766_2,plain,
    ! [U_2310,U_2309,U_2308] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2308),U_2309)),U_2310) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2308),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2309),U_2310)),
    inference(variable_rename,[status(thm)],[f_766_1]) ).

fof(f_766_3,plain,
    ! [U_2308,U_2309,U_2310] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2308),U_2309)),U_2310) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2308),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2309),U_2310)),
    inference(definitional_conversion,[status(esa)],[f_766_2]) ).

cnf(f_766_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2308),U_2309)),U_2310) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2308),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2309),U_2310)),
    inference(clausify,[status(thm)],[f_766_3]) ).

fof(f_767_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_767_2,plain,
    ! [U_2312,U_2311] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2311),U_2312) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2312),U_2311),
    inference(variable_rename,[status(thm)],[f_767_1]) ).

fof(f_767_3,plain,
    ! [U_2311,U_2312] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2311),U_2312) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2312),U_2311),
    inference(definitional_conversion,[status(esa)],[f_767_2]) ).

cnf(f_767_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2311),U_2312) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2312),U_2311),
    inference(clausify,[status(thm)],[f_767_3]) ).

fof(f_768_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)
        | V_m_2 != V_n_2 )
      & ( V_m_2 = V_n_2
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_int__int__eq]) ).

fof(f_768_2,plain,
    ! [U_2314,U_2313] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2313) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2314)
        | U_2313 != U_2314 )
      & ( U_2313 = U_2314
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2313) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2314) ) ),
    inference(variable_rename,[status(thm)],[f_768_1]) ).

fof(f_768_3,plain,
    ( ! [U_2318,U_2316] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2316) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2318)
        | U_2316 != U_2318 )
    & ! [U_2317,U_2315] :
        ( U_2315 = U_2317
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2315) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2317) ) ),
    inference(miniscope,[status(thm)],[f_768_2]) ).

fof(f_768_4,plain,
    ( ! [U_2316,U_2318] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2316) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2318)
        | U_2316 != U_2318 )
    & ! [U_2317,U_2315] :
        ( U_2315 = U_2317
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2315) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2317) ) ),
    inference(definitional_conversion,[status(esa)],[f_768_3]) ).

cnf(f_768_5,plain,
    ( U_2315 = U_2317
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2315) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2317) ),
    inference(clausify,[status(thm)],[f_768_4]) ).

cnf(f_768_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2316) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2318)
    | U_2316 != U_2318 ),
    inference(clausify,[status(thm)],[f_768_4]) ).

fof(f_769_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),
    inference(fof_nnf,[status(thm)],[fact_zmult__int]) ).

fof(f_769_2,plain,
    ! [U_2320,U_2319] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2319)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2320)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2319),U_2320)),
    inference(variable_rename,[status(thm)],[f_769_1]) ).

fof(f_769_3,plain,
    ! [U_2319,U_2320] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2319)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2320)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2319),U_2320)),
    inference(definitional_conversion,[status(esa)],[f_769_2]) ).

cnf(f_769_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2319)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2320)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2319),U_2320)),
    inference(clausify,[status(thm)],[f_769_3]) ).

fof(f_770_1,plain,
    ! [V_n,V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),
    inference(fof_nnf,[status(thm)],[fact_int__mult]) ).

fof(f_770_2,plain,
    ! [U_2322,U_2321] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2321),U_2322)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2321)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2322)),
    inference(variable_rename,[status(thm)],[f_770_1]) ).

fof(f_770_3,plain,
    ! [U_2321,U_2322] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2321),U_2322)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2321)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2322)),
    inference(definitional_conversion,[status(esa)],[f_770_2]) ).

cnf(f_770_4,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2321),U_2322)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2321)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2322)),
    inference(clausify,[status(thm)],[f_770_3]) ).

fof(f_771_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_771_2,plain,
    ! [U_2326,U_2325,U_2324,U_2323] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2323),U_2325),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2324),U_2326))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2325,U_2326)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2323,U_2324) ),
    inference(variable_rename,[status(thm)],[f_771_1]) ).

fof(f_771_3,plain,
    ! [U_2323,U_2324,U_2325,U_2326] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2323),U_2325),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2324),U_2326))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2325,U_2326)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2323,U_2324) ),
    inference(definitional_conversion,[status(esa)],[f_771_2]) ).

cnf(f_771_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2323),U_2325),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2324),U_2326))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2325,U_2326)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2323,U_2324) ),
    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_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_772_2,plain,
    ! [U_2329,U_2328,U_2327] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2329),U_2327),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2329),U_2328))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2327,U_2328) ),
    inference(variable_rename,[status(thm)],[f_772_1]) ).

fof(f_772_3,plain,
    ! [U_2329,U_2328,U_2327] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2329),U_2327),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2329),U_2328))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2327,U_2328) ),
    inference(definitional_conversion,[status(esa)],[f_772_2]) ).

cnf(f_772_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2329),U_2327),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2329),U_2328))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2327,U_2328) ),
    inference(clausify,[status(thm)],[f_772_3]) ).

fof(f_773_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_773_2,plain,
    ! [U_2332,U_2331,U_2330] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2330),U_2332),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2331),U_2332))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2330,U_2331) ),
    inference(variable_rename,[status(thm)],[f_773_1]) ).

fof(f_773_3,plain,
    ! [U_2330,U_2331,U_2332] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2330),U_2332),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2331),U_2332))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2330,U_2331) ),
    inference(definitional_conversion,[status(esa)],[f_773_2]) ).

cnf(f_773_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2330),U_2332),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2331),U_2332))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2330,U_2331) ),
    inference(clausify,[status(thm)],[f_773_3]) ).

fof(f_774_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_774_2,plain,
    ! [U_2333] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2333,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2333),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2333),U_2333))),
    inference(variable_rename,[status(thm)],[f_774_1]) ).

fof(f_774_3,plain,
    ! [U_2333] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2333,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2333),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2333),U_2333))),
    inference(definitional_conversion,[status(esa)],[f_774_2]) ).

cnf(f_774_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2333,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2333),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2333),U_2333))),
    inference(clausify,[status(thm)],[f_774_3]) ).

fof(f_775_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_775_2,plain,
    ! [U_2334] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2334,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2334),U_2334)),
    inference(variable_rename,[status(thm)],[f_775_1]) ).

fof(f_775_3,plain,
    ! [U_2334] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2334,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2334),U_2334)),
    inference(definitional_conversion,[status(esa)],[f_775_2]) ).

cnf(f_775_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2334,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2334),U_2334)),
    inference(clausify,[status(thm)],[f_775_3]) ).

fof(f_776_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_776_2,plain,
    ! [U_2337,U_2336,U_2335] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2335)),U_2336) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2335)),U_2337)
        | U_2336 != U_2337 )
      & ( U_2336 = U_2337
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2335)),U_2336) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2335)),U_2337) ) ),
    inference(variable_rename,[status(thm)],[f_776_1]) ).

fof(f_776_3,plain,
    ( ! [U_2343,U_2341] :
        ( ! [U_2339] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2339)),U_2341) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2339)),U_2343)
        | U_2341 != U_2343 )
    & ! [U_2342,U_2340] :
        ( ! [U_2338] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2338)),U_2340) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2338)),U_2342)
        | U_2340 = U_2342 ) ),
    inference(miniscope,[status(thm)],[f_776_2]) ).

fof(f_776_4,plain,
    ( ! [U_2343,U_2339,U_2341] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2339)),U_2341) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2339)),U_2343)
        | U_2341 != U_2343 )
    & ! [U_2342,U_2340,U_2338] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2338)),U_2340) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2338)),U_2342)
        | U_2340 = U_2342 ) ),
    inference(definitional_conversion,[status(esa)],[f_776_3]) ).

cnf(f_776_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2338)),U_2340) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2338)),U_2342)
    | U_2340 = U_2342 ),
    inference(clausify,[status(thm)],[f_776_4]) ).

cnf(f_776_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2339)),U_2341) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2339)),U_2343)
    | U_2341 != U_2343 ),
    inference(clausify,[status(thm)],[f_776_4]) ).

fof(f_777_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_777_2,plain,
    ! [U_2346,U_2345,U_2344] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2344,U_2345)),U_2346) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2344),U_2346),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2345),U_2346)),
    inference(variable_rename,[status(thm)],[f_777_1]) ).

fof(f_777_3,plain,
    ! [U_2344,U_2345,U_2346] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2344,U_2345)),U_2346) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2344),U_2346),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2345),U_2346)),
    inference(definitional_conversion,[status(esa)],[f_777_2]) ).

cnf(f_777_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2344,U_2345)),U_2346) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2344),U_2346),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2345),U_2346)),
    inference(clausify,[status(thm)],[f_777_3]) ).

fof(f_778_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_778_2,plain,
    ! [U_2349,U_2348,U_2347] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2347),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2348,U_2349)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2347),U_2348),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2347),U_2349)),
    inference(variable_rename,[status(thm)],[f_778_1]) ).

fof(f_778_3,plain,
    ! [U_2347,U_2348,U_2349] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2347),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2348,U_2349)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2347),U_2348),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2347),U_2349)),
    inference(definitional_conversion,[status(esa)],[f_778_2]) ).

cnf(f_778_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2347),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2348,U_2349)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2347),U_2348),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2347),U_2349)),
    inference(clausify,[status(thm)],[f_778_3]) ).

fof(f_779_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)
        | V_x_2 != V_y_2 )
      & ( V_x_2 = V_y_2
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__relations_I1_J]) ).

fof(f_779_2,plain,
    ! [U_2351,U_2350] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2350) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2351)
        | U_2350 != U_2351 )
      & ( U_2350 = U_2351
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2350) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2351) ) ),
    inference(variable_rename,[status(thm)],[f_779_1]) ).

fof(f_779_3,plain,
    ( ! [U_2355,U_2353] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2353) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2355)
        | U_2353 != U_2355 )
    & ! [U_2354,U_2352] :
        ( U_2352 = U_2354
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2352) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2354) ) ),
    inference(miniscope,[status(thm)],[f_779_2]) ).

fof(f_779_4,plain,
    ( ! [U_2353,U_2355] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2353) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2355)
        | U_2353 != U_2355 )
    & ! [U_2354,U_2352] :
        ( U_2352 = U_2354
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2352) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2354) ) ),
    inference(definitional_conversion,[status(esa)],[f_779_3]) ).

cnf(f_779_5,plain,
    ( U_2352 = U_2354
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2352) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2354) ),
    inference(clausify,[status(thm)],[f_779_4]) ).

cnf(f_779_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2353) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2355)
    | U_2353 != U_2355 ),
    inference(clausify,[status(thm)],[f_779_4]) ).

fof(f_780_1,plain,
    ! [V_y,V_x] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y)),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J]) ).

fof(f_780_2,plain,
    ! [U_2357,U_2356] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2356)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2357)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2356),U_2357)),
    inference(variable_rename,[status(thm)],[f_780_1]) ).

fof(f_780_3,plain,
    ! [U_2356,U_2357] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2356)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2357)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2356),U_2357)),
    inference(definitional_conversion,[status(esa)],[f_780_2]) ).

cnf(f_780_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2356)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2357)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2356),U_2357)),
    inference(clausify,[status(thm)],[f_780_3]) ).

fof(f_781_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_781_2,plain,
    ! [U_2358] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_2358) = U_2358,
    inference(variable_rename,[status(thm)],[f_781_1]) ).

fof(f_781_3,plain,
    ! [U_2358] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_2358) = U_2358,
    inference(definitional_conversion,[status(esa)],[f_781_2]) ).

cnf(f_781_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_2358) = U_2358,
    inference(clausify,[status(thm)],[f_781_3]) ).

fof(f_782_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_782_2,plain,
    ! [U_2359] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2359) = U_2359,
    inference(variable_rename,[status(thm)],[f_782_1]) ).

fof(f_782_3,plain,
    ! [U_2359] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2359) = U_2359,
    inference(definitional_conversion,[status(esa)],[f_782_2]) ).

cnf(f_782_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2359) = U_2359,
    inference(clausify,[status(thm)],[f_782_3]) ).

fof(f_783_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_783_2,plain,
    ! [U_2361,U_2360] :
      ( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2360),U_2361)
        | U_2361 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2360 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ( U_2361 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & U_2360 = 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_2360),U_2361) ) ),
    inference(variable_rename,[status(thm)],[f_783_1]) ).

fof(f_783_3,plain,
    ( ! [U_2365,U_2363] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2363),U_2365)
        | U_2365 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2363 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_2364,U_2362] :
        ( ( U_2364 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & U_2362 = 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_2362),U_2364) ) ),
    inference(miniscope,[status(thm)],[f_783_2]) ).

fof(f_783_4,plain,
    ( ! [U_2364,U_2362] :
        ( U_2364 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP202(U_2364,U_2362) )
    & ! [U_2364,U_2362] :
        ( U_2362 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP202(U_2364,U_2362) )
    & ! [U_2365,U_2363] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2363),U_2365)
        | U_2365 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2363 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_2364,U_2362] :
        ( sP202(U_2364,U_2362)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2362),U_2364) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP202])],[f_783_3]) ).

cnf(f_783_5,plain,
    ( sP202(U_2364,U_2362)
    | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2362),U_2364) ),
    inference(clausify,[status(thm)],[f_783_4]) ).

cnf(f_783_6,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2363),U_2365)
    | U_2365 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_2363 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_783_4]) ).

cnf(f_783_7,plain,
    ( U_2362 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP202(U_2364,U_2362) ),
    inference(clausify,[status(thm)],[f_783_4]) ).

cnf(f_783_8,plain,
    ( U_2364 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP202(U_2364,U_2362) ),
    inference(clausify,[status(thm)],[f_783_4]) ).

fof(f_784_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_784_2,plain,
    ! [U_2366] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2366),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2366,
    inference(variable_rename,[status(thm)],[f_784_1]) ).

fof(f_784_3,plain,
    ! [U_2366] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2366),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2366,
    inference(definitional_conversion,[status(esa)],[f_784_2]) ).

cnf(f_784_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2366),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2366,
    inference(clausify,[status(thm)],[f_784_3]) ).

fof(f_785_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_785_2,plain,
    ! [U_2368,U_2367] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2367),U_2368) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2368 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2367 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ( U_2368 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & U_2367 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2367),U_2368) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_785_1]) ).

fof(f_785_3,plain,
    ( ! [U_2372,U_2370] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2370),U_2372) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2372 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2370 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_2371,U_2369] :
        ( ( U_2371 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & U_2369 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2369),U_2371) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_785_2]) ).

fof(f_785_4,plain,
    ( ! [U_2371,U_2369] :
        ( U_2371 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP203(U_2371,U_2369) )
    & ! [U_2371,U_2369] :
        ( U_2369 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP203(U_2371,U_2369) )
    & ! [U_2372,U_2370] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2370),U_2372) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2372 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2370 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_2371,U_2369] :
        ( sP203(U_2371,U_2369)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2369),U_2371) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP203])],[f_785_3]) ).

cnf(f_785_5,plain,
    ( sP203(U_2371,U_2369)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2369),U_2371) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_785_4]) ).

cnf(f_785_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2370),U_2372) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_2372 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_2370 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_785_4]) ).

cnf(f_785_7,plain,
    ( U_2369 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP203(U_2371,U_2369) ),
    inference(clausify,[status(thm)],[f_785_4]) ).

cnf(f_785_8,plain,
    ( U_2371 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP203(U_2371,U_2369) ),
    inference(clausify,[status(thm)],[f_785_4]) ).

fof(f_786_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_786_2,plain,
    ! [U_2374,U_2373] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(U_2373)),c_RComplete_Onatfloor(U_2374)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2373),U_2374)))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2374)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2373) ),
    inference(variable_rename,[status(thm)],[f_786_1]) ).

fof(f_786_3,plain,
    ! [U_2373,U_2374] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(U_2373)),c_RComplete_Onatfloor(U_2374)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2373),U_2374)))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2374)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2373) ),
    inference(definitional_conversion,[status(esa)],[f_786_2]) ).

cnf(f_786_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_2373)),c_RComplete_Onatfloor(U_2374)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2373),U_2374)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2374)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2373) ),
    inference(clausify,[status(thm)],[f_786_3]) ).

fof(f_787_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_787_2,plain,
    ! [U_2376,U_2375] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2375),U_2376) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_2376 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_2375 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( ( U_2376 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_2375 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2375),U_2376) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_787_1]) ).

fof(f_787_3,plain,
    ( ! [U_2380,U_2378] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2378),U_2380) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_2380 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_2378 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    & ! [U_2379,U_2377] :
        ( ( U_2379 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_2377 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2377),U_2379) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_787_2]) ).

fof(f_787_4,plain,
    ( ! [U_2377,U_2379] :
        ( U_2379 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP204(U_2377,U_2379) )
    & ! [U_2377,U_2379] :
        ( U_2377 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP204(U_2377,U_2379) )
    & ! [U_2380,U_2378] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2378),U_2380) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_2380 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_2378 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    & ! [U_2377,U_2379] :
        ( sP204(U_2377,U_2379)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2377),U_2379) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP204])],[f_787_3]) ).

cnf(f_787_5,plain,
    ( sP204(U_2377,U_2379)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2377),U_2379) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_787_4]) ).

cnf(f_787_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2378),U_2380) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_2380 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_2378 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_787_4]) ).

cnf(f_787_7,plain,
    ( U_2377 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP204(U_2377,U_2379) ),
    inference(clausify,[status(thm)],[f_787_4]) ).

cnf(f_787_8,plain,
    ( U_2379 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP204(U_2377,U_2379) ),
    inference(clausify,[status(thm)],[f_787_4]) ).

fof(f_788_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_788_2,plain,
    ! [U_2382,U_2381] :
      ( ( 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_2381),U_2382))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2382)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2381) )
      & ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2382)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2381) )
        | ~ 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_2381),U_2382)) ) ),
    inference(variable_rename,[status(thm)],[f_788_1]) ).

fof(f_788_3,plain,
    ( ! [U_2386,U_2384] :
        ( 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_2384),U_2386))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2386)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2384) )
    & ! [U_2385,U_2383] :
        ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2385)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2383) )
        | ~ 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_2383),U_2385)) ) ),
    inference(miniscope,[status(thm)],[f_788_2]) ).

fof(f_788_4,plain,
    ( ! [U_2383,U_2385] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2385)
        | ~ sP205(U_2383,U_2385) )
    & ! [U_2383,U_2385] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2383)
        | ~ sP205(U_2383,U_2385) )
    & ! [U_2386,U_2384] :
        ( 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_2384),U_2386))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2386)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2384) )
    & ! [U_2383,U_2385] :
        ( sP205(U_2383,U_2385)
        | ~ 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_2383),U_2385)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP205])],[f_788_3]) ).

cnf(f_788_5,plain,
    ( sP205(U_2383,U_2385)
    | ~ 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_2383),U_2385)) ),
    inference(clausify,[status(thm)],[f_788_4]) ).

cnf(f_788_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_2384),U_2386))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2386)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2384) ),
    inference(clausify,[status(thm)],[f_788_4]) ).

cnf(f_788_7,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2383)
    | ~ sP205(U_2383,U_2385) ),
    inference(clausify,[status(thm)],[f_788_4]) ).

cnf(f_788_8,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2385)
    | ~ sP205(U_2383,U_2385) ),
    inference(clausify,[status(thm)],[f_788_4]) ).

fof(f_789_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_789_2,plain,
    ! [U_2389,U_2388,U_2387] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2387),U_2388),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2387),U_2389))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2388,U_2389)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2387) )
      & ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2388,U_2389)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2387) )
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2387),U_2388),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2387),U_2389)) ) ),
    inference(variable_rename,[status(thm)],[f_789_1]) ).

fof(f_789_3,plain,
    ( ! [U_2395,U_2393,U_2391] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2391),U_2393),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2391),U_2395))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2393,U_2395)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2391) )
    & ! [U_2394,U_2392,U_2390] :
        ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2392,U_2394)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2390) )
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2390),U_2392),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2390),U_2394)) ) ),
    inference(miniscope,[status(thm)],[f_789_2]) ).

fof(f_789_4,plain,
    ( ! [U_2394,U_2390,U_2392] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2392,U_2394)
        | ~ sP206(U_2394,U_2390,U_2392) )
    & ! [U_2394,U_2390,U_2392] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2390)
        | ~ sP206(U_2394,U_2390,U_2392) )
    & ! [U_2395,U_2391,U_2393] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2391),U_2393),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2391),U_2395))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2393,U_2395)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2391) )
    & ! [U_2394,U_2390,U_2392] :
        ( sP206(U_2394,U_2390,U_2392)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2390),U_2392),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2390),U_2394)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP206])],[f_789_3]) ).

cnf(f_789_5,plain,
    ( sP206(U_2394,U_2390,U_2392)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2390),U_2392),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2390),U_2394)) ),
    inference(clausify,[status(thm)],[f_789_4]) ).

cnf(f_789_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2391),U_2393),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2391),U_2395))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2393,U_2395)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2391) ),
    inference(clausify,[status(thm)],[f_789_4]) ).

cnf(f_789_7,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2390)
    | ~ sP206(U_2394,U_2390,U_2392) ),
    inference(clausify,[status(thm)],[f_789_4]) ).

cnf(f_789_8,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2392,U_2394)
    | ~ sP206(U_2394,U_2390,U_2392) ),
    inference(clausify,[status(thm)],[f_789_4]) ).

fof(f_790_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_790_2,plain,
    ! [U_2398,U_2397,U_2396] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2396),U_2397),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2398),U_2397))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2396,U_2398)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2397) )
      & ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2396,U_2398)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2397) )
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2396),U_2397),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2398),U_2397)) ) ),
    inference(variable_rename,[status(thm)],[f_790_1]) ).

fof(f_790_3,plain,
    ( ! [U_2404,U_2402,U_2400] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2400),U_2402),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2404),U_2402))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2400,U_2404)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2402) )
    & ! [U_2403,U_2401,U_2399] :
        ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2399,U_2403)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2401) )
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2399),U_2401),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2403),U_2401)) ) ),
    inference(miniscope,[status(thm)],[f_790_2]) ).

fof(f_790_4,plain,
    ( ! [U_2399,U_2401,U_2403] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2399,U_2403)
        | ~ sP207(U_2399,U_2401,U_2403) )
    & ! [U_2399,U_2401,U_2403] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2401)
        | ~ sP207(U_2399,U_2401,U_2403) )
    & ! [U_2400,U_2402,U_2404] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2400),U_2402),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2404),U_2402))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2400,U_2404)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2402) )
    & ! [U_2399,U_2401,U_2403] :
        ( sP207(U_2399,U_2401,U_2403)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2399),U_2401),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2403),U_2401)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP207])],[f_790_3]) ).

cnf(f_790_5,plain,
    ( sP207(U_2399,U_2401,U_2403)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2399),U_2401),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2403),U_2401)) ),
    inference(clausify,[status(thm)],[f_790_4]) ).

cnf(f_790_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2400),U_2402),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2404),U_2402))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2400,U_2404)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2402) ),
    inference(clausify,[status(thm)],[f_790_4]) ).

cnf(f_790_7,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2401)
    | ~ sP207(U_2399,U_2401,U_2403) ),
    inference(clausify,[status(thm)],[f_790_4]) ).

cnf(f_790_8,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2399,U_2403)
    | ~ sP207(U_2399,U_2401,U_2403) ),
    inference(clausify,[status(thm)],[f_790_4]) ).

fof(f_791_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_791_2,plain,
    ! [U_2407,U_2406,U_2405] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2405),U_2407),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2406),U_2407))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2407)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2405,U_2406) ),
    inference(variable_rename,[status(thm)],[f_791_1]) ).

fof(f_791_3,plain,
    ! [U_2405,U_2406,U_2407] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2405),U_2407),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2406),U_2407))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2407)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2405,U_2406) ),
    inference(definitional_conversion,[status(esa)],[f_791_2]) ).

cnf(f_791_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2405),U_2407),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2406),U_2407))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2407)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2405,U_2406) ),
    inference(clausify,[status(thm)],[f_791_3]) ).

fof(f_792_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_792_2,plain,
    ! [U_2410,U_2409,U_2408] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2410),U_2408),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2410),U_2409))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2410)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2408,U_2409) ),
    inference(variable_rename,[status(thm)],[f_792_1]) ).

fof(f_792_3,plain,
    ! [U_2408,U_2410,U_2409] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2410),U_2408),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2410),U_2409))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2410)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2408,U_2409) ),
    inference(definitional_conversion,[status(esa)],[f_792_2]) ).

cnf(f_792_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2410),U_2408),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2410),U_2409))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2410)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2408,U_2409) ),
    inference(clausify,[status(thm)],[f_792_3]) ).

fof(f_793_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_793_2,plain,
    ! [U_2413,U_2412,U_2411] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2411),U_2412),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2411),U_2413))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2412,U_2413)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2411) ),
    inference(variable_rename,[status(thm)],[f_793_1]) ).

fof(f_793_3,plain,
    ! [U_2412,U_2411,U_2413] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2411),U_2412),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2411),U_2413))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2412,U_2413)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2411) ),
    inference(definitional_conversion,[status(esa)],[f_793_2]) ).

cnf(f_793_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2411),U_2412),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2411),U_2413))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2412,U_2413)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2411) ),
    inference(clausify,[status(thm)],[f_793_3]) ).

fof(f_794_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_794_2,plain,
    ! [U_2415,U_2414] :
      ( 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_2414),U_2415))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2415)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2414) ),
    inference(variable_rename,[status(thm)],[f_794_1]) ).

fof(f_794_3,plain,
    ! [U_2414,U_2415] :
      ( 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_2414),U_2415))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2415)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2414) ),
    inference(definitional_conversion,[status(esa)],[f_794_2]) ).

cnf(f_794_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_2414),U_2415))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2415)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2414) ),
    inference(clausify,[status(thm)],[f_794_3]) ).

fof(f_795_1,plain,
    ! [V_y_2,V_x_2,V_za_2] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_za_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_za_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_za_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_za_2)) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2) ),
    inference(fof_nnf,[status(thm)],[fact_real__mult__less__iff1]) ).

fof(f_795_2,plain,
    ! [U_2418,U_2417,U_2416] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2417),U_2416),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2418),U_2416))
          | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2417,U_2418) )
        & ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2417,U_2418)
          | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2417),U_2416),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2418),U_2416)) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2416) ),
    inference(variable_rename,[status(thm)],[f_795_1]) ).

fof(f_795_3,plain,
    ( ! [U_2418,U_2417,U_2416] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2417),U_2416),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2418),U_2416))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2417,U_2418)
        | ~ sP208(U_2418,U_2417,U_2416) )
    & ! [U_2418,U_2417,U_2416] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2417,U_2418)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2417),U_2416),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2418),U_2416))
        | ~ sP208(U_2418,U_2417,U_2416) )
    & ! [U_2418,U_2417,U_2416] :
        ( sP208(U_2418,U_2417,U_2416)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2416) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP208])],[f_795_2]) ).

cnf(f_795_4,plain,
    ( sP208(U_2418,U_2417,U_2416)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2416) ),
    inference(clausify,[status(thm)],[f_795_3]) ).

cnf(f_795_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2417,U_2418)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2417),U_2416),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2418),U_2416))
    | ~ sP208(U_2418,U_2417,U_2416) ),
    inference(clausify,[status(thm)],[f_795_3]) ).

cnf(f_795_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2417),U_2416),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2418),U_2416))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2417,U_2418)
    | ~ sP208(U_2418,U_2417,U_2416) ),
    inference(clausify,[status(thm)],[f_795_3]) ).

fof(f_796_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_796_2,plain,
    ! [U_2421,U_2420,U_2419] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2419)),U_2420),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2419)),U_2421))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2420,U_2421) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2420,U_2421)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2419)),U_2420),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2419)),U_2421)) ) ),
    inference(variable_rename,[status(thm)],[f_796_1]) ).

fof(f_796_3,plain,
    ( ! [U_2427,U_2425] :
        ( ! [U_2423] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2423)),U_2425),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2423)),U_2427))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2425,U_2427) )
    & ! [U_2426,U_2424] :
        ( ! [U_2422] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2422)),U_2424),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2422)),U_2426))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2424,U_2426) ) ),
    inference(miniscope,[status(thm)],[f_796_2]) ).

fof(f_796_4,plain,
    ( ! [U_2427,U_2423,U_2425] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2423)),U_2425),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2423)),U_2427))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2425,U_2427) )
    & ! [U_2422,U_2426,U_2424] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2422)),U_2424),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2422)),U_2426))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2424,U_2426) ) ),
    inference(definitional_conversion,[status(esa)],[f_796_3]) ).

cnf(f_796_5,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2422)),U_2424),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2422)),U_2426))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2424,U_2426) ),
    inference(clausify,[status(thm)],[f_796_4]) ).

cnf(f_796_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2423)),U_2425),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2423)),U_2427))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2425,U_2427) ),
    inference(clausify,[status(thm)],[f_796_4]) ).

fof(f_797_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_797_2,plain,
    ! [U_2429,U_2428] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2428),c_Nat_OSuc(U_2429)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2428,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2428),U_2429)),
    inference(variable_rename,[status(thm)],[f_797_1]) ).

fof(f_797_3,plain,
    ! [U_2428,U_2429] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2428),c_Nat_OSuc(U_2429)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2428,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2428),U_2429)),
    inference(definitional_conversion,[status(esa)],[f_797_2]) ).

cnf(f_797_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2428),c_Nat_OSuc(U_2429)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2428,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2428),U_2429)),
    inference(clausify,[status(thm)],[f_797_3]) ).

fof(f_798_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_798_2,plain,
    ! [U_2431,U_2430] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2430)),U_2431) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2431,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2430),U_2431)),
    inference(variable_rename,[status(thm)],[f_798_1]) ).

fof(f_798_3,plain,
    ! [U_2430,U_2431] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2430)),U_2431) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2431,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2430),U_2431)),
    inference(definitional_conversion,[status(esa)],[f_798_2]) ).

cnf(f_798_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2430)),U_2431) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2431,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2430),U_2431)),
    inference(clausify,[status(thm)],[f_798_3]) ).

fof(f_799_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_799_2,plain,
    ! [U_2434,U_2433,U_2432] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2432)),U_2433),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2432)),U_2434))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2433,U_2434) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2433,U_2434)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2432)),U_2433),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2432)),U_2434)) ) ),
    inference(variable_rename,[status(thm)],[f_799_1]) ).

fof(f_799_3,plain,
    ( ! [U_2440,U_2438] :
        ( ! [U_2436] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2436)),U_2438),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2436)),U_2440))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2438,U_2440) )
    & ! [U_2439,U_2437] :
        ( ! [U_2435] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2435)),U_2437),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2435)),U_2439))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2437,U_2439) ) ),
    inference(miniscope,[status(thm)],[f_799_2]) ).

fof(f_799_4,plain,
    ( ! [U_2440,U_2436,U_2438] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2436)),U_2438),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2436)),U_2440))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2438,U_2440) )
    & ! [U_2437,U_2435,U_2439] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2435)),U_2437),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2435)),U_2439))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2437,U_2439) ) ),
    inference(definitional_conversion,[status(esa)],[f_799_3]) ).

cnf(f_799_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_2435)),U_2437),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2435)),U_2439))
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2437,U_2439) ),
    inference(clausify,[status(thm)],[f_799_4]) ).

cnf(f_799_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_2436)),U_2438),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2436)),U_2440))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2438,U_2440) ),
    inference(clausify,[status(thm)],[f_799_4]) ).

fof(f_800_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_800_2,plain,
    ! [U_2442,U_2441] :
      ( U_2441 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | U_2442 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      | U_2441 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2441),U_2442) ),
    inference(variable_rename,[status(thm)],[f_800_1]) ).

fof(f_800_3,plain,
    ! [U_2442,U_2441] :
      ( U_2441 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | U_2442 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      | U_2441 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2441),U_2442) ),
    inference(definitional_conversion,[status(esa)],[f_800_2]) ).

cnf(f_800_4,plain,
    ( U_2441 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_2442 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_2441 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2441),U_2442) ),
    inference(clausify,[status(thm)],[f_800_3]) ).

fof(f_801_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_801_2,plain,
    ! [U_2444,U_2443] :
      ( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2443),U_2443),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2444),U_2444)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | U_2444 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | U_2443 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( ( U_2444 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
          & U_2443 = 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_2443),U_2443),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2444),U_2444)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(variable_rename,[status(thm)],[f_801_1]) ).

fof(f_801_3,plain,
    ( ! [U_2448,U_2446] :
        ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2446),U_2446),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2448),U_2448)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | U_2448 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | U_2446 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
    & ! [U_2447,U_2445] :
        ( ( U_2447 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
          & U_2445 = 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_2445),U_2445),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2447),U_2447)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(miniscope,[status(thm)],[f_801_2]) ).

fof(f_801_4,plain,
    ( ! [U_2445,U_2447] :
        ( U_2447 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | ~ sP209(U_2445,U_2447) )
    & ! [U_2445,U_2447] :
        ( U_2445 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | ~ sP209(U_2445,U_2447) )
    & ! [U_2448,U_2446] :
        ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2446),U_2446),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2448),U_2448)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | U_2448 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | U_2446 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
    & ! [U_2445,U_2447] :
        ( sP209(U_2445,U_2447)
        | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2445),U_2445),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2447),U_2447)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP209])],[f_801_3]) ).

cnf(f_801_5,plain,
    ( sP209(U_2445,U_2447)
    | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2445),U_2445),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2447),U_2447)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(clausify,[status(thm)],[f_801_4]) ).

cnf(f_801_6,plain,
    ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2446),U_2446),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2448),U_2448)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | U_2448 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | U_2446 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(clausify,[status(thm)],[f_801_4]) ).

cnf(f_801_7,plain,
    ( U_2445 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | ~ sP209(U_2445,U_2447) ),
    inference(clausify,[status(thm)],[f_801_4]) ).

cnf(f_801_8,plain,
    ( U_2447 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | ~ sP209(U_2445,U_2447) ),
    inference(clausify,[status(thm)],[f_801_4]) ).

fof(f_802_1,plain,
    ! [V_b,V_a] : c_Complex_Oexpi(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(V_a)),c_Complex_Oexpi(V_b)),
    inference(fof_nnf,[status(thm)],[fact_expi__add]) ).

fof(f_802_2,plain,
    ! [U_2450,U_2449] : c_Complex_Oexpi(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_2449,U_2450)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(U_2449)),c_Complex_Oexpi(U_2450)),
    inference(variable_rename,[status(thm)],[f_802_1]) ).

fof(f_802_3,plain,
    ! [U_2449,U_2450] : c_Complex_Oexpi(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_2449,U_2450)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(U_2449)),c_Complex_Oexpi(U_2450)),
    inference(definitional_conversion,[status(esa)],[f_802_2]) ).

cnf(f_802_4,plain,
    c_Complex_Oexpi(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_2449,U_2450)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(U_2449)),c_Complex_Oexpi(U_2450)),
    inference(clausify,[status(thm)],[f_802_3]) ).

fof(f_803_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_803_2,plain,
    ! [U_2452,U_2451] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2451,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2452),U_2451))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2452)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2451) ),
    inference(variable_rename,[status(thm)],[f_803_1]) ).

fof(f_803_3,plain,
    ! [U_2452,U_2451] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2451,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2452),U_2451))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2452)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2451) ),
    inference(definitional_conversion,[status(esa)],[f_803_2]) ).

cnf(f_803_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2451,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2452),U_2451))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2452)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2451) ),
    inference(clausify,[status(thm)],[f_803_3]) ).

fof(f_804_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_804_2,plain,
    ! [U_2454,U_2453] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2453,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2453),U_2454))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2454)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2453) ),
    inference(variable_rename,[status(thm)],[f_804_1]) ).

fof(f_804_3,plain,
    ! [U_2454,U_2453] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2453,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2453),U_2454))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2454)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2453) ),
    inference(definitional_conversion,[status(esa)],[f_804_2]) ).

cnf(f_804_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2453,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2453),U_2454))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2454)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2453) ),
    inference(clausify,[status(thm)],[f_804_3]) ).

fof(f_805_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_805_2,plain,
    ! [U_2456,U_2455] :
      ( 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_2456),U_2455))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2456)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2455) ),
    inference(variable_rename,[status(thm)],[f_805_1]) ).

fof(f_805_3,plain,
    ! [U_2456,U_2455] :
      ( 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_2456),U_2455))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2456)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2455) ),
    inference(definitional_conversion,[status(esa)],[f_805_2]) ).

cnf(f_805_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_2456),U_2455))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2456)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2455) ),
    inference(clausify,[status(thm)],[f_805_3]) ).

fof(f_806_1,plain,
    ! [V_y_2,V_x_2,V_za_2] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_za_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_za_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_za_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_za_2),V_y_2)) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2) ),
    inference(fof_nnf,[status(thm)],[fact_real__mult__le__cancel__iff2]) ).

fof(f_806_2,plain,
    ! [U_2459,U_2458,U_2457] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2457),U_2458),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2457),U_2459))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2458,U_2459) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2458,U_2459)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2457),U_2458),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2457),U_2459)) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2457) ),
    inference(variable_rename,[status(thm)],[f_806_1]) ).

fof(f_806_3,plain,
    ( ! [U_2458,U_2459,U_2457] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2457),U_2458),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2457),U_2459))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2458,U_2459)
        | ~ sP210(U_2458,U_2459,U_2457) )
    & ! [U_2458,U_2459,U_2457] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2458,U_2459)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2457),U_2458),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2457),U_2459))
        | ~ sP210(U_2458,U_2459,U_2457) )
    & ! [U_2458,U_2459,U_2457] :
        ( sP210(U_2458,U_2459,U_2457)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2457) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP210])],[f_806_2]) ).

cnf(f_806_4,plain,
    ( sP210(U_2458,U_2459,U_2457)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2457) ),
    inference(clausify,[status(thm)],[f_806_3]) ).

cnf(f_806_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2458,U_2459)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2457),U_2458),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2457),U_2459))
    | ~ sP210(U_2458,U_2459,U_2457) ),
    inference(clausify,[status(thm)],[f_806_3]) ).

cnf(f_806_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2457),U_2458),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2457),U_2459))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2458,U_2459)
    | ~ sP210(U_2458,U_2459,U_2457) ),
    inference(clausify,[status(thm)],[f_806_3]) ).

fof(f_807_1,plain,
    ! [V_y_2,V_x_2,V_za_2] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_za_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_za_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_za_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_za_2)) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2) ),
    inference(fof_nnf,[status(thm)],[fact_real__mult__le__cancel__iff1]) ).

fof(f_807_2,plain,
    ! [U_2462,U_2461,U_2460] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2461),U_2460),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2462),U_2460))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2461,U_2462) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2461,U_2462)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2461),U_2460),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2462),U_2460)) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2460) ),
    inference(variable_rename,[status(thm)],[f_807_1]) ).

fof(f_807_3,plain,
    ( ! [U_2462,U_2461,U_2460] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2461),U_2460),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2462),U_2460))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2461,U_2462)
        | ~ sP211(U_2462,U_2461,U_2460) )
    & ! [U_2462,U_2461,U_2460] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2461,U_2462)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2461),U_2460),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2462),U_2460))
        | ~ sP211(U_2462,U_2461,U_2460) )
    & ! [U_2462,U_2461,U_2460] :
        ( sP211(U_2462,U_2461,U_2460)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2460) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP211])],[f_807_2]) ).

cnf(f_807_4,plain,
    ( sP211(U_2462,U_2461,U_2460)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2460) ),
    inference(clausify,[status(thm)],[f_807_3]) ).

cnf(f_807_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2461,U_2462)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2461),U_2460),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2462),U_2460))
    | ~ sP211(U_2462,U_2461,U_2460) ),
    inference(clausify,[status(thm)],[f_807_3]) ).

cnf(f_807_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2461),U_2460),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2462),U_2460))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2461,U_2462)
    | ~ sP211(U_2462,U_2461,U_2460) ),
    inference(clausify,[status(thm)],[f_807_3]) ).

fof(f_808_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_808_2,plain,
    ! [U_2464,U_2463] :
      ( ( 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_2463),U_2464))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2464)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2463) )
      & ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2464)
          & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2463) )
        | ~ 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_2463),U_2464)) ) ),
    inference(variable_rename,[status(thm)],[f_808_1]) ).

fof(f_808_3,plain,
    ( ! [U_2468,U_2466] :
        ( 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_2466),U_2468))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2468)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2466) )
    & ! [U_2467,U_2465] :
        ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2467)
          & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2465) )
        | ~ 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_2465),U_2467)) ) ),
    inference(miniscope,[status(thm)],[f_808_2]) ).

fof(f_808_4,plain,
    ( ! [U_2467,U_2465] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2467)
        | ~ sP212(U_2467,U_2465) )
    & ! [U_2467,U_2465] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2465)
        | ~ sP212(U_2467,U_2465) )
    & ! [U_2468,U_2466] :
        ( 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_2466),U_2468))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2468)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2466) )
    & ! [U_2467,U_2465] :
        ( sP212(U_2467,U_2465)
        | ~ 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_2465),U_2467)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP212])],[f_808_3]) ).

cnf(f_808_5,plain,
    ( sP212(U_2467,U_2465)
    | ~ 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_2465),U_2467)) ),
    inference(clausify,[status(thm)],[f_808_4]) ).

cnf(f_808_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_2466),U_2468))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2468)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2466) ),
    inference(clausify,[status(thm)],[f_808_4]) ).

cnf(f_808_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2465)
    | ~ sP212(U_2467,U_2465) ),
    inference(clausify,[status(thm)],[f_808_4]) ).

cnf(f_808_8,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2467)
    | ~ sP212(U_2467,U_2465) ),
    inference(clausify,[status(thm)],[f_808_4]) ).

fof(f_809_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_809_2,plain,
    ! [U_2471,U_2470,U_2469] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2469),U_2470),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2471),U_2470))
        | ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2469,U_2471)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2470) ) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2469,U_2471)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2470)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2469),U_2470),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2471),U_2470)) ) ),
    inference(variable_rename,[status(thm)],[f_809_1]) ).

fof(f_809_3,plain,
    ( ! [U_2477,U_2475,U_2473] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2473),U_2475),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2477),U_2475))
        | ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2473,U_2477)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2475) ) )
    & ! [U_2476,U_2474,U_2472] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2472,U_2476)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2474)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2472),U_2474),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2476),U_2474)) ) ),
    inference(miniscope,[status(thm)],[f_809_2]) ).

fof(f_809_4,plain,
    ( ! [U_2475,U_2473,U_2477] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2473,U_2477)
        | ~ sP213(U_2475,U_2473,U_2477) )
    & ! [U_2475,U_2473,U_2477] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2475)
        | ~ sP213(U_2475,U_2473,U_2477) )
    & ! [U_2475,U_2473,U_2477] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2473),U_2475),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2477),U_2475))
        | sP213(U_2475,U_2473,U_2477) )
    & ! [U_2476,U_2472,U_2474] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2472,U_2476)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2474)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2472),U_2474),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2476),U_2474)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP213])],[f_809_3]) ).

cnf(f_809_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2472,U_2476)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2474)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2472),U_2474),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2476),U_2474)) ),
    inference(clausify,[status(thm)],[f_809_4]) ).

cnf(f_809_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2473),U_2475),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2477),U_2475))
    | sP213(U_2475,U_2473,U_2477) ),
    inference(clausify,[status(thm)],[f_809_4]) ).

cnf(f_809_7,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2475)
    | ~ sP213(U_2475,U_2473,U_2477) ),
    inference(clausify,[status(thm)],[f_809_4]) ).

cnf(f_809_8,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2473,U_2477)
    | ~ sP213(U_2475,U_2473,U_2477) ),
    inference(clausify,[status(thm)],[f_809_4]) ).

fof(f_810_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_810_2,plain,
    ! [U_2480,U_2479,U_2478] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2478),U_2479),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2478),U_2480))
        | ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2479,U_2480)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2478) ) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2479,U_2480)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2478)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2478),U_2479),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2478),U_2480)) ) ),
    inference(variable_rename,[status(thm)],[f_810_1]) ).

fof(f_810_3,plain,
    ( ! [U_2486,U_2484,U_2482] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2482),U_2484),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2482),U_2486))
        | ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2484,U_2486)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2482) ) )
    & ! [U_2485,U_2483,U_2481] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2483,U_2485)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2481)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2481),U_2483),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2481),U_2485)) ) ),
    inference(miniscope,[status(thm)],[f_810_2]) ).

fof(f_810_4,plain,
    ( ! [U_2486,U_2482,U_2484] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2484,U_2486)
        | ~ sP214(U_2486,U_2482,U_2484) )
    & ! [U_2486,U_2482,U_2484] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2482)
        | ~ sP214(U_2486,U_2482,U_2484) )
    & ! [U_2486,U_2482,U_2484] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2482),U_2484),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2482),U_2486))
        | sP214(U_2486,U_2482,U_2484) )
    & ! [U_2485,U_2481,U_2483] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2483,U_2485)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2481)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2481),U_2483),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2481),U_2485)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP214])],[f_810_3]) ).

cnf(f_810_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2483,U_2485)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2481)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2481),U_2483),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2481),U_2485)) ),
    inference(clausify,[status(thm)],[f_810_4]) ).

cnf(f_810_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2482),U_2484),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2482),U_2486))
    | sP214(U_2486,U_2482,U_2484) ),
    inference(clausify,[status(thm)],[f_810_4]) ).

cnf(f_810_7,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2482)
    | ~ sP214(U_2486,U_2482,U_2484) ),
    inference(clausify,[status(thm)],[f_810_4]) ).

cnf(f_810_8,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2484,U_2486)
    | ~ sP214(U_2486,U_2482,U_2484) ),
    inference(clausify,[status(thm)],[f_810_4]) ).

fof(f_811_1,plain,
    ! [V_y,V_x,V_c] :
      ( V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y)))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(fof_nnf,[status(thm)],[fact_rabs__ratiotest__lemma]) ).

fof(f_811_2,plain,
    ! [U_2489,U_2488,U_2487] :
      ( U_2488 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_2488),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2487),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_2489)))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2487,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(variable_rename,[status(thm)],[f_811_1]) ).

fof(f_811_3,plain,
    ! [U_2489,U_2487,U_2488] :
      ( U_2488 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_2488),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2487),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_2489)))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2487,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(definitional_conversion,[status(esa)],[f_811_2]) ).

cnf(f_811_4,plain,
    ( U_2488 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_2488),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2487),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_2489)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2487,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(clausify,[status(thm)],[f_811_3]) ).

fof(f_812_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_812_2,plain,
    ! [U_2493,U_2492,U_2491,U_2490] :
      ( U_2492 = c_Groups_Ozero__class_Ozero(U_2490)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2490,U_2492),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2491),c_RealVector_Onorm__class_Onorm(U_2490,U_2493)))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2491,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
      | ~ class_RealVector_Oreal__normed__vector(U_2490) ),
    inference(variable_rename,[status(thm)],[f_812_1]) ).

fof(f_812_3,plain,
    ! [U_2491,U_2490,U_2492,U_2493] :
      ( U_2492 = c_Groups_Ozero__class_Ozero(U_2490)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2490,U_2492),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2491),c_RealVector_Onorm__class_Onorm(U_2490,U_2493)))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2491,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
      | ~ class_RealVector_Oreal__normed__vector(U_2490) ),
    inference(definitional_conversion,[status(esa)],[f_812_2]) ).

cnf(f_812_4,plain,
    ( U_2492 = c_Groups_Ozero__class_Ozero(U_2490)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2490,U_2492),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2491),c_RealVector_Onorm__class_Onorm(U_2490,U_2493)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2491,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | ~ class_RealVector_Oreal__normed__vector(U_2490) ),
    inference(clausify,[status(thm)],[f_812_3]) ).

fof(f_813_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_813_2,plain,
    ! [U_2495,U_2494] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2494),U_2495) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2495,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2494,c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_2495))
        | U_2494 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2494),U_2495) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2494 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_813_1]) ).

fof(f_813_3,plain,
    ( ! [U_2499,U_2497] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2497),U_2499) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2499,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2497,c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_2499))
        | U_2497 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_2498,U_2496] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2496),U_2498) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2496 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_813_2]) ).

fof(f_813_4,plain,
    ( ! [U_2499,U_2497] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2497),U_2499) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2499,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2497,c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_2499))
        | U_2497 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_2496,U_2498] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2496),U_2498) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2496 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_813_3]) ).

cnf(f_813_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2496),U_2498) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_2496 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_813_4]) ).

cnf(f_813_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2497),U_2499) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2499,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2497,c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_2499))
    | U_2497 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_813_4]) ).

fof(f_814_1,plain,
    ! [V_v_H,V_v] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) ) ),
    inference(fof_nnf,[status(thm)],[fact_mult__nat__number__of]) ).

fof(f_814_2,plain,
    ! [U_2501,U_2500] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2500)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2501)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2500),U_2501))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2500,c_Int_OPls) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2500)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2501)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2500,c_Int_OPls) ) ),
    inference(variable_rename,[status(thm)],[f_814_1]) ).

fof(f_814_3,plain,
    ( ! [U_2505,U_2503] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2503)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2505)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2503),U_2505))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2503,c_Int_OPls) )
    & ! [U_2504,U_2502] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2502)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2504)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2502,c_Int_OPls) ) ),
    inference(miniscope,[status(thm)],[f_814_2]) ).

fof(f_814_4,plain,
    ( ! [U_2503,U_2505] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2503)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2505)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2503),U_2505))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2503,c_Int_OPls) )
    & ! [U_2502,U_2504] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2502)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2504)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2502,c_Int_OPls) ) ),
    inference(definitional_conversion,[status(esa)],[f_814_3]) ).

cnf(f_814_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2502)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2504)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2502,c_Int_OPls) ),
    inference(clausify,[status(thm)],[f_814_4]) ).

cnf(f_814_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2503)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2505)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2503),U_2505))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2503,c_Int_OPls) ),
    inference(clausify,[status(thm)],[f_814_4]) ).

fof(f_815_1,plain,
    ! [V_k,V_v_H,V_v] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H))),V_k)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)),V_k)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__number__of__mult__left]) ).

fof(f_815_2,plain,
    ! [U_2508,U_2507,U_2506] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2506)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2507)),U_2508)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2506),U_2507))),U_2508)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2506,c_Int_OPls) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2506)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2507)),U_2508)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2506,c_Int_OPls) ) ),
    inference(variable_rename,[status(thm)],[f_815_1]) ).

fof(f_815_3,plain,
    ( ! [U_2514,U_2512,U_2510] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2510)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2512)),U_2514)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2510),U_2512))),U_2514)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2510,c_Int_OPls) )
    & ! [U_2513,U_2511,U_2509] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2509)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2511)),U_2513)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2509,c_Int_OPls) ) ),
    inference(miniscope,[status(thm)],[f_815_2]) ).

fof(f_815_4,plain,
    ( ! [U_2510,U_2512,U_2514] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2510)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2512)),U_2514)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2510),U_2512))),U_2514)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2510,c_Int_OPls) )
    & ! [U_2511,U_2509,U_2513] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2509)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2511)),U_2513)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2509,c_Int_OPls) ) ),
    inference(definitional_conversion,[status(esa)],[f_815_3]) ).

cnf(f_815_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2509)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2511)),U_2513)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2509,c_Int_OPls) ),
    inference(clausify,[status(thm)],[f_815_4]) ).

cnf(f_815_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2510)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2512)),U_2514)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2510),U_2512))),U_2514)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2510,c_Int_OPls) ),
    inference(clausify,[status(thm)],[f_815_4]) ).

fof(f_816_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_816_2,plain,
    ! [U_2517,U_2516,U_2515] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2516)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2515)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2517,U_2515)
      | ~ 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_2515),U_2516),U_2517)) ),
    inference(variable_rename,[status(thm)],[f_816_1]) ).

fof(f_816_3,plain,
    ! [U_2515,U_2516,U_2517] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2516)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2515)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2517,U_2515)
      | ~ 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_2515),U_2516),U_2517)) ),
    inference(definitional_conversion,[status(esa)],[f_816_2]) ).

cnf(f_816_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2516)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2515)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2517,U_2515)
    | ~ 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_2515),U_2516),U_2517)) ),
    inference(clausify,[status(thm)],[f_816_3]) ).

fof(f_817_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_817_2,plain,
    ! [U_2520,U_2519,U_2518] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2519,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_2518)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2520)
      | ~ 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_2518),U_2519),U_2520),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(variable_rename,[status(thm)],[f_817_1]) ).

fof(f_817_3,plain,
    ! [U_2520,U_2518,U_2519] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2519,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_2518)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2520)
      | ~ 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_2518),U_2519),U_2520),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(definitional_conversion,[status(esa)],[f_817_2]) ).

cnf(f_817_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2519,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_2518)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2520)
    | ~ 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_2518),U_2519),U_2520),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(clausify,[status(thm)],[f_817_3]) ).

fof(f_818_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_818_2,plain,
    ! [U_2525,U_2524,U_2523,U_2522,U_2521] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2522,U_2524)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2525,U_2521)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2523,U_2521)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2523)
      | ~ 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_2521),U_2522),U_2523),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2521),U_2524),U_2525)) ),
    inference(variable_rename,[status(thm)],[f_818_1]) ).

fof(f_818_3,plain,
    ! [U_2521,U_2522,U_2523,U_2524,U_2525] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2522,U_2524)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2525,U_2521)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2523,U_2521)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2523)
      | ~ 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_2521),U_2522),U_2523),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2521),U_2524),U_2525)) ),
    inference(definitional_conversion,[status(esa)],[f_818_2]) ).

cnf(f_818_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2522,U_2524)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2525,U_2521)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2523,U_2521)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2523)
    | ~ 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_2521),U_2522),U_2523),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2521),U_2524),U_2525)) ),
    inference(clausify,[status(thm)],[f_818_3]) ).

fof(f_819_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_819_2,plain,
    ! [U_2531,U_2530,U_2529,U_2528,U_2527,U_2526] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2527,U_2530)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2529,U_2526)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2529)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2528)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2531,U_2529)
      | ~ 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_2529),U_2530),U_2531))
      | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2526),U_2527),U_2528) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2529),U_2530),U_2531) ),
    inference(variable_rename,[status(thm)],[f_819_1]) ).

fof(f_819_3,plain,
    ! [U_2527,U_2526,U_2530,U_2529,U_2531,U_2528] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2527,U_2530)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2529,U_2526)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2529)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2528)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2531,U_2529)
      | ~ 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_2529),U_2530),U_2531))
      | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2526),U_2527),U_2528) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2529),U_2530),U_2531) ),
    inference(definitional_conversion,[status(esa)],[f_819_2]) ).

cnf(f_819_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2527,U_2530)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2529,U_2526)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2529)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2528)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2531,U_2529)
    | ~ 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_2529),U_2530),U_2531))
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2526),U_2527),U_2528) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2529),U_2530),U_2531) ),
    inference(clausify,[status(thm)],[f_819_3]) ).

fof(f_820_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_820_2,plain,
    ! [U_2536,U_2535,U_2534,U_2533,U_2532] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2535,U_2533)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2532,U_2534)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2532,U_2536)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2536,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_2532),U_2533),U_2534),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2532),U_2535),U_2536)) ),
    inference(variable_rename,[status(thm)],[f_820_1]) ).

fof(f_820_3,plain,
    ! [U_2533,U_2532,U_2536,U_2535,U_2534] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2535,U_2533)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2532,U_2534)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2532,U_2536)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2536,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_2532),U_2533),U_2534),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2532),U_2535),U_2536)) ),
    inference(definitional_conversion,[status(esa)],[f_820_2]) ).

cnf(f_820_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2535,U_2533)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2532,U_2534)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2532,U_2536)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2536,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_2532),U_2533),U_2534),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2532),U_2535),U_2536)) ),
    inference(clausify,[status(thm)],[f_820_3]) ).

