Z3---4.15.1.THM-Prf.s

%------------------------------------------------------------------------------
% File     : Z3---4.15.1
% Problem  : SWW276+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_E %s %d THM

% Computer : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sat Jun 21 05:36:45 AM UTC 2025

% Result   : Theorem 1.15s 1.36s
% Output   : Proof 1.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :  102
% Syntax   : Number of formulae    :  244 (  81 unt;   0 typ;   0 def)
%            Number of atoms       : 1010 ( 542 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives : 1261 ( 543   ~; 472   |;  12   &)
%                                         ( 170 <=>;  64  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :   10 (   2 avg)
%            Number of FOOLs       :   48 (  48 