fof(f_821_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_821_2,plain,
    ! [U_2541,U_2540,U_2539,U_2538,U_2537] :
      ( ( ( 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_2537),U_2539),U_2540),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2538),U_2539),U_2541))
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2540,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_2538,U_2537)),U_2539),U_2541)) )
        & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2540,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_2538,U_2537)),U_2539),U_2541))
          | ~ 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_2537),U_2539),U_2540),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2538),U_2539),U_2541)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2537,U_2538) ),
    inference(variable_rename,[status(thm)],[f_821_1]) ).

fof(f_821_3,plain,
    ( ! [U_2537,U_2541,U_2539,U_2538,U_2540] :
        ( 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_2537),U_2539),U_2540),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2538),U_2539),U_2541))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2540,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_2538,U_2537)),U_2539),U_2541))
        | ~ sP215(U_2537,U_2541,U_2539,U_2538,U_2540) )
    & ! [U_2537,U_2541,U_2539,U_2538,U_2540] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2540,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_2538,U_2537)),U_2539),U_2541))
        | ~ 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_2537),U_2539),U_2540),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2538),U_2539),U_2541))
        | ~ sP215(U_2537,U_2541,U_2539,U_2538,U_2540) )
    & ! [U_2537,U_2541,U_2539,U_2538,U_2540] :
        ( sP215(U_2537,U_2541,U_2539,U_2538,U_2540)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2537,U_2538) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP215])],[f_821_2]) ).

cnf(f_821_4,plain,
    ( sP215(U_2537,U_2541,U_2539,U_2538,U_2540)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2537,U_2538) ),
    inference(clausify,[status(thm)],[f_821_3]) ).

cnf(f_821_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2540,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_2538,U_2537)),U_2539),U_2541))
    | ~ 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_2537),U_2539),U_2540),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2538),U_2539),U_2541))
    | ~ sP215(U_2537,U_2541,U_2539,U_2538,U_2540) ),
    inference(clausify,[status(thm)],[f_821_3]) ).

cnf(f_821_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_2537),U_2539),U_2540),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2538),U_2539),U_2541))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2540,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_2538,U_2537)),U_2539),U_2541))
    | ~ sP215(U_2537,U_2541,U_2539,U_2538,U_2540) ),
    inference(clausify,[status(thm)],[f_821_3]) ).

fof(f_822_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_822_2,plain,
    ! [U_2546,U_2545,U_2544,U_2543,U_2542] :
      ( ( ( 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_2543),U_2544),U_2545),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2542),U_2544),U_2546))
          | ~ 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_2543,U_2542)),U_2544),U_2545),U_2546) )
        & ( 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_2543,U_2542)),U_2544),U_2545),U_2546)
          | ~ 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_2543),U_2544),U_2545),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2542),U_2544),U_2546)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2542,U_2543) ),
    inference(variable_rename,[status(thm)],[f_822_1]) ).

fof(f_822_3,plain,
    ( ! [U_2543,U_2544,U_2545,U_2546,U_2542] :
        ( 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_2543),U_2544),U_2545),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2542),U_2544),U_2546))
        | ~ 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_2543,U_2542)),U_2544),U_2545),U_2546)
        | ~ sP216(U_2543,U_2544,U_2545,U_2546,U_2542) )
    & ! [U_2543,U_2544,U_2545,U_2546,U_2542] :
        ( 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_2543,U_2542)),U_2544),U_2545),U_2546)
        | ~ 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_2543),U_2544),U_2545),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2542),U_2544),U_2546))
        | ~ sP216(U_2543,U_2544,U_2545,U_2546,U_2542) )
    & ! [U_2543,U_2544,U_2545,U_2546,U_2542] :
        ( sP216(U_2543,U_2544,U_2545,U_2546,U_2542)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2542,U_2543) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP216])],[f_822_2]) ).

cnf(f_822_4,plain,
    ( sP216(U_2543,U_2544,U_2545,U_2546,U_2542)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2542,U_2543) ),
    inference(clausify,[status(thm)],[f_822_3]) ).

cnf(f_822_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_2543,U_2542)),U_2544),U_2545),U_2546)
    | ~ 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_2543),U_2544),U_2545),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2542),U_2544),U_2546))
    | ~ sP216(U_2543,U_2544,U_2545,U_2546,U_2542) ),
    inference(clausify,[status(thm)],[f_822_3]) ).

cnf(f_822_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_2543),U_2544),U_2545),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2542),U_2544),U_2546))
    | ~ 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_2543,U_2542)),U_2544),U_2545),U_2546)
    | ~ sP216(U_2543,U_2544,U_2545,U_2546,U_2542) ),
    inference(clausify,[status(thm)],[f_822_3]) ).

fof(f_823_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_823_2,plain,
    ! [U_2549,U_2548,U_2547] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2547),U_2548) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2547),U_2549)
        | ( U_2548 != U_2549
          & U_2547 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( U_2548 = U_2549
        | U_2547 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2547),U_2548) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2547),U_2549) ) ),
    inference(variable_rename,[status(thm)],[f_823_1]) ).

fof(f_823_3,plain,
    ( ! [U_2555,U_2553,U_2551] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2551),U_2553) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2551),U_2555)
        | ( U_2553 != U_2555
          & U_2551 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_2554,U_2552,U_2550] :
        ( U_2552 = U_2554
        | U_2550 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2550),U_2552) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2550),U_2554) ) ),
    inference(miniscope,[status(thm)],[f_823_2]) ).

fof(f_823_4,plain,
    ( ! [U_2555,U_2553,U_2551] :
        ( U_2553 != U_2555
        | ~ sP217(U_2555,U_2553,U_2551) )
    & ! [U_2555,U_2553,U_2551] :
        ( U_2551 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP217(U_2555,U_2553,U_2551) )
    & ! [U_2555,U_2553,U_2551] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2551),U_2553) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2551),U_2555)
        | sP217(U_2555,U_2553,U_2551) )
    & ! [U_2552,U_2554,U_2550] :
        ( U_2552 = U_2554
        | U_2550 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2550),U_2552) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2550),U_2554) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP217])],[f_823_3]) ).

cnf(f_823_5,plain,
    ( U_2552 = U_2554
    | U_2550 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2550),U_2552) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2550),U_2554) ),
    inference(clausify,[status(thm)],[f_823_4]) ).

cnf(f_823_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2551),U_2553) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2551),U_2555)
    | sP217(U_2555,U_2553,U_2551) ),
    inference(clausify,[status(thm)],[f_823_4]) ).

cnf(f_823_7,plain,
    ( U_2551 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP217(U_2555,U_2553,U_2551) ),
    inference(clausify,[status(thm)],[f_823_4]) ).

cnf(f_823_8,plain,
    ( U_2553 != U_2555
    | ~ sP217(U_2555,U_2553,U_2551) ),
    inference(clausify,[status(thm)],[f_823_4]) ).

fof(f_824_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_824_2,plain,
    ! [U_2559,U_2558,U_2557,U_2556] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2556),U_2557),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2558),U_2557),U_2559)) = 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_2556,U_2558)),U_2557),U_2559),
    inference(variable_rename,[status(thm)],[f_824_1]) ).

fof(f_824_3,plain,
    ! [U_2557,U_2558,U_2556,U_2559] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2556),U_2557),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2558),U_2557),U_2559)) = 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_2556,U_2558)),U_2557),U_2559),
    inference(definitional_conversion,[status(esa)],[f_824_2]) ).

cnf(f_824_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2556),U_2557),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2558),U_2557),U_2559)) = 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_2556,U_2558)),U_2557),U_2559),
    inference(clausify,[status(thm)],[f_824_3]) ).

fof(f_825_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_825_2,plain,
    ! [U_2562,U_2561,U_2560] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2560),U_2561),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2560),U_2562))
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2561,U_2562) )
        & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2561,U_2562)
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2560),U_2561),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2560),U_2562)) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2560) ),
    inference(variable_rename,[status(thm)],[f_825_1]) ).

fof(f_825_3,plain,
    ( ! [U_2562,U_2561,U_2560] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2560),U_2561),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2560),U_2562))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2561,U_2562)
        | ~ sP218(U_2562,U_2561,U_2560) )
    & ! [U_2562,U_2561,U_2560] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2561,U_2562)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2560),U_2561),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2560),U_2562))
        | ~ sP218(U_2562,U_2561,U_2560) )
    & ! [U_2562,U_2561,U_2560] :
        ( sP218(U_2562,U_2561,U_2560)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2560) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP218])],[f_825_2]) ).

cnf(f_825_4,plain,
    ( sP218(U_2562,U_2561,U_2560)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2560) ),
    inference(clausify,[status(thm)],[f_825_3]) ).

cnf(f_825_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2561,U_2562)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2560),U_2561),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2560),U_2562))
    | ~ sP218(U_2562,U_2561,U_2560) ),
    inference(clausify,[status(thm)],[f_825_3]) ).

cnf(f_825_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2560),U_2561),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2560),U_2562))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2561,U_2562)
    | ~ sP218(U_2562,U_2561,U_2560) ),
    inference(clausify,[status(thm)],[f_825_3]) ).

fof(f_826_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_826_2,plain,
    ! [U_2565,U_2564,U_2563] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2563),U_2564) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2563),U_2565)
          | U_2564 != U_2565 )
        & ( U_2564 = U_2565
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2563),U_2564) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2563),U_2565) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2563) ),
    inference(variable_rename,[status(thm)],[f_826_1]) ).

fof(f_826_3,plain,
    ( ! [U_2565,U_2563,U_2564] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2563),U_2564) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2563),U_2565)
        | U_2564 != U_2565
        | ~ sP219(U_2565,U_2563,U_2564) )
    & ! [U_2565,U_2563,U_2564] :
        ( U_2564 = U_2565
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2563),U_2564) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2563),U_2565)
        | ~ sP219(U_2565,U_2563,U_2564) )
    & ! [U_2565,U_2563,U_2564] :
        ( sP219(U_2565,U_2563,U_2564)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2563) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP219])],[f_826_2]) ).

cnf(f_826_4,plain,
    ( sP219(U_2565,U_2563,U_2564)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2563) ),
    inference(clausify,[status(thm)],[f_826_3]) ).

cnf(f_826_5,plain,
    ( U_2564 = U_2565
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2563),U_2564) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2563),U_2565)
    | ~ sP219(U_2565,U_2563,U_2564) ),
    inference(clausify,[status(thm)],[f_826_3]) ).

cnf(f_826_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2563),U_2564) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2563),U_2565)
    | U_2564 != U_2565
    | ~ sP219(U_2565,U_2563,U_2564) ),
    inference(clausify,[status(thm)],[f_826_3]) ).

fof(f_827_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_827_2,plain,
    ! [U_2568,U_2567,U_2566] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2566),U_2567),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2566),U_2568))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2567,U_2568) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2567,U_2568)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2566),U_2567),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2566),U_2568)) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2566) ),
    inference(variable_rename,[status(thm)],[f_827_1]) ).

fof(f_827_3,plain,
    ( ! [U_2567,U_2566,U_2568] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2566),U_2567),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2566),U_2568))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2567,U_2568)
        | ~ sP220(U_2567,U_2566,U_2568) )
    & ! [U_2567,U_2566,U_2568] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2567,U_2568)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2566),U_2567),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2566),U_2568))
        | ~ sP220(U_2567,U_2566,U_2568) )
    & ! [U_2567,U_2566,U_2568] :
        ( sP220(U_2567,U_2566,U_2568)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2566) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP220])],[f_827_2]) ).

cnf(f_827_4,plain,
    ( sP220(U_2567,U_2566,U_2568)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2566) ),
    inference(clausify,[status(thm)],[f_827_3]) ).

cnf(f_827_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2567,U_2568)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2566),U_2567),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2566),U_2568))
    | ~ sP220(U_2567,U_2566,U_2568) ),
    inference(clausify,[status(thm)],[f_827_3]) ).

cnf(f_827_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2566),U_2567),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2566),U_2568))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2567,U_2568)
    | ~ sP220(U_2567,U_2566,U_2568) ),
    inference(clausify,[status(thm)],[f_827_3]) ).

fof(f_828_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_828_2,plain,
    ! [U_2573,U_2572,U_2571,U_2570,U_2569] :
      ( ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2569),U_2571),U_2572) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2570),U_2571),U_2573)
          | U_2572 != 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_2570,U_2569)),U_2571),U_2573) )
        & ( U_2572 = 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_2570,U_2569)),U_2571),U_2573)
          | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2569),U_2571),U_2572) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2570),U_2571),U_2573) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2569,U_2570) ),
    inference(variable_rename,[status(thm)],[f_828_1]) ).

fof(f_828_3,plain,
    ( ! [U_2570,U_2571,U_2569,U_2572,U_2573] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2569),U_2571),U_2572) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2570),U_2571),U_2573)
        | U_2572 != 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_2570,U_2569)),U_2571),U_2573)
        | ~ sP221(U_2570,U_2571,U_2569,U_2572,U_2573) )
    & ! [U_2570,U_2571,U_2569,U_2572,U_2573] :
        ( U_2572 = 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_2570,U_2569)),U_2571),U_2573)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2569),U_2571),U_2572) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2570),U_2571),U_2573)
        | ~ sP221(U_2570,U_2571,U_2569,U_2572,U_2573) )
    & ! [U_2570,U_2571,U_2569,U_2572,U_2573] :
        ( sP221(U_2570,U_2571,U_2569,U_2572,U_2573)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2569,U_2570) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP221])],[f_828_2]) ).

cnf(f_828_4,plain,
    ( sP221(U_2570,U_2571,U_2569,U_2572,U_2573)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2569,U_2570) ),
    inference(clausify,[status(thm)],[f_828_3]) ).

cnf(f_828_5,plain,
    ( U_2572 = 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_2570,U_2569)),U_2571),U_2573)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2569),U_2571),U_2572) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2570),U_2571),U_2573)
    | ~ sP221(U_2570,U_2571,U_2569,U_2572,U_2573) ),
    inference(clausify,[status(thm)],[f_828_3]) ).

cnf(f_828_6,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2569),U_2571),U_2572) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2570),U_2571),U_2573)
    | U_2572 != 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_2570,U_2569)),U_2571),U_2573)
    | ~ sP221(U_2570,U_2571,U_2569,U_2572,U_2573) ),
    inference(clausify,[status(thm)],[f_828_3]) ).

fof(f_829_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_829_2,plain,
    ! [U_2578,U_2577,U_2576,U_2575,U_2574] :
      ( 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_2574),U_2576),U_2577),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2575),U_2576),U_2578)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2577,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_2575,U_2574)),U_2576),U_2578))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2574,U_2575) ),
    inference(variable_rename,[status(thm)],[f_829_1]) ).

fof(f_829_3,plain,
    ! [U_2575,U_2574,U_2577,U_2578,U_2576] :
      ( 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_2574),U_2576),U_2577),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2575),U_2576),U_2578)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2577,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_2575,U_2574)),U_2576),U_2578))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2574,U_2575) ),
    inference(definitional_conversion,[status(esa)],[f_829_2]) ).

cnf(f_829_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_2574),U_2576),U_2577),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2575),U_2576),U_2578)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2577,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_2575,U_2574)),U_2576),U_2578))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2574,U_2575) ),
    inference(clausify,[status(thm)],[f_829_3]) ).

fof(f_830_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_830_2,plain,
    ! [U_2583,U_2582,U_2581,U_2580,U_2579] :
      ( ( ( 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_2579),U_2581),U_2582),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2580),U_2581),U_2583))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2582,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_2580,U_2579)),U_2581),U_2583)) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2582,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_2580,U_2579)),U_2581),U_2583))
          | ~ 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_2579),U_2581),U_2582),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2580),U_2581),U_2583)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2579,U_2580) ),
    inference(variable_rename,[status(thm)],[f_830_1]) ).

fof(f_830_3,plain,
    ( ! [U_2579,U_2581,U_2580,U_2582,U_2583] :
        ( 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_2579),U_2581),U_2582),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2580),U_2581),U_2583))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2582,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_2580,U_2579)),U_2581),U_2583))
        | ~ sP222(U_2579,U_2581,U_2580,U_2582,U_2583) )
    & ! [U_2579,U_2581,U_2580,U_2582,U_2583] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2582,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_2580,U_2579)),U_2581),U_2583))
        | ~ 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_2579),U_2581),U_2582),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2580),U_2581),U_2583))
        | ~ sP222(U_2579,U_2581,U_2580,U_2582,U_2583) )
    & ! [U_2579,U_2581,U_2580,U_2582,U_2583] :
        ( sP222(U_2579,U_2581,U_2580,U_2582,U_2583)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2579,U_2580) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP222])],[f_830_2]) ).

cnf(f_830_4,plain,
    ( sP222(U_2579,U_2581,U_2580,U_2582,U_2583)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2579,U_2580) ),
    inference(clausify,[status(thm)],[f_830_3]) ).

cnf(f_830_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2582,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_2580,U_2579)),U_2581),U_2583))
    | ~ 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_2579),U_2581),U_2582),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2580),U_2581),U_2583))
    | ~ sP222(U_2579,U_2581,U_2580,U_2582,U_2583) ),
    inference(clausify,[status(thm)],[f_830_3]) ).

cnf(f_830_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_2579),U_2581),U_2582),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2580),U_2581),U_2583))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2582,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_2580,U_2579)),U_2581),U_2583))
    | ~ sP222(U_2579,U_2581,U_2580,U_2582,U_2583) ),
    inference(clausify,[status(thm)],[f_830_3]) ).

fof(f_831_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_831_2,plain,
    ! [U_2588,U_2587,U_2586,U_2585,U_2584] :
      ( ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2585),U_2586),U_2587) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2584),U_2586),U_2588)
          | 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_2585,U_2584)),U_2586),U_2587) != U_2588 )
        & ( 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_2585,U_2584)),U_2586),U_2587) = U_2588
          | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2585),U_2586),U_2587) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2584),U_2586),U_2588) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2584,U_2585) ),
    inference(variable_rename,[status(thm)],[f_831_1]) ).

fof(f_831_3,plain,
    ( ! [U_2585,U_2586,U_2588,U_2587,U_2584] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2585),U_2586),U_2587) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2584),U_2586),U_2588)
        | 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_2585,U_2584)),U_2586),U_2587) != U_2588
        | ~ sP223(U_2585,U_2586,U_2588,U_2587,U_2584) )
    & ! [U_2585,U_2586,U_2588,U_2587,U_2584] :
        ( 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_2585,U_2584)),U_2586),U_2587) = U_2588
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2585),U_2586),U_2587) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2584),U_2586),U_2588)
        | ~ sP223(U_2585,U_2586,U_2588,U_2587,U_2584) )
    & ! [U_2585,U_2586,U_2588,U_2587,U_2584] :
        ( sP223(U_2585,U_2586,U_2588,U_2587,U_2584)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2584,U_2585) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP223])],[f_831_2]) ).

cnf(f_831_4,plain,
    ( sP223(U_2585,U_2586,U_2588,U_2587,U_2584)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2584,U_2585) ),
    inference(clausify,[status(thm)],[f_831_3]) ).

cnf(f_831_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_2585,U_2584)),U_2586),U_2587) = U_2588
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2585),U_2586),U_2587) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2584),U_2586),U_2588)
    | ~ sP223(U_2585,U_2586,U_2588,U_2587,U_2584) ),
    inference(clausify,[status(thm)],[f_831_3]) ).

cnf(f_831_6,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2585),U_2586),U_2587) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2584),U_2586),U_2588)
    | 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_2585,U_2584)),U_2586),U_2587) != U_2588
    | ~ sP223(U_2585,U_2586,U_2588,U_2587,U_2584) ),
    inference(clausify,[status(thm)],[f_831_3]) ).

fof(f_832_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_832_2,plain,
    ! [U_2593,U_2592,U_2591,U_2590,U_2589] :
      ( 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_2590),U_2591),U_2592),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2589),U_2591),U_2593)) = 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_2590,U_2589)),U_2591),U_2592),U_2593)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2589,U_2590) ),
    inference(variable_rename,[status(thm)],[f_832_1]) ).

fof(f_832_3,plain,
    ! [U_2591,U_2592,U_2593,U_2589,U_2590] :
      ( 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_2590),U_2591),U_2592),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2589),U_2591),U_2593)) = 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_2590,U_2589)),U_2591),U_2592),U_2593)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2589,U_2590) ),
    inference(definitional_conversion,[status(esa)],[f_832_2]) ).

cnf(f_832_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_2590),U_2591),U_2592),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2589),U_2591),U_2593)) = 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_2590,U_2589)),U_2591),U_2592),U_2593)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2589,U_2590) ),
    inference(clausify,[status(thm)],[f_832_3]) ).

fof(f_833_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_833_2,plain,
    ! [U_2598,U_2597,U_2596,U_2595,U_2594] :
      ( ( ( 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_2595),U_2596),U_2597),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2594),U_2596),U_2598))
          | ~ 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_2595,U_2594)),U_2596),U_2597),U_2598) )
        & ( 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_2595,U_2594)),U_2596),U_2597),U_2598)
          | ~ 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_2595),U_2596),U_2597),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2594),U_2596),U_2598)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2594,U_2595) ),
    inference(variable_rename,[status(thm)],[f_833_1]) ).

fof(f_833_3,plain,
    ( ! [U_2594,U_2596,U_2595,U_2597,U_2598] :
        ( 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_2595),U_2596),U_2597),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2594),U_2596),U_2598))
        | ~ 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_2595,U_2594)),U_2596),U_2597),U_2598)
        | ~ sP224(U_2594,U_2596,U_2595,U_2597,U_2598) )
    & ! [U_2594,U_2596,U_2595,U_2597,U_2598] :
        ( 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_2595,U_2594)),U_2596),U_2597),U_2598)
        | ~ 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_2595),U_2596),U_2597),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2594),U_2596),U_2598))
        | ~ sP224(U_2594,U_2596,U_2595,U_2597,U_2598) )
    & ! [U_2594,U_2596,U_2595,U_2597,U_2598] :
        ( sP224(U_2594,U_2596,U_2595,U_2597,U_2598)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2594,U_2595) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP224])],[f_833_2]) ).

cnf(f_833_4,plain,
    ( sP224(U_2594,U_2596,U_2595,U_2597,U_2598)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2594,U_2595) ),
    inference(clausify,[status(thm)],[f_833_3]) ).

cnf(f_833_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_2595,U_2594)),U_2596),U_2597),U_2598)
    | ~ 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_2595),U_2596),U_2597),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2594),U_2596),U_2598))
    | ~ sP224(U_2594,U_2596,U_2595,U_2597,U_2598) ),
    inference(clausify,[status(thm)],[f_833_3]) ).

cnf(f_833_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_2595),U_2596),U_2597),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2594),U_2596),U_2598))
    | ~ 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_2595,U_2594)),U_2596),U_2597),U_2598)
    | ~ sP224(U_2594,U_2596,U_2595,U_2597,U_2598) ),
    inference(clausify,[status(thm)],[f_833_3]) ).

fof(f_834_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_834_2,plain,
    ! [U_2599] :
      ( ( ~ 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_2599),U_2599))
        | U_2599 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( U_2599 = 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_2599),U_2599)) ) ),
    inference(variable_rename,[status(thm)],[f_834_1]) ).

fof(f_834_3,plain,
    ( ! [U_2601] :
        ( ~ 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_2601),U_2601))
        | U_2601 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
    & ! [U_2600] :
        ( U_2600 = 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_2600),U_2600)) ) ),
    inference(miniscope,[status(thm)],[f_834_2]) ).

fof(f_834_4,plain,
    ( ! [U_2601] :
        ( ~ 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_2601),U_2601))
        | U_2601 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
    & ! [U_2600] :
        ( U_2600 = 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_2600),U_2600)) ) ),
    inference(definitional_conversion,[status(esa)],[f_834_3]) ).

cnf(f_834_5,plain,
    ( U_2600 = 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_2600),U_2600)) ),
    inference(clausify,[status(thm)],[f_834_4]) ).

cnf(f_834_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_2601),U_2601))
    | U_2601 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(clausify,[status(thm)],[f_834_4]) ).

fof(f_835_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_835_2,plain,
    ! [U_2605,U_2604] :
      ( ? [U_2603] :
          ( ! [U_2602] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2604,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2604),U_2602),U_2605)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2604,U_2602)),U_2603))
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2603) )
      | ~ class_RealVector_Oreal__normed__algebra(U_2604) ),
    inference(variable_rename,[status(thm)],[f_835_1]) ).

fof(f_835_3,plain,
    ! [U_2605,U_2604] :
      ( ( ! [U_2602] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2604,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2604),U_2602),U_2605)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2604,U_2602)),sK61(U_2605,U_2604)))
        & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK61(U_2605,U_2604)) )
      | ~ class_RealVector_Oreal__normed__algebra(U_2604) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_2603,sK61(U_2605,U_2604))],[f_835_2]) ).

fof(f_835_4,plain,
    ( ! [U_2604,U_2602,U_2605] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2604,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2604),U_2602),U_2605)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2604,U_2602)),sK61(U_2605,U_2604)))
        | ~ sP225(U_2604,U_2602,U_2605) )
    & ! [U_2604,U_2602,U_2605] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK61(U_2605,U_2604))
        | ~ sP225(U_2604,U_2602,U_2605) )
    & ! [U_2604,U_2602,U_2605] :
        ( sP225(U_2604,U_2602,U_2605)
        | ~ class_RealVector_Oreal__normed__algebra(U_2604) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP225])],[f_835_3]) ).

cnf(f_835_5,plain,
    ( sP225(U_2604,U_2602,U_2605)
    | ~ class_RealVector_Oreal__normed__algebra(U_2604) ),
    inference(clausify,[status(thm)],[f_835_4]) ).

cnf(f_835_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK61(U_2605,U_2604))
    | ~ sP225(U_2604,U_2602,U_2605) ),
    inference(clausify,[status(thm)],[f_835_4]) ).

cnf(f_835_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2604,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2604),U_2602),U_2605)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2604,U_2602)),sK61(U_2605,U_2604)))
    | ~ sP225(U_2604,U_2602,U_2605) ),
    inference(clausify,[status(thm)],[f_835_4]) ).

fof(f_836_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_836_2,plain,
    ! [U_2609] :
      ( ? [U_2608] :
          ( ! [U_2607,U_2606] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2609,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2609),U_2607),U_2606)),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_2609,U_2607)),c_RealVector_Onorm__class_Onorm(U_2609,U_2606))),U_2608))
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2608) )
      | ~ class_RealVector_Oreal__normed__algebra(U_2609) ),
    inference(variable_rename,[status(thm)],[f_836_1]) ).

fof(f_836_3,plain,
    ! [U_2609] :
      ( ( ! [U_2607,U_2606] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2609,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2609),U_2607),U_2606)),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_2609,U_2607)),c_RealVector_Onorm__class_Onorm(U_2609,U_2606))),sK62(U_2609)))
        & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK62(U_2609)) )
      | ~ class_RealVector_Oreal__normed__algebra(U_2609) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_2608,sK62(U_2609))],[f_836_2]) ).

fof(f_836_4,plain,
    ( ! [U_2607,U_2606,U_2609] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2609,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2609),U_2607),U_2606)),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_2609,U_2607)),c_RealVector_Onorm__class_Onorm(U_2609,U_2606))),sK62(U_2609)))
        | ~ sP226(U_2607,U_2606,U_2609) )
    & ! [U_2607,U_2606,U_2609] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK62(U_2609))
        | ~ sP226(U_2607,U_2606,U_2609) )
    & ! [U_2607,U_2606,U_2609] :
        ( sP226(U_2607,U_2606,U_2609)
        | ~ class_RealVector_Oreal__normed__algebra(U_2609) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP226])],[f_836_3]) ).

cnf(f_836_5,plain,
    ( sP226(U_2607,U_2606,U_2609)
    | ~ class_RealVector_Oreal__normed__algebra(U_2609) ),
    inference(clausify,[status(thm)],[f_836_4]) ).

cnf(f_836_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK62(U_2609))
    | ~ sP226(U_2607,U_2606,U_2609) ),
    inference(clausify,[status(thm)],[f_836_4]) ).

cnf(f_836_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2609,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2609),U_2607),U_2606)),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_2609,U_2607)),c_RealVector_Onorm__class_Onorm(U_2609,U_2606))),sK62(U_2609)))
    | ~ sP226(U_2607,U_2606,U_2609) ),
    inference(clausify,[status(thm)],[f_836_4]) ).

fof(f_837_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_837_2,plain,
    ! [U_2613,U_2612] :
      ( ? [U_2611] :
          ( ! [U_2610] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2612,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2612),U_2613),U_2610)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2612,U_2610)),U_2611))
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2611) )
      | ~ class_RealVector_Oreal__normed__algebra(U_2612) ),
    inference(variable_rename,[status(thm)],[f_837_1]) ).

fof(f_837_3,plain,
    ! [U_2613,U_2612] :
      ( ( ! [U_2610] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2612,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2612),U_2613),U_2610)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2612,U_2610)),sK63(U_2613,U_2612)))
        & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK63(U_2613,U_2612)) )
      | ~ class_RealVector_Oreal__normed__algebra(U_2612) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_2611,sK63(U_2613,U_2612))],[f_837_2]) ).

fof(f_837_4,plain,
    ( ! [U_2610,U_2612,U_2613] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2612,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2612),U_2613),U_2610)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2612,U_2610)),sK63(U_2613,U_2612)))
        | ~ sP227(U_2610,U_2612,U_2613) )
    & ! [U_2610,U_2612,U_2613] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK63(U_2613,U_2612))
        | ~ sP227(U_2610,U_2612,U_2613) )
    & ! [U_2610,U_2612,U_2613] :
        ( sP227(U_2610,U_2612,U_2613)
        | ~ class_RealVector_Oreal__normed__algebra(U_2612) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP227])],[f_837_3]) ).

cnf(f_837_5,plain,
    ( sP227(U_2610,U_2612,U_2613)
    | ~ class_RealVector_Oreal__normed__algebra(U_2612) ),
    inference(clausify,[status(thm)],[f_837_4]) ).

cnf(f_837_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK63(U_2613,U_2612))
    | ~ sP227(U_2610,U_2612,U_2613) ),
    inference(clausify,[status(thm)],[f_837_4]) ).

cnf(f_837_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2612,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2612),U_2613),U_2610)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2612,U_2610)),sK63(U_2613,U_2612)))
    | ~ sP227(U_2610,U_2612,U_2613) ),
    inference(clausify,[status(thm)],[f_837_4]) ).

fof(f_838_1,plain,
    ! [V_k_2,V_P_2,V_da_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_da_2))))
          | ~ hBOOL(hAPP(V_P_2,B_x)) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
      | ? [B_x] :
          ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B_x,V_da_2)))
          & hBOOL(hAPP(V_P_2,B_x)) )
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_da_2) ),
    inference(fof_nnf,[status(thm)],[fact_decr__mult__lemma]) ).

fof(f_838_2,plain,
    ! [U_2618,U_2617,U_2616] :
      ( ! [U_2615] :
          ( hBOOL(hAPP(U_2617,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2615,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2618),U_2616))))
          | ~ hBOOL(hAPP(U_2617,U_2615)) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2618)
      | ? [U_2614] :
          ( ~ hBOOL(hAPP(U_2617,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2614,U_2616)))
          & hBOOL(hAPP(U_2617,U_2614)) )
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2616) ),
    inference(variable_rename,[status(thm)],[f_838_1]) ).

fof(f_838_3,plain,
    ! [U_2618,U_2617,U_2616] :
      ( ! [U_2615] :
          ( hBOOL(hAPP(U_2617,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2615,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2618),U_2616))))
          | ~ hBOOL(hAPP(U_2617,U_2615)) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2618)
      | ( ~ hBOOL(hAPP(U_2617,c_Groups_Ominus__class_Ominus(tc_Int_Oint,sK64(U_2618,U_2617,U_2616),U_2616)))
        & hBOOL(hAPP(U_2617,sK64(U_2618,U_2617,U_2616))) )
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2616) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_2614,sK64(U_2618,U_2617,U_2616))],[f_838_2]) ).

fof(f_838_4,plain,
    ( ! [U_2616,U_2617,U_2618] :
        ( ~ hBOOL(hAPP(U_2617,c_Groups_Ominus__class_Ominus(tc_Int_Oint,sK64(U_2618,U_2617,U_2616),U_2616)))
        | ~ sP228(U_2616,U_2617,U_2618) )
    & ! [U_2616,U_2617,U_2618] :
        ( hBOOL(hAPP(U_2617,sK64(U_2618,U_2617,U_2616)))
        | ~ sP228(U_2616,U_2617,U_2618) )
    & ! [U_2615,U_2616,U_2617,U_2618] :
        ( hBOOL(hAPP(U_2617,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2615,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2618),U_2616))))
        | ~ hBOOL(hAPP(U_2617,U_2615))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2618)
        | sP228(U_2616,U_2617,U_2618)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2616) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP228])],[f_838_3]) ).

cnf(f_838_5,plain,
    ( hBOOL(hAPP(U_2617,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2615,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2618),U_2616))))
    | ~ hBOOL(hAPP(U_2617,U_2615))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2618)
    | sP228(U_2616,U_2617,U_2618)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2616) ),
    inference(clausify,[status(thm)],[f_838_4]) ).

cnf(f_838_6,plain,
    ( hBOOL(hAPP(U_2617,sK64(U_2618,U_2617,U_2616)))
    | ~ sP228(U_2616,U_2617,U_2618) ),
    inference(clausify,[status(thm)],[f_838_4]) ).

cnf(f_838_7,plain,
    ( ~ hBOOL(hAPP(U_2617,c_Groups_Ominus__class_Ominus(tc_Int_Oint,sK64(U_2618,U_2617,U_2616),U_2616)))
    | ~ sP228(U_2616,U_2617,U_2618) ),
    inference(clausify,[status(thm)],[f_838_4]) ).

fof(f_839_1,plain,
    ! [V_k_2,V_P_2,V_da_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_da_2))))
          | ~ hBOOL(hAPP(V_P_2,B_x)) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
      | ? [B_x] :
          ( ~ hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B_x,V_da_2)))
          & hBOOL(hAPP(V_P_2,B_x)) )
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_da_2) ),
    inference(fof_nnf,[status(thm)],[fact_incr__mult__lemma]) ).

fof(f_839_2,plain,
    ! [U_2623,U_2622,U_2621] :
      ( ! [U_2620] :
          ( hBOOL(hAPP(U_2622,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2620,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2623),U_2621))))
          | ~ hBOOL(hAPP(U_2622,U_2620)) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2623)
      | ? [U_2619] :
          ( ~ hBOOL(hAPP(U_2622,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2619,U_2621)))
          & hBOOL(hAPP(U_2622,U_2619)) )
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2621) ),
    inference(variable_rename,[status(thm)],[f_839_1]) ).

fof(f_839_3,plain,
    ! [U_2623,U_2622,U_2621] :
      ( ! [U_2620] :
          ( hBOOL(hAPP(U_2622,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2620,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2623),U_2621))))
          | ~ hBOOL(hAPP(U_2622,U_2620)) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2623)
      | ( ~ hBOOL(hAPP(U_2622,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sK65(U_2623,U_2622,U_2621),U_2621)))
        & hBOOL(hAPP(U_2622,sK65(U_2623,U_2622,U_2621))) )
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2621) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_2619,sK65(U_2623,U_2622,U_2621))],[f_839_2]) ).

fof(f_839_4,plain,
    ( ! [U_2621,U_2622,U_2623] :
        ( ~ hBOOL(hAPP(U_2622,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sK65(U_2623,U_2622,U_2621),U_2621)))
        | ~ sP229(U_2621,U_2622,U_2623) )
    & ! [U_2621,U_2622,U_2623] :
        ( hBOOL(hAPP(U_2622,sK65(U_2623,U_2622,U_2621)))
        | ~ sP229(U_2621,U_2622,U_2623) )
    & ! [U_2621,U_2622,U_2623,U_2620] :
        ( hBOOL(hAPP(U_2622,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2620,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2623),U_2621))))
        | ~ hBOOL(hAPP(U_2622,U_2620))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2623)
        | sP229(U_2621,U_2622,U_2623)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2621) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP229])],[f_839_3]) ).

cnf(f_839_5,plain,
    ( hBOOL(hAPP(U_2622,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2620,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2623),U_2621))))
    | ~ hBOOL(hAPP(U_2622,U_2620))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2623)
    | sP229(U_2621,U_2622,U_2623)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2621) ),
    inference(clausify,[status(thm)],[f_839_4]) ).

cnf(f_839_6,plain,
    ( hBOOL(hAPP(U_2622,sK65(U_2623,U_2622,U_2621)))
    | ~ sP229(U_2621,U_2622,U_2623) ),
    inference(clausify,[status(thm)],[f_839_4]) ).

cnf(f_839_7,plain,
    ( ~ hBOOL(hAPP(U_2622,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sK65(U_2623,U_2622,U_2621),U_2621)))
    | ~ sP229(U_2621,U_2622,U_2623) ),
    inference(clausify,[status(thm)],[f_839_4]) ).

fof(f_840_1,plain,
    ! [V_k] :
      ( ? [B_n] :
          ( V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B_n) )
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__imp__eq__int]) ).

fof(f_840_2,plain,
    ! [U_2625] :
      ( ? [U_2624] :
          ( U_2625 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2624)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2624) )
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2625) ),
    inference(variable_rename,[status(thm)],[f_840_1]) ).

fof(f_840_3,plain,
    ! [U_2625] :
      ( ( U_2625 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK66(U_2625))
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),sK66(U_2625)) )
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2625) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_2624,sK66(U_2625))],[f_840_2]) ).

fof(f_840_4,plain,
    ( ! [U_2625] :
        ( U_2625 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK66(U_2625))
        | ~ sP230(U_2625) )
    & ! [U_2625] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),sK66(U_2625))
        | ~ sP230(U_2625) )
    & ! [U_2625] :
        ( sP230(U_2625)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2625) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP230])],[f_840_3]) ).

cnf(f_840_5,plain,
    ( sP230(U_2625)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2625) ),
    inference(clausify,[status(thm)],[f_840_4]) ).

cnf(f_840_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),sK66(U_2625))
    | ~ sP230(U_2625) ),
    inference(clausify,[status(thm)],[f_840_4]) ).

cnf(f_840_7,plain,
    ( U_2625 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK66(U_2625))
    | ~ sP230(U_2625) ),
    inference(clausify,[status(thm)],[f_840_4]) ).

fof(f_841_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_841_2,plain,
    ! [U_2629] :
      ( ? [U_2628] :
          ( ! [U_2627,U_2626] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2629,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2629),U_2627),U_2626)),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_2629,U_2627)),c_RealVector_Onorm__class_Onorm(U_2629,U_2626))),U_2628))
          & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2628) )
      | ~ class_RealVector_Oreal__normed__algebra(U_2629) ),
    inference(variable_rename,[status(thm)],[f_841_1]) ).

fof(f_841_3,plain,
    ! [U_2629] :
      ( ( ! [U_2627,U_2626] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2629,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2629),U_2627),U_2626)),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_2629,U_2627)),c_RealVector_Onorm__class_Onorm(U_2629,U_2626))),sK67(U_2629)))
        & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK67(U_2629)) )
      | ~ class_RealVector_Oreal__normed__algebra(U_2629) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_2628,sK67(U_2629))],[f_841_2]) ).

fof(f_841_4,plain,
    ( ! [U_2627,U_2626,U_2629] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2629,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2629),U_2627),U_2626)),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_2629,U_2627)),c_RealVector_Onorm__class_Onorm(U_2629,U_2626))),sK67(U_2629)))
        | ~ sP231(U_2627,U_2626,U_2629) )
    & ! [U_2627,U_2626,U_2629] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK67(U_2629))
        | ~ sP231(U_2627,U_2626,U_2629) )
    & ! [U_2627,U_2626,U_2629] :
        ( sP231(U_2627,U_2626,U_2629)
        | ~ class_RealVector_Oreal__normed__algebra(U_2629) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP231])],[f_841_3]) ).

cnf(f_841_5,plain,
    ( sP231(U_2627,U_2626,U_2629)
    | ~ class_RealVector_Oreal__normed__algebra(U_2629) ),
    inference(clausify,[status(thm)],[f_841_4]) ).

cnf(f_841_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK67(U_2629))
    | ~ sP231(U_2627,U_2626,U_2629) ),
    inference(clausify,[status(thm)],[f_841_4]) ).

cnf(f_841_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2629,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2629),U_2627),U_2626)),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_2629,U_2627)),c_RealVector_Onorm__class_Onorm(U_2629,U_2626))),sK67(U_2629)))
    | ~ sP231(U_2627,U_2626,U_2629) ),
    inference(clausify,[status(thm)],[f_841_4]) ).

fof(f_842_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_842_2,plain,
    ! [U_2633,U_2632] :
      ( ? [U_2631] :
          ( ! [U_2630] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2632,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2632),U_2630),U_2633)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2632,U_2630)),U_2631))
          & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2631) )
      | ~ class_RealVector_Oreal__normed__algebra(U_2632) ),
    inference(variable_rename,[status(thm)],[f_842_1]) ).

fof(f_842_3,plain,
    ! [U_2633,U_2632] :
      ( ( ! [U_2630] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2632,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2632),U_2630),U_2633)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2632,U_2630)),sK68(U_2633,U_2632)))
        & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK68(U_2633,U_2632)) )
      | ~ class_RealVector_Oreal__normed__algebra(U_2632) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_2631,sK68(U_2633,U_2632))],[f_842_2]) ).

fof(f_842_4,plain,
    ( ! [U_2630,U_2632,U_2633] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2632,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2632),U_2630),U_2633)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2632,U_2630)),sK68(U_2633,U_2632)))
        | ~ sP232(U_2630,U_2632,U_2633) )
    & ! [U_2630,U_2632,U_2633] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK68(U_2633,U_2632))
        | ~ sP232(U_2630,U_2632,U_2633) )
    & ! [U_2630,U_2632,U_2633] :
        ( sP232(U_2630,U_2632,U_2633)
        | ~ class_RealVector_Oreal__normed__algebra(U_2632) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP232])],[f_842_3]) ).

cnf(f_842_5,plain,
    ( sP232(U_2630,U_2632,U_2633)
    | ~ class_RealVector_Oreal__normed__algebra(U_2632) ),
    inference(clausify,[status(thm)],[f_842_4]) ).

cnf(f_842_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK68(U_2633,U_2632))
    | ~ sP232(U_2630,U_2632,U_2633) ),
    inference(clausify,[status(thm)],[f_842_4]) ).

cnf(f_842_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2632,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2632),U_2630),U_2633)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2632,U_2630)),sK68(U_2633,U_2632)))
    | ~ sP232(U_2630,U_2632,U_2633) ),
    inference(clausify,[status(thm)],[f_842_4]) ).

fof(f_843_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_843_2,plain,
    ! [U_2637,U_2636] :
      ( ? [U_2635] :
          ( ! [U_2634] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2636,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2636),U_2637),U_2634)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2636,U_2634)),U_2635))
          & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2635) )
      | ~ class_RealVector_Oreal__normed__algebra(U_2636) ),
    inference(variable_rename,[status(thm)],[f_843_1]) ).

fof(f_843_3,plain,
    ! [U_2637,U_2636] :
      ( ( ! [U_2634] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2636,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2636),U_2637),U_2634)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2636,U_2634)),sK69(U_2637,U_2636)))
        & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK69(U_2637,U_2636)) )
      | ~ class_RealVector_Oreal__normed__algebra(U_2636) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_2635,sK69(U_2637,U_2636))],[f_843_2]) ).

fof(f_843_4,plain,
    ( ! [U_2634,U_2636,U_2637] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2636,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2636),U_2637),U_2634)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2636,U_2634)),sK69(U_2637,U_2636)))
        | ~ sP233(U_2634,U_2636,U_2637) )
    & ! [U_2634,U_2636,U_2637] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK69(U_2637,U_2636))
        | ~ sP233(U_2634,U_2636,U_2637) )
    & ! [U_2634,U_2636,U_2637] :
        ( sP233(U_2634,U_2636,U_2637)
        | ~ class_RealVector_Oreal__normed__algebra(U_2636) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP233])],[f_843_3]) ).

cnf(f_843_5,plain,
    ( sP233(U_2634,U_2636,U_2637)
    | ~ class_RealVector_Oreal__normed__algebra(U_2636) ),
    inference(clausify,[status(thm)],[f_843_4]) ).

cnf(f_843_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK69(U_2637,U_2636))
    | ~ sP233(U_2634,U_2636,U_2637) ),
    inference(clausify,[status(thm)],[f_843_4]) ).

cnf(f_843_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2636,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2636),U_2637),U_2634)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2636,U_2634)),sK69(U_2637,U_2636)))
    | ~ sP233(U_2634,U_2636,U_2637) ),
    inference(clausify,[status(thm)],[f_843_4]) ).

fof(f_844_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),hAPP(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_844_2,plain,
    ! [U_2639,U_2638] :
      ( 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),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_2639)),U_2638),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_2638,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),U_2639))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2638) ),
    inference(variable_rename,[status(thm)],[f_844_1]) ).

fof(f_844_3,plain,
    ! [U_2638,U_2639] :
      ( 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),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_2639)),U_2638),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_2638,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),U_2639))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2638) ),
    inference(definitional_conversion,[status(esa)],[f_844_2]) ).

cnf(f_844_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),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_2639)),U_2638),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_2638,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),U_2639))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2638) ),
    inference(clausify,[status(thm)],[f_844_3]) ).

fof(f_845_1,plain,
    ! [V_a,V_n] : c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(V_n))),V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)),V_a))),
    inference(fof_nnf,[status(thm)],[fact_cis__real__of__nat__Suc__mult]) ).

fof(f_845_2,plain,
    ! [U_2641,U_2640] : c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_2640))),U_2641)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(U_2641)),c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_2640)),U_2641))),
    inference(variable_rename,[status(thm)],[f_845_1]) ).

fof(f_845_3,plain,
    ! [U_2640,U_2641] : c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_2640))),U_2641)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(U_2641)),c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_2640)),U_2641))),
    inference(definitional_conversion,[status(esa)],[f_845_2]) ).

cnf(f_845_4,plain,
    c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_2640))),U_2641)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(U_2641)),c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_2640)),U_2641))),
    inference(clausify,[status(thm)],[f_845_3]) ).

fof(f_846_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_846_2,plain,
    ! [U_2643,U_2642] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2642),U_2643),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_2642)
      | ~ class_Rings_Ocomm__semiring__1(U_2642) ),
    inference(variable_rename,[status(thm)],[f_846_1]) ).

fof(f_846_3,plain,
    ! [U_2642,U_2643] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2642),U_2643),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_2642)
      | ~ class_Rings_Ocomm__semiring__1(U_2642) ),
    inference(definitional_conversion,[status(esa)],[f_846_2]) ).

cnf(f_846_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2642),U_2643),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_2642)
    | ~ class_Rings_Ocomm__semiring__1(U_2642) ),
    inference(clausify,[status(thm)],[f_846_3]) ).

fof(f_847_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_847_2,plain,
    ! [U_2646,U_2645,U_2644] :
      ( c_RealVector_Onorm__class_Onorm(U_2644,hAPP(hAPP(c_Power_Opower__class_Opower(U_2644),U_2645),U_2646)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2644,U_2645)),U_2646)
      | ~ class_RealVector_Oreal__normed__div__algebra(U_2644) ),
    inference(variable_rename,[status(thm)],[f_847_1]) ).

fof(f_847_3,plain,
    ! [U_2644,U_2645,U_2646] :
      ( c_RealVector_Onorm__class_Onorm(U_2644,hAPP(hAPP(c_Power_Opower__class_Opower(U_2644),U_2645),U_2646)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2644,U_2645)),U_2646)
      | ~ class_RealVector_Oreal__normed__div__algebra(U_2644) ),
    inference(definitional_conversion,[status(esa)],[f_847_2]) ).

cnf(f_847_4,plain,
    ( c_RealVector_Onorm__class_Onorm(U_2644,hAPP(hAPP(c_Power_Opower__class_Opower(U_2644),U_2645),U_2646)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2644,U_2645)),U_2646)
    | ~ class_RealVector_Oreal__normed__div__algebra(U_2644) ),
    inference(clausify,[status(thm)],[f_847_3]) ).

fof(f_848_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_848_2,plain,
    ! [U_2649,U_2648,U_2647] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2647,hAPP(hAPP(c_Power_Opower__class_Opower(U_2647),U_2648),U_2649)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2647,U_2648)),U_2649))
      | ~ class_RealVector_Oreal__normed__algebra__1(U_2647) ),
    inference(variable_rename,[status(thm)],[f_848_1]) ).

fof(f_848_3,plain,
    ! [U_2647,U_2648,U_2649] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2647,hAPP(hAPP(c_Power_Opower__class_Opower(U_2647),U_2648),U_2649)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2647,U_2648)),U_2649))
      | ~ class_RealVector_Oreal__normed__algebra__1(U_2647) ),
    inference(definitional_conversion,[status(esa)],[f_848_2]) ).

cnf(f_848_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2647,hAPP(hAPP(c_Power_Opower__class_Opower(U_2647),U_2648),U_2649)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2647,U_2648)),U_2649))
    | ~ class_RealVector_Oreal__normed__algebra__1(U_2647) ),
    inference(clausify,[status(thm)],[f_848_3]) ).

fof(f_849_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_849_2,plain,
    ! [U_2651,U_2650] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2650),U_2651),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2651
      | ~ class_Rings_Ocomm__semiring__1(U_2650) ),
    inference(variable_rename,[status(thm)],[f_849_1]) ).

fof(f_849_3,plain,
    ! [U_2650,U_2651] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2650),U_2651),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2651
      | ~ class_Rings_Ocomm__semiring__1(U_2650) ),
    inference(definitional_conversion,[status(esa)],[f_849_2]) ).

cnf(f_849_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2650),U_2651),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2651
    | ~ class_Rings_Ocomm__semiring__1(U_2650) ),
    inference(clausify,[status(thm)],[f_849_3]) ).

fof(f_850_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_850_2,plain,
    ! [U_2655,U_2654,U_2653,U_2652] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2652),hAPP(hAPP(c_Power_Opower__class_Opower(U_2652),U_2653),U_2654)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2652),U_2653),U_2655)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2652),U_2653),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2654,U_2655))
      | ~ class_Rings_Ocomm__semiring__1(U_2652) ),
    inference(variable_rename,[status(thm)],[f_850_1]) ).

fof(f_850_3,plain,
    ! [U_2652,U_2653,U_2654,U_2655] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2652),hAPP(hAPP(c_Power_Opower__class_Opower(U_2652),U_2653),U_2654)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2652),U_2653),U_2655)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2652),U_2653),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2654,U_2655))
      | ~ class_Rings_Ocomm__semiring__1(U_2652) ),
    inference(definitional_conversion,[status(esa)],[f_850_2]) ).

cnf(f_850_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2652),hAPP(hAPP(c_Power_Opower__class_Opower(U_2652),U_2653),U_2654)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2652),U_2653),U_2655)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2652),U_2653),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2654,U_2655))
    | ~ class_Rings_Ocomm__semiring__1(U_2652) ),
    inference(clausify,[status(thm)],[f_850_3]) ).

fof(f_851_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_851_2,plain,
    ! [U_2658,U_2657,U_2656] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2656),hAPP(hAPP(c_Power_Opower__class_Opower(U_2656),U_2657),U_2658)),U_2657) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2656),U_2657),c_Nat_OSuc(U_2658))
      | ~ class_Rings_Ocomm__semiring__1(U_2656) ),
    inference(variable_rename,[status(thm)],[f_851_1]) ).

fof(f_851_3,plain,
    ! [U_2656,U_2657,U_2658] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2656),hAPP(hAPP(c_Power_Opower__class_Opower(U_2656),U_2657),U_2658)),U_2657) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2656),U_2657),c_Nat_OSuc(U_2658))
      | ~ class_Rings_Ocomm__semiring__1(U_2656) ),
    inference(definitional_conversion,[status(esa)],[f_851_2]) ).

cnf(f_851_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2656),hAPP(hAPP(c_Power_Opower__class_Opower(U_2656),U_2657),U_2658)),U_2657) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2656),U_2657),c_Nat_OSuc(U_2658))
    | ~ class_Rings_Ocomm__semiring__1(U_2656) ),
    inference(clausify,[status(thm)],[f_851_3]) ).

fof(f_852_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_852_2,plain,
    ! [U_2661,U_2660,U_2659] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2659),U_2660),hAPP(hAPP(c_Power_Opower__class_Opower(U_2659),U_2660),U_2661)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2659),U_2660),c_Nat_OSuc(U_2661))
      | ~ class_Rings_Ocomm__semiring__1(U_2659) ),
    inference(variable_rename,[status(thm)],[f_852_1]) ).

fof(f_852_3,plain,
    ! [U_2659,U_2660,U_2661] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2659),U_2660),hAPP(hAPP(c_Power_Opower__class_Opower(U_2659),U_2660),U_2661)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2659),U_2660),c_Nat_OSuc(U_2661))
      | ~ class_Rings_Ocomm__semiring__1(U_2659) ),
    inference(definitional_conversion,[status(esa)],[f_852_2]) ).

cnf(f_852_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2659),U_2660),hAPP(hAPP(c_Power_Opower__class_Opower(U_2659),U_2660),U_2661)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2659),U_2660),c_Nat_OSuc(U_2661))
    | ~ class_Rings_Ocomm__semiring__1(U_2659) ),
    inference(clausify,[status(thm)],[f_852_3]) ).

fof(f_853_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_853_2,plain,
    ! [U_2664,U_2663,U_2662] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2662),U_2663),c_Nat_OSuc(U_2664)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2662),U_2663),hAPP(hAPP(c_Power_Opower__class_Opower(U_2662),U_2663),U_2664))
      | ~ class_Rings_Ocomm__semiring__1(U_2662) ),
    inference(variable_rename,[status(thm)],[f_853_1]) ).

fof(f_853_3,plain,
    ! [U_2662,U_2663,U_2664] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2662),U_2663),c_Nat_OSuc(U_2664)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2662),U_2663),hAPP(hAPP(c_Power_Opower__class_Opower(U_2662),U_2663),U_2664))
      | ~ class_Rings_Ocomm__semiring__1(U_2662) ),
    inference(definitional_conversion,[status(esa)],[f_853_2]) ).

cnf(f_853_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2662),U_2663),c_Nat_OSuc(U_2664)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2662),U_2663),hAPP(hAPP(c_Power_Opower__class_Opower(U_2662),U_2663),U_2664))
    | ~ class_Rings_Ocomm__semiring__1(U_2662) ),
    inference(clausify,[status(thm)],[f_853_3]) ).

fof(f_854_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_854_2,plain,
    ! [U_2668,U_2667,U_2666,U_2665] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2665),hAPP(hAPP(c_Power_Opower__class_Opower(U_2665),U_2666),U_2667)),U_2668) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2665),U_2666),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2667),U_2668))
      | ~ class_Rings_Ocomm__semiring__1(U_2665) ),
    inference(variable_rename,[status(thm)],[f_854_1]) ).

fof(f_854_3,plain,
    ! [U_2665,U_2666,U_2667,U_2668] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2665),hAPP(hAPP(c_Power_Opower__class_Opower(U_2665),U_2666),U_2667)),U_2668) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2665),U_2666),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2667),U_2668))
      | ~ class_Rings_Ocomm__semiring__1(U_2665) ),
    inference(definitional_conversion,[status(esa)],[f_854_2]) ).

cnf(f_854_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2665),hAPP(hAPP(c_Power_Opower__class_Opower(U_2665),U_2666),U_2667)),U_2668) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2665),U_2666),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2667),U_2668))
    | ~ class_Rings_Ocomm__semiring__1(U_2665) ),
    inference(clausify,[status(thm)],[f_854_3]) ).

fof(f_855_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_855_2,plain,
    ! [U_2672,U_2671,U_2670,U_2669] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2669),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2669),U_2670),U_2671)),U_2672) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2669),hAPP(hAPP(c_Power_Opower__class_Opower(U_2669),U_2670),U_2672)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2669),U_2671),U_2672))
      | ~ class_Rings_Ocomm__semiring__1(U_2669) ),
    inference(variable_rename,[status(thm)],[f_855_1]) ).

fof(f_855_3,plain,
    ! [U_2669,U_2670,U_2671,U_2672] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2669),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2669),U_2670),U_2671)),U_2672) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2669),hAPP(hAPP(c_Power_Opower__class_Opower(U_2669),U_2670),U_2672)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2669),U_2671),U_2672))
      | ~ class_Rings_Ocomm__semiring__1(U_2669) ),
    inference(definitional_conversion,[status(esa)],[f_855_2]) ).

cnf(f_855_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2669),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2669),U_2670),U_2671)),U_2672) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2669),hAPP(hAPP(c_Power_Opower__class_Opower(U_2669),U_2670),U_2672)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2669),U_2671),U_2672))
    | ~ class_Rings_Ocomm__semiring__1(U_2669) ),
    inference(clausify,[status(thm)],[f_855_3]) ).

fof(f_856_1,plain,
    ! [V_wa_2,V_a_2,T_a] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2)) = c_Groups_Ozero__class_Ozero(T_a)
          | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
          | hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_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__number__of]) ).

fof(f_856_2,plain,
    ! [U_2675,U_2674,U_2673] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2673),U_2674),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2675)) = c_Groups_Ozero__class_Ozero(U_2673)
          | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2675) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | U_2674 != c_Groups_Ozero__class_Ozero(U_2673) )
        & ( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2675) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & U_2674 = c_Groups_Ozero__class_Ozero(U_2673) )
          | hAPP(hAPP(c_Power_Opower__class_Opower(U_2673),U_2674),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2675)) != c_Groups_Ozero__class_Ozero(U_2673) ) )
      | ~ class_Rings_Ozero__neq__one(U_2673)
      | ~ class_Rings_Ono__zero__divisors(U_2673)
      | ~ class_Rings_Omult__zero(U_2673)
      | ~ class_Power_Opower(U_2673) ),
    inference(variable_rename,[status(thm)],[f_856_1]) ).

fof(f_856_3,plain,
    ( ! [U_2673,U_2674,U_2675] :
        ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2675) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP234(U_2673,U_2674,U_2675) )
    & ! [U_2673,U_2674,U_2675] :
        ( U_2674 = c_Groups_Ozero__class_Ozero(U_2673)
        | ~ sP234(U_2673,U_2674,U_2675) )
    & ! [U_2673,U_2674,U_2675] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2673),U_2674),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2675)) = c_Groups_Ozero__class_Ozero(U_2673)
        | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2675) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2674 != c_Groups_Ozero__class_Ozero(U_2673)
        | ~ sP235(U_2673,U_2674,U_2675) )
    & ! [U_2673,U_2674,U_2675] :
        ( sP234(U_2673,U_2674,U_2675)
        | hAPP(hAPP(c_Power_Opower__class_Opower(U_2673),U_2674),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2675)) != c_Groups_Ozero__class_Ozero(U_2673)
        | ~ sP235(U_2673,U_2674,U_2675) )
    & ! [U_2673,U_2674,U_2675] :
        ( sP235(U_2673,U_2674,U_2675)
        | ~ class_Rings_Ozero__neq__one(U_2673)
        | ~ class_Rings_Ono__zero__divisors(U_2673)
        | ~ class_Rings_Omult__zero(U_2673)
        | ~ class_Power_Opower(U_2673) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP234,sP235])],[f_856_2]) ).

cnf(f_856_4,plain,
    ( sP235(U_2673,U_2674,U_2675)
    | ~ class_Rings_Ozero__neq__one(U_2673)
    | ~ class_Rings_Ono__zero__divisors(U_2673)
    | ~ class_Rings_Omult__zero(U_2673)
    | ~ class_Power_Opower(U_2673) ),
    inference(clausify,[status(thm)],[f_856_3]) ).

cnf(f_856_5,plain,
    ( sP234(U_2673,U_2674,U_2675)
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_2673),U_2674),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2675)) != c_Groups_Ozero__class_Ozero(U_2673)
    | ~ sP235(U_2673,U_2674,U_2675) ),
    inference(clausify,[status(thm)],[f_856_3]) ).

cnf(f_856_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2673),U_2674),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2675)) = c_Groups_Ozero__class_Ozero(U_2673)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2675) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_2674 != c_Groups_Ozero__class_Ozero(U_2673)
    | ~ sP235(U_2673,U_2674,U_2675) ),
    inference(clausify,[status(thm)],[f_856_3]) ).

cnf(f_856_7,plain,
    ( U_2674 = c_Groups_Ozero__class_Ozero(U_2673)
    | ~ sP234(U_2673,U_2674,U_2675) ),
    inference(clausify,[status(thm)],[f_856_3]) ).

cnf(f_856_8,plain,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2675) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP234(U_2673,U_2674,U_2675) ),
    inference(clausify,[status(thm)],[f_856_3]) ).

fof(f_857_1,plain,
    ! [V_b,V_a] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),c_Complex_Ocis(V_b)) = c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a,V_b)),
    inference(fof_nnf,[status(thm)],[fact_cis__mult]) ).

fof(f_857_2,plain,
    ! [U_2677,U_2676] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(U_2676)),c_Complex_Ocis(U_2677)) = c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2676,U_2677)),
    inference(variable_rename,[status(thm)],[f_857_1]) ).

fof(f_857_3,plain,
    ! [U_2677,U_2676] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(U_2676)),c_Complex_Ocis(U_2677)) = c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2676,U_2677)),
    inference(definitional_conversion,[status(esa)],[f_857_2]) ).

cnf(f_857_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(U_2676)),c_Complex_Ocis(U_2677)) = c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2676,U_2677)),
    inference(clausify,[status(thm)],[f_857_3]) ).

fof(f_858_1,plain,
    c_Complex_Ocis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[fact_cis__zero]) ).

fof(f_858_2,plain,
    c_Complex_Ocis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_858_1]) ).

cnf(f_858_3,plain,
    c_Complex_Ocis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_858_2]) ).

fof(f_859_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_859_2,plain,
    ! [U_2680,U_2679,U_2678] :
      ( c_Orderings_Oord__class_Oless__eq(U_2678,hAPP(hAPP(c_Power_Opower__class_Opower(U_2678),U_2679),c_Nat_OSuc(U_2680)),U_2679)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2678,U_2679,c_Groups_Oone__class_Oone(U_2678))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2678,c_Groups_Ozero__class_Ozero(U_2678),U_2679)
      | ~ class_Rings_Olinordered__semidom(U_2678) ),
    inference(variable_rename,[status(thm)],[f_859_1]) ).

fof(f_859_3,plain,
    ! [U_2680,U_2678,U_2679] :
      ( c_Orderings_Oord__class_Oless__eq(U_2678,hAPP(hAPP(c_Power_Opower__class_Opower(U_2678),U_2679),c_Nat_OSuc(U_2680)),U_2679)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2678,U_2679,c_Groups_Oone__class_Oone(U_2678))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2678,c_Groups_Ozero__class_Ozero(U_2678),U_2679)
      | ~ class_Rings_Olinordered__semidom(U_2678) ),
    inference(definitional_conversion,[status(esa)],[f_859_2]) ).

cnf(f_859_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2678,hAPP(hAPP(c_Power_Opower__class_Opower(U_2678),U_2679),c_Nat_OSuc(U_2680)),U_2679)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2678,U_2679,c_Groups_Oone__class_Oone(U_2678))
    | ~ c_Orderings_Oord__class_Oless__eq(U_2678,c_Groups_Ozero__class_Ozero(U_2678),U_2679)
    | ~ class_Rings_Olinordered__semidom(U_2678) ),
    inference(clausify,[status(thm)],[f_859_3]) ).

fof(f_860_1,plain,
    ! [V_w,T_a] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w)) = c_Groups_Ozero__class_Ozero(T_a)
          | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w)) = c_Groups_Oone__class_Oone(T_a)
          | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w) != 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__number__of]) ).

fof(f_860_2,plain,
    ! [U_2682,U_2681] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2681),c_Groups_Ozero__class_Ozero(U_2681)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2682)) = c_Groups_Ozero__class_Ozero(U_2681)
          | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2682) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2681),c_Groups_Ozero__class_Ozero(U_2681)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2682)) = c_Groups_Oone__class_Oone(U_2681)
          | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2682) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ class_Rings_Osemiring__0(U_2681)
      | ~ class_Power_Opower(U_2681) ),
    inference(variable_rename,[status(thm)],[f_860_1]) ).

fof(f_860_3,plain,
    ( ! [U_2681,U_2682] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2681),c_Groups_Ozero__class_Ozero(U_2681)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2682)) = c_Groups_Ozero__class_Ozero(U_2681)
        | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2682) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP236(U_2681,U_2682) )
    & ! [U_2681,U_2682] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2681),c_Groups_Ozero__class_Ozero(U_2681)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2682)) = c_Groups_Oone__class_Oone(U_2681)
        | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2682) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP236(U_2681,U_2682) )
    & ! [U_2681,U_2682] :
        ( sP236(U_2681,U_2682)
        | ~ class_Rings_Osemiring__0(U_2681)
        | ~ class_Power_Opower(U_2681) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP236])],[f_860_2]) ).

cnf(f_860_4,plain,
    ( sP236(U_2681,U_2682)
    | ~ class_Rings_Osemiring__0(U_2681)
    | ~ class_Power_Opower(U_2681) ),
    inference(clausify,[status(thm)],[f_860_3]) ).

cnf(f_860_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2681),c_Groups_Ozero__class_Ozero(U_2681)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2682)) = c_Groups_Oone__class_Oone(U_2681)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2682) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP236(U_2681,U_2682) ),
    inference(clausify,[status(thm)],[f_860_3]) ).

cnf(f_860_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2681),c_Groups_Ozero__class_Ozero(U_2681)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2682)) = c_Groups_Ozero__class_Ozero(U_2681)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2682) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP236(U_2681,U_2682) ),
    inference(clausify,[status(thm)],[f_860_3]) ).

fof(f_861_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_861_2,plain,
    ! [U_2685,U_2684,U_2683] :
      ( c_Groups_Ominus__class_Ominus(U_2683,hAPP(hAPP(c_Power_Opower__class_Opower(U_2683),U_2684),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_2683),U_2685),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2683),c_Groups_Ominus__class_Ominus(U_2683,U_2684,U_2685)),c_Groups_Oplus__class_Oplus(U_2683,U_2684,U_2685))
      | ~ class_Rings_Ocomm__ring__1(U_2683) ),
    inference(variable_rename,[status(thm)],[f_861_1]) ).

fof(f_861_3,plain,
    ! [U_2683,U_2684,U_2685] :
      ( c_Groups_Ominus__class_Ominus(U_2683,hAPP(hAPP(c_Power_Opower__class_Opower(U_2683),U_2684),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_2683),U_2685),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2683),c_Groups_Ominus__class_Ominus(U_2683,U_2684,U_2685)),c_Groups_Oplus__class_Oplus(U_2683,U_2684,U_2685))
      | ~ class_Rings_Ocomm__ring__1(U_2683) ),
    inference(definitional_conversion,[status(esa)],[f_861_2]) ).

cnf(f_861_4,plain,
    ( c_Groups_Ominus__class_Ominus(U_2683,hAPP(hAPP(c_Power_Opower__class_Opower(U_2683),U_2684),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_2683),U_2685),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2683),c_Groups_Ominus__class_Ominus(U_2683,U_2684,U_2685)),c_Groups_Oplus__class_Oplus(U_2683,U_2684,U_2685))
    | ~ class_Rings_Ocomm__ring__1(U_2683) ),
    inference(clausify,[status(thm)],[f_861_3]) ).

fof(f_862_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_862_2,plain,
    ! [U_2688,U_2687,U_2686] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2686),hAPP(hAPP(c_Power_Opower__class_Opower(U_2686),U_2688),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2687,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_2688) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2686),U_2688),U_2687)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2687)
      | ~ class_Groups_Omonoid__mult(U_2686) ),
    inference(variable_rename,[status(thm)],[f_862_1]) ).

fof(f_862_3,plain,
    ! [U_2686,U_2687,U_2688] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2686),hAPP(hAPP(c_Power_Opower__class_Opower(U_2686),U_2688),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2687,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_2688) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2686),U_2688),U_2687)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2687)
      | ~ class_Groups_Omonoid__mult(U_2686) ),
    inference(definitional_conversion,[status(esa)],[f_862_2]) ).

cnf(f_862_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2686),hAPP(hAPP(c_Power_Opower__class_Opower(U_2686),U_2688),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2687,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_2688) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2686),U_2688),U_2687)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2687)
    | ~ class_Groups_Omonoid__mult(U_2686) ),
    inference(clausify,[status(thm)],[f_862_3]) ).

fof(f_863_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_863_2,plain,
    ! [U_2691,U_2690,U_2689] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2689),U_2691),U_2690) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2689),U_2691),hAPP(hAPP(c_Power_Opower__class_Opower(U_2689),U_2691),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2690,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
          | U_2690 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2689),U_2691),U_2690) = c_Groups_Oone__class_Oone(U_2689)
          | U_2690 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ class_Power_Opower(U_2689) ),
    inference(variable_rename,[status(thm)],[f_863_1]) ).

fof(f_863_3,plain,
    ( ! [U_2689,U_2690,U_2691] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2689),U_2691),U_2690) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2689),U_2691),hAPP(hAPP(c_Power_Opower__class_Opower(U_2689),U_2691),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2690,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | U_2690 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP237(U_2689,U_2690,U_2691) )
    & ! [U_2689,U_2690,U_2691] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2689),U_2691),U_2690) = c_Groups_Oone__class_Oone(U_2689)
        | U_2690 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP237(U_2689,U_2690,U_2691) )
    & ! [U_2689,U_2690,U_2691] :
        ( sP237(U_2689,U_2690,U_2691)
        | ~ class_Power_Opower(U_2689) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP237])],[f_863_2]) ).

cnf(f_863_4,plain,
    ( sP237(U_2689,U_2690,U_2691)
    | ~ class_Power_Opower(U_2689) ),
    inference(clausify,[status(thm)],[f_863_3]) ).

cnf(f_863_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2689),U_2691),U_2690) = c_Groups_Oone__class_Oone(U_2689)
    | U_2690 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP237(U_2689,U_2690,U_2691) ),
    inference(clausify,[status(thm)],[f_863_3]) ).

cnf(f_863_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2689),U_2691),U_2690) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2689),U_2691),hAPP(hAPP(c_Power_Opower__class_Opower(U_2689),U_2691),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2690,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | U_2690 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP237(U_2689,U_2690,U_2691) ),
    inference(clausify,[status(thm)],[f_863_3]) ).

fof(f_864_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_864_2,plain,
    ! [U_2695,U_2694,U_2693,U_2692] :
      ( c_Orderings_Oord__class_Oless(U_2692,hAPP(hAPP(c_Power_Opower__class_Opower(U_2692),U_2693),U_2695),hAPP(hAPP(c_Power_Opower__class_Opower(U_2692),U_2694),U_2695))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2695)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2692,c_Groups_Ozero__class_Ozero(U_2692),U_2693)
      | ~ c_Orderings_Oord__class_Oless(U_2692,U_2693,U_2694)
      | ~ class_Rings_Olinordered__semidom(U_2692) ),
    inference(variable_rename,[status(thm)],[f_864_1]) ).

fof(f_864_3,plain,
    ! [U_2692,U_2694,U_2695,U_2693] :
      ( c_Orderings_Oord__class_Oless(U_2692,hAPP(hAPP(c_Power_Opower__class_Opower(U_2692),U_2693),U_2695),hAPP(hAPP(c_Power_Opower__class_Opower(U_2692),U_2694),U_2695))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2695)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2692,c_Groups_Ozero__class_Ozero(U_2692),U_2693)
      | ~ c_Orderings_Oord__class_Oless(U_2692,U_2693,U_2694)
      | ~ class_Rings_Olinordered__semidom(U_2692) ),
    inference(definitional_conversion,[status(esa)],[f_864_2]) ).

cnf(f_864_4,plain,
    ( c_Orderings_Oord__class_Oless(U_2692,hAPP(hAPP(c_Power_Opower__class_Opower(U_2692),U_2693),U_2695),hAPP(hAPP(c_Power_Opower__class_Opower(U_2692),U_2694),U_2695))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2695)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2692,c_Groups_Ozero__class_Ozero(U_2692),U_2693)
    | ~ c_Orderings_Oord__class_Oless(U_2692,U_2693,U_2694)
    | ~ class_Rings_Olinordered__semidom(U_2692) ),
    inference(clausify,[status(thm)],[f_864_3]) ).

fof(f_865_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)),
    inference(fof_nnf,[status(thm)],[fact_zpower__int]) ).

fof(f_865_2,plain,
    ! [U_2697,U_2696] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2696)),U_2697) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2696),U_2697)),
    inference(variable_rename,[status(thm)],[f_865_1]) ).

fof(f_865_3,plain,
    ! [U_2696,U_2697] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2696)),U_2697) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2696),U_2697)),
    inference(definitional_conversion,[status(esa)],[f_865_2]) ).

cnf(f_865_4,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2696)),U_2697) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2696),U_2697)),
    inference(clausify,[status(thm)],[f_865_3]) ).

fof(f_866_1,plain,
    ! [V_n,V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n),
    inference(fof_nnf,[status(thm)],[fact_int__power]) ).

fof(f_866_2,plain,
    ! [U_2699,U_2698] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2698),U_2699)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2698)),U_2699),
    inference(variable_rename,[status(thm)],[f_866_1]) ).

fof(f_866_3,plain,
    ! [U_2699,U_2698] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2698),U_2699)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2698)),U_2699),
    inference(definitional_conversion,[status(esa)],[f_866_2]) ).

cnf(f_866_4,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2698),U_2699)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2698)),U_2699),
    inference(clausify,[status(thm)],[f_866_3]) ).

fof(f_867_1,plain,
    ! [V_n,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x),V_n)),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J]) ).

fof(f_867_2,plain,
    ! [U_2701,U_2700] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2700)),U_2701) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2700),U_2701)),
    inference(variable_rename,[status(thm)],[f_867_1]) ).

fof(f_867_3,plain,
    ! [U_2700,U_2701] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2700)),U_2701) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2700),U_2701)),
    inference(definitional_conversion,[status(esa)],[f_867_2]) ).

cnf(f_867_4,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2700)),U_2701) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2700),U_2701)),
    inference(clausify,[status(thm)],[f_867_3]) ).

fof(f_868_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_868_2,plain,
    ! [U_2703,U_2702] :
      ( 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_2702),U_2703))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2702) ),
    inference(variable_rename,[status(thm)],[f_868_1]) ).

fof(f_868_3,plain,
    ! [U_2702,U_2703] :
      ( 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_2702),U_2703))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2702) ),
    inference(definitional_conversion,[status(esa)],[f_868_2]) ).

cnf(f_868_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_2702),U_2703))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2702) ),
    inference(clausify,[status(thm)],[f_868_3]) ).

fof(f_869_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_869_2,plain,
    ! [U_2705,U_2704] :
      ( ( 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_2704),U_2705))
        | ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2704)
          & U_2705 != 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_2704)
        | U_2705 = 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_2704),U_2705)) ) ),
    inference(variable_rename,[status(thm)],[f_869_1]) ).

fof(f_869_3,plain,
    ( ! [U_2709,U_2707] :
        ( 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_2707),U_2709))
        | ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2707)
          & U_2709 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_2708,U_2706] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2706)
        | U_2708 = 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_2706),U_2708)) ) ),
    inference(miniscope,[status(thm)],[f_869_2]) ).

fof(f_869_4,plain,
    ( ! [U_2707,U_2709] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2707)
        | ~ sP238(U_2707,U_2709) )
    & ! [U_2707,U_2709] :
        ( U_2709 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP238(U_2707,U_2709) )
    & ! [U_2707,U_2709] :
        ( 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_2707),U_2709))
        | sP238(U_2707,U_2709) )
    & ! [U_2706,U_2708] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2706)
        | U_2708 = 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_2706),U_2708)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP238])],[f_869_3]) ).

cnf(f_869_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2706)
    | U_2708 = 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_2706),U_2708)) ),
    inference(clausify,[status(thm)],[f_869_4]) ).

cnf(f_869_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_2707),U_2709))
    | sP238(U_2707,U_2709) ),
    inference(clausify,[status(thm)],[f_869_4]) ).

cnf(f_869_7,plain,
    ( U_2709 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP238(U_2707,U_2709) ),
    inference(clausify,[status(thm)],[f_869_4]) ).

cnf(f_869_8,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2707)
    | ~ sP238(U_2707,U_2709) ),
    inference(clausify,[status(thm)],[f_869_4]) ).

fof(f_870_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_870_2,plain,
    ! [U_2711,U_2710] :
      ( 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_2710),U_2711))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2710) ),
    inference(variable_rename,[status(thm)],[f_870_1]) ).

fof(f_870_3,plain,
    ! [U_2710,U_2711] :
      ( 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_2710),U_2711))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2710) ),
    inference(definitional_conversion,[status(esa)],[f_870_2]) ).

cnf(f_870_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_2710),U_2711))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2710) ),
    inference(clausify,[status(thm)],[f_870_3]) ).

fof(f_871_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_871_2,plain,
    ! [U_2713,U_2712] :
      ( ( 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_2712),U_2713))
        | ( U_2713 != 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_2712) ) )
      & ( U_2713 = 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_2712)
        | ~ 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_2712),U_2713)) ) ),
    inference(variable_rename,[status(thm)],[f_871_1]) ).

fof(f_871_3,plain,
    ( ! [U_2717,U_2715] :
        ( 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_2715),U_2717))
        | ( U_2717 != 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_2715) ) )
    & ! [U_2716,U_2714] :
        ( U_2716 = 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_2714)
        | ~ 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_2714),U_2716)) ) ),
    inference(miniscope,[status(thm)],[f_871_2]) ).

fof(f_871_4,plain,
    ( ! [U_2715,U_2717] :
        ( U_2717 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP239(U_2715,U_2717) )
    & ! [U_2715,U_2717] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2715)
        | ~ sP239(U_2715,U_2717) )
    & ! [U_2715,U_2717] :
        ( 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_2715),U_2717))
        | sP239(U_2715,U_2717) )
    & ! [U_2716,U_2714] :
        ( U_2716 = 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_2714)
        | ~ 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_2714),U_2716)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP239])],[f_871_3]) ).

cnf(f_871_5,plain,
    ( U_2716 = 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_2714)
    | ~ 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_2714),U_2716)) ),
    inference(clausify,[status(thm)],[f_871_4]) ).

cnf(f_871_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_2715),U_2717))
    | sP239(U_2715,U_2717) ),
    inference(clausify,[status(thm)],[f_871_4]) ).

cnf(f_871_7,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2715)
    | ~ sP239(U_2715,U_2717) ),
    inference(clausify,[status(thm)],[f_871_4]) ).

cnf(f_871_8,plain,
    ( U_2717 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP239(U_2715,U_2717) ),
    inference(clausify,[status(thm)],[f_871_4]) ).

fof(f_872_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_872_2,plain,
    ! [U_2720,U_2719,U_2718] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2719,U_2720)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2718),U_2719),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2718),U_2720))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2718) ),
    inference(variable_rename,[status(thm)],[f_872_1]) ).

fof(f_872_3,plain,
    ! [U_2720,U_2718,U_2719] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2719,U_2720)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2718),U_2719),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2718),U_2720))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2718) ),
    inference(definitional_conversion,[status(esa)],[f_872_2]) ).

cnf(f_872_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2719,U_2720)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2718),U_2719),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2718),U_2720))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2718) ),
    inference(clausify,[status(thm)],[f_872_3]) ).

fof(f_873_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_873_2,plain,
    ! [U_2721] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2721) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_873_1]) ).

fof(f_873_3,plain,
    ! [U_2721] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2721) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_873_2]) ).

cnf(f_873_4,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2721) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_873_3]) ).

fof(f_874_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_874_2,plain,
    ! [U_2723,U_2722] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2722),U_2723) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( U_2722 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_2723 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( U_2722 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_2723 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2722),U_2723) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_874_1]) ).

fof(f_874_3,plain,
    ( ! [U_2727,U_2725] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2725),U_2727) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( U_2725 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_2727 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_2726,U_2724] :
        ( U_2724 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_2726 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2724),U_2726) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_874_2]) ).

fof(f_874_4,plain,
    ( ! [U_2727,U_2725] :
        ( U_2725 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP240(U_2727,U_2725) )
    & ! [U_2727,U_2725] :
        ( U_2727 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP240(U_2727,U_2725) )
    & ! [U_2727,U_2725] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2725),U_2727) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | sP240(U_2727,U_2725) )
    & ! [U_2726,U_2724] :
        ( U_2724 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_2726 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2724),U_2726) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP240])],[f_874_3]) ).

cnf(f_874_5,plain,
    ( U_2724 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_2726 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2724),U_2726) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_874_4]) ).

cnf(f_874_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2725),U_2727) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | sP240(U_2727,U_2725) ),
    inference(clausify,[status(thm)],[f_874_4]) ).

cnf(f_874_7,plain,
    ( U_2727 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP240(U_2727,U_2725) ),
    inference(clausify,[status(thm)],[f_874_4]) ).

cnf(f_874_8,plain,
    ( U_2725 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP240(U_2727,U_2725) ),
    inference(clausify,[status(thm)],[f_874_4]) ).

fof(f_875_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m)),V_n) = hAPP(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_875_2,plain,
    ! [U_2729,U_2728] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_2728)),U_2729) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2728),U_2729)),
    inference(variable_rename,[status(thm)],[f_875_1]) ).

fof(f_875_3,plain,
    ! [U_2728,U_2729] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_2728)),U_2729) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2728),U_2729)),
    inference(definitional_conversion,[status(esa)],[f_875_2]) ).

cnf(f_875_4,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_2728)),U_2729) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2728),U_2729)),
    inference(clausify,[status(thm)],[f_875_3]) ).

fof(f_876_1,plain,
    ! [V_n,V_m] : hAPP(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),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m)),V_n),
    inference(fof_nnf,[status(thm)],[fact_real__of__nat__power]) ).

fof(f_876_2,plain,
    ! [U_2731,U_2730] : hAPP(c_RealDef_Oreal(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2730),U_2731)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_2730)),U_2731),
    inference(variable_rename,[status(thm)],[f_876_1]) ).

fof(f_876_3,plain,
    ! [U_2730,U_2731] : hAPP(c_RealDef_Oreal(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2730),U_2731)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_2730)),U_2731),
    inference(definitional_conversion,[status(esa)],[f_876_2]) ).

cnf(f_876_4,plain,
    hAPP(c_RealDef_Oreal(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2730),U_2731)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_2730)),U_2731),
    inference(clausify,[status(thm)],[f_876_3]) ).

fof(f_877_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_877_2,plain,
    ! [U_2734,U_2733,U_2732] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2732),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2733,U_2734)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2732),U_2733)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2732),U_2734)),
    inference(variable_rename,[status(thm)],[f_877_1]) ).

fof(f_877_3,plain,
    ! [U_2732,U_2733,U_2734] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2732),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2733,U_2734)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2732),U_2733)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2732),U_2734)),
    inference(definitional_conversion,[status(esa)],[f_877_2]) ).

cnf(f_877_4,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2732),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2733,U_2734)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2732),U_2733)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2732),U_2734)),
    inference(clausify,[status(thm)],[f_877_3]) ).

fof(f_878_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_878_2,plain,
    ! [U_2737,U_2736,U_2735] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2735),U_2736)),U_2737) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2735),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2736),U_2737)),
    inference(variable_rename,[status(thm)],[f_878_1]) ).

fof(f_878_3,plain,
    ! [U_2735,U_2736,U_2737] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2735),U_2736)),U_2737) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2735),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2736),U_2737)),
    inference(definitional_conversion,[status(esa)],[f_878_2]) ).

cnf(f_878_4,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2735),U_2736)),U_2737) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2735),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2736),U_2737)),
    inference(clausify,[status(thm)],[f_878_3]) ).

fof(f_879_1,plain,
    ! [V_wa_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),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2)))
        | ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
          & c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_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_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_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),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__power__nat__eq__number__of]) ).

fof(f_879_2,plain,
    ! [U_2739,U_2738] :
      ( ( 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_2738),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2739)))
        | ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2738)
          & c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2739) != 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_2738)
        | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2739) = 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_2738),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2739))) ) ),
    inference(variable_rename,[status(thm)],[f_879_1]) ).

fof(f_879_3,plain,
    ( ! [U_2743,U_2741] :
        ( 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_2741),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2743)))
        | ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2741)
          & c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2743) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_2742,U_2740] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2740)
        | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2742) = 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_2740),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2742))) ) ),
    inference(miniscope,[status(thm)],[f_879_2]) ).

fof(f_879_4,plain,
    ( ! [U_2741,U_2743] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2741)
        | ~ sP241(U_2741,U_2743) )
    & ! [U_2741,U_2743] :
        ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2743) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP241(U_2741,U_2743) )
    & ! [U_2741,U_2743] :
        ( 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_2741),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2743)))
        | sP241(U_2741,U_2743) )
    & ! [U_2742,U_2740] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2740)
        | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2742) = 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_2740),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2742))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP241])],[f_879_3]) ).

cnf(f_879_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2740)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2742) = 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_2740),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2742))) ),
    inference(clausify,[status(thm)],[f_879_4]) ).

cnf(f_879_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_2741),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2743)))
    | sP241(U_2741,U_2743) ),
    inference(clausify,[status(thm)],[f_879_4]) ).

cnf(f_879_7,plain,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2743) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP241(U_2741,U_2743) ),
    inference(clausify,[status(thm)],[f_879_4]) ).

cnf(f_879_8,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2741)
    | ~ sP241(U_2741,U_2743) ),
    inference(clausify,[status(thm)],[f_879_4]) ).

fof(f_880_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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x)),V_n)),
    inference(fof_nnf,[status(thm)],[fact_zero__le__zpower__abs]) ).

fof(f_880_2,plain,
    ! [U_2745,U_2744] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2744)),U_2745)),
    inference(variable_rename,[status(thm)],[f_880_1]) ).

fof(f_880_3,plain,
    ! [U_2744,U_2745] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2744)),U_2745)),
    inference(definitional_conversion,[status(esa)],[f_880_2]) ).

cnf(f_880_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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2744)),U_2745)),
    inference(clausify,[status(thm)],[f_880_3]) ).

fof(f_881_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 != hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)) ),
    inference(fof_nnf,[status(thm)],[fact_natfloor__power]) ).

fof(f_881_2,plain,
    ! [U_2747,U_2746] :
      ( c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2746),U_2747)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(U_2746)),U_2747)
      | U_2746 != hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(U_2746)) ),
    inference(variable_rename,[status(thm)],[f_881_1]) ).

fof(f_881_3,plain,
    ! [U_2747,U_2746] :
      ( c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2746),U_2747)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(U_2746)),U_2747)
      | U_2746 != hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(U_2746)) ),
    inference(definitional_conversion,[status(esa)],[f_881_2]) ).

cnf(f_881_4,plain,
    ( c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2746),U_2747)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(U_2746)),U_2747)
    | U_2746 != hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(U_2746)) ),
    inference(clausify,[status(thm)],[f_881_3]) ).

fof(f_882_1,plain,
    ! [V_n,V_a] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),V_n) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)),V_a)),
    inference(fof_nnf,[status(thm)],[fact_DeMoivre]) ).

fof(f_882_2,plain,
    ! [U_2749,U_2748] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(U_2748)),U_2749) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_2749)),U_2748)),
    inference(variable_rename,[status(thm)],[f_882_1]) ).

fof(f_882_3,plain,
    ! [U_2748,U_2749] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(U_2748)),U_2749) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_2749)),U_2748)),
    inference(definitional_conversion,[status(esa)],[f_882_2]) ).

cnf(f_882_4,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(U_2748)),U_2749) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_2749)),U_2748)),
    inference(clausify,[status(thm)],[f_882_3]) ).

fof(f_883_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_883_2,plain,
    ! [U_2751,U_2750] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2751),U_2750) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2751),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2751),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2750,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | U_2750 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2751),U_2750) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2750 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_883_1]) ).

fof(f_883_3,plain,
    ( ! [U_2755,U_2753] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2755),U_2753) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2755),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2755),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2753,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | U_2753 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_2754,U_2752] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2754),U_2752) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2752 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_883_2]) ).

fof(f_883_4,plain,
    ( ! [U_2753,U_2755] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2755),U_2753) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2755),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2755),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2753,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | U_2753 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_2754,U_2752] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2754),U_2752) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2752 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_883_3]) ).

cnf(f_883_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2754),U_2752) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_2752 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_883_4]) ).

cnf(f_883_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2755),U_2753) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2755),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2755),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2753,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | U_2753 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_883_4]) ).

fof(f_884_1,plain,
    ! [V_n_2,V_x_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)),V_n_2))
        | ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_x_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__zpower__abs__iff]) ).

fof(f_884_2,plain,
    ! [U_2757,U_2756] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2756)),U_2757))
        | ( U_2757 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_2756 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( U_2757 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2756 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2756)),U_2757)) ) ),
    inference(variable_rename,[status(thm)],[f_884_1]) ).

fof(f_884_3,plain,
    ( ! [U_2761,U_2759] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2759)),U_2761))
        | ( U_2761 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_2759 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_2760,U_2758] :
        ( U_2760 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2758 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2758)),U_2760)) ) ),
    inference(miniscope,[status(thm)],[f_884_2]) ).

fof(f_884_4,plain,
    ( ! [U_2761,U_2759] :
        ( U_2761 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP242(U_2761,U_2759) )
    & ! [U_2761,U_2759] :
        ( U_2759 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP242(U_2761,U_2759) )
    & ! [U_2761,U_2759] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2759)),U_2761))
        | sP242(U_2761,U_2759) )
    & ! [U_2760,U_2758] :
        ( U_2760 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2758 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2758)),U_2760)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP242])],[f_884_3]) ).

cnf(f_884_5,plain,
    ( U_2760 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_2758 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2758)),U_2760)) ),
    inference(clausify,[status(thm)],[f_884_4]) ).

cnf(f_884_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2759)),U_2761))
    | sP242(U_2761,U_2759) ),
    inference(clausify,[status(thm)],[f_884_4]) ).

cnf(f_884_7,plain,
    ( U_2759 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP242(U_2761,U_2759) ),
    inference(clausify,[status(thm)],[f_884_4]) ).

cnf(f_884_8,plain,
    ( U_2761 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP242(U_2761,U_2759) ),
    inference(clausify,[status(thm)],[f_884_4]) ).

fof(f_885_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_885_2,plain,
    ! [U_2764,U_2763,U_2762] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2762),U_2763),U_2764) != c_Groups_Ozero__class_Ozero(U_2762)
      | U_2763 = c_Groups_Ozero__class_Ozero(U_2762)
      | ~ class_Rings_Oring__1__no__zero__divisors(U_2762) ),
    inference(variable_rename,[status(thm)],[f_885_1]) ).

fof(f_885_3,plain,
    ! [U_2762,U_2763,U_2764] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2762),U_2763),U_2764) != c_Groups_Ozero__class_Ozero(U_2762)
      | U_2763 = c_Groups_Ozero__class_Ozero(U_2762)
      | ~ class_Rings_Oring__1__no__zero__divisors(U_2762) ),
    inference(definitional_conversion,[status(esa)],[f_885_2]) ).

cnf(f_885_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2762),U_2763),U_2764) != c_Groups_Ozero__class_Ozero(U_2762)
    | U_2763 = c_Groups_Ozero__class_Ozero(U_2762)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_2762) ),
    inference(clausify,[status(thm)],[f_885_3]) ).

fof(f_886_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_886_2,plain,
    ! [U_2767,U_2766,U_2765] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2765),hAPP(hAPP(c_Power_Opower__class_Opower(U_2765),U_2766),U_2767)),U_2766) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2765),U_2766),hAPP(hAPP(c_Power_Opower__class_Opower(U_2765),U_2766),U_2767))
      | ~ class_Groups_Omonoid__mult(U_2765) ),
    inference(variable_rename,[status(thm)],[f_886_1]) ).

fof(f_886_3,plain,
    ! [U_2765,U_2766,U_2767] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2765),hAPP(hAPP(c_Power_Opower__class_Opower(U_2765),U_2766),U_2767)),U_2766) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2765),U_2766),hAPP(hAPP(c_Power_Opower__class_Opower(U_2765),U_2766),U_2767))
      | ~ class_Groups_Omonoid__mult(U_2765) ),
    inference(definitional_conversion,[status(esa)],[f_886_2]) ).

cnf(f_886_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2765),hAPP(hAPP(c_Power_Opower__class_Opower(U_2765),U_2766),U_2767)),U_2766) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2765),U_2766),hAPP(hAPP(c_Power_Opower__class_Opower(U_2765),U_2766),U_2767))
    | ~ class_Groups_Omonoid__mult(U_2765) ),
    inference(clausify,[status(thm)],[f_886_3]) ).

fof(f_887_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_887_2,plain,
    ! [U_2771,U_2770,U_2769,U_2768] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2768),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2768),U_2769),U_2770)),U_2771) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2768),hAPP(hAPP(c_Power_Opower__class_Opower(U_2768),U_2769),U_2771)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2768),U_2770),U_2771))
      | ~ class_Groups_Ocomm__monoid__mult(U_2768) ),
    inference(variable_rename,[status(thm)],[f_887_1]) ).

fof(f_887_3,plain,
    ! [U_2768,U_2769,U_2770,U_2771] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2768),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2768),U_2769),U_2770)),U_2771) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2768),hAPP(hAPP(c_Power_Opower__class_Opower(U_2768),U_2769),U_2771)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2768),U_2770),U_2771))
      | ~ class_Groups_Ocomm__monoid__mult(U_2768) ),
    inference(definitional_conversion,[status(esa)],[f_887_2]) ).

cnf(f_887_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2768),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2768),U_2769),U_2770)),U_2771) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2768),hAPP(hAPP(c_Power_Opower__class_Opower(U_2768),U_2769),U_2771)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2768),U_2770),U_2771))
    | ~ class_Groups_Ocomm__monoid__mult(U_2768) ),
    inference(clausify,[status(thm)],[f_887_3]) ).

fof(f_888_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_888_2,plain,
    ! [U_2773,U_2772] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2772),c_Groups_Oone__class_Oone(U_2772)),U_2773) = c_Groups_Oone__class_Oone(U_2772)
      | ~ class_Groups_Omonoid__mult(U_2772) ),
    inference(variable_rename,[status(thm)],[f_888_1]) ).

fof(f_888_3,plain,
    ! [U_2773,U_2772] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2772),c_Groups_Oone__class_Oone(U_2772)),U_2773) = c_Groups_Oone__class_Oone(U_2772)
      | ~ class_Groups_Omonoid__mult(U_2772) ),
    inference(definitional_conversion,[status(esa)],[f_888_2]) ).

cnf(f_888_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2772),c_Groups_Oone__class_Oone(U_2772)),U_2773) = c_Groups_Oone__class_Oone(U_2772)
    | ~ class_Groups_Omonoid__mult(U_2772) ),
    inference(clausify,[status(thm)],[f_888_3]) ).

fof(f_889_1,plain,
    ! [V_n,V_a,T_a] :
      ( c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n)
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__abs]) ).

fof(f_889_2,plain,
    ! [U_2776,U_2775,U_2774] :
      ( c_Groups_Oabs__class_Oabs(U_2774,hAPP(hAPP(c_Power_Opower__class_Opower(U_2774),U_2775),U_2776)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2774),c_Groups_Oabs__class_Oabs(U_2774,U_2775)),U_2776)
      | ~ class_Rings_Olinordered__idom(U_2774) ),
    inference(variable_rename,[status(thm)],[f_889_1]) ).

fof(f_889_3,plain,
    ! [U_2774,U_2775,U_2776] :
      ( c_Groups_Oabs__class_Oabs(U_2774,hAPP(hAPP(c_Power_Opower__class_Opower(U_2774),U_2775),U_2776)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2774),c_Groups_Oabs__class_Oabs(U_2774,U_2775)),U_2776)
      | ~ class_Rings_Olinordered__idom(U_2774) ),
    inference(definitional_conversion,[status(esa)],[f_889_2]) ).

cnf(f_889_4,plain,
    ( c_Groups_Oabs__class_Oabs(U_2774,hAPP(hAPP(c_Power_Opower__class_Opower(U_2774),U_2775),U_2776)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2774),c_Groups_Oabs__class_Oabs(U_2774,U_2775)),U_2776)
    | ~ class_Rings_Olinordered__idom(U_2774) ),
    inference(clausify,[status(thm)],[f_889_3]) ).

fof(f_890_1,plain,
    ! [V_n,V_m,T_a] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),V_n)
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__power]) ).

fof(f_890_2,plain,
    ! [U_2779,U_2778,U_2777] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2777),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2778),U_2779)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2777),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2777),U_2778)),U_2779)
      | ~ class_Rings_Osemiring__1(U_2777) ),
    inference(variable_rename,[status(thm)],[f_890_1]) ).

fof(f_890_3,plain,
    ! [U_2777,U_2778,U_2779] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2777),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2778),U_2779)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2777),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2777),U_2778)),U_2779)
      | ~ class_Rings_Osemiring__1(U_2777) ),
    inference(definitional_conversion,[status(esa)],[f_890_2]) ).

cnf(f_890_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2777),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2778),U_2779)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2777),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2777),U_2778)),U_2779)
    | ~ class_Rings_Osemiring__1(U_2777) ),
    inference(clausify,[status(thm)],[f_890_3]) ).

fof(f_891_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_891_2,plain,
    ! [U_2783,U_2782,U_2781,U_2780] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2780),U_2781),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2782),U_2783)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2780),hAPP(hAPP(c_Power_Opower__class_Opower(U_2780),U_2781),U_2782)),U_2783)
      | ~ class_Groups_Omonoid__mult(U_2780) ),
    inference(variable_rename,[status(thm)],[f_891_1]) ).

fof(f_891_3,plain,
    ! [U_2780,U_2781,U_2782,U_2783] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2780),U_2781),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2782),U_2783)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2780),hAPP(hAPP(c_Power_Opower__class_Opower(U_2780),U_2781),U_2782)),U_2783)
      | ~ class_Groups_Omonoid__mult(U_2780) ),
    inference(definitional_conversion,[status(esa)],[f_891_2]) ).

cnf(f_891_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2780),U_2781),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2782),U_2783)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2780),hAPP(hAPP(c_Power_Opower__class_Opower(U_2780),U_2781),U_2782)),U_2783)
    | ~ class_Groups_Omonoid__mult(U_2780) ),
    inference(clausify,[status(thm)],[f_891_3]) ).

fof(f_892_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_892_2,plain,
    ! [U_2785,U_2784] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2784),U_2785),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2785
      | ~ class_Groups_Omonoid__mult(U_2784) ),
    inference(variable_rename,[status(thm)],[f_892_1]) ).

fof(f_892_3,plain,
    ! [U_2784,U_2785] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2784),U_2785),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2785
      | ~ class_Groups_Omonoid__mult(U_2784) ),
    inference(definitional_conversion,[status(esa)],[f_892_2]) ).

cnf(f_892_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2784),U_2785),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2785
    | ~ class_Groups_Omonoid__mult(U_2784) ),
    inference(clausify,[status(thm)],[f_892_3]) ).

fof(f_893_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_893_2,plain,
    ! [U_2788,U_2787,U_2786] :
      ( c_Orderings_Oord__class_Oless__eq(U_2786,c_Groups_Ozero__class_Ozero(U_2786),hAPP(hAPP(c_Power_Opower__class_Opower(U_2786),U_2787),U_2788))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2786,c_Groups_Ozero__class_Ozero(U_2786),U_2787)
      | ~ class_Rings_Olinordered__semidom(U_2786) ),
    inference(variable_rename,[status(thm)],[f_893_1]) ).

fof(f_893_3,plain,
    ! [U_2786,U_2787,U_2788] :
      ( c_Orderings_Oord__class_Oless__eq(U_2786,c_Groups_Ozero__class_Ozero(U_2786),hAPP(hAPP(c_Power_Opower__class_Opower(U_2786),U_2787),U_2788))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2786,c_Groups_Ozero__class_Ozero(U_2786),U_2787)
      | ~ class_Rings_Olinordered__semidom(U_2786) ),
    inference(definitional_conversion,[status(esa)],[f_893_2]) ).

cnf(f_893_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2786,c_Groups_Ozero__class_Ozero(U_2786),hAPP(hAPP(c_Power_Opower__class_Opower(U_2786),U_2787),U_2788))
    | ~ c_Orderings_Oord__class_Oless__eq(U_2786,c_Groups_Ozero__class_Ozero(U_2786),U_2787)
    | ~ class_Rings_Olinordered__semidom(U_2786) ),
    inference(clausify,[status(thm)],[f_893_3]) ).

fof(f_894_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_894_2,plain,
    ! [U_2792,U_2791,U_2790,U_2789] :
      ( c_Orderings_Oord__class_Oless__eq(U_2789,hAPP(hAPP(c_Power_Opower__class_Opower(U_2789),U_2790),U_2792),hAPP(hAPP(c_Power_Opower__class_Opower(U_2789),U_2791),U_2792))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2789,c_Groups_Ozero__class_Ozero(U_2789),U_2790)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2789,U_2790,U_2791)
      | ~ class_Rings_Olinordered__semidom(U_2789) ),
    inference(variable_rename,[status(thm)],[f_894_1]) ).

fof(f_894_3,plain,
    ! [U_2789,U_2790,U_2791,U_2792] :
      ( c_Orderings_Oord__class_Oless__eq(U_2789,hAPP(hAPP(c_Power_Opower__class_Opower(U_2789),U_2790),U_2792),hAPP(hAPP(c_Power_Opower__class_Opower(U_2789),U_2791),U_2792))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2789,c_Groups_Ozero__class_Ozero(U_2789),U_2790)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2789,U_2790,U_2791)
      | ~ class_Rings_Olinordered__semidom(U_2789) ),
    inference(definitional_conversion,[status(esa)],[f_894_2]) ).

cnf(f_894_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2789,hAPP(hAPP(c_Power_Opower__class_Opower(U_2789),U_2790),U_2792),hAPP(hAPP(c_Power_Opower__class_Opower(U_2789),U_2791),U_2792))
    | ~ c_Orderings_Oord__class_Oless__eq(U_2789,c_Groups_Ozero__class_Ozero(U_2789),U_2790)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2789,U_2790,U_2791)
    | ~ class_Rings_Olinordered__semidom(U_2789) ),
    inference(clausify,[status(thm)],[f_894_3]) ).

fof(f_895_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_895_2,plain,
    ! [U_2795,U_2794,U_2793] :
      ( c_Orderings_Oord__class_Oless(U_2793,c_Groups_Ozero__class_Ozero(U_2793),hAPP(hAPP(c_Power_Opower__class_Opower(U_2793),U_2794),U_2795))
      | ~ c_Orderings_Oord__class_Oless(U_2793,c_Groups_Ozero__class_Ozero(U_2793),U_2794)
      | ~ class_Rings_Olinordered__semidom(U_2793) ),
    inference(variable_rename,[status(thm)],[f_895_1]) ).

fof(f_895_3,plain,
    ! [U_2795,U_2793,U_2794] :
      ( c_Orderings_Oord__class_Oless(U_2793,c_Groups_Ozero__class_Ozero(U_2793),hAPP(hAPP(c_Power_Opower__class_Opower(U_2793),U_2794),U_2795))
      | ~ c_Orderings_Oord__class_Oless(U_2793,c_Groups_Ozero__class_Ozero(U_2793),U_2794)
      | ~ class_Rings_Olinordered__semidom(U_2793) ),
    inference(definitional_conversion,[status(esa)],[f_895_2]) ).

cnf(f_895_4,plain,
    ( c_Orderings_Oord__class_Oless(U_2793,c_Groups_Ozero__class_Ozero(U_2793),hAPP(hAPP(c_Power_Opower__class_Opower(U_2793),U_2794),U_2795))
    | ~ c_Orderings_Oord__class_Oless(U_2793,c_Groups_Ozero__class_Ozero(U_2793),U_2794)
    | ~ class_Rings_Olinordered__semidom(U_2793) ),
    inference(clausify,[status(thm)],[f_895_3]) ).

fof(f_896_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_896_2,plain,
    ! [U_2798,U_2797,U_2796] :
      ( c_Orderings_Oord__class_Oless__eq(U_2796,c_Groups_Oone__class_Oone(U_2796),hAPP(hAPP(c_Power_Opower__class_Opower(U_2796),U_2797),U_2798))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2796,c_Groups_Oone__class_Oone(U_2796),U_2797)
      | ~ class_Rings_Olinordered__semidom(U_2796) ),
    inference(variable_rename,[status(thm)],[f_896_1]) ).

fof(f_896_3,plain,
    ! [U_2797,U_2796,U_2798] :
      ( c_Orderings_Oord__class_Oless__eq(U_2796,c_Groups_Oone__class_Oone(U_2796),hAPP(hAPP(c_Power_Opower__class_Opower(U_2796),U_2797),U_2798))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2796,c_Groups_Oone__class_Oone(U_2796),U_2797)
      | ~ class_Rings_Olinordered__semidom(U_2796) ),
    inference(definitional_conversion,[status(esa)],[f_896_2]) ).

cnf(f_896_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2796,c_Groups_Oone__class_Oone(U_2796),hAPP(hAPP(c_Power_Opower__class_Opower(U_2796),U_2797),U_2798))
    | ~ c_Orderings_Oord__class_Oless__eq(U_2796,c_Groups_Oone__class_Oone(U_2796),U_2797)
    | ~ class_Rings_Olinordered__semidom(U_2796) ),
    inference(clausify,[status(thm)],[f_896_3]) ).

fof(f_897_1,plain,
    ! [V_n_2,V_m_2,V_a_2,T_a] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_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_a_2),V_m_2) != hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) ) )
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a_2)
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__inject__exp]) ).

fof(f_897_2,plain,
    ! [U_2802,U_2801,U_2800,U_2799] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2799),U_2800),U_2801) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2799),U_2800),U_2802)
          | U_2801 != U_2802 )
        & ( U_2801 = U_2802
          | hAPP(hAPP(c_Power_Opower__class_Opower(U_2799),U_2800),U_2801) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2799),U_2800),U_2802) ) )
      | ~ c_Orderings_Oord__class_Oless(U_2799,c_Groups_Oone__class_Oone(U_2799),U_2800)
      | ~ class_Rings_Olinordered__semidom(U_2799) ),
    inference(variable_rename,[status(thm)],[f_897_1]) ).

fof(f_897_3,plain,
    ( ! [U_2799,U_2800,U_2801,U_2802] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2799),U_2800),U_2801) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2799),U_2800),U_2802)
        | U_2801 != U_2802
        | ~ sP243(U_2799,U_2800,U_2801,U_2802) )
    & ! [U_2799,U_2800,U_2801,U_2802] :
        ( U_2801 = U_2802
        | hAPP(hAPP(c_Power_Opower__class_Opower(U_2799),U_2800),U_2801) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2799),U_2800),U_2802)
        | ~ sP243(U_2799,U_2800,U_2801,U_2802) )
    & ! [U_2799,U_2800,U_2801,U_2802] :
        ( sP243(U_2799,U_2800,U_2801,U_2802)
        | ~ c_Orderings_Oord__class_Oless(U_2799,c_Groups_Oone__class_Oone(U_2799),U_2800)
        | ~ class_Rings_Olinordered__semidom(U_2799) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP243])],[f_897_2]) ).

cnf(f_897_4,plain,
    ( sP243(U_2799,U_2800,U_2801,U_2802)
    | ~ c_Orderings_Oord__class_Oless(U_2799,c_Groups_Oone__class_Oone(U_2799),U_2800)
    | ~ class_Rings_Olinordered__semidom(U_2799) ),
    inference(clausify,[status(thm)],[f_897_3]) ).

cnf(f_897_5,plain,
    ( U_2801 = U_2802
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_2799),U_2800),U_2801) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2799),U_2800),U_2802)
    | ~ sP243(U_2799,U_2800,U_2801,U_2802) ),
    inference(clausify,[status(thm)],[f_897_3]) ).

cnf(f_897_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2799),U_2800),U_2801) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2799),U_2800),U_2802)
    | U_2801 != U_2802
    | ~ sP243(U_2799,U_2800,U_2801,U_2802) ),
    inference(clausify,[status(thm)],[f_897_3]) ).

fof(f_898_1,plain,
    ! [V_n_2,V_a_2,T_a] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a)
          | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
          | hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_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_898_2,plain,
    ! [U_2805,U_2804,U_2803] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2803),U_2804),U_2805) = c_Groups_Ozero__class_Ozero(U_2803)
          | U_2805 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | U_2804 != c_Groups_Ozero__class_Ozero(U_2803) )
        & ( ( U_2805 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & U_2804 = c_Groups_Ozero__class_Ozero(U_2803) )
          | hAPP(hAPP(c_Power_Opower__class_Opower(U_2803),U_2804),U_2805) != c_Groups_Ozero__class_Ozero(U_2803) ) )
      | ~ class_Rings_Ozero__neq__one(U_2803)
      | ~ class_Rings_Ono__zero__divisors(U_2803)
      | ~ class_Rings_Omult__zero(U_2803)
      | ~ class_Power_Opower(U_2803) ),
    inference(variable_rename,[status(thm)],[f_898_1]) ).

fof(f_898_3,plain,
    ( ! [U_2805,U_2804,U_2803] :
        ( U_2805 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP244(U_2805,U_2804,U_2803) )
    & ! [U_2805,U_2804,U_2803] :
        ( U_2804 = c_Groups_Ozero__class_Ozero(U_2803)
        | ~ sP244(U_2805,U_2804,U_2803) )
    & ! [U_2805,U_2804,U_2803] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2803),U_2804),U_2805) = c_Groups_Ozero__class_Ozero(U_2803)
        | U_2805 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2804 != c_Groups_Ozero__class_Ozero(U_2803)
        | ~ sP245(U_2805,U_2804,U_2803) )
    & ! [U_2805,U_2804,U_2803] :
        ( sP244(U_2805,U_2804,U_2803)
        | hAPP(hAPP(c_Power_Opower__class_Opower(U_2803),U_2804),U_2805) != c_Groups_Ozero__class_Ozero(U_2803)
        | ~ sP245(U_2805,U_2804,U_2803) )
    & ! [U_2805,U_2804,U_2803] :
        ( sP245(U_2805,U_2804,U_2803)
        | ~ class_Rings_Ozero__neq__one(U_2803)
        | ~ class_Rings_Ono__zero__divisors(U_2803)
        | ~ class_Rings_Omult__zero(U_2803)
        | ~ class_Power_Opower(U_2803) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP244,sP245])],[f_898_2]) ).

cnf(f_898_4,plain,
    ( sP245(U_2805,U_2804,U_2803)
    | ~ class_Rings_Ozero__neq__one(U_2803)
    | ~ class_Rings_Ono__zero__divisors(U_2803)
    | ~ class_Rings_Omult__zero(U_2803)
    | ~ class_Power_Opower(U_2803) ),
    inference(clausify,[status(thm)],[f_898_3]) ).

cnf(f_898_5,plain,
    ( sP244(U_2805,U_2804,U_2803)
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_2803),U_2804),U_2805) != c_Groups_Ozero__class_Ozero(U_2803)
    | ~ sP245(U_2805,U_2804,U_2803) ),
    inference(clausify,[status(thm)],[f_898_3]) ).

cnf(f_898_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2803),U_2804),U_2805) = c_Groups_Ozero__class_Ozero(U_2803)
    | U_2805 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_2804 != c_Groups_Ozero__class_Ozero(U_2803)
    | ~ sP245(U_2805,U_2804,U_2803) ),
    inference(clausify,[status(thm)],[f_898_3]) ).

cnf(f_898_7,plain,
    ( U_2804 = c_Groups_Ozero__class_Ozero(U_2803)
    | ~ sP244(U_2805,U_2804,U_2803) ),
    inference(clausify,[status(thm)],[f_898_3]) ).

cnf(f_898_8,plain,
    ( U_2805 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP244(U_2805,U_2804,U_2803) ),
    inference(clausify,[status(thm)],[f_898_3]) ).

fof(f_899_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_899_2,plain,
    ! [U_2807,U_2806] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2806),c_Groups_Ozero__class_Ozero(U_2806)),c_Nat_OSuc(U_2807)) = c_Groups_Ozero__class_Ozero(U_2806)
      | ~ class_Rings_Osemiring__0(U_2806)
      | ~ class_Power_Opower(U_2806) ),
    inference(variable_rename,[status(thm)],[f_899_1]) ).

fof(f_899_3,plain,
    ! [U_2807,U_2806] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2806),c_Groups_Ozero__class_Ozero(U_2806)),c_Nat_OSuc(U_2807)) = c_Groups_Ozero__class_Ozero(U_2806)
      | ~ class_Rings_Osemiring__0(U_2806)
      | ~ class_Power_Opower(U_2806) ),
    inference(definitional_conversion,[status(esa)],[f_899_2]) ).

cnf(f_899_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2806),c_Groups_Ozero__class_Ozero(U_2806)),c_Nat_OSuc(U_2807)) = c_Groups_Ozero__class_Ozero(U_2806)
    | ~ class_Rings_Osemiring__0(U_2806)
    | ~ class_Power_Opower(U_2806) ),
    inference(clausify,[status(thm)],[f_899_3]) ).

fof(f_900_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_900_2,plain,
    ! [U_2810,U_2809,U_2808] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2808),U_2809),c_Nat_OSuc(U_2810)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2808),U_2809),hAPP(hAPP(c_Power_Opower__class_Opower(U_2808),U_2809),U_2810))
      | ~ class_Power_Opower(U_2808) ),
    inference(variable_rename,[status(thm)],[f_900_1]) ).

fof(f_900_3,plain,
    ! [U_2808,U_2809,U_2810] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2808),U_2809),c_Nat_OSuc(U_2810)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2808),U_2809),hAPP(hAPP(c_Power_Opower__class_Opower(U_2808),U_2809),U_2810))
      | ~ class_Power_Opower(U_2808) ),
    inference(definitional_conversion,[status(esa)],[f_900_2]) ).

cnf(f_900_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2808),U_2809),c_Nat_OSuc(U_2810)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2808),U_2809),hAPP(hAPP(c_Power_Opower__class_Opower(U_2808),U_2809),U_2810))
    | ~ class_Power_Opower(U_2808) ),
    inference(clausify,[status(thm)],[f_900_3]) ).

fof(f_901_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_901_2,plain,
    ! [U_2813,U_2812,U_2811] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2811),U_2812),c_Nat_OSuc(U_2813)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2811),hAPP(hAPP(c_Power_Opower__class_Opower(U_2811),U_2812),U_2813)),U_2812)
      | ~ class_Groups_Omonoid__mult(U_2811) ),
    inference(variable_rename,[status(thm)],[f_901_1]) ).

fof(f_901_3,plain,
    ! [U_2811,U_2812,U_2813] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2811),U_2812),c_Nat_OSuc(U_2813)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2811),hAPP(hAPP(c_Power_Opower__class_Opower(U_2811),U_2812),U_2813)),U_2812)
      | ~ class_Groups_Omonoid__mult(U_2811) ),
    inference(definitional_conversion,[status(esa)],[f_901_2]) ).

cnf(f_901_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2811),U_2812),c_Nat_OSuc(U_2813)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2811),hAPP(hAPP(c_Power_Opower__class_Opower(U_2811),U_2812),U_2813)),U_2812)
    | ~ class_Groups_Omonoid__mult(U_2811) ),
    inference(clausify,[status(thm)],[f_901_3]) ).

fof(f_902_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_902_2,plain,
    ! [U_2815,U_2814] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2814),U_2815),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_2814)
      | ~ class_Power_Opower(U_2814) ),
    inference(variable_rename,[status(thm)],[f_902_1]) ).

fof(f_902_3,plain,
    ! [U_2814,U_2815] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2814),U_2815),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_2814)
      | ~ class_Power_Opower(U_2814) ),
    inference(definitional_conversion,[status(esa)],[f_902_2]) ).

cnf(f_902_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2814),U_2815),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_2814)
    | ~ class_Power_Opower(U_2814) ),
    inference(clausify,[status(thm)],[f_902_3]) ).

fof(f_903_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_903_2,plain,
    ! [U_2819,U_2818,U_2817,U_2816] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2816),U_2817),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2818,U_2819)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2816),hAPP(hAPP(c_Power_Opower__class_Opower(U_2816),U_2817),U_2818)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2816),U_2817),U_2819))
      | ~ class_Groups_Omonoid__mult(U_2816) ),
    inference(variable_rename,[status(thm)],[f_903_1]) ).

fof(f_903_3,plain,
    ! [U_2816,U_2817,U_2818,U_2819] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2816),U_2817),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2818,U_2819)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2816),hAPP(hAPP(c_Power_Opower__class_Opower(U_2816),U_2817),U_2818)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2816),U_2817),U_2819))
      | ~ class_Groups_Omonoid__mult(U_2816) ),
    inference(definitional_conversion,[status(esa)],[f_903_2]) ).

cnf(f_903_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2816),U_2817),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2818,U_2819)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2816),hAPP(hAPP(c_Power_Opower__class_Opower(U_2816),U_2817),U_2818)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2816),U_2817),U_2819))
    | ~ class_Groups_Omonoid__mult(U_2816) ),
    inference(clausify,[status(thm)],[f_903_3]) ).

fof(f_904_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_904_2,plain,
    ! [U_2823,U_2822,U_2821,U_2820] :
      ( c_Orderings_Oord__class_Oless(U_2820,U_2821,U_2823)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2820,c_Groups_Ozero__class_Ozero(U_2820),U_2823)
      | ~ c_Orderings_Oord__class_Oless(U_2820,hAPP(hAPP(c_Power_Opower__class_Opower(U_2820),U_2821),U_2822),hAPP(hAPP(c_Power_Opower__class_Opower(U_2820),U_2823),U_2822))
      | ~ class_Rings_Olinordered__semidom(U_2820) ),
    inference(variable_rename,[status(thm)],[f_904_1]) ).

fof(f_904_3,plain,
    ! [U_2820,U_2821,U_2822,U_2823] :
      ( c_Orderings_Oord__class_Oless(U_2820,U_2821,U_2823)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2820,c_Groups_Ozero__class_Ozero(U_2820),U_2823)
      | ~ c_Orderings_Oord__class_Oless(U_2820,hAPP(hAPP(c_Power_Opower__class_Opower(U_2820),U_2821),U_2822),hAPP(hAPP(c_Power_Opower__class_Opower(U_2820),U_2823),U_2822))
      | ~ class_Rings_Olinordered__semidom(U_2820) ),
    inference(definitional_conversion,[status(esa)],[f_904_2]) ).

cnf(f_904_4,plain,
    ( c_Orderings_Oord__class_Oless(U_2820,U_2821,U_2823)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2820,c_Groups_Ozero__class_Ozero(U_2820),U_2823)
    | ~ c_Orderings_Oord__class_Oless(U_2820,hAPP(hAPP(c_Power_Opower__class_Opower(U_2820),U_2821),U_2822),hAPP(hAPP(c_Power_Opower__class_Opower(U_2820),U_2823),U_2822))
    | ~ class_Rings_Olinordered__semidom(U_2820) ),
    inference(clausify,[status(thm)],[f_904_3]) ).

fof(f_905_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_905_2,plain,
    ! [U_2827,U_2826,U_2825,U_2824] :
      ( U_2825 = U_2827
      | ~ c_Orderings_Oord__class_Oless__eq(U_2824,c_Groups_Ozero__class_Ozero(U_2824),U_2827)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2824,c_Groups_Ozero__class_Ozero(U_2824),U_2825)
      | hAPP(hAPP(c_Power_Opower__class_Opower(U_2824),U_2825),c_Nat_OSuc(U_2826)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2824),U_2827),c_Nat_OSuc(U_2826))
      | ~ class_Rings_Olinordered__semidom(U_2824) ),
    inference(variable_rename,[status(thm)],[f_905_1]) ).

fof(f_905_3,plain,
    ! [U_2826,U_2824,U_2825,U_2827] :
      ( U_2825 = U_2827
      | ~ c_Orderings_Oord__class_Oless__eq(U_2824,c_Groups_Ozero__class_Ozero(U_2824),U_2827)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2824,c_Groups_Ozero__class_Ozero(U_2824),U_2825)
      | hAPP(hAPP(c_Power_Opower__class_Opower(U_2824),U_2825),c_Nat_OSuc(U_2826)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2824),U_2827),c_Nat_OSuc(U_2826))
      | ~ class_Rings_Olinordered__semidom(U_2824) ),
    inference(definitional_conversion,[status(esa)],[f_905_2]) ).

cnf(f_905_4,plain,
    ( U_2825 = U_2827
    | ~ c_Orderings_Oord__class_Oless__eq(U_2824,c_Groups_Ozero__class_Ozero(U_2824),U_2827)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2824,c_Groups_Ozero__class_Ozero(U_2824),U_2825)
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_2824),U_2825),c_Nat_OSuc(U_2826)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2824),U_2827),c_Nat_OSuc(U_2826))
    | ~ class_Rings_Olinordered__semidom(U_2824) ),
    inference(clausify,[status(thm)],[f_905_3]) ).

fof(f_906_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_906_2,plain,
    ! [U_2831,U_2830,U_2829,U_2828] :
      ( c_Orderings_Oord__class_Oless__eq(U_2828,U_2829,U_2831)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2828,c_Groups_Ozero__class_Ozero(U_2828),U_2831)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2828,hAPP(hAPP(c_Power_Opower__class_Opower(U_2828),U_2829),c_Nat_OSuc(U_2830)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2828),U_2831),c_Nat_OSuc(U_2830)))
      | ~ class_Rings_Olinordered__semidom(U_2828) ),
    inference(variable_rename,[status(thm)],[f_906_1]) ).

fof(f_906_3,plain,
    ! [U_2831,U_2829,U_2830,U_2828] :
      ( c_Orderings_Oord__class_Oless__eq(U_2828,U_2829,U_2831)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2828,c_Groups_Ozero__class_Ozero(U_2828),U_2831)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2828,hAPP(hAPP(c_Power_Opower__class_Opower(U_2828),U_2829),c_Nat_OSuc(U_2830)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2828),U_2831),c_Nat_OSuc(U_2830)))
      | ~ class_Rings_Olinordered__semidom(U_2828) ),
    inference(definitional_conversion,[status(esa)],[f_906_2]) ).

cnf(f_906_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2828,U_2829,U_2831)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2828,c_Groups_Ozero__class_Ozero(U_2828),U_2831)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2828,hAPP(hAPP(c_Power_Opower__class_Opower(U_2828),U_2829),c_Nat_OSuc(U_2830)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2828),U_2831),c_Nat_OSuc(U_2830)))
    | ~ class_Rings_Olinordered__semidom(U_2828) ),
    inference(clausify,[status(thm)],[f_906_3]) ).

fof(f_907_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_907_2,plain,
    ! [U_2834,U_2833,U_2832] :
      ( c_Orderings_Oord__class_Oless(U_2832,hAPP(hAPP(c_Power_Opower__class_Opower(U_2832),U_2833),U_2834),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2832),U_2833),hAPP(hAPP(c_Power_Opower__class_Opower(U_2832),U_2833),U_2834)))
      | ~ c_Orderings_Oord__class_Oless(U_2832,c_Groups_Oone__class_Oone(U_2832),U_2833)
      | ~ class_Rings_Olinordered__semidom(U_2832) ),
    inference(variable_rename,[status(thm)],[f_907_1]) ).

fof(f_907_3,plain,
    ! [U_2832,U_2833,U_2834] :
      ( c_Orderings_Oord__class_Oless(U_2832,hAPP(hAPP(c_Power_Opower__class_Opower(U_2832),U_2833),U_2834),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2832),U_2833),hAPP(hAPP(c_Power_Opower__class_Opower(U_2832),U_2833),U_2834)))
      | ~ c_Orderings_Oord__class_Oless(U_2832,c_Groups_Oone__class_Oone(U_2832),U_2833)
      | ~ class_Rings_Olinordered__semidom(U_2832) ),
    inference(definitional_conversion,[status(esa)],[f_907_2]) ).

cnf(f_907_4,plain,
    ( c_Orderings_Oord__class_Oless(U_2832,hAPP(hAPP(c_Power_Opower__class_Opower(U_2832),U_2833),U_2834),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2832),U_2833),hAPP(hAPP(c_Power_Opower__class_Opower(U_2832),U_2833),U_2834)))
    | ~ c_Orderings_Oord__class_Oless(U_2832,c_Groups_Oone__class_Oone(U_2832),U_2833)
    | ~ class_Rings_Olinordered__semidom(U_2832) ),
    inference(clausify,[status(thm)],[f_907_3]) ).

fof(f_908_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_908_2,plain,
    ! [U_2837,U_2836,U_2835] :
      ( c_Orderings_Oord__class_Oless(U_2835,c_Groups_Oone__class_Oone(U_2835),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2835),U_2836),hAPP(hAPP(c_Power_Opower__class_Opower(U_2835),U_2836),U_2837)))
      | ~ c_Orderings_Oord__class_Oless(U_2835,c_Groups_Oone__class_Oone(U_2835),U_2836)
      | ~ class_Rings_Olinordered__semidom(U_2835) ),
    inference(variable_rename,[status(thm)],[f_908_1]) ).

fof(f_908_3,plain,
    ! [U_2835,U_2836,U_2837] :
      ( c_Orderings_Oord__class_Oless(U_2835,c_Groups_Oone__class_Oone(U_2835),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2835),U_2836),hAPP(hAPP(c_Power_Opower__class_Opower(U_2835),U_2836),U_2837)))
      | ~ c_Orderings_Oord__class_Oless(U_2835,c_Groups_Oone__class_Oone(U_2835),U_2836)
      | ~ class_Rings_Olinordered__semidom(U_2835) ),
    inference(definitional_conversion,[status(esa)],[f_908_2]) ).

cnf(f_908_4,plain,
    ( c_Orderings_Oord__class_Oless(U_2835,c_Groups_Oone__class_Oone(U_2835),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2835),U_2836),hAPP(hAPP(c_Power_Opower__class_Opower(U_2835),U_2836),U_2837)))
    | ~ c_Orderings_Oord__class_Oless(U_2835,c_Groups_Oone__class_Oone(U_2835),U_2836)
    | ~ class_Rings_Olinordered__semidom(U_2835) ),
    inference(clausify,[status(thm)],[f_908_3]) ).

fof(f_909_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_909_2,plain,
    ! [U_2839,U_2838] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2838),c_Groups_Ozero__class_Ozero(U_2838)),U_2839) = c_Groups_Ozero__class_Ozero(U_2838)
          | U_2839 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2838),c_Groups_Ozero__class_Ozero(U_2838)),U_2839) = c_Groups_Oone__class_Oone(U_2838)
          | U_2839 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ class_Rings_Osemiring__0(U_2838)
      | ~ class_Power_Opower(U_2838) ),
    inference(variable_rename,[status(thm)],[f_909_1]) ).

fof(f_909_3,plain,
    ( ! [U_2839,U_2838] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2838),c_Groups_Ozero__class_Ozero(U_2838)),U_2839) = c_Groups_Ozero__class_Ozero(U_2838)
        | U_2839 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP246(U_2839,U_2838) )
    & ! [U_2839,U_2838] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2838),c_Groups_Ozero__class_Ozero(U_2838)),U_2839) = c_Groups_Oone__class_Oone(U_2838)
        | U_2839 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP246(U_2839,U_2838) )
    & ! [U_2839,U_2838] :
        ( sP246(U_2839,U_2838)
        | ~ class_Rings_Osemiring__0(U_2838)
        | ~ class_Power_Opower(U_2838) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP246])],[f_909_2]) ).

cnf(f_909_4,plain,
    ( sP246(U_2839,U_2838)
    | ~ class_Rings_Osemiring__0(U_2838)
    | ~ class_Power_Opower(U_2838) ),
    inference(clausify,[status(thm)],[f_909_3]) ).

cnf(f_909_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2838),c_Groups_Ozero__class_Ozero(U_2838)),U_2839) = c_Groups_Oone__class_Oone(U_2838)
    | U_2839 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP246(U_2839,U_2838) ),
    inference(clausify,[status(thm)],[f_909_3]) ).

cnf(f_909_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2838),c_Groups_Ozero__class_Ozero(U_2838)),U_2839) = c_Groups_Ozero__class_Ozero(U_2838)
    | U_2839 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP246(U_2839,U_2838) ),
    inference(clausify,[status(thm)],[f_909_3]) ).

fof(f_910_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),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__le__power__abs]) ).

fof(f_910_2,plain,
    ! [U_2842,U_2841,U_2840] :
      ( c_Orderings_Oord__class_Oless__eq(U_2840,c_Groups_Ozero__class_Ozero(U_2840),hAPP(hAPP(c_Power_Opower__class_Opower(U_2840),c_Groups_Oabs__class_Oabs(U_2840,U_2841)),U_2842))
      | ~ class_Rings_Olinordered__idom(U_2840) ),
    inference(variable_rename,[status(thm)],[f_910_1]) ).

fof(f_910_3,plain,
    ! [U_2840,U_2842,U_2841] :
      ( c_Orderings_Oord__class_Oless__eq(U_2840,c_Groups_Ozero__class_Ozero(U_2840),hAPP(hAPP(c_Power_Opower__class_Opower(U_2840),c_Groups_Oabs__class_Oabs(U_2840,U_2841)),U_2842))
      | ~ class_Rings_Olinordered__idom(U_2840) ),
    inference(definitional_conversion,[status(esa)],[f_910_2]) ).

cnf(f_910_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2840,c_Groups_Ozero__class_Ozero(U_2840),hAPP(hAPP(c_Power_Opower__class_Opower(U_2840),c_Groups_Oabs__class_Oabs(U_2840,U_2841)),U_2842))
    | ~ class_Rings_Olinordered__idom(U_2840) ),
    inference(clausify,[status(thm)],[f_910_3]) ).

fof(f_911_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_911_2,plain,
    ! [U_2845,U_2844,U_2843] :
      ( c_Orderings_Oord__class_Oless(U_2843,c_Groups_Oone__class_Oone(U_2843),hAPP(hAPP(c_Power_Opower__class_Opower(U_2843),U_2844),c_Nat_OSuc(U_2845)))
      | ~ c_Orderings_Oord__class_Oless(U_2843,c_Groups_Oone__class_Oone(U_2843),U_2844)
      | ~ class_Rings_Olinordered__semidom(U_2843) ),
    inference(variable_rename,[status(thm)],[f_911_1]) ).

fof(f_911_3,plain,
    ! [U_2843,U_2844,U_2845] :
      ( c_Orderings_Oord__class_Oless(U_2843,c_Groups_Oone__class_Oone(U_2843),hAPP(hAPP(c_Power_Opower__class_Opower(U_2843),U_2844),c_Nat_OSuc(U_2845)))
      | ~ c_Orderings_Oord__class_Oless(U_2843,c_Groups_Oone__class_Oone(U_2843),U_2844)
      | ~ class_Rings_Olinordered__semidom(U_2843) ),
    inference(definitional_conversion,[status(esa)],[f_911_2]) ).

cnf(f_911_4,plain,
    ( c_Orderings_Oord__class_Oless(U_2843,c_Groups_Oone__class_Oone(U_2843),hAPP(hAPP(c_Power_Opower__class_Opower(U_2843),U_2844),c_Nat_OSuc(U_2845)))
    | ~ c_Orderings_Oord__class_Oless(U_2843,c_Groups_Oone__class_Oone(U_2843),U_2844)
    | ~ class_Rings_Olinordered__semidom(U_2843) ),
    inference(clausify,[status(thm)],[f_911_3]) ).

fof(f_912_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_912_2,plain,
    ! [U_2849,U_2848,U_2847,U_2846] :
      ( c_Orderings_Oord__class_Oless(U_2846,hAPP(hAPP(c_Power_Opower__class_Opower(U_2846),U_2849),U_2847),hAPP(hAPP(c_Power_Opower__class_Opower(U_2846),U_2849),U_2848))
      | ~ c_Orderings_Oord__class_Oless(U_2846,c_Groups_Oone__class_Oone(U_2846),U_2849)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2847,U_2848)
      | ~ class_Rings_Olinordered__semidom(U_2846) ),
    inference(variable_rename,[status(thm)],[f_912_1]) ).

fof(f_912_3,plain,
    ! [U_2846,U_2847,U_2848,U_2849] :
      ( c_Orderings_Oord__class_Oless(U_2846,hAPP(hAPP(c_Power_Opower__class_Opower(U_2846),U_2849),U_2847),hAPP(hAPP(c_Power_Opower__class_Opower(U_2846),U_2849),U_2848))
      | ~ c_Orderings_Oord__class_Oless(U_2846,c_Groups_Oone__class_Oone(U_2846),U_2849)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2847,U_2848)
      | ~ class_Rings_Olinordered__semidom(U_2846) ),
    inference(definitional_conversion,[status(esa)],[f_912_2]) ).

cnf(f_912_4,plain,
    ( c_Orderings_Oord__class_Oless(U_2846,hAPP(hAPP(c_Power_Opower__class_Opower(U_2846),U_2849),U_2847),hAPP(hAPP(c_Power_Opower__class_Opower(U_2846),U_2849),U_2848))
    | ~ c_Orderings_Oord__class_Oless(U_2846,c_Groups_Oone__class_Oone(U_2846),U_2849)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2847,U_2848)
    | ~ class_Rings_Olinordered__semidom(U_2846) ),
    inference(clausify,[status(thm)],[f_912_3]) ).

fof(f_913_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_913_2,plain,
    ! [U_2853,U_2852,U_2851,U_2850] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2852,U_2853)
      | ~ c_Orderings_Oord__class_Oless(U_2850,hAPP(hAPP(c_Power_Opower__class_Opower(U_2850),U_2851),U_2852),hAPP(hAPP(c_Power_Opower__class_Opower(U_2850),U_2851),U_2853))
      | ~ c_Orderings_Oord__class_Oless(U_2850,c_Groups_Oone__class_Oone(U_2850),U_2851)
      | ~ class_Rings_Olinordered__semidom(U_2850) ),
    inference(variable_rename,[status(thm)],[f_913_1]) ).

fof(f_913_3,plain,
    ! [U_2852,U_2850,U_2851,U_2853] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2852,U_2853)
      | ~ c_Orderings_Oord__class_Oless(U_2850,hAPP(hAPP(c_Power_Opower__class_Opower(U_2850),U_2851),U_2852),hAPP(hAPP(c_Power_Opower__class_Opower(U_2850),U_2851),U_2853))
      | ~ c_Orderings_Oord__class_Oless(U_2850,c_Groups_Oone__class_Oone(U_2850),U_2851)
      | ~ class_Rings_Olinordered__semidom(U_2850) ),
    inference(definitional_conversion,[status(esa)],[f_913_2]) ).

cnf(f_913_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2852,U_2853)
    | ~ c_Orderings_Oord__class_Oless(U_2850,hAPP(hAPP(c_Power_Opower__class_Opower(U_2850),U_2851),U_2852),hAPP(hAPP(c_Power_Opower__class_Opower(U_2850),U_2851),U_2853))
    | ~ c_Orderings_Oord__class_Oless(U_2850,c_Groups_Oone__class_Oone(U_2850),U_2851)
    | ~ class_Rings_Olinordered__semidom(U_2850) ),
    inference(clausify,[status(thm)],[f_913_3]) ).

fof(f_914_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_914_2,plain,
    ! [U_2857,U_2856,U_2855,U_2854] :
      ( ( ( c_Orderings_Oord__class_Oless(U_2854,hAPP(hAPP(c_Power_Opower__class_Opower(U_2854),U_2855),U_2856),hAPP(hAPP(c_Power_Opower__class_Opower(U_2854),U_2855),U_2857))
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2856,U_2857) )
        & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2856,U_2857)
          | ~ c_Orderings_Oord__class_Oless(U_2854,hAPP(hAPP(c_Power_Opower__class_Opower(U_2854),U_2855),U_2856),hAPP(hAPP(c_Power_Opower__class_Opower(U_2854),U_2855),U_2857)) ) )
      | ~ c_Orderings_Oord__class_Oless(U_2854,c_Groups_Oone__class_Oone(U_2854),U_2855)
      | ~ class_Rings_Olinordered__semidom(U_2854) ),
    inference(variable_rename,[status(thm)],[f_914_1]) ).

fof(f_914_3,plain,
    ( ! [U_2855,U_2857,U_2854,U_2856] :
        ( c_Orderings_Oord__class_Oless(U_2854,hAPP(hAPP(c_Power_Opower__class_Opower(U_2854),U_2855),U_2856),hAPP(hAPP(c_Power_Opower__class_Opower(U_2854),U_2855),U_2857))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2856,U_2857)
        | ~ sP247(U_2855,U_2857,U_2854,U_2856) )
    & ! [U_2855,U_2857,U_2854,U_2856] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2856,U_2857)
        | ~ c_Orderings_Oord__class_Oless(U_2854,hAPP(hAPP(c_Power_Opower__class_Opower(U_2854),U_2855),U_2856),hAPP(hAPP(c_Power_Opower__class_Opower(U_2854),U_2855),U_2857))
        | ~ sP247(U_2855,U_2857,U_2854,U_2856) )
    & ! [U_2855,U_2857,U_2854,U_2856] :
        ( sP247(U_2855,U_2857,U_2854,U_2856)
        | ~ c_Orderings_Oord__class_Oless(U_2854,c_Groups_Oone__class_Oone(U_2854),U_2855)
        | ~ class_Rings_Olinordered__semidom(U_2854) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP247])],[f_914_2]) ).

cnf(f_914_4,plain,
    ( sP247(U_2855,U_2857,U_2854,U_2856)
    | ~ c_Orderings_Oord__class_Oless(U_2854,c_Groups_Oone__class_Oone(U_2854),U_2855)
    | ~ class_Rings_Olinordered__semidom(U_2854) ),
    inference(clausify,[status(thm)],[f_914_3]) ).

cnf(f_914_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2856,U_2857)
    | ~ c_Orderings_Oord__class_Oless(U_2854,hAPP(hAPP(c_Power_Opower__class_Opower(U_2854),U_2855),U_2856),hAPP(hAPP(c_Power_Opower__class_Opower(U_2854),U_2855),U_2857))
    | ~ sP247(U_2855,U_2857,U_2854,U_2856) ),
    inference(clausify,[status(thm)],[f_914_3]) ).

cnf(f_914_6,plain,
    ( c_Orderings_Oord__class_Oless(U_2854,hAPP(hAPP(c_Power_Opower__class_Opower(U_2854),U_2855),U_2856),hAPP(hAPP(c_Power_Opower__class_Opower(U_2854),U_2855),U_2857))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2856,U_2857)
    | ~ sP247(U_2855,U_2857,U_2854,U_2856) ),
    inference(clausify,[status(thm)],[f_914_3]) ).

fof(f_915_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_915_2,plain,
    ! [U_2861,U_2860,U_2859,U_2858] :
      ( c_Orderings_Oord__class_Oless__eq(U_2858,hAPP(hAPP(c_Power_Opower__class_Opower(U_2858),U_2861),U_2859),hAPP(hAPP(c_Power_Opower__class_Opower(U_2858),U_2861),U_2860))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2858,c_Groups_Oone__class_Oone(U_2858),U_2861)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2859,U_2860)
      | ~ class_Rings_Olinordered__semidom(U_2858) ),
    inference(variable_rename,[status(thm)],[f_915_1]) ).

fof(f_915_3,plain,
    ! [U_2859,U_2861,U_2860,U_2858] :
      ( c_Orderings_Oord__class_Oless__eq(U_2858,hAPP(hAPP(c_Power_Opower__class_Opower(U_2858),U_2861),U_2859),hAPP(hAPP(c_Power_Opower__class_Opower(U_2858),U_2861),U_2860))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2858,c_Groups_Oone__class_Oone(U_2858),U_2861)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2859,U_2860)
      | ~ class_Rings_Olinordered__semidom(U_2858) ),
    inference(definitional_conversion,[status(esa)],[f_915_2]) ).

cnf(f_915_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2858,hAPP(hAPP(c_Power_Opower__class_Opower(U_2858),U_2861),U_2859),hAPP(hAPP(c_Power_Opower__class_Opower(U_2858),U_2861),U_2860))
    | ~ c_Orderings_Oord__class_Oless__eq(U_2858,c_Groups_Oone__class_Oone(U_2858),U_2861)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2859,U_2860)
    | ~ class_Rings_Olinordered__semidom(U_2858) ),
    inference(clausify,[status(thm)],[f_915_3]) ).

fof(f_916_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_916_2,plain,
    ! [U_2864,U_2863,U_2862] :
      ( c_Orderings_Oord__class_Oless(U_2862,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2862),U_2863),hAPP(hAPP(c_Power_Opower__class_Opower(U_2862),U_2863),U_2864)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2862),U_2863),U_2864))
      | ~ c_Orderings_Oord__class_Oless(U_2862,U_2863,c_Groups_Oone__class_Oone(U_2862))
      | ~ c_Orderings_Oord__class_Oless(U_2862,c_Groups_Ozero__class_Ozero(U_2862),U_2863)
      | ~ class_Rings_Olinordered__semidom(U_2862) ),
    inference(variable_rename,[status(thm)],[f_916_1]) ).

fof(f_916_3,plain,
    ! [U_2862,U_2863,U_2864] :
      ( c_Orderings_Oord__class_Oless(U_2862,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2862),U_2863),hAPP(hAPP(c_Power_Opower__class_Opower(U_2862),U_2863),U_2864)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2862),U_2863),U_2864))
      | ~ c_Orderings_Oord__class_Oless(U_2862,U_2863,c_Groups_Oone__class_Oone(U_2862))
      | ~ c_Orderings_Oord__class_Oless(U_2862,c_Groups_Ozero__class_Ozero(U_2862),U_2863)
      | ~ class_Rings_Olinordered__semidom(U_2862) ),
    inference(definitional_conversion,[status(esa)],[f_916_2]) ).

cnf(f_916_4,plain,
    ( c_Orderings_Oord__class_Oless(U_2862,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2862),U_2863),hAPP(hAPP(c_Power_Opower__class_Opower(U_2862),U_2863),U_2864)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2862),U_2863),U_2864))
    | ~ c_Orderings_Oord__class_Oless(U_2862,U_2863,c_Groups_Oone__class_Oone(U_2862))
    | ~ c_Orderings_Oord__class_Oless(U_2862,c_Groups_Ozero__class_Ozero(U_2862),U_2863)
    | ~ class_Rings_Olinordered__semidom(U_2862) ),
    inference(clausify,[status(thm)],[f_916_3]) ).

fof(f_917_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_917_2,plain,
    ! [U_2867,U_2866,U_2865] :
      ( c_Orderings_Oord__class_Oless(U_2865,hAPP(hAPP(c_Power_Opower__class_Opower(U_2865),U_2866),c_Nat_OSuc(U_2867)),c_Groups_Oone__class_Oone(U_2865))
      | ~ c_Orderings_Oord__class_Oless(U_2865,U_2866,c_Groups_Oone__class_Oone(U_2865))
      | ~ c_Orderings_Oord__class_Oless(U_2865,c_Groups_Ozero__class_Ozero(U_2865),U_2866)
      | ~ class_Rings_Olinordered__semidom(U_2865) ),
    inference(variable_rename,[status(thm)],[f_917_1]) ).

fof(f_917_3,plain,
    ! [U_2867,U_2866,U_2865] :
      ( c_Orderings_Oord__class_Oless(U_2865,hAPP(hAPP(c_Power_Opower__class_Opower(U_2865),U_2866),c_Nat_OSuc(U_2867)),c_Groups_Oone__class_Oone(U_2865))
      | ~ c_Orderings_Oord__class_Oless(U_2865,U_2866,c_Groups_Oone__class_Oone(U_2865))
      | ~ c_Orderings_Oord__class_Oless(U_2865,c_Groups_Ozero__class_Ozero(U_2865),U_2866)
      | ~ class_Rings_Olinordered__semidom(U_2865) ),
    inference(definitional_conversion,[status(esa)],[f_917_2]) ).

cnf(f_917_4,plain,
    ( c_Orderings_Oord__class_Oless(U_2865,hAPP(hAPP(c_Power_Opower__class_Opower(U_2865),U_2866),c_Nat_OSuc(U_2867)),c_Groups_Oone__class_Oone(U_2865))
    | ~ c_Orderings_Oord__class_Oless(U_2865,U_2866,c_Groups_Oone__class_Oone(U_2865))
    | ~ c_Orderings_Oord__class_Oless(U_2865,c_Groups_Ozero__class_Ozero(U_2865),U_2866)
    | ~ class_Rings_Olinordered__semidom(U_2865) ),
    inference(clausify,[status(thm)],[f_917_3]) ).

fof(f_918_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_918_2,plain,
    ! [U_2871,U_2870,U_2869,U_2868] :
      ( c_Orderings_Oord__class_Oless(U_2868,hAPP(hAPP(c_Power_Opower__class_Opower(U_2868),U_2871),U_2870),hAPP(hAPP(c_Power_Opower__class_Opower(U_2868),U_2871),U_2869))
      | ~ c_Orderings_Oord__class_Oless(U_2868,U_2871,c_Groups_Oone__class_Oone(U_2868))
      | ~ c_Orderings_Oord__class_Oless(U_2868,c_Groups_Ozero__class_Ozero(U_2868),U_2871)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2869,U_2870)
      | ~ class_Rings_Olinordered__semidom(U_2868) ),
    inference(variable_rename,[status(thm)],[f_918_1]) ).

fof(f_918_3,plain,
    ! [U_2870,U_2869,U_2868,U_2871] :
      ( c_Orderings_Oord__class_Oless(U_2868,hAPP(hAPP(c_Power_Opower__class_Opower(U_2868),U_2871),U_2870),hAPP(hAPP(c_Power_Opower__class_Opower(U_2868),U_2871),U_2869))
      | ~ c_Orderings_Oord__class_Oless(U_2868,U_2871,c_Groups_Oone__class_Oone(U_2868))
      | ~ c_Orderings_Oord__class_Oless(U_2868,c_Groups_Ozero__class_Ozero(U_2868),U_2871)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2869,U_2870)
      | ~ class_Rings_Olinordered__semidom(U_2868) ),
    inference(definitional_conversion,[status(esa)],[f_918_2]) ).

cnf(f_918_4,plain,
    ( c_Orderings_Oord__class_Oless(U_2868,hAPP(hAPP(c_Power_Opower__class_Opower(U_2868),U_2871),U_2870),hAPP(hAPP(c_Power_Opower__class_Opower(U_2868),U_2871),U_2869))
    | ~ c_Orderings_Oord__class_Oless(U_2868,U_2871,c_Groups_Oone__class_Oone(U_2868))
    | ~ c_Orderings_Oord__class_Oless(U_2868,c_Groups_Ozero__class_Ozero(U_2868),U_2871)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2869,U_2870)
    | ~ class_Rings_Olinordered__semidom(U_2868) ),
    inference(clausify,[status(thm)],[f_918_3]) ).

fof(f_919_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_919_2,plain,
    ! [U_2875,U_2874,U_2873,U_2872] :
      ( U_2873 = U_2875
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2874)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2872,c_Groups_Ozero__class_Ozero(U_2872),U_2875)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2872,c_Groups_Ozero__class_Ozero(U_2872),U_2873)
      | hAPP(hAPP(c_Power_Opower__class_Opower(U_2872),U_2873),U_2874) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2872),U_2875),U_2874)
      | ~ class_Rings_Olinordered__semidom(U_2872) ),
    inference(variable_rename,[status(thm)],[f_919_1]) ).

fof(f_919_3,plain,
    ! [U_2873,U_2875,U_2872,U_2874] :
      ( U_2873 = U_2875
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2874)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2872,c_Groups_Ozero__class_Ozero(U_2872),U_2875)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2872,c_Groups_Ozero__class_Ozero(U_2872),U_2873)
      | hAPP(hAPP(c_Power_Opower__class_Opower(U_2872),U_2873),U_2874) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2872),U_2875),U_2874)
      | ~ class_Rings_Olinordered__semidom(U_2872) ),
    inference(definitional_conversion,[status(esa)],[f_919_2]) ).

cnf(f_919_4,plain,
    ( U_2873 = U_2875
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2874)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2872,c_Groups_Ozero__class_Ozero(U_2872),U_2875)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2872,c_Groups_Ozero__class_Ozero(U_2872),U_2873)
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_2872),U_2873),U_2874) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2872),U_2875),U_2874)
    | ~ class_Rings_Olinordered__semidom(U_2872) ),
    inference(clausify,[status(thm)],[f_919_3]) ).

fof(f_920_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_920_2,plain,
    ! [U_2879,U_2878,U_2877,U_2876] :
      ( c_Orderings_Oord__class_Oless__eq(U_2876,hAPP(hAPP(c_Power_Opower__class_Opower(U_2876),U_2879),U_2878),hAPP(hAPP(c_Power_Opower__class_Opower(U_2876),U_2879),U_2877))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2876,U_2879,c_Groups_Oone__class_Oone(U_2876))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2876,c_Groups_Ozero__class_Ozero(U_2876),U_2879)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2877,U_2878)
      | ~ class_Rings_Olinordered__semidom(U_2876) ),
    inference(variable_rename,[status(thm)],[f_920_1]) ).

fof(f_920_3,plain,
    ! [U_2879,U_2878,U_2877,U_2876] :
      ( c_Orderings_Oord__class_Oless__eq(U_2876,hAPP(hAPP(c_Power_Opower__class_Opower(U_2876),U_2879),U_2878),hAPP(hAPP(c_Power_Opower__class_Opower(U_2876),U_2879),U_2877))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2876,U_2879,c_Groups_Oone__class_Oone(U_2876))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2876,c_Groups_Ozero__class_Ozero(U_2876),U_2879)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2877,U_2878)
      | ~ class_Rings_Olinordered__semidom(U_2876) ),
    inference(definitional_conversion,[status(esa)],[f_920_2]) ).

cnf(f_920_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2876,hAPP(hAPP(c_Power_Opower__class_Opower(U_2876),U_2879),U_2878),hAPP(hAPP(c_Power_Opower__class_Opower(U_2876),U_2879),U_2877))
    | ~ c_Orderings_Oord__class_Oless__eq(U_2876,U_2879,c_Groups_Oone__class_Oone(U_2876))
    | ~ c_Orderings_Oord__class_Oless__eq(U_2876,c_Groups_Ozero__class_Ozero(U_2876),U_2879)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2877,U_2878)
    | ~ class_Rings_Olinordered__semidom(U_2876) ),
    inference(clausify,[status(thm)],[f_920_3]) ).

fof(f_921_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_921_2,plain,
    ! [U_2883,U_2882,U_2881,U_2880] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2882,U_2883)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2880,hAPP(hAPP(c_Power_Opower__class_Opower(U_2880),U_2881),U_2882),hAPP(hAPP(c_Power_Opower__class_Opower(U_2880),U_2881),U_2883))
      | ~ c_Orderings_Oord__class_Oless(U_2880,c_Groups_Oone__class_Oone(U_2880),U_2881)
      | ~ class_Rings_Olinordered__semidom(U_2880) ),
    inference(variable_rename,[status(thm)],[f_921_1]) ).

fof(f_921_3,plain,
    ! [U_2883,U_2880,U_2882,U_2881] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2882,U_2883)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2880,hAPP(hAPP(c_Power_Opower__class_Opower(U_2880),U_2881),U_2882),hAPP(hAPP(c_Power_Opower__class_Opower(U_2880),U_2881),U_2883))
      | ~ c_Orderings_Oord__class_Oless(U_2880,c_Groups_Oone__class_Oone(U_2880),U_2881)
      | ~ class_Rings_Olinordered__semidom(U_2880) ),
    inference(definitional_conversion,[status(esa)],[f_921_2]) ).

cnf(f_921_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2882,U_2883)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2880,hAPP(hAPP(c_Power_Opower__class_Opower(U_2880),U_2881),U_2882),hAPP(hAPP(c_Power_Opower__class_Opower(U_2880),U_2881),U_2883))
    | ~ c_Orderings_Oord__class_Oless(U_2880,c_Groups_Oone__class_Oone(U_2880),U_2881)
    | ~ class_Rings_Olinordered__semidom(U_2880) ),
    inference(clausify,[status(thm)],[f_921_3]) ).

fof(f_922_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_922_2,plain,
    ! [U_2887,U_2886,U_2885,U_2884] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_2884,hAPP(hAPP(c_Power_Opower__class_Opower(U_2884),U_2885),U_2886),hAPP(hAPP(c_Power_Opower__class_Opower(U_2884),U_2885),U_2887))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2886,U_2887) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2886,U_2887)
          | ~ c_Orderings_Oord__class_Oless__eq(U_2884,hAPP(hAPP(c_Power_Opower__class_Opower(U_2884),U_2885),U_2886),hAPP(hAPP(c_Power_Opower__class_Opower(U_2884),U_2885),U_2887)) ) )
      | ~ c_Orderings_Oord__class_Oless(U_2884,c_Groups_Oone__class_Oone(U_2884),U_2885)
      | ~ class_Rings_Olinordered__semidom(U_2884) ),
    inference(variable_rename,[status(thm)],[f_922_1]) ).

fof(f_922_3,plain,
    ( ! [U_2885,U_2884,U_2886,U_2887] :
        ( c_Orderings_Oord__class_Oless__eq(U_2884,hAPP(hAPP(c_Power_Opower__class_Opower(U_2884),U_2885),U_2886),hAPP(hAPP(c_Power_Opower__class_Opower(U_2884),U_2885),U_2887))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2886,U_2887)
        | ~ sP248(U_2885,U_2884,U_2886,U_2887) )
    & ! [U_2885,U_2884,U_2886,U_2887] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2886,U_2887)
        | ~ c_Orderings_Oord__class_Oless__eq(U_2884,hAPP(hAPP(c_Power_Opower__class_Opower(U_2884),U_2885),U_2886),hAPP(hAPP(c_Power_Opower__class_Opower(U_2884),U_2885),U_2887))
        | ~ sP248(U_2885,U_2884,U_2886,U_2887) )
    & ! [U_2885,U_2884,U_2886,U_2887] :
        ( sP248(U_2885,U_2884,U_2886,U_2887)
        | ~ c_Orderings_Oord__class_Oless(U_2884,c_Groups_Oone__class_Oone(U_2884),U_2885)
        | ~ class_Rings_Olinordered__semidom(U_2884) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP248])],[f_922_2]) ).

cnf(f_922_4,plain,
    ( sP248(U_2885,U_2884,U_2886,U_2887)
    | ~ c_Orderings_Oord__class_Oless(U_2884,c_Groups_Oone__class_Oone(U_2884),U_2885)
    | ~ class_Rings_Olinordered__semidom(U_2884) ),
    inference(clausify,[status(thm)],[f_922_3]) ).

cnf(f_922_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2886,U_2887)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2884,hAPP(hAPP(c_Power_Opower__class_Opower(U_2884),U_2885),U_2886),hAPP(hAPP(c_Power_Opower__class_Opower(U_2884),U_2885),U_2887))
    | ~ sP248(U_2885,U_2884,U_2886,U_2887) ),
    inference(clausify,[status(thm)],[f_922_3]) ).

cnf(f_922_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2884,hAPP(hAPP(c_Power_Opower__class_Opower(U_2884),U_2885),U_2886),hAPP(hAPP(c_Power_Opower__class_Opower(U_2884),U_2885),U_2887))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2886,U_2887)
    | ~ sP248(U_2885,U_2884,U_2886,U_2887) ),
    inference(clausify,[status(thm)],[f_922_3]) ).

fof(f_923_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_923_2,plain,
    ! [U_2890,U_2889,U_2888] :
      ( c_Orderings_Oord__class_Oless(U_2888,c_Groups_Oone__class_Oone(U_2888),hAPP(hAPP(c_Power_Opower__class_Opower(U_2888),U_2889),U_2890))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2890)
      | ~ c_Orderings_Oord__class_Oless(U_2888,c_Groups_Oone__class_Oone(U_2888),U_2889)
      | ~ class_Rings_Olinordered__semidom(U_2888) ),
    inference(variable_rename,[status(thm)],[f_923_1]) ).

fof(f_923_3,plain,
    ! [U_2889,U_2890,U_2888] :
      ( c_Orderings_Oord__class_Oless(U_2888,c_Groups_Oone__class_Oone(U_2888),hAPP(hAPP(c_Power_Opower__class_Opower(U_2888),U_2889),U_2890))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2890)
      | ~ c_Orderings_Oord__class_Oless(U_2888,c_Groups_Oone__class_Oone(U_2888),U_2889)
      | ~ class_Rings_Olinordered__semidom(U_2888) ),
    inference(definitional_conversion,[status(esa)],[f_923_2]) ).

cnf(f_923_4,plain,
    ( c_Orderings_Oord__class_Oless(U_2888,c_Groups_Oone__class_Oone(U_2888),hAPP(hAPP(c_Power_Opower__class_Opower(U_2888),U_2889),U_2890))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2890)
    | ~ c_Orderings_Oord__class_Oless(U_2888,c_Groups_Oone__class_Oone(U_2888),U_2889)
    | ~ class_Rings_Olinordered__semidom(U_2888) ),
    inference(clausify,[status(thm)],[f_923_3]) ).

fof(f_924_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_924_2,plain,
    ! [U_2894,U_2893,U_2892,U_2891] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2891),U_2894),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2893),U_2892)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2891),hAPP(hAPP(c_Power_Opower__class_Opower(U_2891),U_2894),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2893,U_2892))),U_2894)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2892,U_2893)
      | ~ class_Groups_Omonoid__mult(U_2891) ),
    inference(variable_rename,[status(thm)],[f_924_1]) ).

fof(f_924_3,plain,
    ! [U_2892,U_2891,U_2893,U_2894] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2891),U_2894),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2893),U_2892)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2891),hAPP(hAPP(c_Power_Opower__class_Opower(U_2891),U_2894),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2893,U_2892))),U_2894)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2892,U_2893)
      | ~ class_Groups_Omonoid__mult(U_2891) ),
    inference(definitional_conversion,[status(esa)],[f_924_2]) ).

cnf(f_924_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2891),U_2894),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2893),U_2892)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2891),hAPP(hAPP(c_Power_Opower__class_Opower(U_2891),U_2894),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2893,U_2892))),U_2894)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2892,U_2893)
    | ~ class_Groups_Omonoid__mult(U_2891) ),
    inference(clausify,[status(thm)],[f_924_3]) ).

fof(f_925_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_925_2,plain,
    ! [U_2897,U_2896] :
      ( ? [U_2895] : 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_2896),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),U_2895),U_2897)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | U_2897 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | U_2896 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    inference(variable_rename,[status(thm)],[f_925_1]) ).

fof(f_925_3,plain,
    ! [U_2897,U_2896] :
      ( 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_2896),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),sK70(U_2897,U_2896)),U_2897)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | U_2897 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | U_2896 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_2895,sK70(U_2897,U_2896))],[f_925_2]) ).

fof(f_925_4,plain,
    ! [U_2896,U_2897] :
      ( 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_2896),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),sK70(U_2897,U_2896)),U_2897)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | U_2897 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | U_2896 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    inference(definitional_conversion,[status(esa)],[f_925_3]) ).

cnf(f_925_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_2896),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),sK70(U_2897,U_2896)),U_2897)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    | U_2897 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_2896 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    inference(clausify,[status(thm)],[f_925_4]) ).

fof(f_926_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_926_2,plain,
    ! [U_2898] :
      ( c_Power_Opower__class_Opower(U_2898) = c_Power_Opower_Opower(U_2898,c_Groups_Oone__class_Oone(U_2898),c_Groups_Otimes__class_Otimes(U_2898))
      | ~ class_Power_Opower(U_2898) ),
    inference(variable_rename,[status(thm)],[f_926_1]) ).

fof(f_926_3,plain,
    ! [U_2898] :
      ( c_Power_Opower__class_Opower(U_2898) = c_Power_Opower_Opower(U_2898,c_Groups_Oone__class_Oone(U_2898),c_Groups_Otimes__class_Otimes(U_2898))
      | ~ class_Power_Opower(U_2898) ),
    inference(definitional_conversion,[status(esa)],[f_926_2]) ).

cnf(f_926_4,plain,
    ( c_Power_Opower__class_Opower(U_2898) = c_Power_Opower_Opower(U_2898,c_Groups_Oone__class_Oone(U_2898),c_Groups_Otimes__class_Otimes(U_2898))
    | ~ class_Power_Opower(U_2898) ),
    inference(clausify,[status(thm)],[f_926_3]) ).

fof(f_927_1,plain,
    ! [V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2,
    inference(fof_nnf,[status(thm)],[fact_power_Opower_Opower__0]) ).

fof(f_927_2,plain,
    ! [U_2902,U_2901,U_2900,U_2899] : hAPP(hAPP(c_Power_Opower_Opower(U_2899,U_2900,U_2901),U_2902),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_2900,
    inference(variable_rename,[status(thm)],[f_927_1]) ).

fof(f_927_3,plain,
    ! [U_2899,U_2900,U_2901,U_2902] : hAPP(hAPP(c_Power_Opower_Opower(U_2899,U_2900,U_2901),U_2902),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_2900,
    inference(definitional_conversion,[status(esa)],[f_927_2]) ).

cnf(f_927_4,plain,
    hAPP(hAPP(c_Power_Opower_Opower(U_2899,U_2900,U_2901),U_2902),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_2900,
    inference(clausify,[status(thm)],[f_927_3]) ).

fof(f_928_1,plain,
    ! [V_n_2,V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Nat_OSuc(V_n_2)) = hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),V_n_2)),
    inference(fof_nnf,[status(thm)],[fact_power_Opower_Opower__Suc]) ).

fof(f_928_2,plain,
    ! [U_2907,U_2906,U_2905,U_2904,U_2903] : hAPP(hAPP(c_Power_Opower_Opower(U_2903,U_2904,U_2905),U_2906),c_Nat_OSuc(U_2907)) = hAPP(hAPP(U_2905,U_2906),hAPP(hAPP(c_Power_Opower_Opower(U_2903,U_2904,U_2905),U_2906),U_2907)),
    inference(variable_rename,[status(thm)],[f_928_1]) ).

fof(f_928_3,plain,
    ! [U_2903,U_2904,U_2905,U_2906,U_2907] : hAPP(hAPP(c_Power_Opower_Opower(U_2903,U_2904,U_2905),U_2906),c_Nat_OSuc(U_2907)) = hAPP(hAPP(U_2905,U_2906),hAPP(hAPP(c_Power_Opower_Opower(U_2903,U_2904,U_2905),U_2906),U_2907)),
    inference(definitional_conversion,[status(esa)],[f_928_2]) ).

cnf(f_928_4,plain,
    hAPP(hAPP(c_Power_Opower_Opower(U_2903,U_2904,U_2905),U_2906),c_Nat_OSuc(U_2907)) = hAPP(hAPP(U_2905,U_2906),hAPP(hAPP(c_Power_Opower_Opower(U_2903,U_2904,U_2905),U_2906),U_2907)),
    inference(clausify,[status(thm)],[f_928_3]) ).

fof(f_929_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),hAPP(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),hAPP(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_929_2,plain,
    ! [U_2910,U_2909] :
      ( ? [U_2908] :
          ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2910,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(U_2908))),U_2909))
          & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_2908)),U_2909),U_2910) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2910)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2909) ),
    inference(variable_rename,[status(thm)],[f_929_1]) ).

fof(f_929_3,plain,
    ! [U_2910,U_2909] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2910,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(sK71(U_2910,U_2909)))),U_2909))
        & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),sK71(U_2910,U_2909))),U_2909),U_2910) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2910)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2909) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_2908,sK71(U_2910,U_2909))],[f_929_2]) ).

fof(f_929_4,plain,
    ( ! [U_2909,U_2910] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2910,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(sK71(U_2910,U_2909)))),U_2909))
        | ~ sP249(U_2909,U_2910) )
    & ! [U_2909,U_2910] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),sK71(U_2910,U_2909))),U_2909),U_2910)
        | ~ sP249(U_2909,U_2910) )
    & ! [U_2909,U_2910] :
        ( sP249(U_2909,U_2910)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2910)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2909) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP249])],[f_929_3]) ).

cnf(f_929_5,plain,
    ( sP249(U_2909,U_2910)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2910)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2909) ),
    inference(clausify,[status(thm)],[f_929_4]) ).

cnf(f_929_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),sK71(U_2910,U_2909))),U_2909),U_2910)
    | ~ sP249(U_2909,U_2910) ),
    inference(clausify,[status(thm)],[f_929_4]) ).

cnf(f_929_7,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2910,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(sK71(U_2910,U_2909)))),U_2909))
    | ~ sP249(U_2909,U_2910) ),
    inference(clausify,[status(thm)],[f_929_4]) ).

fof(f_930_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_930_2,plain,
    ! [U_2912,U_2911] :
      ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2912),U_2911),U_2912) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2912),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2911,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_2912)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2911) ),
    inference(variable_rename,[status(thm)],[f_930_1]) ).

fof(f_930_3,plain,
    ! [U_2912,U_2911] :
      ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2912),U_2911),U_2912) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2912),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2911,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_2912)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2911) ),
    inference(definitional_conversion,[status(esa)],[f_930_2]) ).

cnf(f_930_4,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2912),U_2911),U_2912) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2912),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2911,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_2912)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2911) ),
    inference(clausify,[status(thm)],[f_930_3]) ).

fof(f_931_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_931_2,plain,
    ! [U_2915,U_2914,U_2913] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2914,U_2915),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2913,U_2915))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2915,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2913,U_2914) ),
    inference(variable_rename,[status(thm)],[f_931_1]) ).

fof(f_931_3,plain,
    ! [U_2914,U_2915,U_2913] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2914,U_2915),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2913,U_2915))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2915,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2913,U_2914) ),
    inference(definitional_conversion,[status(esa)],[f_931_2]) ).

cnf(f_931_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2914,U_2915),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2913,U_2915))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2915,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2913,U_2914) ),
    inference(clausify,[status(thm)],[f_931_3]) ).

fof(f_932_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_932_2,plain,
    ! [U_2918,U_2917,U_2916] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2916,U_2918),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2917,U_2918))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2918)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2916,U_2917) ),
    inference(variable_rename,[status(thm)],[f_932_1]) ).

fof(f_932_3,plain,
    ! [U_2916,U_2917,U_2918] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2916,U_2918),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2917,U_2918))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2918)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2916,U_2917) ),
    inference(definitional_conversion,[status(esa)],[f_932_2]) ).

cnf(f_932_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2916,U_2918),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2917,U_2918))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2918)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2916,U_2917) ),
    inference(clausify,[status(thm)],[f_932_3]) ).

fof(f_933_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_933_2,plain,
    ! [U_2920,U_2919] :
      ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2919,U_2920) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2920,U_2919)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2919,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(variable_rename,[status(thm)],[f_933_1]) ).

fof(f_933_3,plain,
    ! [U_2919,U_2920] :
      ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2919,U_2920) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2920,U_2919)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2919,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(definitional_conversion,[status(esa)],[f_933_2]) ).

cnf(f_933_4,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2919,U_2920) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2920,U_2919)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2919,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(clausify,[status(thm)],[f_933_3]) ).

fof(f_934_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_934_2,plain,
    ! [U_2923,U_2922,U_2921] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2921,U_2922),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2921,U_2923))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2922,U_2923)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2922)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2921,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(variable_rename,[status(thm)],[f_934_1]) ).

fof(f_934_3,plain,
    ! [U_2923,U_2922,U_2921] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2921,U_2922),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2921,U_2923))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2922,U_2923)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2922)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2921,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(definitional_conversion,[status(esa)],[f_934_2]) ).

cnf(f_934_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2921,U_2922),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2921,U_2923))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2922,U_2923)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2922)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2921,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(clausify,[status(thm)],[f_934_3]) ).

fof(f_935_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_935_2,plain,
    ! [U_2925,U_2924] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2924,U_2925),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_2925)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2924,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(variable_rename,[status(thm)],[f_935_1]) ).

fof(f_935_3,plain,
    ! [U_2925,U_2924] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2924,U_2925),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_2925)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2924,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(definitional_conversion,[status(esa)],[f_935_2]) ).

cnf(f_935_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2924,U_2925),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_2925)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2924,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(clausify,[status(thm)],[f_935_3]) ).

fof(f_936_1,plain,
    ! [V_a_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_a_2,V_b_2))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a_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_a_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_936_2,plain,
    ! [U_2927,U_2926] :
      ( ( ( 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_2927,U_2926))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2927,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2927,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_2927,U_2926)) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2926,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(variable_rename,[status(thm)],[f_936_1]) ).

fof(f_936_3,plain,
    ( ! [U_2927,U_2926] :
        ( 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_2927,U_2926))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2927,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ sP250(U_2927,U_2926) )
    & ! [U_2927,U_2926] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2927,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_2927,U_2926))
        | ~ sP250(U_2927,U_2926) )
    & ! [U_2927,U_2926] :
        ( sP250(U_2927,U_2926)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2926,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP250])],[f_936_2]) ).

cnf(f_936_4,plain,
    ( sP250(U_2927,U_2926)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2926,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(clausify,[status(thm)],[f_936_3]) ).

cnf(f_936_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2927,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_2927,U_2926))
    | ~ sP250(U_2927,U_2926) ),
    inference(clausify,[status(thm)],[f_936_3]) ).

cnf(f_936_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_2927,U_2926))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2927,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ sP250(U_2927,U_2926) ),
    inference(clausify,[status(thm)],[f_936_3]) ).

fof(f_937_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_937_2,plain,
    ! [U_2929,U_2928] :
      ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2928,U_2929) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2928,U_2929)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2928) ),
    inference(variable_rename,[status(thm)],[f_937_1]) ).

fof(f_937_3,plain,
    ! [U_2928,U_2929] :
      ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2928,U_2929) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2928,U_2929)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2928) ),
    inference(definitional_conversion,[status(esa)],[f_937_2]) ).

cnf(f_937_4,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2928,U_2929) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2928,U_2929)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2928) ),
    inference(clausify,[status(thm)],[f_937_3]) ).

fof(f_938_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_938_2,plain,
    ! [U_2931,U_2930] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2930,U_2931),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2931,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_2930) ),
    inference(variable_rename,[status(thm)],[f_938_1]) ).

fof(f_938_3,plain,
    ! [U_2930,U_2931] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2930,U_2931),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2931,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_2930) ),
    inference(definitional_conversion,[status(esa)],[f_938_2]) ).

cnf(f_938_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2930,U_2931),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2931,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_2930) ),
    inference(clausify,[status(thm)],[f_938_3]) ).

fof(f_939_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_939_2,plain,
    ! [U_2934,U_2933,U_2932] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2932,U_2934),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2932,U_2933))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2933,U_2934)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2933)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2932) ),
    inference(variable_rename,[status(thm)],[f_939_1]) ).

fof(f_939_3,plain,
    ! [U_2933,U_2932,U_2934] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2932,U_2934),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2932,U_2933))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2933,U_2934)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2933)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2932) ),
    inference(definitional_conversion,[status(esa)],[f_939_2]) ).

cnf(f_939_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2932,U_2934),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2932,U_2933))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2933,U_2934)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2933)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2932) ),
    inference(clausify,[status(thm)],[f_939_3]) ).

fof(f_940_1,plain,
    ! [V_b_2,V_a_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_a_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_a_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_a_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_a_2,V_b_2)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2) ),
    inference(fof_nnf,[status(thm)],[fact_nonneg1__imp__zdiv__pos__iff]) ).

fof(f_940_2,plain,
    ! [U_2936,U_2935] :
      ( ( ( 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_2935,U_2936))
          | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2936)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2936,U_2935) )
        & ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2936)
            & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2936,U_2935) )
          | ~ 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_2935,U_2936)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2935) ),
    inference(variable_rename,[status(thm)],[f_940_1]) ).

fof(f_940_3,plain,
    ( ! [U_2935,U_2936] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2936)
        | ~ sP251(U_2935,U_2936) )
    & ! [U_2935,U_2936] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2936,U_2935)
        | ~ sP251(U_2935,U_2936) )
    & ! [U_2935,U_2936] :
        ( 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_2935,U_2936))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2936)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2936,U_2935)
        | ~ sP252(U_2935,U_2936) )
    & ! [U_2935,U_2936] :
        ( sP251(U_2935,U_2936)
        | ~ 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_2935,U_2936))
        | ~ sP252(U_2935,U_2936) )
    & ! [U_2935,U_2936] :
        ( sP252(U_2935,U_2936)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2935) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP251,sP252])],[f_940_2]) ).

cnf(f_940_4,plain,
    ( sP252(U_2935,U_2936)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2935) ),
    inference(clausify,[status(thm)],[f_940_3]) ).

cnf(f_940_5,plain,
    ( sP251(U_2935,U_2936)
    | ~ 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_2935,U_2936))
    | ~ sP252(U_2935,U_2936) ),
    inference(clausify,[status(thm)],[f_940_3]) ).

cnf(f_940_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_2935,U_2936))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2936)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2936,U_2935)
    | ~ sP252(U_2935,U_2936) ),
    inference(clausify,[status(thm)],[f_940_3]) ).

cnf(f_940_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2936,U_2935)
    | ~ sP251(U_2935,U_2936) ),
    inference(clausify,[status(thm)],[f_940_3]) ).

cnf(f_940_8,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2936)
    | ~ sP251(U_2935,U_2936) ),
    inference(clausify,[status(thm)],[f_940_3]) ).

fof(f_941_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_941_2,plain,
    ! [U_2938,U_2937] :
      ( ( ( 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_2938,U_2937))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2937,U_2938) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2937,U_2938)
          | ~ 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_2938,U_2937)) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2937) ),
    inference(variable_rename,[status(thm)],[f_941_1]) ).

fof(f_941_3,plain,
    ( ! [U_2937,U_2938] :
        ( 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_2938,U_2937))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2937,U_2938)
        | ~ sP253(U_2937,U_2938) )
    & ! [U_2937,U_2938] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2937,U_2938)
        | ~ 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_2938,U_2937))
        | ~ sP253(U_2937,U_2938) )
    & ! [U_2937,U_2938] :
        ( sP253(U_2937,U_2938)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2937) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP253])],[f_941_2]) ).

cnf(f_941_4,plain,
    ( sP253(U_2937,U_2938)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2937) ),
    inference(clausify,[status(thm)],[f_941_3]) ).

cnf(f_941_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2937,U_2938)
    | ~ 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_2938,U_2937))
    | ~ sP253(U_2937,U_2938) ),
    inference(clausify,[status(thm)],[f_941_3]) ).

cnf(f_941_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_2938,U_2937))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2937,U_2938)
    | ~ sP253(U_2937,U_2938) ),
    inference(clausify,[status(thm)],[f_941_3]) ).

fof(f_942_1,plain,
    ! [V_a_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_a_2,V_b_2))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_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_a_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_942_2,plain,
    ! [U_2940,U_2939] :
      ( ( ( 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_2940,U_2939))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2940) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2940)
          | ~ 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_2940,U_2939)) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2939) ),
    inference(variable_rename,[status(thm)],[f_942_1]) ).

fof(f_942_3,plain,
    ( ! [U_2940,U_2939] :
        ( 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_2940,U_2939))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2940)
        | ~ sP254(U_2940,U_2939) )
    & ! [U_2940,U_2939] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2940)
        | ~ 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_2940,U_2939))
        | ~ sP254(U_2940,U_2939) )
    & ! [U_2940,U_2939] :
        ( sP254(U_2940,U_2939)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2939) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP254])],[f_942_2]) ).

cnf(f_942_4,plain,
    ( sP254(U_2940,U_2939)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2939) ),
    inference(clausify,[status(thm)],[f_942_3]) ).

cnf(f_942_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2940)
    | ~ 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_2940,U_2939))
    | ~ sP254(U_2940,U_2939) ),
    inference(clausify,[status(thm)],[f_942_3]) ).

cnf(f_942_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_2940,U_2939))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2940)
    | ~ sP254(U_2940,U_2939) ),
    inference(clausify,[status(thm)],[f_942_3]) ).

fof(f_943_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_943_2,plain,
    ! [U_2942,U_2941] :
      ( ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2941,U_2942) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2942,U_2941)
            | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2941,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
          & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2941,U_2942)
            | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2941) )
          & U_2942 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2942,U_2941)
          & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2941,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
        | ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2941,U_2942)
          & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2941) )
        | U_2942 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2941,U_2942) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_943_1]) ).

fof(f_943_3,plain,
    ( ! [U_2946,U_2944] :
        ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2944,U_2946) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2946,U_2944)
            | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2944,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
          & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2944,U_2946)
            | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2944) )
          & U_2946 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_2945,U_2943] :
        ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2945,U_2943)
          & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2943,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
        | ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2943,U_2945)
          & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2943) )
        | U_2945 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2943,U_2945) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_943_2]) ).

fof(f_943_4,plain,
    ( ! [U_2946,U_2944] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2946,U_2944)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2944,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ sP257(U_2946,U_2944) )
    & ! [U_2946,U_2944] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2944,U_2946)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2944)
        | ~ sP257(U_2946,U_2944) )
    & ! [U_2946,U_2944] :
        ( U_2946 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP257(U_2946,U_2944) )
    & ! [U_2943,U_2945] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2945,U_2943)
        | ~ sP256(U_2943,U_2945) )
    & ! [U_2943,U_2945] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2943,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ sP256(U_2943,U_2945) )
    & ! [U_2943,U_2945] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2943,U_2945)
        | ~ sP255(U_2943,U_2945) )
    & ! [U_2943,U_2945] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2943)
        | ~ sP255(U_2943,U_2945) )
    & ! [U_2946,U_2944] :
        ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2944,U_2946) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | sP257(U_2946,U_2944) )
    & ! [U_2943,U_2945] :
        ( sP256(U_2943,U_2945)
        | sP255(U_2943,U_2945)
        | U_2945 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2943,U_2945) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP255,sP256,sP257])],[f_943_3]) ).

cnf(f_943_5,plain,
    ( sP256(U_2943,U_2945)
    | sP255(U_2943,U_2945)
    | U_2945 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2943,U_2945) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_943_4]) ).

cnf(f_943_6,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2944,U_2946) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | sP257(U_2946,U_2944) ),
    inference(clausify,[status(thm)],[f_943_4]) ).

cnf(f_943_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2943)
    | ~ sP255(U_2943,U_2945) ),
    inference(clausify,[status(thm)],[f_943_4]) ).

cnf(f_943_8,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2943,U_2945)
    | ~ sP255(U_2943,U_2945) ),
    inference(clausify,[status(thm)],[f_943_4]) ).

cnf(f_943_9,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2943,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ sP256(U_2943,U_2945) ),
    inference(clausify,[status(thm)],[f_943_4]) ).

cnf(f_943_10,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2945,U_2943)
    | ~ sP256(U_2943,U_2945) ),
    inference(clausify,[status(thm)],[f_943_4]) ).

cnf(f_943_11,plain,
    ( U_2946 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP257(U_2946,U_2944) ),
    inference(clausify,[status(thm)],[f_943_4]) ).

cnf(f_943_12,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2944,U_2946)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2944)
    | ~ sP257(U_2946,U_2944) ),
    inference(clausify,[status(thm)],[f_943_4]) ).

cnf(f_943_13,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2946,U_2944)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2944,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ sP257(U_2946,U_2944) ),
    inference(clausify,[status(thm)],[f_943_4]) ).

fof(f_944_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_944_2,plain,
    ! [U_2948,U_2947] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2947,U_2948),U_2947)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2948)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2947) ),
    inference(variable_rename,[status(thm)],[f_944_1]) ).

fof(f_944_3,plain,
    ! [U_2947,U_2948] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2947,U_2948),U_2947)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2948)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2947) ),
    inference(definitional_conversion,[status(esa)],[f_944_2]) ).

cnf(f_944_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2947,U_2948),U_2947)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2948)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2947) ),
    inference(clausify,[status(thm)],[f_944_3]) ).

fof(f_945_1,plain,
    ! [V_b,V_a,V_c] :
      ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),V_c)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c) ),
    inference(fof_nnf,[status(thm)],[fact_zdiv__zmult2__eq]) ).

fof(f_945_2,plain,
    ! [U_2951,U_2950,U_2949] :
      ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2950,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2951),U_2949)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2950,U_2951),U_2949)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2949) ),
    inference(variable_rename,[status(thm)],[f_945_1]) ).

fof(f_945_3,plain,
    ! [U_2950,U_2949,U_2951] :
      ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2950,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2951),U_2949)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2950,U_2951),U_2949)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2949) ),
    inference(definitional_conversion,[status(esa)],[f_945_2]) ).

cnf(f_945_4,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2950,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2951),U_2949)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2950,U_2951),U_2949)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2949) ),
    inference(clausify,[status(thm)],[f_945_3]) ).

fof(f_946_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_946_2,plain,
    ! [U_2955,U_2954,U_2953,U_2952] :
      ( c_Divides_Odiv__class_Odiv(U_2952,c_Groups_Oplus__class_Oplus(U_2952,U_2954,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2952),U_2955),U_2953)),U_2953) = c_Groups_Oplus__class_Oplus(U_2952,U_2955,c_Divides_Odiv__class_Odiv(U_2952,U_2954,U_2953))
      | U_2953 = c_Groups_Ozero__class_Ozero(U_2952)
      | ~ class_Divides_Osemiring__div(U_2952) ),
    inference(variable_rename,[status(thm)],[f_946_1]) ).

fof(f_946_3,plain,
    ! [U_2952,U_2953,U_2954,U_2955] :
      ( c_Divides_Odiv__class_Odiv(U_2952,c_Groups_Oplus__class_Oplus(U_2952,U_2954,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2952),U_2955),U_2953)),U_2953) = c_Groups_Oplus__class_Oplus(U_2952,U_2955,c_Divides_Odiv__class_Odiv(U_2952,U_2954,U_2953))
      | U_2953 = c_Groups_Ozero__class_Ozero(U_2952)
      | ~ class_Divides_Osemiring__div(U_2952) ),
    inference(definitional_conversion,[status(esa)],[f_946_2]) ).

cnf(f_946_4,plain,
    ( c_Divides_Odiv__class_Odiv(U_2952,c_Groups_Oplus__class_Oplus(U_2952,U_2954,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2952),U_2955),U_2953)),U_2953) = c_Groups_Oplus__class_Oplus(U_2952,U_2955,c_Divides_Odiv__class_Odiv(U_2952,U_2954,U_2953))
    | U_2953 = c_Groups_Ozero__class_Ozero(U_2952)
    | ~ class_Divides_Osemiring__div(U_2952) ),
    inference(clausify,[status(thm)],[f_946_3]) ).

fof(f_947_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_947_2,plain,
    ! [U_2959,U_2958,U_2957,U_2956] :
      ( c_Divides_Odiv__class_Odiv(U_2956,c_Groups_Oplus__class_Oplus(U_2956,U_2958,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2956),U_2957),U_2959)),U_2957) = c_Groups_Oplus__class_Oplus(U_2956,U_2959,c_Divides_Odiv__class_Odiv(U_2956,U_2958,U_2957))
      | U_2957 = c_Groups_Ozero__class_Ozero(U_2956)
      | ~ class_Divides_Osemiring__div(U_2956) ),
    inference(variable_rename,[status(thm)],[f_947_1]) ).

fof(f_947_3,plain,
    ! [U_2957,U_2956,U_2958,U_2959] :
      ( c_Divides_Odiv__class_Odiv(U_2956,c_Groups_Oplus__class_Oplus(U_2956,U_2958,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2956),U_2957),U_2959)),U_2957) = c_Groups_Oplus__class_Oplus(U_2956,U_2959,c_Divides_Odiv__class_Odiv(U_2956,U_2958,U_2957))
      | U_2957 = c_Groups_Ozero__class_Ozero(U_2956)
      | ~ class_Divides_Osemiring__div(U_2956) ),
    inference(definitional_conversion,[status(esa)],[f_947_2]) ).

cnf(f_947_4,plain,
    ( c_Divides_Odiv__class_Odiv(U_2956,c_Groups_Oplus__class_Oplus(U_2956,U_2958,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2956),U_2957),U_2959)),U_2957) = c_Groups_Oplus__class_Oplus(U_2956,U_2959,c_Divides_Odiv__class_Odiv(U_2956,U_2958,U_2957))
    | U_2957 = c_Groups_Ozero__class_Ozero(U_2956)
    | ~ class_Divides_Osemiring__div(U_2956) ),
    inference(clausify,[status(thm)],[f_947_3]) ).

fof(f_948_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_948_2,plain,
    ! [U_2962,U_2961,U_2960] :
      ( c_Divides_Odiv__class_Odiv(U_2960,c_Groups_Oplus__class_Oplus(U_2960,U_2962,U_2961),U_2961) = c_Groups_Oplus__class_Oplus(U_2960,c_Divides_Odiv__class_Odiv(U_2960,U_2962,U_2961),c_Groups_Oone__class_Oone(U_2960))
      | U_2961 = c_Groups_Ozero__class_Ozero(U_2960)
      | ~ class_Divides_Osemiring__div(U_2960) ),
    inference(variable_rename,[status(thm)],[f_948_1]) ).

fof(f_948_3,plain,
    ! [U_2961,U_2960,U_2962] :
      ( c_Divides_Odiv__class_Odiv(U_2960,c_Groups_Oplus__class_Oplus(U_2960,U_2962,U_2961),U_2961) = c_Groups_Oplus__class_Oplus(U_2960,c_Divides_Odiv__class_Odiv(U_2960,U_2962,U_2961),c_Groups_Oone__class_Oone(U_2960))
      | U_2961 = c_Groups_Ozero__class_Ozero(U_2960)
      | ~ class_Divides_Osemiring__div(U_2960) ),
    inference(definitional_conversion,[status(esa)],[f_948_2]) ).

cnf(f_948_4,plain,
    ( c_Divides_Odiv__class_Odiv(U_2960,c_Groups_Oplus__class_Oplus(U_2960,U_2962,U_2961),U_2961) = c_Groups_Oplus__class_Oplus(U_2960,c_Divides_Odiv__class_Odiv(U_2960,U_2962,U_2961),c_Groups_Oone__class_Oone(U_2960))
    | U_2961 = c_Groups_Ozero__class_Ozero(U_2960)
    | ~ class_Divides_Osemiring__div(U_2960) ),
    inference(clausify,[status(thm)],[f_948_3]) ).

fof(f_949_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_949_2,plain,
    ! [U_2965,U_2964,U_2963] :
      ( c_Divides_Odiv__class_Odiv(U_2963,c_Groups_Oplus__class_Oplus(U_2963,U_2964,U_2965),U_2964) = c_Groups_Oplus__class_Oplus(U_2963,c_Divides_Odiv__class_Odiv(U_2963,U_2965,U_2964),c_Groups_Oone__class_Oone(U_2963))
      | U_2964 = c_Groups_Ozero__class_Ozero(U_2963)
      | ~ class_Divides_Osemiring__div(U_2963) ),
    inference(variable_rename,[status(thm)],[f_949_1]) ).

fof(f_949_3,plain,
    ! [U_2963,U_2964,U_2965] :
      ( c_Divides_Odiv__class_Odiv(U_2963,c_Groups_Oplus__class_Oplus(U_2963,U_2964,U_2965),U_2964) = c_Groups_Oplus__class_Oplus(U_2963,c_Divides_Odiv__class_Odiv(U_2963,U_2965,U_2964),c_Groups_Oone__class_Oone(U_2963))
      | U_2964 = c_Groups_Ozero__class_Ozero(U_2963)
      | ~ class_Divides_Osemiring__div(U_2963) ),
    inference(definitional_conversion,[status(esa)],[f_949_2]) ).

cnf(f_949_4,plain,
    ( c_Divides_Odiv__class_Odiv(U_2963,c_Groups_Oplus__class_Oplus(U_2963,U_2964,U_2965),U_2964) = c_Groups_Oplus__class_Oplus(U_2963,c_Divides_Odiv__class_Odiv(U_2963,U_2965,U_2964),c_Groups_Oone__class_Oone(U_2963))
    | U_2964 = c_Groups_Ozero__class_Ozero(U_2963)
    | ~ class_Divides_Osemiring__div(U_2963) ),
    inference(clausify,[status(thm)],[f_949_3]) ).

fof(f_950_1,plain,
    ! [V_b,V_a,V_c,T_a] :
      ( c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(T_a,V_a,V_b)
      | V_c = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__mult__mult1]) ).

fof(f_950_2,plain,
    ! [U_2969,U_2968,U_2967,U_2966] :
      ( c_Divides_Odiv__class_Odiv(U_2966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2966),U_2967),U_2968),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2966),U_2967),U_2969)) = c_Divides_Odiv__class_Odiv(U_2966,U_2968,U_2969)
      | U_2967 = c_Groups_Ozero__class_Ozero(U_2966)
      | ~ class_Divides_Osemiring__div(U_2966) ),
    inference(variable_rename,[status(thm)],[f_950_1]) ).

fof(f_950_3,plain,
    ! [U_2966,U_2967,U_2968,U_2969] :
      ( c_Divides_Odiv__class_Odiv(U_2966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2966),U_2967),U_2968),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2966),U_2967),U_2969)) = c_Divides_Odiv__class_Odiv(U_2966,U_2968,U_2969)
      | U_2967 = c_Groups_Ozero__class_Ozero(U_2966)
      | ~ class_Divides_Osemiring__div(U_2966) ),
    inference(definitional_conversion,[status(esa)],[f_950_2]) ).

cnf(f_950_4,plain,
    ( c_Divides_Odiv__class_Odiv(U_2966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2966),U_2967),U_2968),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2966),U_2967),U_2969)) = c_Divides_Odiv__class_Odiv(U_2966,U_2968,U_2969)
    | U_2967 = c_Groups_Ozero__class_Ozero(U_2966)
    | ~ class_Divides_Osemiring__div(U_2966) ),
    inference(clausify,[status(thm)],[f_950_3]) ).

fof(f_951_1,plain,
    ! [V_b,V_a,V_c,T_a] :
      ( c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(T_a,V_a,V_b)
      | V_c = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__mult__mult2]) ).

fof(f_951_2,plain,
    ! [U_2973,U_2972,U_2971,U_2970] :
      ( c_Divides_Odiv__class_Odiv(U_2970,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2970),U_2972),U_2971),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2970),U_2973),U_2971)) = c_Divides_Odiv__class_Odiv(U_2970,U_2972,U_2973)
      | U_2971 = c_Groups_Ozero__class_Ozero(U_2970)
      | ~ class_Divides_Osemiring__div(U_2970) ),
    inference(variable_rename,[status(thm)],[f_951_1]) ).

fof(f_951_3,plain,
    ! [U_2970,U_2971,U_2972,U_2973] :
      ( c_Divides_Odiv__class_Odiv(U_2970,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2970),U_2972),U_2971),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2970),U_2973),U_2971)) = c_Divides_Odiv__class_Odiv(U_2970,U_2972,U_2973)
      | U_2971 = c_Groups_Ozero__class_Ozero(U_2970)
      | ~ class_Divides_Osemiring__div(U_2970) ),
    inference(definitional_conversion,[status(esa)],[f_951_2]) ).

cnf(f_951_4,plain,
    ( c_Divides_Odiv__class_Odiv(U_2970,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2970),U_2972),U_2971),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2970),U_2973),U_2971)) = c_Divides_Odiv__class_Odiv(U_2970,U_2972,U_2973)
    | U_2971 = c_Groups_Ozero__class_Ozero(U_2970)
    | ~ class_Divides_Osemiring__div(U_2970) ),
    inference(clausify,[status(thm)],[f_951_3]) ).

fof(f_952_1,plain,
    ! [V_a,V_b,T_a] :
      ( c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b) = V_a
      | V_b = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__mult__self1__is__id]) ).

fof(f_952_2,plain,
    ! [U_2976,U_2975,U_2974] :
      ( c_Divides_Odiv__class_Odiv(U_2974,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2974),U_2975),U_2976),U_2975) = U_2976
      | U_2975 = c_Groups_Ozero__class_Ozero(U_2974)
      | ~ class_Divides_Osemiring__div(U_2974) ),
    inference(variable_rename,[status(thm)],[f_952_1]) ).

fof(f_952_3,plain,
    ! [U_2975,U_2974,U_2976] :
      ( c_Divides_Odiv__class_Odiv(U_2974,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2974),U_2975),U_2976),U_2975) = U_2976
      | U_2975 = c_Groups_Ozero__class_Ozero(U_2974)
      | ~ class_Divides_Osemiring__div(U_2974) ),
    inference(definitional_conversion,[status(esa)],[f_952_2]) ).

cnf(f_952_4,plain,
    ( c_Divides_Odiv__class_Odiv(U_2974,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2974),U_2975),U_2976),U_2975) = U_2976
    | U_2975 = c_Groups_Ozero__class_Ozero(U_2974)
    | ~ class_Divides_Osemiring__div(U_2974) ),
    inference(clausify,[status(thm)],[f_952_3]) ).

fof(f_953_1,plain,
    ! [V_a,V_b,T_a] :
      ( c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b) = V_a
      | V_b = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__mult__self2__is__id]) ).

fof(f_953_2,plain,
    ! [U_2979,U_2978,U_2977] :
      ( c_Divides_Odiv__class_Odiv(U_2977,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2977),U_2979),U_2978),U_2978) = U_2979
      | U_2978 = c_Groups_Ozero__class_Ozero(U_2977)
      | ~ class_Divides_Osemiring__div(U_2977) ),
    inference(variable_rename,[status(thm)],[f_953_1]) ).

fof(f_953_3,plain,
    ! [U_2978,U_2977,U_2979] :
      ( c_Divides_Odiv__class_Odiv(U_2977,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2977),U_2979),U_2978),U_2978) = U_2979
      | U_2978 = c_Groups_Ozero__class_Ozero(U_2977)
      | ~ class_Divides_Osemiring__div(U_2977) ),
    inference(definitional_conversion,[status(esa)],[f_953_2]) ).

cnf(f_953_4,plain,
    ( c_Divides_Odiv__class_Odiv(U_2977,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2977),U_2979),U_2978),U_2978) = U_2979
    | U_2978 = c_Groups_Ozero__class_Ozero(U_2977)
    | ~ class_Divides_Osemiring__div(U_2977) ),
    inference(clausify,[status(thm)],[f_953_3]) ).

fof(f_954_1,plain,
    ! [V_b,V_a,V_c,T_a] :
      ( ( ( c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(T_a,V_a,V_b)
          | V_c = c_Groups_Ozero__class_Ozero(T_a) )
        & ( c_Divides_Odiv__class_Odiv(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_Groups_Ozero__class_Ozero(T_a)
          | V_c != c_Groups_Ozero__class_Ozero(T_a) ) )
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__mult__mult1__if]) ).

fof(f_954_2,plain,
    ! [U_2983,U_2982,U_2981,U_2980] :
      ( ( ( c_Divides_Odiv__class_Odiv(U_2980,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2980),U_2981),U_2982),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2980),U_2981),U_2983)) = c_Divides_Odiv__class_Odiv(U_2980,U_2982,U_2983)
          | U_2981 = c_Groups_Ozero__class_Ozero(U_2980) )
        & ( c_Divides_Odiv__class_Odiv(U_2980,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2980),U_2981),U_2982),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2980),U_2981),U_2983)) = c_Groups_Ozero__class_Ozero(U_2980)
          | U_2981 != c_Groups_Ozero__class_Ozero(U_2980) ) )
      | ~ class_Divides_Osemiring__div(U_2980) ),
    inference(variable_rename,[status(thm)],[f_954_1]) ).

fof(f_954_3,plain,
    ( ! [U_2981,U_2982,U_2980,U_2983] :
        ( c_Divides_Odiv__class_Odiv(U_2980,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2980),U_2981),U_2982),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2980),U_2981),U_2983)) = c_Divides_Odiv__class_Odiv(U_2980,U_2982,U_2983)
        | U_2981 = c_Groups_Ozero__class_Ozero(U_2980)
        | ~ sP258(U_2981,U_2982,U_2980,U_2983) )
    & ! [U_2981,U_2982,U_2980,U_2983] :
        ( c_Divides_Odiv__class_Odiv(U_2980,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2980),U_2981),U_2982),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2980),U_2981),U_2983)) = c_Groups_Ozero__class_Ozero(U_2980)
        | U_2981 != c_Groups_Ozero__class_Ozero(U_2980)
        | ~ sP258(U_2981,U_2982,U_2980,U_2983) )
    & ! [U_2981,U_2982,U_2980,U_2983] :
        ( sP258(U_2981,U_2982,U_2980,U_2983)
        | ~ class_Divides_Osemiring__div(U_2980) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP258])],[f_954_2]) ).

cnf(f_954_4,plain,
    ( sP258(U_2981,U_2982,U_2980,U_2983)
    | ~ class_Divides_Osemiring__div(U_2980) ),
    inference(clausify,[status(thm)],[f_954_3]) ).

cnf(f_954_5,plain,
    ( c_Divides_Odiv__class_Odiv(U_2980,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2980),U_2981),U_2982),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2980),U_2981),U_2983)) = c_Groups_Ozero__class_Ozero(U_2980)
    | U_2981 != c_Groups_Ozero__class_Ozero(U_2980)
    | ~ sP258(U_2981,U_2982,U_2980,U_2983) ),
    inference(clausify,[status(thm)],[f_954_3]) ).

cnf(f_954_6,plain,
    ( c_Divides_Odiv__class_Odiv(U_2980,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2980),U_2981),U_2982),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2980),U_2981),U_2983)) = c_Divides_Odiv__class_Odiv(U_2980,U_2982,U_2983)
    | U_2981 = c_Groups_Ozero__class_Ozero(U_2980)
    | ~ sP258(U_2981,U_2982,U_2980,U_2983) ),
    inference(clausify,[status(thm)],[f_954_3]) ).

fof(f_955_1,plain,
    ! [V_a] :
      ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(fof_nnf,[status(thm)],[fact_zdiv__self]) ).

fof(f_955_2,plain,
    ! [U_2984] :
      ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2984,U_2984) = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | U_2984 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_955_1]) ).

fof(f_955_3,plain,
    ! [U_2984] :
      ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2984,U_2984) = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | U_2984 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(definitional_conversion,[status(esa)],[f_955_2]) ).

cnf(f_955_4,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2984,U_2984) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | U_2984 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_955_3]) ).

fof(f_956_1,plain,
    ! [V_a,T_a] :
      ( c_Divides_Odiv__class_Odiv(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a)
      | V_a = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__self]) ).

fof(f_956_2,plain,
    ! [U_2986,U_2985] :
      ( c_Divides_Odiv__class_Odiv(U_2985,U_2986,U_2986) = c_Groups_Oone__class_Oone(U_2985)
      | U_2986 = c_Groups_Ozero__class_Ozero(U_2985)
      | ~ class_Divides_Osemiring__div(U_2985) ),
    inference(variable_rename,[status(thm)],[f_956_1]) ).

fof(f_956_3,plain,
    ! [U_2985,U_2986] :
      ( c_Divides_Odiv__class_Odiv(U_2985,U_2986,U_2986) = c_Groups_Oone__class_Oone(U_2985)
      | U_2986 = c_Groups_Ozero__class_Ozero(U_2985)
      | ~ class_Divides_Osemiring__div(U_2985) ),
    inference(definitional_conversion,[status(esa)],[f_956_2]) ).

cnf(f_956_4,plain,
    ( c_Divides_Odiv__class_Odiv(U_2985,U_2986,U_2986) = c_Groups_Oone__class_Oone(U_2985)
    | U_2986 = c_Groups_Ozero__class_Ozero(U_2985)
    | ~ class_Divides_Osemiring__div(U_2985) ),
    inference(clausify,[status(thm)],[f_956_3]) ).

fof(f_957_1,plain,
    ! [V_b] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_zdiv__zero]) ).

fof(f_957_2,plain,
    ! [U_2987] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2987) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_957_1]) ).

fof(f_957_3,plain,
    ! [U_2987] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2987) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_957_2]) ).

cnf(f_957_4,plain,
    c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2987) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_957_3]) ).

fof(f_958_1,plain,
    ! [V_a,T_a] :
      ( c_Divides_Odiv__class_Odiv(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__0]) ).

fof(f_958_2,plain,
    ! [U_2989,U_2988] :
      ( c_Divides_Odiv__class_Odiv(U_2988,c_Groups_Ozero__class_Ozero(U_2988),U_2989) = c_Groups_Ozero__class_Ozero(U_2988)
      | ~ class_Divides_Osemiring__div(U_2988) ),
    inference(variable_rename,[status(thm)],[f_958_1]) ).

fof(f_958_3,plain,
    ! [U_2988,U_2989] :
      ( c_Divides_Odiv__class_Odiv(U_2988,c_Groups_Ozero__class_Ozero(U_2988),U_2989) = c_Groups_Ozero__class_Ozero(U_2988)
      | ~ class_Divides_Osemiring__div(U_2988) ),
    inference(definitional_conversion,[status(esa)],[f_958_2]) ).

cnf(f_958_4,plain,
    ( c_Divides_Odiv__class_Odiv(U_2988,c_Groups_Ozero__class_Ozero(U_2988),U_2989) = c_Groups_Ozero__class_Ozero(U_2988)
    | ~ class_Divides_Osemiring__div(U_2988) ),
    inference(clausify,[status(thm)],[f_958_3]) ).

fof(f_959_1,plain,
    ! [V_a,T_a] :
      ( c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__by__0]) ).

fof(f_959_2,plain,
    ! [U_2991,U_2990] :
      ( c_Divides_Odiv__class_Odiv(U_2990,U_2991,c_Groups_Ozero__class_Ozero(U_2990)) = c_Groups_Ozero__class_Ozero(U_2990)
      | ~ class_Divides_Osemiring__div(U_2990) ),
    inference(variable_rename,[status(thm)],[f_959_1]) ).

fof(f_959_3,plain,
    ! [U_2990,U_2991] :
      ( c_Divides_Odiv__class_Odiv(U_2990,U_2991,c_Groups_Ozero__class_Ozero(U_2990)) = c_Groups_Ozero__class_Ozero(U_2990)
      | ~ class_Divides_Osemiring__div(U_2990) ),
    inference(definitional_conversion,[status(esa)],[f_959_2]) ).

cnf(f_959_4,plain,
    ( c_Divides_Odiv__class_Odiv(U_2990,U_2991,c_Groups_Ozero__class_Ozero(U_2990)) = c_Groups_Ozero__class_Ozero(U_2990)
    | ~ class_Divides_Osemiring__div(U_2990) ),
    inference(clausify,[status(thm)],[f_959_3]) ).

fof(f_960_1,plain,
    ! [V_y,V_x] :
      ( 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_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_Divides_Otransfer__nat__int__function__closures_I1_J]) ).

fof(f_960_2,plain,
    ! [U_2993,U_2992] :
      ( 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_2992,U_2993))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2993)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2992) ),
    inference(variable_rename,[status(thm)],[f_960_1]) ).

fof(f_960_3,plain,
    ! [U_2993,U_2992] :
      ( 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_2992,U_2993))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2993)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2992) ),
    inference(definitional_conversion,[status(esa)],[f_960_2]) ).

cnf(f_960_4,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_2992,U_2993))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2993)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2992) ),
    inference(clausify,[status(thm)],[f_960_3]) ).

fof(f_961_1,plain,
    ! [V_a_2,V_b_2] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
          | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
        & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
          | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),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_2) ),
    inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__neg__iff]) ).

fof(f_961_2,plain,
    ! [U_2995,U_2994] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2995,U_2994),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
          | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2995,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
        & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2995,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
          | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2995,U_2994),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_2994) ),
    inference(variable_rename,[status(thm)],[f_961_1]) ).

fof(f_961_3,plain,
    ( ! [U_2995,U_2994] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2995,U_2994),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2995,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ sP259(U_2995,U_2994) )
    & ! [U_2995,U_2994] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2995,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2995,U_2994),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ sP259(U_2995,U_2994) )
    & ! [U_2995,U_2994] :
        ( sP259(U_2995,U_2994)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2994) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP259])],[f_961_2]) ).

cnf(f_961_4,plain,
    ( sP259(U_2995,U_2994)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2994) ),
    inference(clausify,[status(thm)],[f_961_3]) ).

cnf(f_961_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2995,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2995,U_2994),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ sP259(U_2995,U_2994) ),
    inference(clausify,[status(thm)],[f_961_3]) ).

cnf(f_961_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2995,U_2994),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2995,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ sP259(U_2995,U_2994) ),
    inference(clausify,[status(thm)],[f_961_3]) ).

fof(f_962_1,plain,
    ! [V_a_2,V_b_2] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),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_a_2) )
        & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2)
          | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) )
      | ~ 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__neg__iff]) ).

fof(f_962_2,plain,
    ! [U_2997,U_2996] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2997,U_2996),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_2997) )
        & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2997)
          | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2997,U_2996),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2996,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(variable_rename,[status(thm)],[f_962_1]) ).

fof(f_962_3,plain,
    ( ! [U_2996,U_2997] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2997,U_2996),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_2997)
        | ~ sP260(U_2996,U_2997) )
    & ! [U_2996,U_2997] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2997)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2997,U_2996),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ sP260(U_2996,U_2997) )
    & ! [U_2996,U_2997] :
        ( sP260(U_2996,U_2997)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2996,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP260])],[f_962_2]) ).

cnf(f_962_4,plain,
    ( sP260(U_2996,U_2997)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2996,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(clausify,[status(thm)],[f_962_3]) ).

cnf(f_962_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2997)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2997,U_2996),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ sP260(U_2996,U_2997) ),
    inference(clausify,[status(thm)],[f_962_3]) ).

cnf(f_962_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2997,U_2996),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_2997)
    | ~ sP260(U_2996,U_2997) ),
    inference(clausify,[status(thm)],[f_962_3]) ).

fof(f_963_1,plain,
    ! [V_b,V_a] :
      ( c_Orderings_Oord__class_Oless(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(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(fof_nnf,[status(thm)],[fact_div__neg__pos__less0]) ).

fof(f_963_2,plain,
    ! [U_2999,U_2998] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2998,U_2999),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_2999)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2998,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(variable_rename,[status(thm)],[f_963_1]) ).

fof(f_963_3,plain,
    ! [U_2998,U_2999] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2998,U_2999),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_2999)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2998,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(definitional_conversion,[status(esa)],[f_963_2]) ).

cnf(f_963_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2998,U_2999),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_2999)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2998,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(clausify,[status(thm)],[f_963_3]) ).

fof(f_964_1,plain,
    ! [V_a,T_a] :
      ( c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__by__1]) ).

fof(f_964_2,plain,
    ! [U_3001,U_3000] :
      ( c_Divides_Odiv__class_Odiv(U_3000,U_3001,c_Groups_Oone__class_Oone(U_3000)) = U_3001
      | ~ class_Divides_Osemiring__div(U_3000) ),
    inference(variable_rename,[status(thm)],[f_964_1]) ).

fof(f_964_3,plain,
    ! [U_3000,U_3001] :
      ( c_Divides_Odiv__class_Odiv(U_3000,U_3001,c_Groups_Oone__class_Oone(U_3000)) = U_3001
      | ~ class_Divides_Osemiring__div(U_3000) ),
    inference(definitional_conversion,[status(esa)],[f_964_2]) ).

cnf(f_964_4,plain,
    ( c_Divides_Odiv__class_Odiv(U_3000,U_3001,c_Groups_Oone__class_Oone(U_3000)) = U_3001
    | ~ class_Divides_Osemiring__div(U_3000) ),
    inference(clausify,[status(thm)],[f_964_3]) ).

fof(f_965_1,plain,
    ! [V_r_1,V_y,V_b_1,V_a_1] :
      ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_1,V_b_1) = V_y
      | V_b_1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r_1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
          | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_1,V_r_1) )
        & ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1) )
      | ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_1,V_b_1)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_1) )
        & c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1) )
      | V_a_1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y),V_r_1) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__div__eq]) ).

fof(f_965_2,plain,
    ! [U_3005,U_3004,U_3003,U_3002] :
      ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3002,U_3003) = U_3004
      | U_3003 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3005,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
          | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3003,U_3005) )
        & ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3003) )
      | ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3005,U_3003)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3005) )
        & c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3003) )
      | U_3002 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3003),U_3004),U_3005) ),
    inference(variable_rename,[status(thm)],[f_965_1]) ).

fof(f_965_3,plain,
    ( ! [U_3003,U_3005] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3005,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3003,U_3005)
        | ~ sP262(U_3003,U_3005) )
    & ! [U_3003,U_3005] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3003)
        | ~ sP262(U_3003,U_3005) )
    & ! [U_3003,U_3005] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3005,U_3003)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3005)
        | ~ sP261(U_3003,U_3005) )
    & ! [U_3003,U_3005] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3003)
        | ~ sP261(U_3003,U_3005) )
    & ! [U_3004,U_3002,U_3003,U_3005] :
        ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3002,U_3003) = U_3004
        | U_3003 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | sP262(U_3003,U_3005)
        | sP261(U_3003,U_3005)
        | U_3002 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3003),U_3004),U_3005) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP261,sP262])],[f_965_2]) ).

cnf(f_965_4,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3002,U_3003) = U_3004
    | U_3003 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | sP262(U_3003,U_3005)
    | sP261(U_3003,U_3005)
    | U_3002 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3003),U_3004),U_3005) ),
    inference(clausify,[status(thm)],[f_965_3]) ).

cnf(f_965_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3003)
    | ~ sP261(U_3003,U_3005) ),
    inference(clausify,[status(thm)],[f_965_3]) ).

cnf(f_965_6,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3005,U_3003)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3005)
    | ~ sP261(U_3003,U_3005) ),
    inference(clausify,[status(thm)],[f_965_3]) ).

cnf(f_965_7,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3003)
    | ~ sP262(U_3003,U_3005) ),
    inference(clausify,[status(thm)],[f_965_3]) ).

cnf(f_965_8,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3005,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3003,U_3005)
    | ~ sP262(U_3003,U_3005) ),
    inference(clausify,[status(thm)],[f_965_3]) ).

fof(f_966_1,plain,
    ! [V_k_2,V_n_2,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))
        | ( ? [B_i] :
              ( ~ hBOOL(hAPP(V_P_2,B_i))
              & ? [B_j] :
                  ( V_n_2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i),B_j)
                  & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B_j,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
                  & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,B_j) ) )
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
        | ( ? [B_i] :
              ( ~ hBOOL(hAPP(V_P_2,B_i))
              & ? [B_j] :
                  ( V_n_2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i),B_j)
                  & c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j,V_k_2)
                  & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B_j) ) )
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2) )
        | ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( ( ( ! [B_i] :
                ( hBOOL(hAPP(V_P_2,B_i))
                | ! [B_j] :
                    ( V_n_2 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i),B_j)
                    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B_j,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
                    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,B_j) ) )
            | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
          & ( ! [B_i] :
                ( hBOOL(hAPP(V_P_2,B_i))
                | ! [B_j] :
                    ( V_n_2 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i),B_j)
                    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j,V_k_2)
                    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B_j) ) )
            | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2) )
          & ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_split__zdiv]) ).

fof(f_966_2,plain,
    ! [U_3016,U_3015,U_3014] :
      ( ( hBOOL(hAPP(U_3014,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3015,U_3016)))
        | ( ? [U_3013] :
              ( ~ hBOOL(hAPP(U_3014,U_3013))
              & ? [U_3012] :
                  ( U_3015 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3016),U_3013),U_3012)
                  & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3012,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
                  & c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3016,U_3012) ) )
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3016,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
        | ( ? [U_3011] :
              ( ~ hBOOL(hAPP(U_3014,U_3011))
              & ? [U_3010] :
                  ( U_3015 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3016),U_3011),U_3010)
                  & c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3010,U_3016)
                  & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3010) ) )
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3016) )
        | ( ~ hBOOL(hAPP(U_3014,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_3016 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( ( ( ! [U_3009] :
                ( hBOOL(hAPP(U_3014,U_3009))
                | ! [U_3008] :
                    ( U_3015 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3016),U_3009),U_3008)
                    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3008,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
                    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3016,U_3008) ) )
            | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3016,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
          & ( ! [U_3007] :
                ( hBOOL(hAPP(U_3014,U_3007))
                | ! [U_3006] :
                    ( U_3015 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3016),U_3007),U_3006)
                    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3006,U_3016)
                    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3006) ) )
            | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3016) )
          & ( hBOOL(hAPP(U_3014,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_3016 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3014,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3015,U_3016))) ) ),
    inference(variable_rename,[status(thm)],[f_966_1]) ).

fof(f_966_3,plain,
    ( ! [U_3022,U_3020,U_3018] :
        ( hBOOL(hAPP(U_3018,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3020,U_3022)))
        | ( ? [U_3013] :
              ( ~ hBOOL(hAPP(U_3018,U_3013))
              & ? [U_3012] :
                  ( U_3020 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3022),U_3013),U_3012)
                  & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3012,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
                  & c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3022,U_3012) ) )
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3022,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
        | ( ? [U_3011] :
              ( ~ hBOOL(hAPP(U_3018,U_3011))
              & ? [U_3010] :
                  ( U_3020 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3022),U_3011),U_3010)
                  & c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3010,U_3022)
                  & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3010) ) )
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3022) )
        | ( ~ hBOOL(hAPP(U_3018,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_3022 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_3021,U_3019,U_3017] :
        ( ( ( ! [U_3009] :
                ( hBOOL(hAPP(U_3017,U_3009))
                | ! [U_3008] :
                    ( U_3019 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3021),U_3009),U_3008)
                    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3008,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
                    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3021,U_3008) ) )
            | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3021,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
          & ( ! [U_3007] :
                ( hBOOL(hAPP(U_3017,U_3007))
                | ! [U_3006] :
                    ( U_3019 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3021),U_3007),U_3006)
                    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3006,U_3021)
                    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3006) ) )
            | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3021) )
          & ( hBOOL(hAPP(U_3017,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_3021 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3017,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3019,U_3021))) ) ),
    inference(miniscope,[status(thm)],[f_966_2]) ).

fof(f_966_4,plain,
    ( ! [U_3022,U_3020,U_3018] :
        ( hBOOL(hAPP(U_3018,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3020,U_3022)))
        | ( ? [U_3013] :
              ( ~ hBOOL(hAPP(U_3018,U_3013))
              & ? [U_3012] :
                  ( U_3020 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3022),U_3013),U_3012)
                  & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3012,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
                  & c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3022,U_3012) ) )
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3022,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
        | ( ~ hBOOL(hAPP(U_3018,sK72(U_3022,U_3020,U_3018)))
          & ? [U_3010] :
              ( U_3020 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3022),sK72(U_3022,U_3020,U_3018)),U_3010)
              & c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3010,U_3022)
              & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3010) )
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3022) )
        | ( ~ hBOOL(hAPP(U_3018,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_3022 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_3021,U_3019,U_3017] :
        ( ( ( ! [U_3009] :
                ( hBOOL(hAPP(U_3017,U_3009))
                | ! [U_3008] :
                    ( U_3019 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3021),U_3009),U_3008)
                    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3008,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
                    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3021,U_3008) ) )
            | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3021,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
          & ( ! [U_3007] :
                ( hBOOL(hAPP(U_3017,U_3007))
                | ! [U_3006] :
                    ( U_3019 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3021),U_3007),U_3006)
                    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3006,U_3021)
                    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3006) ) )
            | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3021) )
          & ( hBOOL(hAPP(U_3017,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_3021 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3017,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3019,U_3021))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_3011,sK72(U_3022,U_3020,U_3018))],[f_966_3]) ).

fof(f_966_5,plain,
    ( ! [U_3022,U_3020,U_3018] :
        ( hBOOL(hAPP(U_3018,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3020,U_3022)))
        | ( ? [U_3013] :
              ( ~ hBOOL(hAPP(U_3018,U_3013))
              & ? [U_3012] :
                  ( U_3020 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3022),U_3013),U_3012)
                  & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3012,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
                  & c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3022,U_3012) ) )
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3022,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
        | ( ~ hBOOL(hAPP(U_3018,sK72(U_3022,U_3020,U_3018)))
          & U_3020 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3022),sK72(U_3022,U_3020,U_3018)),sK73(U_3022,U_3020,U_3018))
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,sK73(U_3022,U_3020,U_3018),U_3022)
          & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK73(U_3022,U_3020,U_3018))
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3022) )
        | ( ~ hBOOL(hAPP(U_3018,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_3022 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_3021,U_3019,U_3017] :
        ( ( ( ! [U_3009] :
                ( hBOOL(hAPP(U_3017,U_3009))
                | ! [U_3008] :
                    ( U_3019 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3021),U_3009),U_3008)
                    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3008,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
                    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3021,U_3008) ) )
            | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3021,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
          & ( ! [U_3007] :
                ( hBOOL(hAPP(U_3017,U_3007))
                | ! [U_3006] :
                    ( U_3019 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3021),U_3007),U_3006)
                    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3006,U_3021)
                    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3006) ) )
            | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3021) )
          & ( hBOOL(hAPP(U_3017,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_3021 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3017,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3019,U_3021))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_3010,sK73(U_3022,U_3020,U_3018))],[f_966_4]) ).

fof(f_966_6,plain,
    ( ! [U_3022,U_3020,U_3018] :
        ( hBOOL(hAPP(U_3018,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3020,U_3022)))
        | ( ~ hBOOL(hAPP(U_3018,sK74(U_3022,U_3020,U_3018)))
          & ? [U_3012] :
              ( U_3020 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3022),sK74(U_3022,U_3020,U_3018)),U_3012)
              & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3012,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
              & c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3022,U_3012) )
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3022,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
        | ( ~ hBOOL(hAPP(U_3018,sK72(U_3022,U_3020,U_3018)))
          & U_3020 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3022),sK72(U_3022,U_3020,U_3018)),sK73(U_3022,U_3020,U_3018))
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,sK73(U_3022,U_3020,U_3018),U_3022)
          & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK73(U_3022,U_3020,U_3018))
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3022) )
        | ( ~ hBOOL(hAPP(U_3018,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_3022 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_3021,U_3019,U_3017] :
        ( ( ( ! [U_3009] :
                ( hBOOL(hAPP(U_3017,U_3009))
                | ! [U_3008] :
                    ( U_3019 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3021),U_3009),U_3008)
                    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3008,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
                    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3021,U_3008) ) )
            | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3021,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
          & ( ! [U_3007] :
                ( hBOOL(hAPP(U_3017,U_3007))
                | ! [U_3006] :
                    ( U_3019 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3021),U_3007),U_3006)
                    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3006,U_3021)
                    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3006) ) )
            | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3021) )
          & ( hBOOL(hAPP(U_3017,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_3021 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3017,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3019,U_3021))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_3013,sK74(U_3022,U_3020,U_3018))],[f_966_5]) ).

fof(f_966_7,plain,
    ( ! [U_3022,U_3020,U_3018] :
        ( hBOOL(hAPP(U_3018,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3020,U_3022)))
        | ( ~ hBOOL(hAPP(U_3018,sK74(U_3022,U_3020,U_3018)))
          & U_3020 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3022),sK74(U_3022,U_3020,U_3018)),sK75(U_3022,U_3020,U_3018))
          & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK75(U_3022,U_3020,U_3018),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3022,sK75(U_3022,U_3020,U_3018))
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3022,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
        | ( ~ hBOOL(hAPP(U_3018,sK72(U_3022,U_3020,U_3018)))
          & U_3020 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3022),sK72(U_3022,U_3020,U_3018)),sK73(U_3022,U_3020,U_3018))
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,sK73(U_3022,U_3020,U_3018),U_3022)
          & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK73(U_3022,U_3020,U_3018))
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3022) )
        | ( ~ hBOOL(hAPP(U_3018,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_3022 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_3021,U_3019,U_3017] :
        ( ( ( ! [U_3009] :
                ( hBOOL(hAPP(U_3017,U_3009))
                | ! [U_3008] :
                    ( U_3019 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3021),U_3009),U_3008)
                    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3008,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
                    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3021,U_3008) ) )
            | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3021,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
          & ( ! [U_3007] :
                ( hBOOL(hAPP(U_3017,U_3007))
                | ! [U_3006] :
                    ( U_3019 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3021),U_3007),U_3006)
                    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3006,U_3021)
                    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3006) ) )
            | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3021) )
          & ( hBOOL(hAPP(U_3017,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_3021 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3017,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3019,U_3021))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_3012,sK75(U_3022,U_3020,U_3018))],[f_966_6]) ).

fof(f_966_8,plain,
    ( ! [U_3022,U_3018,U_3020] :
        ( ~ hBOOL(hAPP(U_3018,sK74(U_3022,U_3020,U_3018)))
        | ~ sP266(U_3022,U_3018,U_3020) )
    & ! [U_3022,U_3018,U_3020] :
        ( U_3020 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3022),sK74(U_3022,U_3020,U_3018)),sK75(U_3022,U_3020,U_3018))
        | ~ sP266(U_3022,U_3018,U_3020) )
    & ! [U_3022,U_3018,U_3020] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK75(U_3022,U_3020,U_3018),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ sP266(U_3022,U_3018,U_3020) )
    & ! [U_3022,U_3018,U_3020] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3022,sK75(U_3022,U_3020,U_3018))
        | ~ sP266(U_3022,U_3018,U_3020) )
    & ! [U_3022,U_3018,U_3020] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3022,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ sP266(U_3022,U_3018,U_3020) )
    & ! [U_3022,U_3018,U_3020] :
        ( ~ hBOOL(hAPP(U_3018,sK72(U_3022,U_3020,U_3018)))
        | ~ sP265(U_3022,U_3018,U_3020) )
    & ! [U_3022,U_3018,U_3020] :
        ( U_3020 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3022),sK72(U_3022,U_3020,U_3018)),sK73(U_3022,U_3020,U_3018))
        | ~ sP265(U_3022,U_3018,U_3020) )
    & ! [U_3022,U_3018,U_3020] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,sK73(U_3022,U_3020,U_3018),U_3022)
        | ~ sP265(U_3022,U_3018,U_3020) )
    & ! [U_3022,U_3018,U_3020] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK73(U_3022,U_3020,U_3018))
        | ~ sP265(U_3022,U_3018,U_3020) )
    & ! [U_3022,U_3018,U_3020] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3022)
        | ~ sP265(U_3022,U_3018,U_3020) )
    & ! [U_3022,U_3018] :
        ( ~ hBOOL(hAPP(U_3018,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP264(U_3022,U_3018) )
    & ! [U_3022,U_3018] :
        ( U_3022 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP264(U_3022,U_3018) )
    & ! [U_3006,U_3008,U_3007,U_3009,U_3017,U_3021,U_3019] :
        ( hBOOL(hAPP(U_3017,U_3009))
        | U_3019 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3021),U_3009),U_3008)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3008,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3021,U_3008)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3021,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ sP263(U_3006,U_3008,U_3007,U_3009,U_3017,U_3021,U_3019) )
    & ! [U_3006,U_3008,U_3007,U_3009,U_3017,U_3021,U_3019] :
        ( hBOOL(hAPP(U_3017,U_3007))
        | U_3019 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3021),U_3007),U_3006)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3006,U_3021)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3006)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3021)
        | ~ sP263(U_3006,U_3008,U_3007,U_3009,U_3017,U_3021,U_3019) )
    & ! [U_3006,U_3008,U_3007,U_3009,U_3017,U_3021,U_3019] :
        ( hBOOL(hAPP(U_3017,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | U_3021 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP263(U_3006,U_3008,U_3007,U_3009,U_3017,U_3021,U_3019) )
    & ! [U_3022,U_3018,U_3020] :
        ( hBOOL(hAPP(U_3018,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3020,U_3022)))
        | sP266(U_3022,U_3018,U_3020)
        | sP265(U_3022,U_3018,U_3020)
        | sP264(U_3022,U_3018) )
    & ! [U_3006,U_3008,U_3007,U_3009,U_3017,U_3021,U_3019] :
        ( sP263(U_3006,U_3008,U_3007,U_3009,U_3017,U_3021,U_3019)
        | ~ hBOOL(hAPP(U_3017,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3019,U_3021))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP263,sP264,sP265,sP266])],[f_966_7]) ).

cnf(f_966_9,plain,
    ( sP263(U_3006,U_3008,U_3007,U_3009,U_3017,U_3021,U_3019)
    | ~ hBOOL(hAPP(U_3017,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3019,U_3021))) ),
    inference(clausify,[status(thm)],[f_966_8]) ).

cnf(f_966_10,plain,
    ( hBOOL(hAPP(U_3018,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3020,U_3022)))
    | sP266(U_3022,U_3018,U_3020)
    | sP265(U_3022,U_3018,U_3020)
    | sP264(U_3022,U_3018) ),
    inference(clausify,[status(thm)],[f_966_8]) ).

cnf(f_966_11,plain,
    ( hBOOL(hAPP(U_3017,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_3021 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP263(U_3006,U_3008,U_3007,U_3009,U_3017,U_3021,U_3019) ),
    inference(clausify,[status(thm)],[f_966_8]) ).

cnf(f_966_12,plain,
    ( hBOOL(hAPP(U_3017,U_3007))
    | U_3019 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3021),U_3007),U_3006)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3006,U_3021)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3006)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3021)
    | ~ sP263(U_3006,U_3008,U_3007,U_3009,U_3017,U_3021,U_3019) ),
    inference(clausify,[status(thm)],[f_966_8]) ).

cnf(f_966_13,plain,
    ( hBOOL(hAPP(U_3017,U_3009))
    | U_3019 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3021),U_3009),U_3008)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3008,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3021,U_3008)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3021,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ sP263(U_3006,U_3008,U_3007,U_3009,U_3017,U_3021,U_3019) ),
    inference(clausify,[status(thm)],[f_966_8]) ).

cnf(f_966_14,plain,
    ( U_3022 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP264(U_3022,U_3018) ),
    inference(clausify,[status(thm)],[f_966_8]) ).

cnf(f_966_15,plain,
    ( ~ hBOOL(hAPP(U_3018,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP264(U_3022,U_3018) ),
    inference(clausify,[status(thm)],[f_966_8]) ).

cnf(f_966_16,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3022)
    | ~ sP265(U_3022,U_3018,U_3020) ),
    inference(clausify,[status(thm)],[f_966_8]) ).

cnf(f_966_17,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK73(U_3022,U_3020,U_3018))
    | ~ sP265(U_3022,U_3018,U_3020) ),
    inference(clausify,[status(thm)],[f_966_8]) ).

cnf(f_966_18,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,sK73(U_3022,U_3020,U_3018),U_3022)
    | ~ sP265(U_3022,U_3018,U_3020) ),
    inference(clausify,[status(thm)],[f_966_8]) ).

cnf(f_966_19,plain,
    ( U_3020 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3022),sK72(U_3022,U_3020,U_3018)),sK73(U_3022,U_3020,U_3018))
    | ~ sP265(U_3022,U_3018,U_3020) ),
    inference(clausify,[status(thm)],[f_966_8]) ).

cnf(f_966_20,plain,
    ( ~ hBOOL(hAPP(U_3018,sK72(U_3022,U_3020,U_3018)))
    | ~ sP265(U_3022,U_3018,U_3020) ),
    inference(clausify,[status(thm)],[f_966_8]) ).

cnf(f_966_21,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3022,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ sP266(U_3022,U_3018,U_3020) ),
    inference(clausify,[status(thm)],[f_966_8]) ).

cnf(f_966_22,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3022,sK75(U_3022,U_3020,U_3018))
    | ~ sP266(U_3022,U_3018,U_3020) ),
    inference(clausify,[status(thm)],[f_966_8]) ).

cnf(f_966_23,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK75(U_3022,U_3020,U_3018),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ sP266(U_3022,U_3018,U_3020) ),
    inference(clausify,[status(thm)],[f_966_8]) ).

cnf(f_966_24,plain,
    ( U_3020 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3022),sK74(U_3022,U_3020,U_3018)),sK75(U_3022,U_3020,U_3018))
    | ~ sP266(U_3022,U_3018,U_3020) ),
    inference(clausify,[status(thm)],[f_966_8]) ).

cnf(f_966_25,plain,
    ( ~ hBOOL(hAPP(U_3018,sK74(U_3022,U_3020,U_3018)))
    | ~ sP266(U_3022,U_3018,U_3020) ),
    inference(clausify,[status(thm)],[f_966_8]) ).

fof(f_967_1,plain,
    ! [V_n,V_a,V_r] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Orcis(V_r,V_a)),V_n) = c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_r),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)),V_a)),
    inference(fof_nnf,[status(thm)],[fact_DeMoivre2]) ).

fof(f_967_2,plain,
    ! [U_3025,U_3024,U_3023] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Orcis(U_3023,U_3024)),U_3025) = c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_3023),U_3025),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_3025)),U_3024)),
    inference(variable_rename,[status(thm)],[f_967_1]) ).

fof(f_967_3,plain,
    ! [U_3023,U_3024,U_3025] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Orcis(U_3023,U_3024)),U_3025) = c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_3023),U_3025),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_3025)),U_3024)),
    inference(definitional_conversion,[status(esa)],[f_967_2]) ).

cnf(f_967_4,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Orcis(U_3023,U_3024)),U_3025) = c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_3023),U_3025),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_3025)),U_3024)),
    inference(clausify,[status(thm)],[f_967_3]) ).

fof(f_968_1,plain,
    ! [V_a,V_n] :
      ( ? [B_x] :
          ( ! [B_y] :
              ( B_y = B_x
              | hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_y),V_n) != V_a
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_y) )
          & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_x),V_n) = V_a
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_x) )
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ),
    inference(fof_nnf,[status(thm)],[fact_realpow__pos__nth__unique]) ).

fof(f_968_2,plain,
    ! [U_3029,U_3028] :
      ( ? [U_3027] :
          ( ! [U_3026] :
              ( U_3026 = U_3027
              | hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_3026),U_3028) != U_3029
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3026) )
          & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_3027),U_3028) = U_3029
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3027) )
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3029)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3028) ),
    inference(variable_rename,[status(thm)],[f_968_1]) ).

fof(f_968_3,plain,
    ! [U_3029,U_3028] :
      ( ( ! [U_3026] :
            ( U_3026 = sK76(U_3029,U_3028)
            | hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_3026),U_3028) != U_3029
            | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3026) )
        & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sK76(U_3029,U_3028)),U_3028) = U_3029
        & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK76(U_3029,U_3028)) )
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3029)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3028) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_3027,sK76(U_3029,U_3028))],[f_968_2]) ).

fof(f_968_4,plain,
    ( ! [U_3028,U_3029,U_3026] :
        ( U_3026 = sK76(U_3029,U_3028)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_3026),U_3028) != U_3029
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3026)
        | ~ sP267(U_3028,U_3029,U_3026) )
    & ! [U_3028,U_3029,U_3026] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sK76(U_3029,U_3028)),U_3028) = U_3029
        | ~ sP267(U_3028,U_3029,U_3026) )
    & ! [U_3028,U_3029,U_3026] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK76(U_3029,U_3028))
        | ~ sP267(U_3028,U_3029,U_3026) )
    & ! [U_3028,U_3029,U_3026] :
        ( sP267(U_3028,U_3029,U_3026)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3029)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3028) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP267])],[f_968_3]) ).

cnf(f_968_5,plain,
    ( sP267(U_3028,U_3029,U_3026)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3029)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3028) ),
    inference(clausify,[status(thm)],[f_968_4]) ).

cnf(f_968_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK76(U_3029,U_3028))
    | ~ sP267(U_3028,U_3029,U_3026) ),
    inference(clausify,[status(thm)],[f_968_4]) ).

cnf(f_968_7,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sK76(U_3029,U_3028)),U_3028) = U_3029
    | ~ sP267(U_3028,U_3029,U_3026) ),
    inference(clausify,[status(thm)],[f_968_4]) ).

cnf(f_968_8,plain,
    ( U_3026 = sK76(U_3029,U_3028)
    | hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_3026),U_3028) != U_3029
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3026)
    | ~ sP267(U_3028,U_3029,U_3026) ),
    inference(clausify,[status(thm)],[f_968_4]) ).

fof(f_969_1,plain,
    ! [V_n,V_m,V_k] :
      ( ( c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)
        | V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Divides_Odiv__class_Odiv(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_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__div__cancel__disj]) ).

fof(f_969_2,plain,
    ! [U_3032,U_3031,U_3030] :
      ( ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3030),U_3031),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3030),U_3032)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3031,U_3032)
        | U_3030 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3030),U_3031),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3030),U_3032)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3030 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_969_1]) ).

fof(f_969_3,plain,
    ( ! [U_3038,U_3036,U_3034] :
        ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3034),U_3036),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3034),U_3038)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3036,U_3038)
        | U_3034 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_3037,U_3035,U_3033] :
        ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3033),U_3035),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3033),U_3037)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3033 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_969_2]) ).

fof(f_969_4,plain,
    ( ! [U_3038,U_3034,U_3036] :
        ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3034),U_3036),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3034),U_3038)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3036,U_3038)
        | U_3034 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_3037,U_3033,U_3035] :
        ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3033),U_3035),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3033),U_3037)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3033 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_969_3]) ).

cnf(f_969_5,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3033),U_3035),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3033),U_3037)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_3033 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_969_4]) ).

cnf(f_969_6,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3034),U_3036),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3034),U_3038)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3036,U_3038)
    | U_3034 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_969_4]) ).

fof(f_970_1,plain,
    ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,V_b),V_c),
    inference(fof_nnf,[status(thm)],[fact_div__mult2__eq]) ).

fof(f_970_2,plain,
    ! [U_3041,U_3040,U_3039] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3039,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3040),U_3041)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3039,U_3040),U_3041),
    inference(variable_rename,[status(thm)],[f_970_1]) ).

fof(f_970_3,plain,
    ! [U_3041,U_3039,U_3040] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3039,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3040),U_3041)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3039,U_3040),U_3041),
    inference(definitional_conversion,[status(esa)],[f_970_2]) ).

cnf(f_970_4,plain,
    c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3039,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3040),U_3041)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3039,U_3040),U_3041),
    inference(clausify,[status(thm)],[f_970_3]) ).

fof(f_971_1,plain,
    ! [V_n,V_m] :
      ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,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_div__less]) ).

fof(f_971_2,plain,
    ! [U_3043,U_3042] :
      ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3042,U_3043) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3042,U_3043) ),
    inference(variable_rename,[status(thm)],[f_971_1]) ).

fof(f_971_3,plain,
    ! [U_3042,U_3043] :
      ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3042,U_3043) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3042,U_3043) ),
    inference(definitional_conversion,[status(esa)],[f_971_2]) ).

cnf(f_971_4,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3042,U_3043) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3042,U_3043) ),
    inference(clausify,[status(thm)],[f_971_3]) ).

fof(f_972_1,plain,
    ! [V_m] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = V_m,
    inference(fof_nnf,[status(thm)],[fact_div__1]) ).

fof(f_972_2,plain,
    ! [U_3044] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3044,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = U_3044,
    inference(variable_rename,[status(thm)],[f_972_1]) ).

fof(f_972_3,plain,
    ! [U_3044] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3044,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = U_3044,
    inference(definitional_conversion,[status(esa)],[f_972_2]) ).

cnf(f_972_4,plain,
    c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3044,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = U_3044,
    inference(clausify,[status(thm)],[f_972_3]) ).

fof(f_973_1,plain,
    ! [V_n,V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n),V_m),
    inference(fof_nnf,[status(thm)],[fact_div__le__dividend]) ).

fof(f_973_2,plain,
    ! [U_3046,U_3045] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3045,U_3046),U_3045),
    inference(variable_rename,[status(thm)],[f_973_1]) ).

fof(f_973_3,plain,
    ! [U_3046,U_3045] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3045,U_3046),U_3045),
    inference(definitional_conversion,[status(esa)],[f_973_2]) ).

cnf(f_973_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3045,U_3046),U_3045),
    inference(clausify,[status(thm)],[f_973_3]) ).

fof(f_974_1,plain,
    ! [V_k,V_n,V_m] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_k),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_k))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
    inference(fof_nnf,[status(thm)],[fact_div__le__mono]) ).

fof(f_974_2,plain,
    ! [U_3049,U_3048,U_3047] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3047,U_3049),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3048,U_3049))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3047,U_3048) ),
    inference(variable_rename,[status(thm)],[f_974_1]) ).

fof(f_974_3,plain,
    ! [U_3048,U_3047,U_3049] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3047,U_3049),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3048,U_3049))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3047,U_3048) ),
    inference(definitional_conversion,[status(esa)],[f_974_2]) ).

cnf(f_974_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3047,U_3049),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3048,U_3049))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3047,U_3048) ),
    inference(clausify,[status(thm)],[f_974_3]) ).

fof(f_975_1,plain,
    ! [V_y,V_x] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_x,V_y)),
    inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__int__nat__functions_I1_J]) ).

fof(f_975_2,plain,
    ! [U_3051,U_3050] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3050),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3051)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3050,U_3051)),
    inference(variable_rename,[status(thm)],[f_975_1]) ).

fof(f_975_3,plain,
    ! [U_3050,U_3051] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3050),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3051)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3050,U_3051)),
    inference(definitional_conversion,[status(esa)],[f_975_2]) ).

cnf(f_975_4,plain,
    c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3050),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3051)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3050,U_3051)),
    inference(clausify,[status(thm)],[f_975_3]) ).

fof(f_976_1,plain,
    ! [V_b,V_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,V_b)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b)),
    inference(fof_nnf,[status(thm)],[fact_zdiv__int]) ).

fof(f_976_2,plain,
    ! [U_3053,U_3052] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3052,U_3053)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3052),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3053)),
    inference(variable_rename,[status(thm)],[f_976_1]) ).

fof(f_976_3,plain,
    ! [U_3052,U_3053] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3052,U_3053)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3052),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3053)),
    inference(definitional_conversion,[status(esa)],[f_976_2]) ).

cnf(f_976_4,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3052,U_3053)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3052),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3053)),
    inference(clausify,[status(thm)],[f_976_3]) ).

fof(f_977_1,plain,
    ! [V_m,V_n] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(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_Oone__class_Oone(tc_Nat_Onat),V_n) ),
    inference(fof_nnf,[status(thm)],[fact_div__less__dividend]) ).

fof(f_977_2,plain,
    ! [U_3055,U_3054] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3055,U_3054),U_3055)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3055)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_3054) ),
    inference(variable_rename,[status(thm)],[f_977_1]) ).

fof(f_977_3,plain,
    ! [U_3055,U_3054] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3055,U_3054),U_3055)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3055)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_3054) ),
    inference(definitional_conversion,[status(esa)],[f_977_2]) ).

cnf(f_977_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3055,U_3054),U_3055)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3055)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_3054) ),
    inference(clausify,[status(thm)],[f_977_3]) ).

fof(f_978_1,plain,
    ! [V_n,V_m,V_k] :
      ( c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(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) ),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__div__cancel1]) ).

fof(f_978_2,plain,
    ! [U_3058,U_3057,U_3056] :
      ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3056),U_3057),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3056),U_3058)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3057,U_3058)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3056) ),
    inference(variable_rename,[status(thm)],[f_978_1]) ).

fof(f_978_3,plain,
    ! [U_3057,U_3056,U_3058] :
      ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3056),U_3057),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3056),U_3058)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3057,U_3058)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3056) ),
    inference(definitional_conversion,[status(esa)],[f_978_2]) ).

cnf(f_978_4,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3056),U_3057),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3056),U_3058)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3057,U_3058)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3056) ),
    inference(clausify,[status(thm)],[f_978_3]) ).

fof(f_979_1,plain,
    ! [V_m,V_n] :
      ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n),V_n) = 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_div__mult__self__is__m]) ).

fof(f_979_2,plain,
    ! [U_3060,U_3059] :
      ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3060),U_3059),U_3059) = U_3060
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3059) ),
    inference(variable_rename,[status(thm)],[f_979_1]) ).

fof(f_979_3,plain,
    ! [U_3060,U_3059] :
      ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3060),U_3059),U_3059) = U_3060
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3059) ),
    inference(definitional_conversion,[status(esa)],[f_979_2]) ).

cnf(f_979_4,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3060),U_3059),U_3059) = U_3060
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3059) ),
    inference(clausify,[status(thm)],[f_979_3]) ).

fof(f_980_1,plain,
    ! [V_m,V_n] :
      ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m),V_n) = 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_div__mult__self1__is__m]) ).

fof(f_980_2,plain,
    ! [U_3062,U_3061] :
      ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3061),U_3062),U_3061) = U_3062
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3061) ),
    inference(variable_rename,[status(thm)],[f_980_1]) ).

fof(f_980_3,plain,
    ! [U_3061,U_3062] :
      ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3061),U_3062),U_3061) = U_3062
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3061) ),
    inference(definitional_conversion,[status(esa)],[f_980_2]) ).

cnf(f_980_4,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3061),U_3062),U_3061) = U_3062
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3061) ),
    inference(clausify,[status(thm)],[f_980_3]) ).

fof(f_981_1,plain,
    ! [V_k,V_n,V_m] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_n),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_m))
      | ~ c_Orderings_Oord__class_Oless__eq(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_div__le__mono2]) ).

fof(f_981_2,plain,
    ! [U_3065,U_3064,U_3063] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3065,U_3064),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3065,U_3063))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3063,U_3064)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3063) ),
    inference(variable_rename,[status(thm)],[f_981_1]) ).

fof(f_981_3,plain,
    ! [U_3064,U_3063,U_3065] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3065,U_3064),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3065,U_3063))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3063,U_3064)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3063) ),
    inference(definitional_conversion,[status(esa)],[f_981_2]) ).

cnf(f_981_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3065,U_3064),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3065,U_3063))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3063,U_3064)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3063) ),
    inference(clausify,[status(thm)],[f_981_3]) ).

fof(f_982_1,plain,
    ! [V_a,V_r] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(V_r,V_a)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r),
    inference(fof_nnf,[status(thm)],[fact_complex__mod__rcis]) ).

fof(f_982_2,plain,
    ! [U_3067,U_3066] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(U_3066,U_3067)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_3066),
    inference(variable_rename,[status(thm)],[f_982_1]) ).

fof(f_982_3,plain,
    ! [U_3067,U_3066] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(U_3066,U_3067)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_3066),
    inference(definitional_conversion,[status(esa)],[f_982_2]) ).

cnf(f_982_4,plain,
    c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(U_3066,U_3067)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_3066),
    inference(clausify,[status(thm)],[f_982_3]) ).

fof(f_983_1,plain,
    ! [V_a] : c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[fact_rcis__zero__mod]) ).

fof(f_983_2,plain,
    ! [U_3068] : c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3068) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(variable_rename,[status(thm)],[f_983_1]) ).

fof(f_983_3,plain,
    ! [U_3068] : c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3068) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_983_2]) ).

cnf(f_983_4,plain,
    c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3068) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_983_3]) ).

fof(f_984_1,plain,
    ! [V_a] : c_Complex_Ocis(V_a) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_a),
    inference(fof_nnf,[status(thm)],[fact_cis__rcis__eq]) ).

fof(f_984_2,plain,
    ! [U_3069] : c_Complex_Ocis(U_3069) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_3069),
    inference(variable_rename,[status(thm)],[f_984_1]) ).

fof(f_984_3,plain,
    ! [U_3069] : c_Complex_Ocis(U_3069) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_3069),
    inference(definitional_conversion,[status(esa)],[f_984_2]) ).

cnf(f_984_4,plain,
    c_Complex_Ocis(U_3069) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_3069),
    inference(clausify,[status(thm)],[f_984_3]) ).

fof(f_985_1,plain,
    ! [V_m,V_n] :
      ( ( ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n))
          | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) )
        & ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | ~ 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_n) ),
    inference(fof_nnf,[status(thm)],[fact_div__if]) ).

fof(f_985_2,plain,
    ! [U_3071,U_3070] :
      ( ( ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3071,U_3070) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3071,U_3070),U_3070))
          | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3071,U_3070) )
        & ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3071,U_3070) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3071,U_3070) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3070) ),
    inference(variable_rename,[status(thm)],[f_985_1]) ).

fof(f_985_3,plain,
    ( ! [U_3070,U_3071] :
        ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3071,U_3070) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3071,U_3070),U_3070))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3071,U_3070)
        | ~ sP268(U_3070,U_3071) )
    & ! [U_3070,U_3071] :
        ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3071,U_3070) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3071,U_3070)
        | ~ sP268(U_3070,U_3071) )
    & ! [U_3070,U_3071] :
        ( sP268(U_3070,U_3071)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3070) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP268])],[f_985_2]) ).

cnf(f_985_4,plain,
    ( sP268(U_3070,U_3071)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3070) ),
    inference(clausify,[status(thm)],[f_985_3]) ).

cnf(f_985_5,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3071,U_3070) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3071,U_3070)
    | ~ sP268(U_3070,U_3071) ),
    inference(clausify,[status(thm)],[f_985_3]) ).

cnf(f_985_6,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3071,U_3070) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3071,U_3070),U_3070))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3071,U_3070)
    | ~ sP268(U_3070,U_3071) ),
    inference(clausify,[status(thm)],[f_985_3]) ).

fof(f_986_1,plain,
    ! [V_m,V_n] :
      ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n))
      | 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_n) ),
    inference(fof_nnf,[status(thm)],[fact_div__geq]) ).

fof(f_986_2,plain,
    ! [U_3073,U_3072] :
      ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3073,U_3072) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3073,U_3072),U_3072))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3073,U_3072)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3072) ),
    inference(variable_rename,[status(thm)],[f_986_1]) ).

fof(f_986_3,plain,
    ! [U_3072,U_3073] :
      ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3073,U_3072) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3073,U_3072),U_3072))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3073,U_3072)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3072) ),
    inference(definitional_conversion,[status(esa)],[f_986_2]) ).

cnf(f_986_4,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3073,U_3072) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3073,U_3072),U_3072))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3073,U_3072)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3072) ),
    inference(clausify,[status(thm)],[f_986_3]) ).

fof(f_987_1,plain,
    ! [V_k_2,V_n_2,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n_2,V_k_2)))
        | ( ? [B_i,B_j] :
              ( ~ hBOOL(hAPP(V_P_2,B_i))
              & V_n_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i),B_j)
              & c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_k_2) )
          & V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( ( ( ! [B_i,B_j] :
                ( hBOOL(hAPP(V_P_2,B_i))
                | V_n_2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i),B_j)
                | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_k_2) )
            | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n_2,V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_split__div]) ).

fof(f_987_2,plain,
    ! [U_3080,U_3079,U_3078] :
      ( ( hBOOL(hAPP(U_3078,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3079,U_3080)))
        | ( ? [U_3077,U_3076] :
              ( ~ hBOOL(hAPP(U_3078,U_3077))
              & U_3079 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3080),U_3077),U_3076)
              & c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3076,U_3080) )
          & U_3080 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_3078,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_3080 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( ( ( ! [U_3075,U_3074] :
                ( hBOOL(hAPP(U_3078,U_3075))
                | U_3079 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3080),U_3075),U_3074)
                | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3074,U_3080) )
            | U_3080 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_3078,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_3080 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_3078,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3079,U_3080))) ) ),
    inference(variable_rename,[status(thm)],[f_987_1]) ).

fof(f_987_3,plain,
    ( ! [U_3086,U_3084,U_3082] :
        ( hBOOL(hAPP(U_3082,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3084,U_3086)))
        | ( ? [U_3077,U_3076] :
              ( ~ hBOOL(hAPP(U_3082,U_3077))
              & U_3084 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3086),U_3077),U_3076)
              & c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3076,U_3086) )
          & U_3086 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_3082,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_3086 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_3085,U_3083,U_3081] :
        ( ( ( ! [U_3075,U_3074] :
                ( hBOOL(hAPP(U_3081,U_3075))
                | U_3083 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3085),U_3075),U_3074)
                | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3074,U_3085) )
            | U_3085 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_3081,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_3085 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_3081,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3083,U_3085))) ) ),
    inference(miniscope,[status(thm)],[f_987_2]) ).

fof(f_987_4,plain,
    ( ! [U_3086,U_3084,U_3082] :
        ( hBOOL(hAPP(U_3082,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3084,U_3086)))
        | ( ? [U_3076] :
              ( ~ hBOOL(hAPP(U_3082,sK77(U_3086,U_3084,U_3082)))
              & U_3084 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3086),sK77(U_3086,U_3084,U_3082)),U_3076)
              & c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3076,U_3086) )
          & U_3086 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_3082,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_3086 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_3085,U_3083,U_3081] :
        ( ( ( ! [U_3075,U_3074] :
                ( hBOOL(hAPP(U_3081,U_3075))
                | U_3083 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3085),U_3075),U_3074)
                | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3074,U_3085) )
            | U_3085 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_3081,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_3085 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_3081,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3083,U_3085))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_3077,sK77(U_3086,U_3084,U_3082))],[f_987_3]) ).

fof(f_987_5,plain,
    ( ! [U_3086,U_3084,U_3082] :
        ( hBOOL(hAPP(U_3082,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3084,U_3086)))
        | ( ~ hBOOL(hAPP(U_3082,sK77(U_3086,U_3084,U_3082)))
          & U_3084 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3086),sK77(U_3086,U_3084,U_3082)),sK78(U_3086,U_3084,U_3082))
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK78(U_3086,U_3084,U_3082),U_3086)
          & U_3086 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_3082,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_3086 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_3085,U_3083,U_3081] :
        ( ( ( ! [U_3075,U_3074] :
                ( hBOOL(hAPP(U_3081,U_3075))
                | U_3083 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3085),U_3075),U_3074)
                | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3074,U_3085) )
            | U_3085 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_3081,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_3085 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_3081,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3083,U_3085))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_3076,sK78(U_3086,U_3084,U_3082))],[f_987_4]) ).

fof(f_987_6,plain,
    ( ! [U_3082,U_3084,U_3086] :
        ( ~ hBOOL(hAPP(U_3082,sK77(U_3086,U_3084,U_3082)))
        | ~ sP271(U_3082,U_3084,U_3086) )
    & ! [U_3082,U_3084,U_3086] :
        ( U_3084 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3086),sK77(U_3086,U_3084,U_3082)),sK78(U_3086,U_3084,U_3082))
        | ~ sP271(U_3082,U_3084,U_3086) )
    & ! [U_3082,U_3084,U_3086] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK78(U_3086,U_3084,U_3082),U_3086)
        | ~ sP271(U_3082,U_3084,U_3086) )
    & ! [U_3082,U_3084,U_3086] :
        ( U_3086 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP271(U_3082,U_3084,U_3086) )
    & ! [U_3082,U_3086] :
        ( ~ hBOOL(hAPP(U_3082,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ sP270(U_3082,U_3086) )
    & ! [U_3082,U_3086] :
        ( U_3086 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP270(U_3082,U_3086) )
    & ! [U_3074,U_3085,U_3075,U_3081,U_3083] :
        ( hBOOL(hAPP(U_3081,U_3075))
        | U_3083 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3085),U_3075),U_3074)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3074,U_3085)
        | U_3085 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP269(U_3074,U_3085,U_3075,U_3081,U_3083) )
    & ! [U_3074,U_3085,U_3075,U_3081,U_3083] :
        ( hBOOL(hAPP(U_3081,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | U_3085 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP269(U_3074,U_3085,U_3075,U_3081,U_3083) )
    & ! [U_3082,U_3084,U_3086] :
        ( hBOOL(hAPP(U_3082,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3084,U_3086)))
        | sP271(U_3082,U_3084,U_3086)
        | sP270(U_3082,U_3086) )
    & ! [U_3074,U_3085,U_3075,U_3081,U_3083] :
        ( sP269(U_3074,U_3085,U_3075,U_3081,U_3083)
        | ~ hBOOL(hAPP(U_3081,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3083,U_3085))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP269,sP270,sP271])],[f_987_5]) ).

cnf(f_987_7,plain,
    ( sP269(U_3074,U_3085,U_3075,U_3081,U_3083)
    | ~ hBOOL(hAPP(U_3081,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3083,U_3085))) ),
    inference(clausify,[status(thm)],[f_987_6]) ).

cnf(f_987_8,plain,
    ( hBOOL(hAPP(U_3082,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3084,U_3086)))
    | sP271(U_3082,U_3084,U_3086)
    | sP270(U_3082,U_3086) ),
    inference(clausify,[status(thm)],[f_987_6]) ).

cnf(f_987_9,plain,
    ( hBOOL(hAPP(U_3081,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | U_3085 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP269(U_3074,U_3085,U_3075,U_3081,U_3083) ),
    inference(clausify,[status(thm)],[f_987_6]) ).

cnf(f_987_10,plain,
    ( hBOOL(hAPP(U_3081,U_3075))
    | U_3083 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3085),U_3075),U_3074)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3074,U_3085)
    | U_3085 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP269(U_3074,U_3085,U_3075,U_3081,U_3083) ),
    inference(clausify,[status(thm)],[f_987_6]) ).

cnf(f_987_11,plain,
    ( U_3086 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP270(U_3082,U_3086) ),
    inference(clausify,[status(thm)],[f_987_6]) ).

cnf(f_987_12,plain,
    ( ~ hBOOL(hAPP(U_3082,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ sP270(U_3082,U_3086) ),
    inference(clausify,[status(thm)],[f_987_6]) ).

cnf(f_987_13,plain,
    ( U_3086 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP271(U_3082,U_3084,U_3086) ),
    inference(clausify,[status(thm)],[f_987_6]) ).

cnf(f_987_14,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK78(U_3086,U_3084,U_3082),U_3086)
    | ~ sP271(U_3082,U_3084,U_3086) ),
    inference(clausify,[status(thm)],[f_987_6]) ).

cnf(f_987_15,plain,
    ( U_3084 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3086),sK77(U_3086,U_3084,U_3082)),sK78(U_3086,U_3084,U_3082))
    | ~ sP271(U_3082,U_3084,U_3086) ),
    inference(clausify,[status(thm)],[f_987_6]) ).

cnf(f_987_16,plain,
    ( ~ hBOOL(hAPP(U_3082,sK77(U_3086,U_3084,U_3082)))
    | ~ sP271(U_3082,U_3084,U_3086) ),
    inference(clausify,[status(thm)],[f_987_6]) ).

fof(f_988_1,plain,
    ! [V_m_2,V_q_2,V_n_2] :
      ( ( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),c_Nat_OSuc(V_q_2)))
            & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_q_2),V_m_2) )
          | V_q_2 != c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2) )
        & ( V_q_2 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2)
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),c_Nat_OSuc(V_q_2)))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_q_2),V_m_2) ) )
      | ~ 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_split__div__lemma]) ).

fof(f_988_2,plain,
    ! [U_3089,U_3088,U_3087] :
      ( ( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3089,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3087),c_Nat_OSuc(U_3088)))
            & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3087),U_3088),U_3089) )
          | U_3088 != c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3089,U_3087) )
        & ( U_3088 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3089,U_3087)
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3089,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3087),c_Nat_OSuc(U_3088)))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3087),U_3088),U_3089) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3087) ),
    inference(variable_rename,[status(thm)],[f_988_1]) ).

fof(f_988_3,plain,
    ( ! [U_3089,U_3088,U_3087] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3089,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3087),c_Nat_OSuc(U_3088)))
        | ~ sP272(U_3089,U_3088,U_3087) )
    & ! [U_3089,U_3088,U_3087] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3087),U_3088),U_3089)
        | ~ sP272(U_3089,U_3088,U_3087) )
    & ! [U_3089,U_3088,U_3087] :
        ( sP272(U_3089,U_3088,U_3087)
        | U_3088 != c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3089,U_3087)
        | ~ sP273(U_3089,U_3088,U_3087) )
    & ! [U_3089,U_3088,U_3087] :
        ( U_3088 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3089,U_3087)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3089,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3087),c_Nat_OSuc(U_3088)))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3087),U_3088),U_3089)
        | ~ sP273(U_3089,U_3088,U_3087) )
    & ! [U_3089,U_3088,U_3087] :
        ( sP273(U_3089,U_3088,U_3087)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3087) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP272,sP273])],[f_988_2]) ).

cnf(f_988_4,plain,
    ( sP273(U_3089,U_3088,U_3087)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3087) ),
    inference(clausify,[status(thm)],[f_988_3]) ).

cnf(f_988_5,plain,
    ( U_3088 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3089,U_3087)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3089,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3087),c_Nat_OSuc(U_3088)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3087),U_3088),U_3089)
    | ~ sP273(U_3089,U_3088,U_3087) ),
    inference(clausify,[status(thm)],[f_988_3]) ).

cnf(f_988_6,plain,
    ( sP272(U_3089,U_3088,U_3087)
    | U_3088 != c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3089,U_3087)
    | ~ sP273(U_3089,U_3088,U_3087) ),
    inference(clausify,[status(thm)],[f_988_3]) ).

cnf(f_988_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3087),U_3088),U_3089)
    | ~ sP272(U_3089,U_3088,U_3087) ),
    inference(clausify,[status(thm)],[f_988_3]) ).

cnf(f_988_8,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3089,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3087),c_Nat_OSuc(U_3088)))
    | ~ sP272(U_3089,U_3088,U_3087) ),
    inference(clausify,[status(thm)],[f_988_3]) ).

fof(f_989_1,plain,
    ! [V_n_2,V_m_2,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2)))
        | ( ! [B_q] :
              ( ~ hBOOL(hAPP(V_P_2,B_q))
              | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),c_Nat_OSuc(B_q)))
              | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q),V_m_2) )
          & ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
      & ( ? [B_q] :
            ( hBOOL(hAPP(V_P_2,B_q))
            & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),c_Nat_OSuc(B_q)))
            & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q),V_m_2) )
        | ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ~ hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_split__div_H]) ).

fof(f_989_2,plain,
    ! [U_3094,U_3093,U_3092] :
      ( ( hBOOL(hAPP(U_3092,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3093,U_3094)))
        | ( ! [U_3091] :
              ( ~ hBOOL(hAPP(U_3092,U_3091))
              | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3093,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3094),c_Nat_OSuc(U_3091)))
              | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3094),U_3091),U_3093) )
          & ( ~ hBOOL(hAPP(U_3092,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_3094 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
      & ( ? [U_3090] :
            ( hBOOL(hAPP(U_3092,U_3090))
            & c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3093,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3094),c_Nat_OSuc(U_3090)))
            & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3094),U_3090),U_3093) )
        | ( hBOOL(hAPP(U_3092,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_3094 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ~ hBOOL(hAPP(U_3092,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3093,U_3094))) ) ),
    inference(variable_rename,[status(thm)],[f_989_1]) ).

fof(f_989_3,plain,
    ( ! [U_3100,U_3098,U_3096] :
        ( hBOOL(hAPP(U_3096,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3098,U_3100)))
        | ( ! [U_3091] :
              ( ~ hBOOL(hAPP(U_3096,U_3091))
              | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3098,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3100),c_Nat_OSuc(U_3091)))
              | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3100),U_3091),U_3098) )
          & ( ~ hBOOL(hAPP(U_3096,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_3100 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
    & ! [U_3099,U_3097,U_3095] :
        ( ? [U_3090] :
            ( hBOOL(hAPP(U_3095,U_3090))
            & c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3097,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3099),c_Nat_OSuc(U_3090)))
            & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3099),U_3090),U_3097) )
        | ( hBOOL(hAPP(U_3095,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_3099 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ~ hBOOL(hAPP(U_3095,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3097,U_3099))) ) ),
    inference(miniscope,[status(thm)],[f_989_2]) ).

fof(f_989_4,plain,
    ( ! [U_3100,U_3098,U_3096] :
        ( hBOOL(hAPP(U_3096,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3098,U_3100)))
        | ( ! [U_3091] :
              ( ~ hBOOL(hAPP(U_3096,U_3091))
              | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3098,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3100),c_Nat_OSuc(U_3091)))
              | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3100),U_3091),U_3098) )
          & ( ~ hBOOL(hAPP(U_3096,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_3100 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
    & ! [U_3099,U_3097,U_3095] :
        ( ( hBOOL(hAPP(U_3095,sK79(U_3099,U_3097,U_3095)))
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3097,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3099),c_Nat_OSuc(sK79(U_3099,U_3097,U_3095))))
          & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3099),sK79(U_3099,U_3097,U_3095)),U_3097) )
        | ( hBOOL(hAPP(U_3095,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_3099 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ~ hBOOL(hAPP(U_3095,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3097,U_3099))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_3090,sK79(U_3099,U_3097,U_3095))],[f_989_3]) ).

fof(f_989_5,plain,
    ( ! [U_3091,U_3098,U_3096,U_3100] :
        ( ~ hBOOL(hAPP(U_3096,U_3091))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3098,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3100),c_Nat_OSuc(U_3091)))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3100),U_3091),U_3098)
        | ~ sP276(U_3091,U_3098,U_3096,U_3100) )
    & ! [U_3091,U_3098,U_3096,U_3100] :
        ( ~ hBOOL(hAPP(U_3096,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | U_3100 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP276(U_3091,U_3098,U_3096,U_3100) )
    & ! [U_3095,U_3099,U_3097] :
        ( hBOOL(hAPP(U_3095,sK79(U_3099,U_3097,U_3095)))
        | ~ sP275(U_3095,U_3099,U_3097) )
    & ! [U_3095,U_3099,U_3097] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3097,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3099),c_Nat_OSuc(sK79(U_3099,U_3097,U_3095))))
        | ~ sP275(U_3095,U_3099,U_3097) )
    & ! [U_3095,U_3099,U_3097] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3099),sK79(U_3099,U_3097,U_3095)),U_3097)
        | ~ sP275(U_3095,U_3099,U_3097) )
    & ! [U_3095,U_3099] :
        ( hBOOL(hAPP(U_3095,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ sP274(U_3095,U_3099) )
    & ! [U_3095,U_3099] :
        ( U_3099 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP274(U_3095,U_3099) )
    & ! [U_3091,U_3098,U_3096,U_3100] :
        ( hBOOL(hAPP(U_3096,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3098,U_3100)))
        | sP276(U_3091,U_3098,U_3096,U_3100) )
    & ! [U_3095,U_3099,U_3097] :
        ( sP275(U_3095,U_3099,U_3097)
        | sP274(U_3095,U_3099)
        | ~ hBOOL(hAPP(U_3095,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3097,U_3099))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP274,sP275,sP276])],[f_989_4]) ).

cnf(f_989_6,plain,
    ( sP275(U_3095,U_3099,U_3097)
    | sP274(U_3095,U_3099)
    | ~ hBOOL(hAPP(U_3095,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3097,U_3099))) ),
    inference(clausify,[status(thm)],[f_989_5]) ).

cnf(f_989_7,plain,
    ( hBOOL(hAPP(U_3096,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3098,U_3100)))
    | sP276(U_3091,U_3098,U_3096,U_3100) ),
    inference(clausify,[status(thm)],[f_989_5]) ).

cnf(f_989_8,plain,
    ( U_3099 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP274(U_3095,U_3099) ),
    inference(clausify,[status(thm)],[f_989_5]) ).

cnf(f_989_9,plain,
    ( hBOOL(hAPP(U_3095,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ sP274(U_3095,U_3099) ),
    inference(clausify,[status(thm)],[f_989_5]) ).

cnf(f_989_10,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3099),sK79(U_3099,U_3097,U_3095)),U_3097)
    | ~ sP275(U_3095,U_3099,U_3097) ),
    inference(clausify,[status(thm)],[f_989_5]) ).

cnf(f_989_11,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3097,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3099),c_Nat_OSuc(sK79(U_3099,U_3097,U_3095))))
    | ~ sP275(U_3095,U_3099,U_3097) ),
    inference(clausify,[status(thm)],[f_989_5]) ).

cnf(f_989_12,plain,
    ( hBOOL(hAPP(U_3095,sK79(U_3099,U_3097,U_3095)))
    | ~ sP275(U_3095,U_3099,U_3097) ),
    inference(clausify,[status(thm)],[f_989_5]) ).

cnf(f_989_13,plain,
    ( ~ hBOOL(hAPP(U_3096,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | U_3100 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP276(U_3091,U_3098,U_3096,U_3100) ),
    inference(clausify,[status(thm)],[f_989_5]) ).

cnf(f_989_14,plain,
    ( ~ hBOOL(hAPP(U_3096,U_3091))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3098,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3100),c_Nat_OSuc(U_3091)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3100),U_3091),U_3098)
    | ~ sP276(U_3091,U_3098,U_3096,U_3100) ),
    inference(clausify,[status(thm)],[f_989_5]) ).

fof(f_990_1,plain,
    ! [V_m,V_n] :
      ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,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_le__div__geq]) ).

fof(f_990_2,plain,
    ! [U_3102,U_3101] :
      ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3102,U_3101) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3102,U_3101),U_3101))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3101,U_3102)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3101) ),
    inference(variable_rename,[status(thm)],[f_990_1]) ).

fof(f_990_3,plain,
    ! [U_3101,U_3102] :
      ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3102,U_3101) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3102,U_3101),U_3101))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3101,U_3102)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3101) ),
    inference(definitional_conversion,[status(esa)],[f_990_2]) ).

cnf(f_990_4,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3102,U_3101) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3102,U_3101),U_3101))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3101,U_3102)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3101) ),
    inference(clausify,[status(thm)],[f_990_3]) ).

fof(f_991_1,plain,
    ! [V_b,V_r2,V_a,V_r1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Orcis(V_r1,V_a)),c_Complex_Orcis(V_r2,V_b)) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r1),V_r2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a,V_b)),
    inference(fof_nnf,[status(thm)],[fact_rcis__mult]) ).

fof(f_991_2,plain,
    ! [U_3106,U_3105,U_3104,U_3103] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Orcis(U_3103,U_3104)),c_Complex_Orcis(U_3105,U_3106)) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_3103),U_3105),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_3104,U_3106)),
    inference(variable_rename,[status(thm)],[f_991_1]) ).

fof(f_991_3,plain,
    ! [U_3105,U_3104,U_3103,U_3106] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Orcis(U_3103,U_3104)),c_Complex_Orcis(U_3105,U_3106)) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_3103),U_3105),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_3104,U_3106)),
    inference(definitional_conversion,[status(esa)],[f_991_2]) ).

cnf(f_991_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Orcis(U_3103,U_3104)),c_Complex_Orcis(U_3105,U_3106)) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_3103),U_3105),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_3104,U_3106)),
    inference(clausify,[status(thm)],[f_991_3]) ).

fof(f_992_1,plain,
    ! [V_a,V_n] :
      ( ? [B_r] :
          ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_r),V_n) = V_a
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_r) )
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ),
    inference(fof_nnf,[status(thm)],[fact_realpow__pos__nth]) ).

fof(f_992_2,plain,
    ! [U_3109,U_3108] :
      ( ? [U_3107] :
          ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_3107),U_3108) = U_3109
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3107) )
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3109)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3108) ),
    inference(variable_rename,[status(thm)],[f_992_1]) ).

fof(f_992_3,plain,
    ! [U_3109,U_3108] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sK80(U_3109,U_3108)),U_3108) = U_3109
        & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK80(U_3109,U_3108)) )
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3109)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3108) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_3107,sK80(U_3109,U_3108))],[f_992_2]) ).

fof(f_992_4,plain,
    ( ! [U_3108,U_3109] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sK80(U_3109,U_3108)),U_3108) = U_3109
        | ~ sP277(U_3108,U_3109) )
    & ! [U_3108,U_3109] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK80(U_3109,U_3108))
        | ~ sP277(U_3108,U_3109) )
    & ! [U_3108,U_3109] :
        ( sP277(U_3108,U_3109)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3109)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3108) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP277])],[f_992_3]) ).

cnf(f_992_5,plain,
    ( sP277(U_3108,U_3109)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3109)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3108) ),
    inference(clausify,[status(thm)],[f_992_4]) ).

cnf(f_992_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK80(U_3109,U_3108))
    | ~ sP277(U_3108,U_3109) ),
    inference(clausify,[status(thm)],[f_992_4]) ).

cnf(f_992_7,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sK80(U_3109,U_3108)),U_3108) = U_3109
    | ~ sP277(U_3108,U_3109) ),
    inference(clausify,[status(thm)],[f_992_4]) ).

fof(f_993_1,plain,
    ! [V_y,V_x] :
      ( c_RComplete_Onatfloor(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_y))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_y)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_y)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x) ),
    inference(fof_nnf,[status(thm)],[fact_natfloor__div__nat]) ).

fof(f_993_2,plain,
    ! [U_3111,U_3110] :
      ( c_RComplete_Onatfloor(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_3110,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_3111))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(U_3110),U_3111)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3111)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_3110) ),
    inference(variable_rename,[status(thm)],[f_993_1]) ).

fof(f_993_3,plain,
    ! [U_3111,U_3110] :
      ( c_RComplete_Onatfloor(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_3110,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_3111))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(U_3110),U_3111)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3111)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_3110) ),
    inference(definitional_conversion,[status(esa)],[f_993_2]) ).

cnf(f_993_4,plain,
    ( c_RComplete_Onatfloor(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_3110,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_3111))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(U_3110),U_3111)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3111)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_3110) ),
    inference(clausify,[status(thm)],[f_993_3]) ).

fof(f_994_1,plain,
    ! [V_x,V_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_x)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_x))),
    inference(fof_nnf,[status(thm)],[fact_real__of__nat__div4]) ).

fof(f_994_2,plain,
    ! [U_3113,U_3112] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3112,U_3113)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_3112),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_3113))),
    inference(variable_rename,[status(thm)],[f_994_1]) ).

fof(f_994_3,plain,
    ! [U_3113,U_3112] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3112,U_3113)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_3112),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_3113))),
    inference(definitional_conversion,[status(esa)],[f_994_2]) ).

cnf(f_994_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3112,U_3113)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_3112),hAPP(c_RealDef_Oreal(tc_Nat_Onat),U_3113))),
    inference(clausify,[status(thm)],[f_994_3]) ).

fof(f_995_1,plain,
    ! [V_n,V_a,V_b,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)),V_n) = c_Rings_Oinverse__class_Odivide(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))
      | V_b = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Fields_Ofield(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_nonzero__power__divide]) ).

fof(f_995_2,plain,
    ! [U_3117,U_3116,U_3115,U_3114] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_3114),c_Rings_Oinverse__class_Odivide(U_3114,U_3116,U_3115)),U_3117) = c_Rings_Oinverse__class_Odivide(U_3114,hAPP(hAPP(c_Power_Opower__class_Opower(U_3114),U_3116),U_3117),hAPP(hAPP(c_Power_Opower__class_Opower(U_3114),U_3115),U_3117))
      | U_3115 = c_Groups_Ozero__class_Ozero(U_3114)
      | ~ class_Fields_Ofield(U_3114) ),
    inference(variable_rename,[status(thm)],[f_995_1]) ).

fof(f_995_3,plain,
    ! [U_3114,U_3115,U_3116,U_3117] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_3114),c_Rings_Oinverse__class_Odivide(U_3114,U_3116,U_3115)),U_3117) = c_Rings_Oinverse__class_Odivide(U_3114,hAPP(hAPP(c_Power_Opower__class_Opower(U_3114),U_3116),U_3117),hAPP(hAPP(c_Power_Opower__class_Opower(U_3114),U_3115),U_3117))
      | U_3115 = c_Groups_Ozero__class_Ozero(U_3114)
      | ~ class_Fields_Ofield(U_3114) ),
    inference(definitional_conversion,[status(esa)],[f_995_2]) ).

cnf(f_995_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_3114),c_Rings_Oinverse__class_Odivide(U_3114,U_3116,U_3115)),U_3117) = c_Rings_Oinverse__class_Odivide(U_3114,hAPP(hAPP(c_Power_Opower__class_Opower(U_3114),U_3116),U_3117),hAPP(hAPP(c_Power_Opower__class_Opower(U_3114),U_3115),U_3117))
    | U_3115 = c_Groups_Ozero__class_Ozero(U_3114)
    | ~ class_Fields_Ofield(U_3114) ),
    inference(clausify,[status(thm)],[f_995_3]) ).

fof(f_996_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_996_2,plain,
    ! [U_3118] :
      ( class_Rings_Oidom(tc_Polynomial_Opoly(U_3118))
      | ~ class_Rings_Oidom(U_3118) ),
    inference(variable_rename,[status(thm)],[f_996_1]) ).

fof(f_996_3,plain,
    ! [U_3118] :
      ( class_Rings_Oidom(tc_Polynomial_Opoly(U_3118))
      | ~ class_Rings_Oidom(U_3118) ),
    inference(definitional_conversion,[status(esa)],[f_996_2]) ).

cnf(f_996_4,plain,
    ( class_Rings_Oidom(tc_Polynomial_Opoly(U_3118))
    | ~ class_Rings_Oidom(U_3118) ),
    inference(clausify,[status(thm)],[f_996_3]) ).

fof(f_997_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_997_2,plain,
    ! [U_3119] :
      ( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(U_3119))
      | ~ class_Groups_Ocancel__comm__monoid__add(U_3119) ),
    inference(variable_rename,[status(thm)],[f_997_1]) ).

fof(f_997_3,plain,
    ! [U_3119] :
      ( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(U_3119))
      | ~ class_Groups_Ocancel__comm__monoid__add(U_3119) ),
    inference(definitional_conversion,[status(esa)],[f_997_2]) ).

cnf(f_997_4,plain,
    ( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(U_3119))
    | ~ class_Groups_Ocancel__comm__monoid__add(U_3119) ),
    inference(clausify,[status(thm)],[f_997_3]) ).

fof(f_998_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_998_2,plain,
    ! [U_3120] :
      ( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(U_3120))
      | ~ class_Rings_Ocomm__semiring__0(U_3120) ),
    inference(variable_rename,[status(thm)],[f_998_1]) ).

fof(f_998_3,plain,
    ! [U_3120] :
      ( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(U_3120))
      | ~ class_Rings_Ocomm__semiring__0(U_3120) ),
    inference(definitional_conversion,[status(esa)],[f_998_2]) ).

cnf(f_998_4,plain,
    ( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(U_3120))
    | ~ class_Rings_Ocomm__semiring__0(U_3120) ),
    inference(clausify,[status(thm)],[f_998_3]) ).

fof(f_999_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_999_2,plain,
    ! [U_3121] :
      ( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(U_3121))
      | ~ class_Rings_Ocomm__ring(U_3121) ),
    inference(variable_rename,[status(thm)],[f_999_1]) ).

fof(f_999_3,plain,
    ! [U_3121] :
      ( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(U_3121))
      | ~ class_Rings_Ocomm__ring(U_3121) ),
    inference(definitional_conversion,[status(esa)],[f_999_2]) ).

cnf(f_999_4,plain,
    ( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(U_3121))
    | ~ class_Rings_Ocomm__ring(U_3121) ),
    inference(clausify,[status(thm)],[f_999_3]) ).

fof(f_1000_1,plain,
    class_Rings_Oidom(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Oidom]) ).

fof(f_1000_2,plain,
    class_Rings_Oidom(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1000_1]) ).

cnf(f_1000_3,plain,
    class_Rings_Oidom(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1000_2]) ).

fof(f_1001_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_1001_2,plain,
    class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1001_1]) ).

cnf(f_1001_3,plain,
    class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1001_2]) ).

fof(f_1002_1,plain,
    class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__0]) ).

fof(f_1002_2,plain,
    class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1002_1]) ).

cnf(f_1002_3,plain,
    class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1002_2]) ).

fof(f_1003_1,plain,
    class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__ring]) ).

fof(f_1003_2,plain,
    class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1003_1]) ).

cnf(f_1003_3,plain,
    class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1003_2]) ).

fof(f_1004_1,plain,
    class_Rings_Oidom(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oidom]) ).

fof(f_1004_2,plain,
    class_Rings_Oidom(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1004_1]) ).

cnf(f_1004_3,plain,
    class_Rings_Oidom(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1004_2]) ).

fof(f_1005_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_1005_2,plain,
    class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1005_1]) ).

cnf(f_1005_3,plain,
    class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1005_2]) ).

fof(f_1006_1,plain,
    class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__0]) ).

fof(f_1006_2,plain,
    class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1006_1]) ).

cnf(f_1006_3,plain,
    class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1006_2]) ).

fof(f_1007_1,plain,
    class_Rings_Ocomm__ring(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__ring]) ).

fof(f_1007_2,plain,
    class_Rings_Ocomm__ring(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1007_1]) ).

cnf(f_1007_3,plain,
    class_Rings_Ocomm__ring(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1007_2]) ).

fof(f_1008_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_1008_2,plain,
    class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1008_1]) ).

cnf(f_1008_3,plain,
    class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1008_2]) ).

fof(f_1009_1,plain,
    class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__0]) ).

fof(f_1009_2,plain,
    class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1009_1]) ).

cnf(f_1009_3,plain,
    class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1009_2]) ).

fof(f_1010_1,plain,
    class_Rings_Oidom(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oidom]) ).

fof(f_1010_2,plain,
    class_Rings_Oidom(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1010_1]) ).

cnf(f_1010_3,plain,
    class_Rings_Oidom(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1010_2]) ).

fof(f_1011_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_1011_2,plain,
    class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1011_1]) ).

cnf(f_1011_3,plain,
    class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1011_2]) ).

fof(f_1012_1,plain,
    class_Rings_Ocomm__semiring__0(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring__0]) ).

fof(f_1012_2,plain,
    class_Rings_Ocomm__semiring__0(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1012_1]) ).

cnf(f_1012_3,plain,
    class_Rings_Ocomm__semiring__0(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1012_2]) ).

fof(f_1013_1,plain,
    class_Rings_Ocomm__ring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring]) ).

fof(f_1013_2,plain,
    class_Rings_Ocomm__ring(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1013_1]) ).

cnf(f_1013_3,plain,
    class_Rings_Ocomm__ring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1013_2]) ).

fof(f_1014_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_1014_2,plain,
    ! [U_3123,U_3122] :
      ( class_Orderings_Opreorder(tc_fun(U_3123,U_3122))
      | ~ class_Orderings_Opreorder(U_3122) ),
    inference(variable_rename,[status(thm)],[f_1014_1]) ).

fof(f_1014_3,plain,
    ! [U_3123,U_3122] :
      ( class_Orderings_Opreorder(tc_fun(U_3123,U_3122))
      | ~ class_Orderings_Opreorder(U_3122) ),
    inference(definitional_conversion,[status(esa)],[f_1014_2]) ).

cnf(f_1014_4,plain,
    ( class_Orderings_Opreorder(tc_fun(U_3123,U_3122))
    | ~ class_Orderings_Opreorder(U_3122) ),
    inference(clausify,[status(thm)],[f_1014_3]) ).

fof(f_1015_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_1015_2,plain,
    ! [U_3125,U_3124] :
      ( class_Orderings_Oorder(tc_fun(U_3125,U_3124))
      | ~ class_Orderings_Oorder(U_3124) ),
    inference(variable_rename,[status(thm)],[f_1015_1]) ).

fof(f_1015_3,plain,
    ! [U_3125,U_3124] :
      ( class_Orderings_Oorder(tc_fun(U_3125,U_3124))
      | ~ class_Orderings_Oorder(U_3124) ),
    inference(definitional_conversion,[status(esa)],[f_1015_2]) ).

cnf(f_1015_4,plain,
    ( class_Orderings_Oorder(tc_fun(U_3125,U_3124))
    | ~ class_Orderings_Oorder(U_3124) ),
    inference(clausify,[status(thm)],[f_1015_3]) ).

fof(f_1016_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_1016_2,plain,
    ! [U_3127,U_3126] :
      ( class_Orderings_Oord(tc_fun(U_3127,U_3126))
      | ~ class_Orderings_Oord(U_3126) ),
    inference(variable_rename,[status(thm)],[f_1016_1]) ).

fof(f_1016_3,plain,
    ! [U_3126,U_3127] :
      ( class_Orderings_Oord(tc_fun(U_3127,U_3126))
      | ~ class_Orderings_Oord(U_3126) ),
    inference(definitional_conversion,[status(esa)],[f_1016_2]) ).

cnf(f_1016_4,plain,
    ( class_Orderings_Oord(tc_fun(U_3127,U_3126))
    | ~ class_Orderings_Oord(U_3126) ),
    inference(clausify,[status(thm)],[f_1016_3]) ).

fof(f_1017_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_1017_2,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1017_1]) ).

cnf(f_1017_3,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1017_2]) ).

fof(f_1018_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_1018_2,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1018_1]) ).

cnf(f_1018_3,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1018_2]) ).

fof(f_1019_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_1019_2,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1019_1]) ).

cnf(f_1019_3,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1019_2]) ).

fof(f_1020_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_1020_2,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1020_1]) ).

cnf(f_1020_3,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1020_2]) ).

fof(f_1021_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_1021_2,plain,
    class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1021_1]) ).

cnf(f_1021_3,plain,
    class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1021_2]) ).

fof(f_1022_1,plain,
    class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__strict]) ).

fof(f_1022_2,plain,
    class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1022_1]) ).

cnf(f_1022_3,plain,
    class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1022_2]) ).

fof(f_1023_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_1023_2,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1023_1]) ).

cnf(f_1023_3,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1023_2]) ).

fof(f_1024_1,plain,
    class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__group__add__abs]) ).

fof(f_1024_2,plain,
    class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1024_1]) ).

cnf(f_1024_3,plain,
    class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1024_2]) ).

fof(f_1025_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_1025_2,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1025_1]) ).

cnf(f_1025_3,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1025_2]) ).

fof(f_1026_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_1026_2,plain,
    class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1026_1]) ).

cnf(f_1026_3,plain,
    class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1026_2]) ).

fof(f_1027_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_1027_2,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1027_1]) ).

cnf(f_1027_3,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1027_2]) ).

fof(f_1028_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_1028_2,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1028_1]) ).

cnf(f_1028_3,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1028_2]) ).

fof(f_1029_1,plain,
    class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__cancel__semiring]) ).

fof(f_1029_2,plain,
    class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1029_1]) ).

cnf(f_1029_3,plain,
    class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1029_2]) ).

fof(f_1030_1,plain,
    class_Rings_Olinordered__ring__strict(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring__strict]) ).

fof(f_1030_2,plain,
    class_Rings_Olinordered__ring__strict(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1030_1]) ).

cnf(f_1030_3,plain,
    class_Rings_Olinordered__ring__strict(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1030_2]) ).

fof(f_1031_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_1031_2,plain,
    class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1031_1]) ).

cnf(f_1031_3,plain,
    class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1031_2]) ).

fof(f_1032_1,plain,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__comm__semiring]) ).

fof(f_1032_2,plain,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1032_1]) ).

cnf(f_1032_3,plain,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1032_2]) ).

fof(f_1033_1,plain,
    class_Rings_Olinordered__semiring__1(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1]) ).

fof(f_1033_2,plain,
    class_Rings_Olinordered__semiring__1(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1033_1]) ).

cnf(f_1033_3,plain,
    class_Rings_Olinordered__semiring__1(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1033_2]) ).

fof(f_1034_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_1034_2,plain,
    class_Groups_Oordered__ab__group__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1034_1]) ).

cnf(f_1034_3,plain,
    class_Groups_Oordered__ab__group__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1034_2]) ).

fof(f_1035_1,plain,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocancel__semigroup__add]) ).

fof(f_1035_2,plain,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1035_1]) ).

cnf(f_1035_3,plain,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1035_2]) ).

fof(f_1036_1,plain,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring]) ).

fof(f_1036_2,plain,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1036_1]) ).

cnf(f_1036_3,plain,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1036_2]) ).

fof(f_1037_1,plain,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semidom]) ).

fof(f_1037_2,plain,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1037_1]) ).

cnf(f_1037_3,plain,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1037_2]) ).

fof(f_1038_1,plain,
    class_Groups_Oab__semigroup__mult(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__mult]) ).

fof(f_1038_2,plain,
    class_Groups_Oab__semigroup__mult(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1038_1]) ).

cnf(f_1038_3,plain,
    class_Groups_Oab__semigroup__mult(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1038_2]) ).

fof(f_1039_1,plain,
    class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__mult]) ).

fof(f_1039_2,plain,
    class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1039_1]) ).

cnf(f_1039_3,plain,
    class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1039_2]) ).

fof(f_1040_1,plain,
    class_Groups_Oab__semigroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__add]) ).

fof(f_1040_2,plain,
    class_Groups_Oab__semigroup__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1040_1]) ).

cnf(f_1040_3,plain,
    class_Groups_Oab__semigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1040_2]) ).

fof(f_1041_1,plain,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__semiring]) ).

fof(f_1041_2,plain,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1041_1]) ).

cnf(f_1041_3,plain,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1041_2]) ).

fof(f_1042_1,plain,
    class_Rings_Oordered__ring__abs(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring__abs]) ).

fof(f_1042_2,plain,
    class_Rings_Oordered__ring__abs(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1042_1]) ).

cnf(f_1042_3,plain,
    class_Rings_Oordered__ring__abs(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1042_2]) ).

fof(f_1043_1,plain,
    class_Rings_Ono__zero__divisors(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ono__zero__divisors]) ).

fof(f_1043_2,plain,
    class_Rings_Ono__zero__divisors(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1043_1]) ).

cnf(f_1043_3,plain,
    class_Rings_Ono__zero__divisors(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1043_2]) ).

fof(f_1044_1,plain,
    class_Groups_Ocomm__monoid__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__add]) ).

fof(f_1044_2,plain,
    class_Groups_Ocomm__monoid__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1044_1]) ).

cnf(f_1044_3,plain,
    class_Groups_Ocomm__monoid__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1044_2]) ).

fof(f_1045_1,plain,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring]) ).

fof(f_1045_2,plain,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1045_1]) ).

cnf(f_1045_3,plain,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1045_2]) ).

fof(f_1046_1,plain,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__idom]) ).

fof(f_1046_2,plain,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1046_1]) ).

cnf(f_1046_3,plain,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1046_2]) ).

fof(f_1047_1,plain,
    class_Rings_Ocomm__semiring__1(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring__1]) ).

fof(f_1047_2,plain,
    class_Rings_Ocomm__semiring__1(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1047_1]) ).

cnf(f_1047_3,plain,
    class_Rings_Ocomm__semiring__1(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1047_2]) ).

fof(f_1048_1,plain,
    class_Divides_Osemiring__div(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Divides_Osemiring__div]) ).

fof(f_1048_2,plain,
    class_Divides_Osemiring__div(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1048_1]) ).

cnf(f_1048_3,plain,
    class_Divides_Osemiring__div(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1048_2]) ).

fof(f_1049_1,plain,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring]) ).

fof(f_1049_2,plain,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1049_1]) ).

cnf(f_1049_3,plain,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1049_2]) ).

fof(f_1050_1,plain,
    class_Nat_Osemiring__char__0(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Nat_Osemiring__char__0]) ).

fof(f_1050_2,plain,
    class_Nat_Osemiring__char__0(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1050_1]) ).

cnf(f_1050_3,plain,
    class_Nat_Osemiring__char__0(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1050_2]) ).

fof(f_1051_1,plain,
    class_Groups_Oab__group__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__group__add]) ).

fof(f_1051_2,plain,
    class_Groups_Oab__group__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1051_1]) ).

cnf(f_1051_3,plain,
    class_Groups_Oab__group__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1051_2]) ).

fof(f_1052_1,plain,
    class_Rings_Ozero__neq__one(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ozero__neq__one]) ).

fof(f_1052_2,plain,
    class_Rings_Ozero__neq__one(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1052_1]) ).

cnf(f_1052_3,plain,
    class_Rings_Ozero__neq__one(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1052_2]) ).

fof(f_1053_1,plain,
    class_Rings_Oordered__ring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring]) ).

fof(f_1053_2,plain,
    class_Rings_Oordered__ring(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1053_1]) ).

cnf(f_1053_3,plain,
    class_Rings_Oordered__ring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1053_2]) ).

fof(f_1054_1,plain,
    class_Orderings_Opreorder(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Opreorder]) ).

fof(f_1054_2,plain,
    class_Orderings_Opreorder(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1054_1]) ).

cnf(f_1054_3,plain,
    class_Orderings_Opreorder(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1054_2]) ).

fof(f_1055_1,plain,
    class_Orderings_Olinorder(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Olinorder]) ).

fof(f_1055_2,plain,
    class_Orderings_Olinorder(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1055_1]) ).

cnf(f_1055_3,plain,
    class_Orderings_Olinorder(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1055_2]) ).

fof(f_1056_1,plain,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Omonoid__mult]) ).

fof(f_1056_2,plain,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1056_1]) ).

cnf(f_1056_3,plain,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1056_2]) ).

fof(f_1057_1,plain,
    class_Rings_Ocomm__ring__1(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring__1]) ).

fof(f_1057_2,plain,
    class_Rings_Ocomm__ring__1(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1057_1]) ).

cnf(f_1057_3,plain,
    class_Rings_Ocomm__ring__1(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1057_2]) ).

fof(f_1058_1,plain,
    class_Groups_Omonoid__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Omonoid__add]) ).

fof(f_1058_2,plain,
    class_Groups_Omonoid__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1058_1]) ).

cnf(f_1058_3,plain,
    class_Groups_Omonoid__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1058_2]) ).

fof(f_1059_1,plain,
    class_Rings_Osemiring__1(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Osemiring__1]) ).

fof(f_1059_2,plain,
    class_Rings_Osemiring__1(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1059_1]) ).

cnf(f_1059_3,plain,
    class_Rings_Osemiring__1(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1059_2]) ).

fof(f_1060_1,plain,
    class_Rings_Osemiring__0(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Osemiring__0]) ).

fof(f_1060_2,plain,
    class_Rings_Osemiring__0(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1060_1]) ).

cnf(f_1060_3,plain,
    class_Rings_Osemiring__0(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1060_2]) ).

fof(f_1061_1,plain,
    class_Groups_Ogroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ogroup__add]) ).

fof(f_1061_2,plain,
    class_Groups_Ogroup__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1061_1]) ).

cnf(f_1061_3,plain,
    class_Groups_Ogroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1061_2]) ).

fof(f_1062_1,plain,
    class_Rings_Omult__zero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Omult__zero]) ).

fof(f_1062_2,plain,
    class_Rings_Omult__zero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1062_1]) ).

cnf(f_1062_3,plain,
    class_Rings_Omult__zero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1062_2]) ).

fof(f_1063_1,plain,
    class_Orderings_Oorder(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Oorder]) ).

fof(f_1063_2,plain,
    class_Orderings_Oorder(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1063_1]) ).

cnf(f_1063_3,plain,
    class_Orderings_Oorder(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1063_2]) ).

fof(f_1064_1,plain,
    class_Int_Oring__char__0(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Int_Oring__char__0]) ).

fof(f_1064_2,plain,
    class_Int_Oring__char__0(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1064_1]) ).

cnf(f_1064_3,plain,
    class_Int_Oring__char__0(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1064_2]) ).

fof(f_1065_1,plain,
    class_Int_Onumber__ring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Int_Onumber__ring]) ).

fof(f_1065_2,plain,
    class_Int_Onumber__ring(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1065_1]) ).

cnf(f_1065_3,plain,
    class_Int_Onumber__ring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1065_2]) ).

fof(f_1066_1,plain,
    class_Rings_Osemiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Osemiring]) ).

fof(f_1066_2,plain,
    class_Rings_Osemiring(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1066_1]) ).

cnf(f_1066_3,plain,
    class_Rings_Osemiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1066_2]) ).

fof(f_1067_1,plain,
    class_Orderings_Oord(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Oord]) ).

fof(f_1067_2,plain,
    class_Orderings_Oord(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1067_1]) ).

cnf(f_1067_3,plain,
    class_Orderings_Oord(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1067_2]) ).

fof(f_1068_1,plain,
    class_Rings_Oring__1(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring__1]) ).

fof(f_1068_2,plain,
    class_Rings_Oring__1(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1068_1]) ).

cnf(f_1068_3,plain,
    class_Rings_Oring__1(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1068_2]) ).

fof(f_1069_1,plain,
    class_Power_Opower(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Power_Opower]) ).

fof(f_1069_2,plain,
    class_Power_Opower(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1069_1]) ).

cnf(f_1069_3,plain,
    class_Power_Opower(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1069_2]) ).

fof(f_1070_1,plain,
    class_Groups_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ozero]) ).

fof(f_1070_2,plain,
    class_Groups_Ozero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1070_1]) ).

cnf(f_1070_3,plain,
    class_Groups_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1070_2]) ).

fof(f_1071_1,plain,
    class_Rings_Oring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring]) ).

fof(f_1071_2,plain,
    class_Rings_Oring(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1071_1]) ).

cnf(f_1071_3,plain,
    class_Rings_Oring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1071_2]) ).

fof(f_1072_1,plain,
    class_Int_Onumber(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Int_Onumber]) ).

fof(f_1072_2,plain,
    class_Int_Onumber(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1072_1]) ).

cnf(f_1072_3,plain,
    class_Int_Onumber(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1072_2]) ).

fof(f_1073_1,plain,
    class_Groups_Oone(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oone]) ).

fof(f_1073_2,plain,
    class_Groups_Oone(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1073_1]) ).

cnf(f_1073_3,plain,
    class_Groups_Oone(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1073_2]) ).

fof(f_1074_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_1074_2,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1074_1]) ).

cnf(f_1074_3,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1074_2]) ).

fof(f_1075_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_1075_2,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1075_1]) ).

cnf(f_1075_3,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1075_2]) ).

fof(f_1076_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_1076_2,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1076_1]) ).

cnf(f_1076_3,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1076_2]) ).

fof(f_1077_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_1077_2,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1077_1]) ).

cnf(f_1077_3,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1077_2]) ).

fof(f_1078_1,plain,
    class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring__strict]) ).

fof(f_1078_2,plain,
    class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1078_1]) ).

cnf(f_1078_3,plain,
    class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1078_2]) ).

fof(f_1079_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_1079_2,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1079_1]) ).

cnf(f_1079_3,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1079_2]) ).

fof(f_1080_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_1080_2,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1080_1]) ).

cnf(f_1080_3,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1080_2]) ).

fof(f_1081_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_1081_2,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1081_1]) ).

cnf(f_1081_3,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1081_2]) ).

fof(f_1082_1,plain,
    class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__cancel__semiring]) ).

fof(f_1082_2,plain,
    class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1082_1]) ).

cnf(f_1082_3,plain,
    class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1082_2]) ).

fof(f_1083_1,plain,
    class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__comm__semiring]) ).

fof(f_1083_2,plain,
    class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1083_1]) ).

cnf(f_1083_3,plain,
    class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1083_2]) ).

fof(f_1084_1,plain,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__semigroup__add]) ).

fof(f_1084_2,plain,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1084_1]) ).

cnf(f_1084_3,plain,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1084_2]) ).

fof(f_1085_1,plain,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring]) ).

fof(f_1085_2,plain,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1085_1]) ).

cnf(f_1085_3,plain,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1085_2]) ).

fof(f_1086_1,plain,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]) ).

fof(f_1086_2,plain,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1086_1]) ).

cnf(f_1086_3,plain,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1086_2]) ).

fof(f_1087_1,plain,
    class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__mult]) ).

fof(f_1087_2,plain,
    class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1087_1]) ).

cnf(f_1087_3,plain,
    class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1087_2]) ).

fof(f_1088_1,plain,
    class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__mult]) ).

fof(f_1088_2,plain,
    class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1088_1]) ).

cnf(f_1088_3,plain,
    class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1088_2]) ).

fof(f_1089_1,plain,
    class_Groups_Oab__semigroup__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__add]) ).

fof(f_1089_2,plain,
    class_Groups_Oab__semigroup__add(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1089_1]) ).

cnf(f_1089_3,plain,
    class_Groups_Oab__semigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1089_2]) ).

fof(f_1090_1,plain,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__semiring]) ).

fof(f_1090_2,plain,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1090_1]) ).

cnf(f_1090_3,plain,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1090_2]) ).

fof(f_1091_1,plain,
    class_Rings_Ono__zero__divisors(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ono__zero__divisors]) ).

fof(f_1091_2,plain,
    class_Rings_Ono__zero__divisors(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1091_1]) ).

cnf(f_1091_3,plain,
    class_Rings_Ono__zero__divisors(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1091_2]) ).

fof(f_1092_1,plain,
    class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__add]) ).

fof(f_1092_2,plain,
    class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1092_1]) ).

cnf(f_1092_3,plain,
    class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1092_2]) ).

fof(f_1093_1,plain,
    class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__1]) ).

fof(f_1093_2,plain,
    class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1093_1]) ).

cnf(f_1093_3,plain,
    class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1093_2]) ).

fof(f_1094_1,plain,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Divides_Osemiring__div]) ).

fof(f_1094_2,plain,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1094_1]) ).

cnf(f_1094_3,plain,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1094_2]) ).

fof(f_1095_1,plain,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring]) ).

fof(f_1095_2,plain,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1095_1]) ).

cnf(f_1095_3,plain,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1095_2]) ).

fof(f_1096_1,plain,
    class_Nat_Osemiring__char__0(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Nat_Osemiring__char__0]) ).

fof(f_1096_2,plain,
    class_Nat_Osemiring__char__0(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1096_1]) ).

cnf(f_1096_3,plain,
    class_Nat_Osemiring__char__0(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1096_2]) ).

fof(f_1097_1,plain,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ozero__neq__one]) ).

fof(f_1097_2,plain,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1097_1]) ).

cnf(f_1097_3,plain,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1097_2]) ).

fof(f_1098_1,plain,
    class_Orderings_Opreorder(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]) ).

fof(f_1098_2,plain,
    class_Orderings_Opreorder(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1098_1]) ).

cnf(f_1098_3,plain,
    class_Orderings_Opreorder(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1098_2]) ).

fof(f_1099_1,plain,
    class_Orderings_Olinorder(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]) ).

fof(f_1099_2,plain,
    class_Orderings_Olinorder(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1099_1]) ).

cnf(f_1099_3,plain,
    class_Orderings_Olinorder(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1099_2]) ).

fof(f_1100_1,plain,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__mult]) ).

fof(f_1100_2,plain,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1100_1]) ).

cnf(f_1100_3,plain,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1100_2]) ).

fof(f_1101_1,plain,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]) ).

fof(f_1101_2,plain,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1101_1]) ).

cnf(f_1101_3,plain,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1101_2]) ).

fof(f_1102_1,plain,
    class_Rings_Osemiring__1(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__1]) ).

fof(f_1102_2,plain,
    class_Rings_Osemiring__1(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1102_1]) ).

cnf(f_1102_3,plain,
    class_Rings_Osemiring__1(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1102_2]) ).

fof(f_1103_1,plain,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__0]) ).

fof(f_1103_2,plain,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1103_1]) ).

cnf(f_1103_3,plain,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1103_2]) ).

fof(f_1104_1,plain,
    class_Rings_Omult__zero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Omult__zero]) ).

fof(f_1104_2,plain,
    class_Rings_Omult__zero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1104_1]) ).

cnf(f_1104_3,plain,
    class_Rings_Omult__zero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1104_2]) ).

fof(f_1105_1,plain,
    class_Orderings_Oorder(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]) ).

fof(f_1105_2,plain,
    class_Orderings_Oorder(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1105_1]) ).

cnf(f_1105_3,plain,
    class_Orderings_Oorder(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1105_2]) ).

fof(f_1106_1,plain,
    class_Rings_Osemiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Osemiring]) ).

fof(f_1106_2,plain,
    class_Rings_Osemiring(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1106_1]) ).

cnf(f_1106_3,plain,
    class_Rings_Osemiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1106_2]) ).

fof(f_1107_1,plain,
    class_Orderings_Oord(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Oord]) ).

fof(f_1107_2,plain,
    class_Orderings_Oord(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1107_1]) ).

cnf(f_1107_3,plain,
    class_Orderings_Oord(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1107_2]) ).

fof(f_1108_1,plain,
    class_Power_Opower(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Power_Opower]) ).

fof(f_1108_2,plain,
    class_Power_Opower(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1108_1]) ).

cnf(f_1108_3,plain,
    class_Power_Opower(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1108_2]) ).

fof(f_1109_1,plain,
    class_Groups_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ozero]) ).

fof(f_1109_2,plain,
    class_Groups_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1109_1]) ).

cnf(f_1109_3,plain,
    class_Groups_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1109_2]) ).

fof(f_1110_1,plain,
    class_Int_Onumber(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Int_Onumber]) ).

fof(f_1110_2,plain,
    class_Int_Onumber(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1110_1]) ).

cnf(f_1110_3,plain,
    class_Int_Onumber(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1110_2]) ).

fof(f_1111_1,plain,
    class_Groups_Oone(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oone]) ).

fof(f_1111_2,plain,
    class_Groups_Oone(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1111_1]) ).

cnf(f_1111_3,plain,
    class_Groups_Oone(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1111_2]) ).

fof(f_1112_1,plain,
    class_Orderings_Opreorder(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]) ).

fof(f_1112_2,plain,
    class_Orderings_Opreorder(tc_HOL_Obool),
    inference(definitional_conversion,[status(esa)],[f_1112_1]) ).

cnf(f_1112_3,plain,
    class_Orderings_Opreorder(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_1112_2]) ).

fof(f_1113_1,plain,
    class_Orderings_Oorder(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]) ).

fof(f_1113_2,plain,
    class_Orderings_Oorder(tc_HOL_Obool),
    inference(definitional_conversion,[status(esa)],[f_1113_1]) ).

cnf(f_1113_3,plain,
    class_Orderings_Oorder(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_1113_2]) ).

fof(f_1114_1,plain,
    class_Orderings_Oord(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Oord]) ).

fof(f_1114_2,plain,
    class_Orderings_Oord(tc_HOL_Obool),
    inference(definitional_conversion,[status(esa)],[f_1114_1]) ).

cnf(f_1114_3,plain,
    class_Orderings_Oord(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_1114_2]) ).

fof(f_1115_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_1115_2,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1115_1]) ).

cnf(f_1115_3,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1115_2]) ).

fof(f_1116_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_1116_2,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1116_1]) ).

cnf(f_1116_3,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1116_2]) ).

fof(f_1117_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_1117_2,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1117_1]) ).

cnf(f_1117_3,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1117_2]) ).

fof(f_1118_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_1118_2,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1118_1]) ).

cnf(f_1118_3,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1118_2]) ).

fof(f_1119_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_1119_2,plain,
    class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1119_1]) ).

cnf(f_1119_3,plain,
    class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1119_2]) ).

fof(f_1120_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_1120_2,plain,
    class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1120_1]) ).

cnf(f_1120_3,plain,
    class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1120_2]) ).

fof(f_1121_1,plain,
    class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring__strict]) ).

fof(f_1121_2,plain,
    class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1121_1]) ).

cnf(f_1121_3,plain,
    class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1121_2]) ).

fof(f_1122_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_1122_2,plain,
    class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1122_1]) ).

cnf(f_1122_3,plain,
    class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1122_2]) ).

fof(f_1123_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_1123_2,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1123_1]) ).

cnf(f_1123_3,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1123_2]) ).

fof(f_1124_1,plain,
    class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs]) ).

fof(f_1124_2,plain,
    class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1124_1]) ).

cnf(f_1124_3,plain,
    class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1124_2]) ).

fof(f_1125_1,plain,
    class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__algebra]) ).

fof(f_1125_2,plain,
    class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1125_1]) ).

cnf(f_1125_3,plain,
    class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1125_2]) ).

fof(f_1126_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_1126_2,plain,
    class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1126_1]) ).

cnf(f_1126_3,plain,
    class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1126_2]) ).

fof(f_1127_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_1127_2,plain,
    class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1127_1]) ).

cnf(f_1127_3,plain,
    class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1127_2]) ).

fof(f_1128_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_1128_2,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1128_1]) ).

cnf(f_1128_3,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1128_2]) ).

fof(f_1129_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_1129_2,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1129_1]) ).

cnf(f_1129_3,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1129_2]) ).

fof(f_1130_1,plain,
    class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__cancel__semiring]) ).

fof(f_1130_2,plain,
    class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1130_1]) ).

cnf(f_1130_3,plain,
    class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1130_2]) ).

fof(f_1131_1,plain,
    class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__vector]) ).

fof(f_1131_2,plain,
    class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1131_1]) ).

cnf(f_1131_3,plain,
    class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1131_2]) ).

fof(f_1132_1,plain,
    class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__ring__strict]) ).

fof(f_1132_2,plain,
    class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1132_1]) ).

cnf(f_1132_3,plain,
    class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1132_2]) ).

fof(f_1133_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_1133_2,plain,
    class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1133_1]) ).

cnf(f_1133_3,plain,
    class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1133_2]) ).

fof(f_1134_1,plain,
    class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__comm__semiring]) ).

fof(f_1134_2,plain,
    class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1134_1]) ).

cnf(f_1134_3,plain,
    class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1134_2]) ).

fof(f_1135_1,plain,
    class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring__1]) ).

fof(f_1135_2,plain,
    class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1135_1]) ).

cnf(f_1135_3,plain,
    class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1135_2]) ).

fof(f_1136_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_1136_2,plain,
    class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1136_1]) ).

cnf(f_1136_3,plain,
    class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1136_2]) ).

fof(f_1137_1,plain,
    class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ocancel__semigroup__add]) ).

fof(f_1137_2,plain,
    class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1137_1]) ).

cnf(f_1137_3,plain,
    class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1137_2]) ).

fof(f_1138_1,plain,
    class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring]) ).

fof(f_1138_2,plain,
    class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1138_1]) ).

cnf(f_1138_3,plain,
    class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1138_2]) ).

fof(f_1139_1,plain,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semidom]) ).

fof(f_1139_2,plain,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1139_1]) ).

cnf(f_1139_3,plain,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1139_2]) ).

fof(f_1140_1,plain,
    class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__semigroup__mult]) ).

fof(f_1140_2,plain,
    class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1140_1]) ).

cnf(f_1140_3,plain,
    class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1140_2]) ).

fof(f_1141_1,plain,
    class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ocomm__monoid__mult]) ).

fof(f_1141_2,plain,
    class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1141_1]) ).

cnf(f_1141_3,plain,
    class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1141_2]) ).

fof(f_1142_1,plain,
    class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__semigroup__add]) ).

fof(f_1142_2,plain,
    class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1142_1]) ).

cnf(f_1142_3,plain,
    class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1142_2]) ).

fof(f_1143_1,plain,
    class_Rings_Oordered__semiring(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__semiring]) ).

fof(f_1143_2,plain,
    class_Rings_Oordered__semiring(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1143_1]) ).

cnf(f_1143_3,plain,
    class_Rings_Oordered__semiring(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1143_2]) ).

fof(f_1144_1,plain,
    class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__ring__abs]) ).

fof(f_1144_2,plain,
    class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1144_1]) ).

cnf(f_1144_3,plain,
    class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1144_2]) ).

fof(f_1145_1,plain,
    class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ono__zero__divisors]) ).

fof(f_1145_2,plain,
    class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1145_1]) ).

cnf(f_1145_3,plain,
    class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1145_2]) ).

fof(f_1146_1,plain,
    class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ocomm__monoid__add]) ).

fof(f_1146_2,plain,
    class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1146_1]) ).

cnf(f_1146_3,plain,
    class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1146_2]) ).

fof(f_1147_1,plain,
    class_Rings_Olinordered__ring(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__ring]) ).

fof(f_1147_2,plain,
    class_Rings_Olinordered__ring(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1147_1]) ).

cnf(f_1147_3,plain,
    class_Rings_Olinordered__ring(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1147_2]) ).

fof(f_1148_1,plain,
    class_Rings_Olinordered__idom(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__idom]) ).

fof(f_1148_2,plain,
    class_Rings_Olinordered__idom(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1148_1]) ).

cnf(f_1148_3,plain,
    class_Rings_Olinordered__idom(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1148_2]) ).

fof(f_1149_1,plain,
    class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__1]) ).

fof(f_1149_2,plain,
    class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1149_1]) ).

cnf(f_1149_3,plain,
    class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1149_2]) ).

fof(f_1150_1,plain,
    class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring]) ).

fof(f_1150_2,plain,
    class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1150_1]) ).

cnf(f_1150_3,plain,
    class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1150_2]) ).

fof(f_1151_1,plain,
    class_Nat_Osemiring__char__0(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Nat_Osemiring__char__0]) ).

fof(f_1151_2,plain,
    class_Nat_Osemiring__char__0(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1151_1]) ).

cnf(f_1151_3,plain,
    class_Nat_Osemiring__char__0(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1151_2]) ).

fof(f_1152_1,plain,
    class_Groups_Oab__group__add(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__group__add]) ).

fof(f_1152_2,plain,
    class_Groups_Oab__group__add(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1152_1]) ).

cnf(f_1152_3,plain,
    class_Groups_Oab__group__add(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1152_2]) ).

fof(f_1153_1,plain,
    class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ozero__neq__one]) ).

fof(f_1153_2,plain,
    class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1153_1]) ).

cnf(f_1153_3,plain,
    class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1153_2]) ).

fof(f_1154_1,plain,
    class_Rings_Oordered__ring(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__ring]) ).

fof(f_1154_2,plain,
    class_Rings_Oordered__ring(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1154_1]) ).

cnf(f_1154_3,plain,
    class_Rings_Oordered__ring(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1154_2]) ).

fof(f_1155_1,plain,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).

fof(f_1155_2,plain,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1155_1]) ).

cnf(f_1155_3,plain,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1155_2]) ).

fof(f_1156_1,plain,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]) ).

fof(f_1156_2,plain,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1156_1]) ).

cnf(f_1156_3,plain,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1156_2]) ).

fof(f_1157_1,plain,
    class_Groups_Omonoid__mult(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__mult]) ).

fof(f_1157_2,plain,
    class_Groups_Omonoid__mult(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1157_1]) ).

cnf(f_1157_3,plain,
    class_Groups_Omonoid__mult(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1157_2]) ).

fof(f_1158_1,plain,
    class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__ring__1]) ).

fof(f_1158_2,plain,
    class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1158_1]) ).

cnf(f_1158_3,plain,
    class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1158_2]) ).

fof(f_1159_1,plain,
    class_Groups_Omonoid__add(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__add]) ).

fof(f_1159_2,plain,
    class_Groups_Omonoid__add(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1159_1]) ).

cnf(f_1159_3,plain,
    class_Groups_Omonoid__add(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1159_2]) ).

fof(f_1160_1,plain,
    class_Rings_Osemiring__1(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring__1]) ).

fof(f_1160_2,plain,
    class_Rings_Osemiring__1(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1160_1]) ).

cnf(f_1160_3,plain,
    class_Rings_Osemiring__1(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1160_2]) ).

fof(f_1161_1,plain,
    class_Rings_Osemiring__0(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring__0]) ).

fof(f_1161_2,plain,
    class_Rings_Osemiring__0(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1161_1]) ).

cnf(f_1161_3,plain,
    class_Rings_Osemiring__0(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1161_2]) ).

fof(f_1162_1,plain,
    class_Groups_Ogroup__add(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ogroup__add]) ).

fof(f_1162_2,plain,
    class_Groups_Ogroup__add(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1162_1]) ).

cnf(f_1162_3,plain,
    class_Groups_Ogroup__add(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1162_2]) ).

fof(f_1163_1,plain,
    class_Rings_Omult__zero(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Omult__zero]) ).

fof(f_1163_2,plain,
    class_Rings_Omult__zero(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1163_1]) ).

cnf(f_1163_3,plain,
    class_Rings_Omult__zero(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1163_2]) ).

fof(f_1164_1,plain,
    class_Orderings_Oorder(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]) ).

fof(f_1164_2,plain,
    class_Orderings_Oorder(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1164_1]) ).

cnf(f_1164_3,plain,
    class_Orderings_Oorder(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1164_2]) ).

fof(f_1165_1,plain,
    class_Int_Oring__char__0(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Int_Oring__char__0]) ).

fof(f_1165_2,plain,
    class_Int_Oring__char__0(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1165_1]) ).

cnf(f_1165_3,plain,
    class_Int_Oring__char__0(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1165_2]) ).

fof(f_1166_1,plain,
    class_Int_Onumber__ring(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Int_Onumber__ring]) ).

fof(f_1166_2,plain,
    class_Int_Onumber__ring(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1166_1]) ).

cnf(f_1166_3,plain,
    class_Int_Onumber__ring(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1166_2]) ).

fof(f_1167_1,plain,
    class_Rings_Osemiring(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring]) ).

fof(f_1167_2,plain,
    class_Rings_Osemiring(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1167_1]) ).

cnf(f_1167_3,plain,
    class_Rings_Osemiring(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1167_2]) ).

fof(f_1168_1,plain,
    class_Orderings_Oord(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Orderings_Oord]) ).

fof(f_1168_2,plain,
    class_Orderings_Oord(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1168_1]) ).

cnf(f_1168_3,plain,
    class_Orderings_Oord(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1168_2]) ).

fof(f_1169_1,plain,
    class_Rings_Oring__1(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oring__1]) ).

fof(f_1169_2,plain,
    class_Rings_Oring__1(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1169_1]) ).

cnf(f_1169_3,plain,
    class_Rings_Oring__1(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1169_2]) ).

fof(f_1170_1,plain,
    class_Fields_Ofield(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Fields_Ofield]) ).

fof(f_1170_2,plain,
    class_Fields_Ofield(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1170_1]) ).

cnf(f_1170_3,plain,
    class_Fields_Ofield(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1170_2]) ).

fof(f_1171_1,plain,
    class_Power_Opower(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Power_Opower]) ).

fof(f_1171_2,plain,
    class_Power_Opower(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1171_1]) ).

cnf(f_1171_3,plain,
    class_Power_Opower(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1171_2]) ).

fof(f_1172_1,plain,
    class_Groups_Ozero(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ozero]) ).

fof(f_1172_2,plain,
    class_Groups_Ozero(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1172_1]) ).

cnf(f_1172_3,plain,
    class_Groups_Ozero(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1172_2]) ).

fof(f_1173_1,plain,
    class_Rings_Oring(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oring]) ).

fof(f_1173_2,plain,
    class_Rings_Oring(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1173_1]) ).

cnf(f_1173_3,plain,
    class_Rings_Oring(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1173_2]) ).

fof(f_1174_1,plain,
    class_Int_Onumber(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Int_Onumber]) ).

fof(f_1174_2,plain,
    class_Int_Onumber(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1174_1]) ).

cnf(f_1174_3,plain,
    class_Int_Onumber(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1174_2]) ).

fof(f_1175_1,plain,
    class_Groups_Oone(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oone]) ).

fof(f_1175_2,plain,
    class_Groups_Oone(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1175_1]) ).

cnf(f_1175_3,plain,
    class_Groups_Oone(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1175_2]) ).

fof(f_1176_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_1176_2,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1176_1]) ).

cnf(f_1176_3,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1176_2]) ).

fof(f_1177_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_1177_2,plain,
    class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1177_1]) ).

cnf(f_1177_3,plain,
    class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1177_2]) ).

fof(f_1178_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_1178_2,plain,
    class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1178_1]) ).

cnf(f_1178_3,plain,
    class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1178_2]) ).

fof(f_1179_1,plain,
    class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra]) ).

fof(f_1179_2,plain,
    class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1179_1]) ).

cnf(f_1179_3,plain,
    class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1179_2]) ).

fof(f_1180_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_1180_2,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1180_1]) ).

cnf(f_1180_3,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1180_2]) ).

fof(f_1181_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_1181_2,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1181_1]) ).

cnf(f_1181_3,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1181_2]) ).

fof(f_1182_1,plain,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).

fof(f_1182_2,plain,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1182_1]) ).

cnf(f_1182_3,plain,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1182_2]) ).

fof(f_1183_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_1183_2,plain,
    class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1183_1]) ).

cnf(f_1183_3,plain,
    class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1183_2]) ).

fof(f_1184_1,plain,
    class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add]) ).

fof(f_1184_2,plain,
    class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1184_1]) ).

cnf(f_1184_3,plain,
    class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1184_2]) ).

fof(f_1185_1,plain,
    class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__semigroup__mult]) ).

fof(f_1185_2,plain,
    class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1185_1]) ).

cnf(f_1185_3,plain,
    class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1185_2]) ).

fof(f_1186_1,plain,
    class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult]) ).

fof(f_1186_2,plain,
    class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1186_1]) ).

cnf(f_1186_3,plain,
    class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1186_2]) ).

fof(f_1187_1,plain,
    class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__semigroup__add]) ).

fof(f_1187_2,plain,
    class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1187_1]) ).

cnf(f_1187_3,plain,
    class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1187_2]) ).

fof(f_1188_1,plain,
    class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ono__zero__divisors]) ).

fof(f_1188_2,plain,
    class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1188_1]) ).

cnf(f_1188_3,plain,
    class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1188_2]) ).

fof(f_1189_1,plain,
    class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocomm__monoid__add]) ).

fof(f_1189_2,plain,
    class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1189_1]) ).

cnf(f_1189_3,plain,
    class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1189_2]) ).

fof(f_1190_1,plain,
    class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]) ).

fof(f_1190_2,plain,
    class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1190_1]) ).

cnf(f_1190_3,plain,
    class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1190_2]) ).

fof(f_1191_1,plain,
    class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring]) ).

fof(f_1191_2,plain,
    class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1191_1]) ).

cnf(f_1191_3,plain,
    class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1191_2]) ).

fof(f_1192_1,plain,
    class_Nat_Osemiring__char__0(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Nat_Osemiring__char__0]) ).

fof(f_1192_2,plain,
    class_Nat_Osemiring__char__0(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1192_1]) ).

cnf(f_1192_3,plain,
    class_Nat_Osemiring__char__0(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1192_2]) ).

fof(f_1193_1,plain,
    class_Groups_Oab__group__add(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__group__add]) ).

fof(f_1193_2,plain,
    class_Groups_Oab__group__add(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1193_1]) ).

cnf(f_1193_3,plain,
    class_Groups_Oab__group__add(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1193_2]) ).

fof(f_1194_1,plain,
    class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ozero__neq__one]) ).

fof(f_1194_2,plain,
    class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1194_1]) ).

cnf(f_1194_3,plain,
    class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1194_2]) ).

fof(f_1195_1,plain,
    class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__mult]) ).

fof(f_1195_2,plain,
    class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1195_1]) ).

cnf(f_1195_3,plain,
    class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1195_2]) ).

fof(f_1196_1,plain,
    class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__ring__1]) ).

fof(f_1196_2,plain,
    class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1196_1]) ).

cnf(f_1196_3,plain,
    class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1196_2]) ).

fof(f_1197_1,plain,
    class_Groups_Omonoid__add(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__add]) ).

fof(f_1197_2,plain,
    class_Groups_Omonoid__add(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1197_1]) ).

cnf(f_1197_3,plain,
    class_Groups_Omonoid__add(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1197_2]) ).

fof(f_1198_1,plain,
    class_Rings_Osemiring__1(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring__1]) ).

fof(f_1198_2,plain,
    class_Rings_Osemiring__1(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1198_1]) ).

cnf(f_1198_3,plain,
    class_Rings_Osemiring__1(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1198_2]) ).

fof(f_1199_1,plain,
    class_Rings_Osemiring__0(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring__0]) ).

fof(f_1199_2,plain,
    class_Rings_Osemiring__0(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1199_1]) ).

cnf(f_1199_3,plain,
    class_Rings_Osemiring__0(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1199_2]) ).

fof(f_1200_1,plain,
    class_Groups_Ogroup__add(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ogroup__add]) ).

fof(f_1200_2,plain,
    class_Groups_Ogroup__add(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1200_1]) ).

cnf(f_1200_3,plain,
    class_Groups_Ogroup__add(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1200_2]) ).

fof(f_1201_1,plain,
    class_Rings_Omult__zero(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Omult__zero]) ).

fof(f_1201_2,plain,
    class_Rings_Omult__zero(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1201_1]) ).

cnf(f_1201_3,plain,
    class_Rings_Omult__zero(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1201_2]) ).

fof(f_1202_1,plain,
    class_Int_Oring__char__0(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Int_Oring__char__0]) ).

fof(f_1202_2,plain,
    class_Int_Oring__char__0(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1202_1]) ).

cnf(f_1202_3,plain,
    class_Int_Oring__char__0(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1202_2]) ).

fof(f_1203_1,plain,
    class_Int_Onumber__ring(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Int_Onumber__ring]) ).

fof(f_1203_2,plain,
    class_Int_Onumber__ring(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1203_1]) ).

cnf(f_1203_3,plain,
    class_Int_Onumber__ring(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1203_2]) ).

fof(f_1204_1,plain,
    class_Rings_Osemiring(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring]) ).

fof(f_1204_2,plain,
    class_Rings_Osemiring(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1204_1]) ).

cnf(f_1204_3,plain,
    class_Rings_Osemiring(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1204_2]) ).

fof(f_1205_1,plain,
    class_Rings_Oring__1(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring__1]) ).

fof(f_1205_2,plain,
    class_Rings_Oring__1(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1205_1]) ).

cnf(f_1205_3,plain,
    class_Rings_Oring__1(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1205_2]) ).

fof(f_1206_1,plain,
    class_Fields_Ofield(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Fields_Ofield]) ).

fof(f_1206_2,plain,
    class_Fields_Ofield(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1206_1]) ).

cnf(f_1206_3,plain,
    class_Fields_Ofield(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1206_2]) ).

fof(f_1207_1,plain,
    class_Power_Opower(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Power_Opower]) ).

fof(f_1207_2,plain,
    class_Power_Opower(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1207_1]) ).

cnf(f_1207_3,plain,
    class_Power_Opower(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1207_2]) ).

fof(f_1208_1,plain,
    class_Groups_Ozero(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ozero]) ).

fof(f_1208_2,plain,
    class_Groups_Ozero(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1208_1]) ).

cnf(f_1208_3,plain,
    class_Groups_Ozero(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1208_2]) ).

fof(f_1209_1,plain,
    class_Rings_Oring(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring]) ).

fof(f_1209_2,plain,
    class_Rings_Oring(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1209_1]) ).

cnf(f_1209_3,plain,
    class_Rings_Oring(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1209_2]) ).

fof(f_1210_1,plain,
    class_Int_Onumber(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Int_Onumber]) ).

fof(f_1210_2,plain,
    class_Int_Onumber(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1210_1]) ).

cnf(f_1210_3,plain,
    class_Int_Onumber(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1210_2]) ).

fof(f_1211_1,plain,
    class_Groups_Oone(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Oone]) ).

fof(f_1211_2,plain,
    class_Groups_Oone(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1211_1]) ).

cnf(f_1211_3,plain,
    class_Groups_Oone(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1211_2]) ).

fof(f_1212_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_1212_2,plain,
    ! [U_3128] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(U_3128))
      | ~ class_Rings_Oidom(U_3128) ),
    inference(variable_rename,[status(thm)],[f_1212_1]) ).

fof(f_1212_3,plain,
    ! [U_3128] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(U_3128))
      | ~ class_Rings_Oidom(U_3128) ),
    inference(definitional_conversion,[status(esa)],[f_1212_2]) ).

cnf(f_1212_4,plain,
    ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(U_3128))
    | ~ class_Rings_Oidom(U_3128) ),
    inference(clausify,[status(thm)],[f_1212_3]) ).

fof(f_1213_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_1213_2,plain,
    ! [U_3129] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(U_3129))
      | ~ class_Rings_Olinordered__idom(U_3129) ),
    inference(variable_rename,[status(thm)],[f_1213_1]) ).

fof(f_1213_3,plain,
    ! [U_3129] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(U_3129))
      | ~ class_Rings_Olinordered__idom(U_3129) ),
    inference(definitional_conversion,[status(esa)],[f_1213_2]) ).

cnf(f_1213_4,plain,
    ( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(U_3129))
    | ~ class_Rings_Olinordered__idom(U_3129) ),
    inference(clausify,[status(thm)],[f_1213_3]) ).

fof(f_1214_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_1214_2,plain,
    ! [U_3130] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(U_3130))
      | ~ class_Rings_Olinordered__idom(U_3130) ),
    inference(variable_rename,[status(thm)],[f_1214_1]) ).

fof(f_1214_3,plain,
    ! [U_3130] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(U_3130))
      | ~ class_Rings_Olinordered__idom(U_3130) ),
    inference(definitional_conversion,[status(esa)],[f_1214_2]) ).

cnf(f_1214_4,plain,
    ( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(U_3130))
    | ~ class_Rings_Olinordered__idom(U_3130) ),
    inference(clausify,[status(thm)],[f_1214_3]) ).

fof(f_1215_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_1215_2,plain,
    ! [U_3131] :
      ( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(U_3131))
      | ~ class_Rings_Olinordered__idom(U_3131) ),
    inference(variable_rename,[status(thm)],[f_1215_1]) ).

fof(f_1215_3,plain,
    ! [U_3131] :
      ( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(U_3131))
      | ~ class_Rings_Olinordered__idom(U_3131) ),
    inference(definitional_conversion,[status(esa)],[f_1215_2]) ).

cnf(f_1215_4,plain,
    ( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(U_3131))
    | ~ class_Rings_Olinordered__idom(U_3131) ),
    inference(clausify,[status(thm)],[f_1215_3]) ).

fof(f_1216_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_1216_2,plain,
    ! [U_3132] :
      ( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(U_3132))
      | ~ class_Rings_Olinordered__idom(U_3132) ),
    inference(variable_rename,[status(thm)],[f_1216_1]) ).

fof(f_1216_3,plain,
    ! [U_3132] :
      ( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(U_3132))
      | ~ class_Rings_Olinordered__idom(U_3132) ),
    inference(definitional_conversion,[status(esa)],[f_1216_2]) ).

cnf(f_1216_4,plain,
    ( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(U_3132))
    | ~ class_Rings_Olinordered__idom(U_3132) ),
    inference(clausify,[status(thm)],[f_1216_3]) ).

fof(f_1217_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_1217_2,plain,
    ! [U_3133] :
      ( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(U_3133))
      | ~ class_Rings_Olinordered__idom(U_3133) ),
    inference(variable_rename,[status(thm)],[f_1217_1]) ).

fof(f_1217_3,plain,
    ! [U_3133] :
      ( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(U_3133))
      | ~ class_Rings_Olinordered__idom(U_3133) ),
    inference(definitional_conversion,[status(esa)],[f_1217_2]) ).

cnf(f_1217_4,plain,
    ( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(U_3133))
    | ~ class_Rings_Olinordered__idom(U_3133) ),
    inference(clausify,[status(thm)],[f_1217_3]) ).

fof(f_1218_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_1218_2,plain,
    ! [U_3134] :
      ( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(U_3134))
      | ~ class_Rings_Olinordered__idom(U_3134) ),
    inference(variable_rename,[status(thm)],[f_1218_1]) ).

fof(f_1218_3,plain,
    ! [U_3134] :
      ( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(U_3134))
      | ~ class_Rings_Olinordered__idom(U_3134) ),
    inference(definitional_conversion,[status(esa)],[f_1218_2]) ).

cnf(f_1218_4,plain,
    ( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(U_3134))
    | ~ class_Rings_Olinordered__idom(U_3134) ),
    inference(clausify,[status(thm)],[f_1218_3]) ).

fof(f_1219_1,plain,
    ! [T_1] :
      ( class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Olinordered__idom(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs]) ).

fof(f_1219_2,plain,
    ! [U_3135] :
      ( class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(U_3135))
      | ~ class_Rings_Olinordered__idom(U_3135) ),
    inference(variable_rename,[status(thm)],[f_1219_1]) ).

fof(f_1219_3,plain,
    ! [U_3135] :
      ( class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(U_3135))
      | ~ class_Rings_Olinordered__idom(U_3135) ),
    inference(definitional_conversion,[status(esa)],[f_1219_2]) ).

cnf(f_1219_4,plain,
    ( class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(U_3135))
    | ~ class_Rings_Olinordered__idom(U_3135) ),
    inference(clausify,[status(thm)],[f_1219_3]) ).

fof(f_1220_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_1220_2,plain,
    ! [U_3136] :
      ( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(U_3136))
      | ~ class_Rings_Olinordered__idom(U_3136) ),
    inference(variable_rename,[status(thm)],[f_1220_1]) ).

fof(f_1220_3,plain,
    ! [U_3136] :
      ( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(U_3136))
      | ~ class_Rings_Olinordered__idom(U_3136) ),
    inference(definitional_conversion,[status(esa)],[f_1220_2]) ).

cnf(f_1220_4,plain,
    ( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(U_3136))
    | ~ class_Rings_Olinordered__idom(U_3136) ),
    inference(clausify,[status(thm)],[f_1220_3]) ).

fof(f_1221_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_1221_2,plain,
    ! [U_3137] :
      ( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(U_3137))
      | ~ class_Rings_Olinordered__idom(U_3137) ),
    inference(variable_rename,[status(thm)],[f_1221_1]) ).

fof(f_1221_3,plain,
    ! [U_3137] :
      ( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(U_3137))
      | ~ class_Rings_Olinordered__idom(U_3137) ),
    inference(definitional_conversion,[status(esa)],[f_1221_2]) ).

cnf(f_1221_4,plain,
    ( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(U_3137))
    | ~ class_Rings_Olinordered__idom(U_3137) ),
    inference(clausify,[status(thm)],[f_1221_3]) ).

fof(f_1222_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_1222_2,plain,
    ! [U_3138] :
      ( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(U_3138))
      | ~ class_Groups_Ocancel__comm__monoid__add(U_3138) ),
    inference(variable_rename,[status(thm)],[f_1222_1]) ).

fof(f_1222_3,plain,
    ! [U_3138] :
      ( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(U_3138))
      | ~ class_Groups_Ocancel__comm__monoid__add(U_3138) ),
    inference(definitional_conversion,[status(esa)],[f_1222_2]) ).

cnf(f_1222_4,plain,
    ( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(U_3138))
    | ~ class_Groups_Ocancel__comm__monoid__add(U_3138) ),
    inference(clausify,[status(thm)],[f_1222_3]) ).

fof(f_1223_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_1223_2,plain,
    ! [U_3139] :
      ( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(U_3139))
      | ~ class_Rings_Oidom(U_3139) ),
    inference(variable_rename,[status(thm)],[f_1223_1]) ).

fof(f_1223_3,plain,
    ! [U_3139] :
      ( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(U_3139))
      | ~ class_Rings_Oidom(U_3139) ),
    inference(definitional_conversion,[status(esa)],[f_1223_2]) ).

cnf(f_1223_4,plain,
    ( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(U_3139))
    | ~ class_Rings_Oidom(U_3139) ),
    inference(clausify,[status(thm)],[f_1223_3]) ).

fof(f_1224_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_1224_2,plain,
    ! [U_3140] :
      ( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(U_3140))
      | ~ class_Rings_Olinordered__idom(U_3140) ),
    inference(variable_rename,[status(thm)],[f_1224_1]) ).

fof(f_1224_3,plain,
    ! [U_3140] :
      ( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(U_3140))
      | ~ class_Rings_Olinordered__idom(U_3140) ),
    inference(definitional_conversion,[status(esa)],[f_1224_2]) ).

cnf(f_1224_4,plain,
    ( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(U_3140))
    | ~ class_Rings_Olinordered__idom(U_3140) ),
    inference(clausify,[status(thm)],[f_1224_3]) ).

fof(f_1225_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_1225_2,plain,
    ! [U_3141] :
      ( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(U_3141))
      | ~ class_Rings_Olinordered__idom(U_3141) ),
    inference(variable_rename,[status(thm)],[f_1225_1]) ).

fof(f_1225_3,plain,
    ! [U_3141] :
      ( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(U_3141))
      | ~ class_Rings_Olinordered__idom(U_3141) ),
    inference(definitional_conversion,[status(esa)],[f_1225_2]) ).

cnf(f_1225_4,plain,
    ( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(U_3141))
    | ~ class_Rings_Olinordered__idom(U_3141) ),
    inference(clausify,[status(thm)],[f_1225_3]) ).

fof(f_1226_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_1226_2,plain,
    ! [U_3142] :
      ( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(U_3142))
      | ~ class_Rings_Oidom(U_3142) ),
    inference(variable_rename,[status(thm)],[f_1226_1]) ).

fof(f_1226_3,plain,
    ! [U_3142] :
      ( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(U_3142))
      | ~ class_Rings_Oidom(U_3142) ),
    inference(definitional_conversion,[status(esa)],[f_1226_2]) ).

cnf(f_1226_4,plain,
    ( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(U_3142))
    | ~ class_Rings_Oidom(U_3142) ),
    inference(clausify,[status(thm)],[f_1226_3]) ).

fof(f_1227_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_1227_2,plain,
    ! [U_3143] :
      ( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(U_3143))
      | ~ class_Rings_Olinordered__idom(U_3143) ),
    inference(variable_rename,[status(thm)],[f_1227_1]) ).

fof(f_1227_3,plain,
    ! [U_3143] :
      ( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(U_3143))
      | ~ class_Rings_Olinordered__idom(U_3143) ),
    inference(definitional_conversion,[status(esa)],[f_1227_2]) ).

cnf(f_1227_4,plain,
    ( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(U_3143))
    | ~ class_Rings_Olinordered__idom(U_3143) ),
    inference(clausify,[status(thm)],[f_1227_3]) ).

fof(f_1228_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_1228_2,plain,
    ! [U_3144] :
      ( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(U_3144))
      | ~ class_Rings_Olinordered__idom(U_3144) ),
    inference(variable_rename,[status(thm)],[f_1228_1]) ).

fof(f_1228_3,plain,
    ! [U_3144] :
      ( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(U_3144))
      | ~ class_Rings_Olinordered__idom(U_3144) ),
    inference(definitional_conversion,[status(esa)],[f_1228_2]) ).

cnf(f_1228_4,plain,
    ( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(U_3144))
    | ~ class_Rings_Olinordered__idom(U_3144) ),
    inference(clausify,[status(thm)],[f_1228_3]) ).

fof(f_1229_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_1229_2,plain,
    ! [U_3145] :
      ( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(U_3145))
      | ~ class_Rings_Olinordered__idom(U_3145) ),
    inference(variable_rename,[status(thm)],[f_1229_1]) ).

fof(f_1229_3,plain,
    ! [U_3145] :
      ( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(U_3145))
      | ~ class_Rings_Olinordered__idom(U_3145) ),
    inference(definitional_conversion,[status(esa)],[f_1229_2]) ).

cnf(f_1229_4,plain,
    ( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(U_3145))
    | ~ class_Rings_Olinordered__idom(U_3145) ),
    inference(clausify,[status(thm)],[f_1229_3]) ).

fof(f_1230_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_1230_2,plain,
    ! [U_3146] :
      ( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(U_3146))
      | ~ class_Groups_Ocancel__comm__monoid__add(U_3146) ),
    inference(variable_rename,[status(thm)],[f_1230_1]) ).

fof(f_1230_3,plain,
    ! [U_3146] :
      ( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(U_3146))
      | ~ class_Groups_Ocancel__comm__monoid__add(U_3146) ),
    inference(definitional_conversion,[status(esa)],[f_1230_2]) ).

cnf(f_1230_4,plain,
    ( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(U_3146))
    | ~ class_Groups_Ocancel__comm__monoid__add(U_3146) ),
    inference(clausify,[status(thm)],[f_1230_3]) ).

fof(f_1231_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_1231_2,plain,
    ! [U_3147] :
      ( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(U_3147))
      | ~ class_Rings_Olinordered__idom(U_3147) ),
    inference(variable_rename,[status(thm)],[f_1231_1]) ).

fof(f_1231_3,plain,
    ! [U_3147] :
      ( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(U_3147))
      | ~ class_Rings_Olinordered__idom(U_3147) ),
    inference(definitional_conversion,[status(esa)],[f_1231_2]) ).

cnf(f_1231_4,plain,
    ( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(U_3147))
    | ~ class_Rings_Olinordered__idom(U_3147) ),
    inference(clausify,[status(thm)],[f_1231_3]) ).

fof(f_1232_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_1232_2,plain,
    ! [U_3148] :
      ( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(U_3148))
      | ~ class_Rings_Olinordered__idom(U_3148) ),
    inference(variable_rename,[status(thm)],[f_1232_1]) ).

fof(f_1232_3,plain,
    ! [U_3148] :
      ( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(U_3148))
      | ~ class_Rings_Olinordered__idom(U_3148) ),
    inference(definitional_conversion,[status(esa)],[f_1232_2]) ).

cnf(f_1232_4,plain,
    ( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(U_3148))
    | ~ class_Rings_Olinordered__idom(U_3148) ),
    inference(clausify,[status(thm)],[f_1232_3]) ).

fof(f_1233_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_1233_2,plain,
    ! [U_3149] :
      ( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(U_3149))
      | ~ class_Rings_Ocomm__semiring__0(U_3149) ),
    inference(variable_rename,[status(thm)],[f_1233_1]) ).

fof(f_1233_3,plain,
    ! [U_3149] :
      ( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(U_3149))
      | ~ class_Rings_Ocomm__semiring__0(U_3149) ),
    inference(definitional_conversion,[status(esa)],[f_1233_2]) ).

cnf(f_1233_4,plain,
    ( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(U_3149))
    | ~ class_Rings_Ocomm__semiring__0(U_3149) ),
    inference(clausify,[status(thm)],[f_1233_3]) ).

fof(f_1234_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_1234_2,plain,
    ! [U_3150] :
      ( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(U_3150))
      | ~ class_Rings_Ocomm__semiring__1(U_3150) ),
    inference(variable_rename,[status(thm)],[f_1234_1]) ).

fof(f_1234_3,plain,
    ! [U_3150] :
      ( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(U_3150))
      | ~ class_Rings_Ocomm__semiring__1(U_3150) ),
    inference(definitional_conversion,[status(esa)],[f_1234_2]) ).

cnf(f_1234_4,plain,
    ( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(U_3150))
    | ~ class_Rings_Ocomm__semiring__1(U_3150) ),
    inference(clausify,[status(thm)],[f_1234_3]) ).

fof(f_1235_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_1235_2,plain,
    ! [U_3151] :
      ( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(U_3151))
      | ~ class_Groups_Ocomm__monoid__add(U_3151) ),
    inference(variable_rename,[status(thm)],[f_1235_1]) ).

fof(f_1235_3,plain,
    ! [U_3151] :
      ( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(U_3151))
      | ~ class_Groups_Ocomm__monoid__add(U_3151) ),
    inference(definitional_conversion,[status(esa)],[f_1235_2]) ).

cnf(f_1235_4,plain,
    ( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(U_3151))
    | ~ class_Groups_Ocomm__monoid__add(U_3151) ),
    inference(clausify,[status(thm)],[f_1235_3]) ).

fof(f_1236_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_1236_2,plain,
    ! [U_3152] :
      ( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(U_3152))
      | ~ class_Rings_Olinordered__idom(U_3152) ),
    inference(variable_rename,[status(thm)],[f_1236_1]) ).

fof(f_1236_3,plain,
    ! [U_3152] :
      ( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(U_3152))
      | ~ class_Rings_Olinordered__idom(U_3152) ),
    inference(definitional_conversion,[status(esa)],[f_1236_2]) ).

cnf(f_1236_4,plain,
    ( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(U_3152))
    | ~ class_Rings_Olinordered__idom(U_3152) ),
    inference(clausify,[status(thm)],[f_1236_3]) ).

fof(f_1237_1,plain,
    ! [T_1] :
      ( class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Olinordered__idom(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__ring__abs]) ).

fof(f_1237_2,plain,
    ! [U_3153] :
      ( class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(U_3153))
      | ~ class_Rings_Olinordered__idom(U_3153) ),
    inference(variable_rename,[status(thm)],[f_1237_1]) ).

fof(f_1237_3,plain,
    ! [U_3153] :
      ( class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(U_3153))
      | ~ class_Rings_Olinordered__idom(U_3153) ),
    inference(definitional_conversion,[status(esa)],[f_1237_2]) ).

cnf(f_1237_4,plain,
    ( class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(U_3153))
    | ~ class_Rings_Olinordered__idom(U_3153) ),
    inference(clausify,[status(thm)],[f_1237_3]) ).

fof(f_1238_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_1238_2,plain,
    ! [U_3154] :
      ( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(U_3154))
      | ~ class_Rings_Oidom(U_3154) ),
    inference(variable_rename,[status(thm)],[f_1238_1]) ).

fof(f_1238_3,plain,
    ! [U_3154] :
      ( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(U_3154))
      | ~ class_Rings_Oidom(U_3154) ),
    inference(definitional_conversion,[status(esa)],[f_1238_2]) ).

cnf(f_1238_4,plain,
    ( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(U_3154))
    | ~ class_Rings_Oidom(U_3154) ),
    inference(clausify,[status(thm)],[f_1238_3]) ).

fof(f_1239_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_1239_2,plain,
    ! [U_3155] :
      ( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(U_3155))
      | ~ class_Groups_Ocomm__monoid__add(U_3155) ),
    inference(variable_rename,[status(thm)],[f_1239_1]) ).

fof(f_1239_3,plain,
    ! [U_3155] :
      ( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(U_3155))
      | ~ class_Groups_Ocomm__monoid__add(U_3155) ),
    inference(definitional_conversion,[status(esa)],[f_1239_2]) ).

cnf(f_1239_4,plain,
    ( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(U_3155))
    | ~ class_Groups_Ocomm__monoid__add(U_3155) ),
    inference(clausify,[status(thm)],[f_1239_3]) ).

fof(f_1240_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_1240_2,plain,
    ! [U_3156] :
      ( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(U_3156))
      | ~ class_Rings_Olinordered__idom(U_3156) ),
    inference(variable_rename,[status(thm)],[f_1240_1]) ).

fof(f_1240_3,plain,
    ! [U_3156] :
      ( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(U_3156))
      | ~ class_Rings_Olinordered__idom(U_3156) ),
    inference(definitional_conversion,[status(esa)],[f_1240_2]) ).

cnf(f_1240_4,plain,
    ( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(U_3156))
    | ~ class_Rings_Olinordered__idom(U_3156) ),
    inference(clausify,[status(thm)],[f_1240_3]) ).

fof(f_1241_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_1241_2,plain,
    ! [U_3157] :
      ( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(U_3157))
      | ~ class_Rings_Olinordered__idom(U_3157) ),
    inference(variable_rename,[status(thm)],[f_1241_1]) ).

fof(f_1241_3,plain,
    ! [U_3157] :
      ( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(U_3157))
      | ~ class_Rings_Olinordered__idom(U_3157) ),
    inference(definitional_conversion,[status(esa)],[f_1241_2]) ).

cnf(f_1241_4,plain,
    ( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(U_3157))
    | ~ class_Rings_Olinordered__idom(U_3157) ),
    inference(clausify,[status(thm)],[f_1241_3]) ).

fof(f_1242_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_1242_2,plain,
    ! [U_3158] :
      ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(U_3158))
      | ~ class_Rings_Ocomm__semiring__1(U_3158) ),
    inference(variable_rename,[status(thm)],[f_1242_1]) ).

fof(f_1242_3,plain,
    ! [U_3158] :
      ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(U_3158))
      | ~ class_Rings_Ocomm__semiring__1(U_3158) ),
    inference(definitional_conversion,[status(esa)],[f_1242_2]) ).

cnf(f_1242_4,plain,
    ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(U_3158))
    | ~ class_Rings_Ocomm__semiring__1(U_3158) ),
    inference(clausify,[status(thm)],[f_1242_3]) ).

fof(f_1243_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_1243_2,plain,
    ! [U_3159] :
      ( class_Divides_Osemiring__div(tc_Polynomial_Opoly(U_3159))
      | ~ class_Fields_Ofield(U_3159) ),
    inference(variable_rename,[status(thm)],[f_1243_1]) ).

fof(f_1243_3,plain,
    ! [U_3159] :
      ( class_Divides_Osemiring__div(tc_Polynomial_Opoly(U_3159))
      | ~ class_Fields_Ofield(U_3159) ),
    inference(definitional_conversion,[status(esa)],[f_1243_2]) ).

cnf(f_1243_4,plain,
    ( class_Divides_Osemiring__div(tc_Polynomial_Opoly(U_3159))
    | ~ class_Fields_Ofield(U_3159) ),
    inference(clausify,[status(thm)],[f_1243_3]) ).

fof(f_1244_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_1244_2,plain,
    ! [U_3160] :
      ( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(U_3160))
      | ~ class_Rings_Ocomm__semiring__0(U_3160) ),
    inference(variable_rename,[status(thm)],[f_1244_1]) ).

fof(f_1244_3,plain,
    ! [U_3160] :
      ( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(U_3160))
      | ~ class_Rings_Ocomm__semiring__0(U_3160) ),
    inference(definitional_conversion,[status(esa)],[f_1244_2]) ).

cnf(f_1244_4,plain,
    ( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(U_3160))
    | ~ class_Rings_Ocomm__semiring__0(U_3160) ),
    inference(clausify,[status(thm)],[f_1244_3]) ).

fof(f_1245_1,plain,
    ! [T_1] :
      ( class_Nat_Osemiring__char__0(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Olinordered__idom(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Nat_Osemiring__char__0]) ).

fof(f_1245_2,plain,
    ! [U_3161] :
      ( class_Nat_Osemiring__char__0(tc_Polynomial_Opoly(U_3161))
      | ~ class_Rings_Olinordered__idom(U_3161) ),
    inference(variable_rename,[status(thm)],[f_1245_1]) ).

fof(f_1245_3,plain,
    ! [U_3161] :
      ( class_Nat_Osemiring__char__0(tc_Polynomial_Opoly(U_3161))
      | ~ class_Rings_Olinordered__idom(U_3161) ),
    inference(definitional_conversion,[status(esa)],[f_1245_2]) ).

cnf(f_1245_4,plain,
    ( class_Nat_Osemiring__char__0(tc_Polynomial_Opoly(U_3161))
    | ~ class_Rings_Olinordered__idom(U_3161) ),
    inference(clausify,[status(thm)],[f_1245_3]) ).

fof(f_1246_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_1246_2,plain,
    ! [U_3162] :
      ( class_Groups_Oab__group__add(tc_Polynomial_Opoly(U_3162))
      | ~ class_Groups_Oab__group__add(U_3162) ),
    inference(variable_rename,[status(thm)],[f_1246_1]) ).

fof(f_1246_3,plain,
    ! [U_3162] :
      ( class_Groups_Oab__group__add(tc_Polynomial_Opoly(U_3162))
      | ~ class_Groups_Oab__group__add(U_3162) ),
    inference(definitional_conversion,[status(esa)],[f_1246_2]) ).

cnf(f_1246_4,plain,
    ( class_Groups_Oab__group__add(tc_Polynomial_Opoly(U_3162))
    | ~ class_Groups_Oab__group__add(U_3162) ),
    inference(clausify,[status(thm)],[f_1246_3]) ).

fof(f_1247_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_1247_2,plain,
    ! [U_3163] :
      ( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(U_3163))
      | ~ class_Rings_Ocomm__semiring__1(U_3163) ),
    inference(variable_rename,[status(thm)],[f_1247_1]) ).

fof(f_1247_3,plain,
    ! [U_3163] :
      ( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(U_3163))
      | ~ class_Rings_Ocomm__semiring__1(U_3163) ),
    inference(definitional_conversion,[status(esa)],[f_1247_2]) ).

cnf(f_1247_4,plain,
    ( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(U_3163))
    | ~ class_Rings_Ocomm__semiring__1(U_3163) ),
    inference(clausify,[status(thm)],[f_1247_3]) ).

fof(f_1248_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_1248_2,plain,
    ! [U_3164] :
      ( class_Rings_Oordered__ring(tc_Polynomial_Opoly(U_3164))
      | ~ class_Rings_Olinordered__idom(U_3164) ),
    inference(variable_rename,[status(thm)],[f_1248_1]) ).

fof(f_1248_3,plain,
    ! [U_3164] :
      ( class_Rings_Oordered__ring(tc_Polynomial_Opoly(U_3164))
      | ~ class_Rings_Olinordered__idom(U_3164) ),
    inference(definitional_conversion,[status(esa)],[f_1248_2]) ).

cnf(f_1248_4,plain,
    ( class_Rings_Oordered__ring(tc_Polynomial_Opoly(U_3164))
    | ~ class_Rings_Olinordered__idom(U_3164) ),
    inference(clausify,[status(thm)],[f_1248_3]) ).

fof(f_1249_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_1249_2,plain,
    ! [U_3165] :
      ( class_Orderings_Opreorder(tc_Polynomial_Opoly(U_3165))
      | ~ class_Rings_Olinordered__idom(U_3165) ),
    inference(variable_rename,[status(thm)],[f_1249_1]) ).

fof(f_1249_3,plain,
    ! [U_3165] :
      ( class_Orderings_Opreorder(tc_Polynomial_Opoly(U_3165))
      | ~ class_Rings_Olinordered__idom(U_3165) ),
    inference(definitional_conversion,[status(esa)],[f_1249_2]) ).

cnf(f_1249_4,plain,
    ( class_Orderings_Opreorder(tc_Polynomial_Opoly(U_3165))
    | ~ class_Rings_Olinordered__idom(U_3165) ),
    inference(clausify,[status(thm)],[f_1249_3]) ).

fof(f_1250_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_1250_2,plain,
    ! [U_3166] :
      ( class_Orderings_Olinorder(tc_Polynomial_Opoly(U_3166))
      | ~ class_Rings_Olinordered__idom(U_3166) ),
    inference(variable_rename,[status(thm)],[f_1250_1]) ).

fof(f_1250_3,plain,
    ! [U_3166] :
      ( class_Orderings_Olinorder(tc_Polynomial_Opoly(U_3166))
      | ~ class_Rings_Olinordered__idom(U_3166) ),
    inference(definitional_conversion,[status(esa)],[f_1250_2]) ).

cnf(f_1250_4,plain,
    ( class_Orderings_Olinorder(tc_Polynomial_Opoly(U_3166))
    | ~ class_Rings_Olinordered__idom(U_3166) ),
    inference(clausify,[status(thm)],[f_1250_3]) ).

fof(f_1251_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_1251_2,plain,
    ! [U_3167] :
      ( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(U_3167))
      | ~ class_Rings_Ocomm__semiring__1(U_3167) ),
    inference(variable_rename,[status(thm)],[f_1251_1]) ).

fof(f_1251_3,plain,
    ! [U_3167] :
      ( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(U_3167))
      | ~ class_Rings_Ocomm__semiring__1(U_3167) ),
    inference(definitional_conversion,[status(esa)],[f_1251_2]) ).

cnf(f_1251_4,plain,
    ( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(U_3167))
    | ~ class_Rings_Ocomm__semiring__1(U_3167) ),
    inference(clausify,[status(thm)],[f_1251_3]) ).

fof(f_1252_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_1252_2,plain,
    ! [U_3168] :
      ( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(U_3168))
      | ~ class_Rings_Ocomm__ring__1(U_3168) ),
    inference(variable_rename,[status(thm)],[f_1252_1]) ).

fof(f_1252_3,plain,
    ! [U_3168] :
      ( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(U_3168))
      | ~ class_Rings_Ocomm__ring__1(U_3168) ),
    inference(definitional_conversion,[status(esa)],[f_1252_2]) ).

cnf(f_1252_4,plain,
    ( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(U_3168))
    | ~ class_Rings_Ocomm__ring__1(U_3168) ),
    inference(clausify,[status(thm)],[f_1252_3]) ).

fof(f_1253_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_1253_2,plain,
    ! [U_3169] :
      ( class_Groups_Omonoid__add(tc_Polynomial_Opoly(U_3169))
      | ~ class_Groups_Ocomm__monoid__add(U_3169) ),
    inference(variable_rename,[status(thm)],[f_1253_1]) ).

fof(f_1253_3,plain,
    ! [U_3169] :
      ( class_Groups_Omonoid__add(tc_Polynomial_Opoly(U_3169))
      | ~ class_Groups_Ocomm__monoid__add(U_3169) ),
    inference(definitional_conversion,[status(esa)],[f_1253_2]) ).

cnf(f_1253_4,plain,
    ( class_Groups_Omonoid__add(tc_Polynomial_Opoly(U_3169))
    | ~ class_Groups_Ocomm__monoid__add(U_3169) ),
    inference(clausify,[status(thm)],[f_1253_3]) ).

fof(f_1254_1,plain,
    ! [T_1] :
      ( class_Rings_Osemiring__1(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Ocomm__semiring__1(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Osemiring__1]) ).

fof(f_1254_2,plain,
    ! [U_3170] :
      ( class_Rings_Osemiring__1(tc_Polynomial_Opoly(U_3170))
      | ~ class_Rings_Ocomm__semiring__1(U_3170) ),
    inference(variable_rename,[status(thm)],[f_1254_1]) ).

fof(f_1254_3,plain,
    ! [U_3170] :
      ( class_Rings_Osemiring__1(tc_Polynomial_Opoly(U_3170))
      | ~ class_Rings_Ocomm__semiring__1(U_3170) ),
    inference(definitional_conversion,[status(esa)],[f_1254_2]) ).

cnf(f_1254_4,plain,
    ( class_Rings_Osemiring__1(tc_Polynomial_Opoly(U_3170))
    | ~ class_Rings_Ocomm__semiring__1(U_3170) ),
    inference(clausify,[status(thm)],[f_1254_3]) ).

fof(f_1255_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_1255_2,plain,
    ! [U_3171] :
      ( class_Rings_Osemiring__0(tc_Polynomial_Opoly(U_3171))
      | ~ class_Rings_Ocomm__semiring__0(U_3171) ),
    inference(variable_rename,[status(thm)],[f_1255_1]) ).

fof(f_1255_3,plain,
    ! [U_3171] :
      ( class_Rings_Osemiring__0(tc_Polynomial_Opoly(U_3171))
      | ~ class_Rings_Ocomm__semiring__0(U_3171) ),
    inference(definitional_conversion,[status(esa)],[f_1255_2]) ).

cnf(f_1255_4,plain,
    ( class_Rings_Osemiring__0(tc_Polynomial_Opoly(U_3171))
    | ~ class_Rings_Ocomm__semiring__0(U_3171) ),
    inference(clausify,[status(thm)],[f_1255_3]) ).

fof(f_1256_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_1256_2,plain,
    ! [U_3172] :
      ( class_Groups_Ogroup__add(tc_Polynomial_Opoly(U_3172))
      | ~ class_Groups_Oab__group__add(U_3172) ),
    inference(variable_rename,[status(thm)],[f_1256_1]) ).

fof(f_1256_3,plain,
    ! [U_3172] :
      ( class_Groups_Ogroup__add(tc_Polynomial_Opoly(U_3172))
      | ~ class_Groups_Oab__group__add(U_3172) ),
    inference(definitional_conversion,[status(esa)],[f_1256_2]) ).

cnf(f_1256_4,plain,
    ( class_Groups_Ogroup__add(tc_Polynomial_Opoly(U_3172))
    | ~ class_Groups_Oab__group__add(U_3172) ),
    inference(clausify,[status(thm)],[f_1256_3]) ).

fof(f_1257_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_1257_2,plain,
    ! [U_3173] :
      ( class_Rings_Omult__zero(tc_Polynomial_Opoly(U_3173))
      | ~ class_Rings_Ocomm__semiring__0(U_3173) ),
    inference(variable_rename,[status(thm)],[f_1257_1]) ).

fof(f_1257_3,plain,
    ! [U_3173] :
      ( class_Rings_Omult__zero(tc_Polynomial_Opoly(U_3173))
      | ~ class_Rings_Ocomm__semiring__0(U_3173) ),
    inference(definitional_conversion,[status(esa)],[f_1257_2]) ).

cnf(f_1257_4,plain,
    ( class_Rings_Omult__zero(tc_Polynomial_Opoly(U_3173))
    | ~ class_Rings_Ocomm__semiring__0(U_3173) ),
    inference(clausify,[status(thm)],[f_1257_3]) ).

fof(f_1258_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_1258_2,plain,
    ! [U_3174] :
      ( class_Orderings_Oorder(tc_Polynomial_Opoly(U_3174))
      | ~ class_Rings_Olinordered__idom(U_3174) ),
    inference(variable_rename,[status(thm)],[f_1258_1]) ).

fof(f_1258_3,plain,
    ! [U_3174] :
      ( class_Orderings_Oorder(tc_Polynomial_Opoly(U_3174))
      | ~ class_Rings_Olinordered__idom(U_3174) ),
    inference(definitional_conversion,[status(esa)],[f_1258_2]) ).

cnf(f_1258_4,plain,
    ( class_Orderings_Oorder(tc_Polynomial_Opoly(U_3174))
    | ~ class_Rings_Olinordered__idom(U_3174) ),
    inference(clausify,[status(thm)],[f_1258_3]) ).

fof(f_1259_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_1259_2,plain,
    ! [U_3175] :
      ( class_Int_Oring__char__0(tc_Polynomial_Opoly(U_3175))
      | ~ class_Rings_Olinordered__idom(U_3175) ),
    inference(variable_rename,[status(thm)],[f_1259_1]) ).

fof(f_1259_3,plain,
    ! [U_3175] :
      ( class_Int_Oring__char__0(tc_Polynomial_Opoly(U_3175))
      | ~ class_Rings_Olinordered__idom(U_3175) ),
    inference(definitional_conversion,[status(esa)],[f_1259_2]) ).

cnf(f_1259_4,plain,
    ( class_Int_Oring__char__0(tc_Polynomial_Opoly(U_3175))
    | ~ class_Rings_Olinordered__idom(U_3175) ),
    inference(clausify,[status(thm)],[f_1259_3]) ).

fof(f_1260_1,plain,
    ! [T_1] :
      ( class_Int_Onumber__ring(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Ocomm__ring__1(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Int_Onumber__ring]) ).

fof(f_1260_2,plain,
    ! [U_3176] :
      ( class_Int_Onumber__ring(tc_Polynomial_Opoly(U_3176))
      | ~ class_Rings_Ocomm__ring__1(U_3176) ),
    inference(variable_rename,[status(thm)],[f_1260_1]) ).

fof(f_1260_3,plain,
    ! [U_3176] :
      ( class_Int_Onumber__ring(tc_Polynomial_Opoly(U_3176))
      | ~ class_Rings_Ocomm__ring__1(U_3176) ),
    inference(definitional_conversion,[status(esa)],[f_1260_2]) ).

cnf(f_1260_4,plain,
    ( class_Int_Onumber__ring(tc_Polynomial_Opoly(U_3176))
    | ~ class_Rings_Ocomm__ring__1(U_3176) ),
    inference(clausify,[status(thm)],[f_1260_3]) ).

fof(f_1261_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_1261_2,plain,
    ! [U_3177] :
      ( class_Rings_Osemiring(tc_Polynomial_Opoly(U_3177))
      | ~ class_Rings_Ocomm__semiring__0(U_3177) ),
    inference(variable_rename,[status(thm)],[f_1261_1]) ).

fof(f_1261_3,plain,
    ! [U_3177] :
      ( class_Rings_Osemiring(tc_Polynomial_Opoly(U_3177))
      | ~ class_Rings_Ocomm__semiring__0(U_3177) ),
    inference(definitional_conversion,[status(esa)],[f_1261_2]) ).

cnf(f_1261_4,plain,
    ( class_Rings_Osemiring(tc_Polynomial_Opoly(U_3177))
    | ~ class_Rings_Ocomm__semiring__0(U_3177) ),
    inference(clausify,[status(thm)],[f_1261_3]) ).

fof(f_1262_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_1262_2,plain,
    ! [U_3178] :
      ( class_Orderings_Oord(tc_Polynomial_Opoly(U_3178))
      | ~ class_Rings_Olinordered__idom(U_3178) ),
    inference(variable_rename,[status(thm)],[f_1262_1]) ).

fof(f_1262_3,plain,
    ! [U_3178] :
      ( class_Orderings_Oord(tc_Polynomial_Opoly(U_3178))
      | ~ class_Rings_Olinordered__idom(U_3178) ),
    inference(definitional_conversion,[status(esa)],[f_1262_2]) ).

cnf(f_1262_4,plain,
    ( class_Orderings_Oord(tc_Polynomial_Opoly(U_3178))
    | ~ class_Rings_Olinordered__idom(U_3178) ),
    inference(clausify,[status(thm)],[f_1262_3]) ).

fof(f_1263_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_1263_2,plain,
    ! [U_3179] :
      ( class_Rings_Oring__1(tc_Polynomial_Opoly(U_3179))
      | ~ class_Rings_Ocomm__ring__1(U_3179) ),
    inference(variable_rename,[status(thm)],[f_1263_1]) ).

fof(f_1263_3,plain,
    ! [U_3179] :
      ( class_Rings_Oring__1(tc_Polynomial_Opoly(U_3179))
      | ~ class_Rings_Ocomm__ring__1(U_3179) ),
    inference(definitional_conversion,[status(esa)],[f_1263_2]) ).

cnf(f_1263_4,plain,
    ( class_Rings_Oring__1(tc_Polynomial_Opoly(U_3179))
    | ~ class_Rings_Ocomm__ring__1(U_3179) ),
    inference(clausify,[status(thm)],[f_1263_3]) ).

fof(f_1264_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_1264_2,plain,
    ! [U_3180] :
      ( class_Power_Opower(tc_Polynomial_Opoly(U_3180))
      | ~ class_Rings_Ocomm__semiring__1(U_3180) ),
    inference(variable_rename,[status(thm)],[f_1264_1]) ).

fof(f_1264_3,plain,
    ! [U_3180] :
      ( class_Power_Opower(tc_Polynomial_Opoly(U_3180))
      | ~ class_Rings_Ocomm__semiring__1(U_3180) ),
    inference(definitional_conversion,[status(esa)],[f_1264_2]) ).

cnf(f_1264_4,plain,
    ( class_Power_Opower(tc_Polynomial_Opoly(U_3180))
    | ~ class_Rings_Ocomm__semiring__1(U_3180) ),
    inference(clausify,[status(thm)],[f_1264_3]) ).

fof(f_1265_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_1265_2,plain,
    ! [U_3181] :
      ( class_Groups_Ozero(tc_Polynomial_Opoly(U_3181))
      | ~ class_Groups_Ozero(U_3181) ),
    inference(variable_rename,[status(thm)],[f_1265_1]) ).

fof(f_1265_3,plain,
    ! [U_3181] :
      ( class_Groups_Ozero(tc_Polynomial_Opoly(U_3181))
      | ~ class_Groups_Ozero(U_3181) ),
    inference(definitional_conversion,[status(esa)],[f_1265_2]) ).

cnf(f_1265_4,plain,
    ( class_Groups_Ozero(tc_Polynomial_Opoly(U_3181))
    | ~ class_Groups_Ozero(U_3181) ),
    inference(clausify,[status(thm)],[f_1265_3]) ).

fof(f_1266_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_1266_2,plain,
    ! [U_3182] :
      ( class_Rings_Oring(tc_Polynomial_Opoly(U_3182))
      | ~ class_Rings_Ocomm__ring(U_3182) ),
    inference(variable_rename,[status(thm)],[f_1266_1]) ).

fof(f_1266_3,plain,
    ! [U_3182] :
      ( class_Rings_Oring(tc_Polynomial_Opoly(U_3182))
      | ~ class_Rings_Ocomm__ring(U_3182) ),
    inference(definitional_conversion,[status(esa)],[f_1266_2]) ).

cnf(f_1266_4,plain,
    ( class_Rings_Oring(tc_Polynomial_Opoly(U_3182))
    | ~ class_Rings_Ocomm__ring(U_3182) ),
    inference(clausify,[status(thm)],[f_1266_3]) ).

fof(f_1267_1,plain,
    ! [T_1] :
      ( class_Int_Onumber(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Ocomm__ring__1(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Int_Onumber]) ).

fof(f_1267_2,plain,
    ! [U_3183] :
      ( class_Int_Onumber(tc_Polynomial_Opoly(U_3183))
      | ~ class_Rings_Ocomm__ring__1(U_3183) ),
    inference(variable_rename,[status(thm)],[f_1267_1]) ).

fof(f_1267_3,plain,
    ! [U_3183] :
      ( class_Int_Onumber(tc_Polynomial_Opoly(U_3183))
      | ~ class_Rings_Ocomm__ring__1(U_3183) ),
    inference(definitional_conversion,[status(esa)],[f_1267_2]) ).

cnf(f_1267_4,plain,
    ( class_Int_Onumber(tc_Polynomial_Opoly(U_3183))
    | ~ class_Rings_Ocomm__ring__1(U_3183) ),
    inference(clausify,[status(thm)],[f_1267_3]) ).

fof(f_1268_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_1268_2,plain,
    ! [U_3184] :
      ( class_Groups_Oone(tc_Polynomial_Opoly(U_3184))
      | ~ class_Rings_Ocomm__semiring__1(U_3184) ),
    inference(variable_rename,[status(thm)],[f_1268_1]) ).

fof(f_1268_3,plain,
    ! [U_3184] :
      ( class_Groups_Oone(tc_Polynomial_Opoly(U_3184))
      | ~ class_Rings_Ocomm__semiring__1(U_3184) ),
    inference(definitional_conversion,[status(esa)],[f_1268_2]) ).

cnf(f_1268_4,plain,
    ( class_Groups_Oone(tc_Polynomial_Opoly(U_3184))
    | ~ class_Rings_Ocomm__semiring__1(U_3184) ),
    inference(clausify,[status(thm)],[f_1268_3]) ).

fof(f_1269_1,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
    inference(negate,[status(cth)],[conj_0]) ).

fof(f_1269_2,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
    inference(definitional_conversion,[status(esa)],[f_1269_1]) ).

cnf(f_1269_3,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
    inference(clausify,[status(thm)],[f_1269_2]) ).

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,
    ( 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_6,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_7,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_8,axiom,
    ( c_RealDef_Oreal(Eq_x_0) = c_RealDef_Oreal(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_9,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_10,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_11,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat__aux(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Nat_Osemiring__1__class_Oof__nat__aux(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_12,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_13,axiom,
    ( c_Groups_Oabs__class_Oabs(Eq_x_0,Eq_x_1) = c_Groups_Oabs__class_Oabs(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_14,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_15,axiom,
    ( c_Int_Onumber__class_Onumber__of(Eq_x_0,Eq_x_1) = c_Int_Onumber__class_Onumber__of(Eq_y_0,Eq_y_1)
    | 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_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_17,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_18,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_19,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_20,axiom,
    ( v_g____(Eq_x_0) = v_g____(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_21,axiom,
    ( c_Int_Osucc(Eq_x_0) = c_Int_Osucc(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_22,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_23,axiom,
    ( c_Int_Opred(Eq_x_0) = c_Int_Opred(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_24,axiom,
    ( c_Complex_Oexpi(Eq_x_0) = c_Complex_Oexpi(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_25,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_26,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(Eq_x_0) = c_Nat_Osemiring__1__class_Oof__nat(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_27,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_28,axiom,
    ( c_Complex_Ocis(Eq_x_0) = c_Complex_Ocis(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_29,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_30,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_31,axiom,
    ( c_Complex_Orcis(Eq_x_0,Eq_x_1) = c_Complex_Orcis(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_Rings_Oinverse__class_Odivide(Eq_x_0,Eq_x_1,Eq_x_2) = c_Rings_Oinverse__class_Odivide(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_33,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_34,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_35,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_36,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_37,axiom,
    ( sK5(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK5(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_38,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_39,axiom,
    ( sK7(Eq_x_0,Eq_x_1) = sK7(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,
    ( 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_41,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_42,axiom,
    ( sK10(Eq_x_0,Eq_x_1) = sK10(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,
    ( 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_44,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_45,axiom,
    ( sK13(Eq_x_0,Eq_x_1) = sK13(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,
    ( sK14(Eq_x_0,Eq_x_1) = sK14(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_47,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_48,axiom,
    ( sK16(Eq_x_0,Eq_x_1) = sK16(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,
    ( 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_50,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_51,axiom,
    ( sK19(Eq_x_0,Eq_x_1) = sK19(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,
    ( sK20(Eq_x_0,Eq_x_1) = sK20(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_53,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_54,axiom,
    ( sK22(Eq_x_0,Eq_x_1) = sK22(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,
    ( sK23(Eq_x_0) = sK23(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_56,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_57,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_58,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_59,axiom,
    ( sK27(Eq_x_0) = sK27(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_60,axiom,
    ( sK28(Eq_x_0) = sK28(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_61,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_62,axiom,
    ( sK30(Eq_x_0) = sK30(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_63,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_64,axiom,
    ( sK32(Eq_x_0) = sK32(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_65,axiom,
    ( sK33(Eq_x_0,Eq_x_1,Eq_x_2) = sK33(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,
    ( sK34(Eq_x_0) = sK34(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_67,axiom,
    ( sK35(Eq_x_0,Eq_x_1,Eq_x_2) = sK35(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_68,axiom,
    ( sK36(Eq_x_0,Eq_x_1) = sK36(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,
    ( sK37(Eq_x_0,Eq_x_1,Eq_x_2) = sK37(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_70,axiom,
    ( sK38(Eq_x_0,Eq_x_1) = sK38(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,
    ( sK39(Eq_x_0,Eq_x_1,Eq_x_2) = sK39(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_72,axiom,
    ( sK40(Eq_x_0,Eq_x_1) = sK40(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_73,axiom,
    ( sK41(Eq_x_0,Eq_x_1,Eq_x_2) = sK41(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_74,axiom,
    ( sK42(Eq_x_0,Eq_x_1) = sK42(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_75,axiom,
    ( sK43(Eq_x_0) = sK43(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_76,axiom,
    ( sK46(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK46(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_77,axiom,
    ( sK47(Eq_x_0,Eq_x_1) = sK47(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_78,axiom,
    ( sK48(Eq_x_0,Eq_x_1,Eq_x_2) = sK48(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_79,axiom,
    ( sK49(Eq_x_0,Eq_x_1) = sK49(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_80,axiom,
    ( sK50(Eq_x_0,Eq_x_1,Eq_x_2) = sK50(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_81,axiom,
    ( sK51(Eq_x_0,Eq_x_1) = sK51(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_82,axiom,
    ( sK52(Eq_x_0,Eq_x_1,Eq_x_2) = sK52(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_83,axiom,
    ( sK53(Eq_x_0,Eq_x_1) = sK53(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_84,axiom,
    ( sK54(Eq_x_0,Eq_x_1,Eq_x_2) = sK54(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_85,axiom,
    ( sK55(Eq_x_0) = sK55(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_86,axiom,
    ( sK56(Eq_x_0) = sK56(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_87,axiom,
    ( sK57(Eq_x_0) = sK57(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_88,axiom,
    ( sK58(Eq_x_0) = sK58(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_89,axiom,
    ( sK59(Eq_x_0,Eq_x_1) = sK59(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_90,axiom,
    ( sK60(Eq_x_0,Eq_x_1) = sK60(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_91,axiom,
    ( sK61(Eq_x_0,Eq_x_1) = sK61(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_92,axiom,
    ( sK62(Eq_x_0) = sK62(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_93,axiom,
    ( sK63(Eq_x_0,Eq_x_1) = sK63(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_94,axiom,
    ( sK64(Eq_x_0,Eq_x_1,Eq_x_2) = sK64(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_95,axiom,
    ( sK65(Eq_x_0,Eq_x_1,Eq_x_2) = sK65(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_96,axiom,
    ( sK66(Eq_x_0) = sK66(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_97,axiom,
    ( sK67(Eq_x_0) = sK67(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_98,axiom,
    ( sK68(Eq_x_0,Eq_x_1) = sK68(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_99,axiom,
    ( sK69(Eq_x_0,Eq_x_1) = sK69(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_100,axiom,
    ( sK70(Eq_x_0,Eq_x_1) = sK70(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_101,axiom,
    ( sK71(Eq_x_0,Eq_x_1) = sK71(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_102,axiom,
    ( sK72(Eq_x_0,Eq_x_1,Eq_x_2) = sK72(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_103,axiom,
    ( sK73(Eq_x_0,Eq_x_1,Eq_x_2) = sK73(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_104,axiom,
    ( sK74(Eq_x_0,Eq_x_1,Eq_x_2) = sK74(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_105,axiom,
    ( sK75(Eq_x_0,Eq_x_1,Eq_x_2) = sK75(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_106,axiom,
    ( sK76(Eq_x_0,Eq_x_1) = sK76(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_107,axiom,
    ( sK77(Eq_x_0,Eq_x_1,Eq_x_2) = sK77(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_108,axiom,
    ( sK78(Eq_x_0,Eq_x_1,Eq_x_2) = sK78(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_109,axiom,
    ( sK79(Eq_x_0,Eq_x_1,Eq_x_2) = sK79(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_110,axiom,
    ( sK80(Eq_x_0,Eq_x_1) = sK80(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_111,axiom,
    ( c_SEQ_Osubseq(Eq_y_0)
    | ~ c_SEQ_Osubseq(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_112,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_113,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_114,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_115,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_116,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_117,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_118,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_119,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_120,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_121,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_122,axiom,
    ( c_SEQ_Odecseq(Eq_y_0,Eq_y_1)
    | ~ c_SEQ_Odecseq(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_123,axiom,
    ( c_SEQ_Oincseq(Eq_y_0,Eq_y_1)
    | ~ c_SEQ_Oincseq(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_124,axiom,
    ( c_SEQ_Omonoseq(Eq_y_0,Eq_y_1)
    | ~ c_SEQ_Omonoseq(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_125,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_126,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_127,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_128,axiom,
    ( class_Rings_Osemiring__1(Eq_y_0)
    | ~ class_Rings_Osemiring__1(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_129,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_130,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_131,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_132,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_133,axiom,
    ( hBOOL(Eq_y_0)
    | ~ hBOOL(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_134,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_135,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_136,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_137,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_138,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_139,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_140,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_141,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_142,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_143,axiom,
    ( class_Int_Onumber(Eq_y_0)
    | ~ class_Int_Onumber(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_144,axiom,
    ( class_Int_Onumber__ring(Eq_y_0)
    | ~ class_Int_Onumber__ring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_145,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_146,axiom,
    ( class_Groups_Oordered__ab__group__add__abs(Eq_y_0)
    | ~ class_Groups_Oordered__ab__group__add__abs(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_147,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_148,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_149,axiom,
    ( c_Nat__Numeral_Oneg(Eq_y_0)
    | ~ c_Nat__Numeral_Oneg(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_150,axiom,
    ( c_SEQ_OBseq(Eq_y_0,Eq_y_1)
    | ~ c_SEQ_OBseq(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,
    ( 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_152,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_153,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_154,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_155,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_156,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_157,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_158,axiom,
    ( class_Nat_Osemiring__char__0(Eq_y_0)
    | ~ class_Nat_Osemiring__char__0(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_159,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_160,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_161,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_162,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_163,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_164,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_165,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_166,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_167,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_168,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_169,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_170,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_171,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_172,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_173,axiom,
    ( class_Rings_Oordered__ring__abs(Eq_y_0)
    | ~ class_Rings_Oordered__ring__abs(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_174,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_175,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_176,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_177,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_178,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_179,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_180,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_181,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_182,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_183,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_184,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_185,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_186,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_187,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_188,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_189,axiom,
    ( sP3(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP3(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,
    ( 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_191,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_192,axiom,
    ( sP6(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP6(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_193,axiom,
    ( sP7(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP7(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_194,axiom,
    ( sP8(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP8(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_195,axiom,
    ( sP9(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP9(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_196,axiom,
    ( sP10(Eq_y_0,Eq_y_1)
    | ~ sP10(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_197,axiom,
    ( sP11(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP11(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_198,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_199,axiom,
    ( sP13(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP13(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_200,axiom,
    ( sP14(Eq_y_0,Eq_y_1)
    | ~ sP14(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_201,axiom,
    ( sP15(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP15(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_202,axiom,
    ( sP16(Eq_y_0,Eq_y_1)
    | ~ sP16(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_203,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_204,axiom,
    ( sP18(Eq_y_0,Eq_y_1)
    | ~ sP18(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_205,axiom,
    ( sP19(Eq_y_0,Eq_y_1)
    | ~ sP19(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_206,axiom,
    ( sP20(Eq_y_0,Eq_y_1)
    | ~ sP20(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_207,axiom,
    ( sP21(Eq_y_0,Eq_y_1)
    | ~ sP21(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_208,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_209,axiom,
    ( sP23(Eq_y_0,Eq_y_1)
    | ~ sP23(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_210,axiom,
    ( sP24(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP24(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,
    ( 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_212,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_213,axiom,
    ( sP27(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP27(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_214,axiom,
    ( sP28(Eq_y_0,Eq_y_1)
    | ~ sP28(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_215,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_216,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_217,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_218,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_219,axiom,
    ( sP33(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP33(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_220,axiom,
    ( sP34(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP34(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_221,axiom,
    ( sP35(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP35(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_222,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_223,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_224,axiom,
    ( sP38(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP38(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_225,axiom,
    ( sP39(Eq_y_0,Eq_y_1)
    | ~ sP39(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_226,axiom,
    ( sP40(Eq_y_0,Eq_y_1)
    | ~ sP40(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_227,axiom,
    ( sP41(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP41(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,
    ( 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_229,axiom,
    ( sP43(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP43(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,
    ( sP44(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP44(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,
    ( sP45(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP45(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_232,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_233,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_234,axiom,
    ( sP48(Eq_y_0,Eq_y_1)
    | ~ sP48(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_235,axiom,
    ( sP49(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP49(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_236,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_237,axiom,
    ( sP51(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP51(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,
    ( 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_239,axiom,
    ( sP53(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP53(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,
    ( sP54(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP54(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,
    ( sP55(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP55(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,
    ( 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_243,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_244,axiom,
    ( sP58(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP58(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_245,axiom,
    ( sP59(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP59(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_246,axiom,
    ( sP60(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP60(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_247,axiom,
    ( sP61(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP61(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_248,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_249,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_250,axiom,
    ( sP64(Eq_y_0,Eq_y_1)
    | ~ sP64(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,
    ( sP65(Eq_y_0,Eq_y_1)
    | ~ sP65(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_252,axiom,
    ( sP66(Eq_y_0,Eq_y_1)
    | ~ sP66(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_253,axiom,
    ( sP67(Eq_y_0,Eq_y_1)
    | ~ sP67(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_254,axiom,
    ( sP68(Eq_y_0,Eq_y_1)
    | ~ sP68(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_255,axiom,
    ( sP69(Eq_y_0,Eq_y_1)
    | ~ sP69(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_256,axiom,
    ( sP70(Eq_y_0,Eq_y_1)
    | ~ sP70(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_257,axiom,
    ( sP71(Eq_y_0,Eq_y_1)
    | ~ sP71(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_258,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_259,axiom,
    ( sP73(Eq_y_0,Eq_y_1)
    | ~ sP73(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_260,axiom,
    ( sP74(Eq_y_0)
    | ~ sP74(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_261,axiom,
    ( sP75(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP75(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_262,axiom,
    ( sP76(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP76(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_263,axiom,
    ( sP77(Eq_y_0,Eq_y_1)
    | ~ sP77(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,
    ( sP78(Eq_y_0,Eq_y_1)
    | ~ sP78(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_265,axiom,
    ( sP79(Eq_y_0,Eq_y_1)
    | ~ sP79(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,
    ( 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_267,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_268,axiom,
    ( sP82(Eq_y_0,Eq_y_1)
    | ~ sP82(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,
    ( sP83(Eq_y_0,Eq_y_1)
    | ~ sP83(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_270,axiom,
    ( sP84(Eq_y_0,Eq_y_1)
    | ~ sP84(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_271,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_272,axiom,
    ( sP86(Eq_y_0,Eq_y_1)
    | ~ sP86(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_273,axiom,
    ( sP87(Eq_y_0,Eq_y_1)
    | ~ sP87(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_274,axiom,
    ( sP88(Eq_y_0,Eq_y_1)
    | ~ sP88(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_275,axiom,
    ( sP89(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP89(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_276,axiom,
    ( sP90(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP90(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_277,axiom,
    ( sP91(Eq_y_0,Eq_y_1)
    | ~ sP91(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_278,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_279,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_280,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_281,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_282,axiom,
    ( sP96(Eq_y_0,Eq_y_1)
    | ~ sP96(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_283,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_284,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_285,axiom,
    ( sP99(Eq_y_0,Eq_y_1)
    | ~ sP99(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_286,axiom,
    ( sP100(Eq_y_0,Eq_y_1)
    | ~ sP100(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_287,axiom,
    ( sP101(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP101(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_288,axiom,
    ( sP102(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP102(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_289,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_290,axiom,
    ( sP104(Eq_y_0,Eq_y_1)
    | ~ sP104(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_291,axiom,
    ( sP105(Eq_y_0)
    | ~ sP105(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_292,axiom,
    ( sP106(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP106(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,
    ( sP107(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP107(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_294,axiom,
    ( sP108(Eq_y_0)
    | ~ sP108(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_295,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_296,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_297,axiom,
    ( sP111(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP111(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_298,axiom,
    ( sP112(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP112(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_299,axiom,
    ( sP113(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP113(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_300,axiom,
    ( sP114(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP114(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_301,axiom,
    ( sP115(Eq_y_0,Eq_y_1)
    | ~ sP115(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_302,axiom,
    ( sP116(Eq_y_0,Eq_y_1)
    | ~ sP116(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_303,axiom,
    ( sP117(Eq_y_0,Eq_y_1)
    | ~ sP117(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_304,axiom,
    ( sP118(Eq_y_0,Eq_y_1)
    | ~ sP118(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_305,axiom,
    ( sP119(Eq_y_0,Eq_y_1)
    | ~ sP119(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_306,axiom,
    ( sP120(Eq_y_0,Eq_y_1)
    | ~ sP120(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_307,axiom,
    ( sP121(Eq_y_0,Eq_y_1)
    | ~ sP121(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_308,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_309,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_310,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_311,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_312,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_313,axiom,
    ( sP127(Eq_y_0,Eq_y_1)
    | ~ sP127(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,
    ( sP128(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP128(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_315,axiom,
    ( sP129(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP129(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_316,axiom,
    ( sP130(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP130(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_317,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_318,axiom,
    ( sP132(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP132(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_319,axiom,
    ( sP133(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP133(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_320,axiom,
    ( sP134(Eq_y_0,Eq_y_1)
    | ~ sP134(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,
    ( sP135(Eq_y_0,Eq_y_1)
    | ~ sP135(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,
    ( sP136(Eq_y_0,Eq_y_1)
    | ~ sP136(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,
    ( sP137(Eq_y_0,Eq_y_1)
    | ~ sP137(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,
    ( sP138(Eq_y_0,Eq_y_1)
    | ~ sP138(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_325,axiom,
    ( sP139(Eq_y_0,Eq_y_1)
    | ~ sP139(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_326,axiom,
    ( sP140(Eq_y_0,Eq_y_1)
    | ~ sP140(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,
    ( sP141(Eq_y_0,Eq_y_1)
    | ~ sP141(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,
    ( sP142(Eq_y_0,Eq_y_1)
    | ~ sP142(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,
    ( 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_330,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_331,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_332,axiom,
    ( sP146(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP146(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_333,axiom,
    ( sP147(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP147(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_334,axiom,
    ( sP148(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP148(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_335,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_336,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_337,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_338,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_339,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_340,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_341,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_342,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_343,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_344,axiom,
    ( sP158(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP158(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,
    ( sP159(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP159(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,
    ( sP160(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP160(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_347,axiom,
    ( sP161(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP161(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_348,axiom,
    ( sP162(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP162(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_349,axiom,
    ( sP163(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP163(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_350,axiom,
    ( sP164(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP164(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_351,axiom,
    ( sP165(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP165(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_352,axiom,
    ( sP166(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP166(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,
    ( sP167(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP167(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_354,axiom,
    ( sP168(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP168(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,
    ( sP169(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP169(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,
    ( 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_357,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_358,axiom,
    ( sP172(Eq_y_0)
    | ~ sP172(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_359,axiom,
    ( sP173(Eq_y_0)
    | ~ sP173(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_360,axiom,
    ( sP174(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP174(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_361,axiom,
    ( sP175(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP175(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_362,axiom,
    ( sP176(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP176(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_363,axiom,
    ( sP177(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP177(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_364,axiom,
    ( sP178(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP178(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_365,axiom,
    ( sP179(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP179(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_366,axiom,
    ( sP180(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP180(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_367,axiom,
    ( sP181(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP181(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,
    ( sP182(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP182(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_369,axiom,
    ( sP183(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP183(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_370,axiom,
    ( sP184(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP184(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_371,axiom,
    ( sP185(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP185(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_372,axiom,
    ( sP186(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP186(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_373,axiom,
    ( sP187(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP187(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_374,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_375,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_376,axiom,
    ( sP190(Eq_y_0,Eq_y_1)
    | ~ sP190(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_377,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_378,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_379,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_380,axiom,
    ( sP194(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP194(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_381,axiom,
    ( sP195(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP195(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_382,axiom,
    ( sP196(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP196(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,
    ( sP197(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP197(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_384,axiom,
    ( sP198(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP198(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,
    ( sP199(Eq_y_0,Eq_y_1)
    | ~ sP199(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,
    ( 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_387,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_388,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_389,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_390,axiom,
    ( sP204(Eq_y_0,Eq_y_1)
    | ~ sP204(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,
    ( sP205(Eq_y_0,Eq_y_1)
    | ~ sP205(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,
    ( 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_393,axiom,
    ( sP207(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP207(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_394,axiom,
    ( sP208(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP208(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_395,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_396,axiom,
    ( sP210(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP210(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_397,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_398,axiom,
    ( sP212(Eq_y_0,Eq_y_1)
    | ~ sP212(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,
    ( sP213(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP213(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,
    ( sP214(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP214(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,
    ( sP215(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP215(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_402,axiom,
    ( sP216(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP216(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_403,axiom,
    ( sP217(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP217(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_404,axiom,
    ( sP218(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP218(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_405,axiom,
    ( sP219(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP219(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_406,axiom,
    ( sP220(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP220(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,
    ( sP221(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP221(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_408,axiom,
    ( sP222(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP222(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_409,axiom,
    ( sP223(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP223(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_410,axiom,
    ( sP224(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP224(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_411,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_412,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_413,axiom,
    ( sP227(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP227(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_414,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_415,axiom,
    ( sP229(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP229(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_416,axiom,
    ( sP230(Eq_y_0)
    | ~ sP230(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_417,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_418,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_419,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_420,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_421,axiom,
    ( sP235(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP235(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_422,axiom,
    ( sP236(Eq_y_0,Eq_y_1)
    | ~ sP236(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,
    ( 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_424,axiom,
    ( sP238(Eq_y_0,Eq_y_1)
    | ~ sP238(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_425,axiom,
    ( sP239(Eq_y_0,Eq_y_1)
    | ~ sP239(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_426,axiom,
    ( sP240(Eq_y_0,Eq_y_1)
    | ~ sP240(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_427,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_428,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_429,axiom,
    ( sP243(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP243(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_430,axiom,
    ( sP244(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP244(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_431,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_432,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_433,axiom,
    ( sP247(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP247(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_434,axiom,
    ( sP248(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP248(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_435,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_436,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_437,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_438,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_439,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_440,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_441,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_442,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_443,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_444,axiom,
    ( sP258(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP258(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_445,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_446,axiom,
    ( sP260(Eq_y_0,Eq_y_1)
    | ~ sP260(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_447,axiom,
    ( sP261(Eq_y_0,Eq_y_1)
    | ~ sP261(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_448,axiom,
    ( sP262(Eq_y_0,Eq_y_1)
    | ~ sP262(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_449,axiom,
    ( sP263(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP263(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
    | 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_450,axiom,
    ( sP264(Eq_y_0,Eq_y_1)
    | ~ sP264(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_451,axiom,
    ( sP265(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP265(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_452,axiom,
    ( sP266(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP266(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_453,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_454,axiom,
    ( sP268(Eq_y_0,Eq_y_1)
    | ~ sP268(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_455,axiom,
    ( sP269(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP269(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_456,axiom,
    ( sP270(Eq_y_0,Eq_y_1)
    | ~ sP270(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_457,axiom,
    ( sP271(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP271(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_458,axiom,
    ( sP272(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP272(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_459,axiom,
    ( sP273(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP273(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_460,axiom,
    ( sP274(Eq_y_0,Eq_y_1)
    | ~ sP274(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_461,axiom,
    ( sP275(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP275(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_462,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_463,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(sat_proved,plain,
    $false,
    inference(cadical,[status(thm)],[]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWW225+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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/10.39  % Computer : n020.cluster.edu
% 0.10/10.39  % Model    : x86_64 x86_64
% 0.10/10.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.39  % Memory   : 8046.5625MB
% 0.10/10.39  % OS       : Linux 6.8.0-71-generic
% 0.10/10.39  % CPULimit : 300
% 0.10/10.39  % WCLimit  : 300
% 0.10/10.39  % DateTime : Sun Sep 20 05:11:44 UTC 2026
% 0.10/10.39  % CPUTime  : 
% 39.62/49.90  % SZS status Theorem for theBenchmark
% 39.62/49.90  % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------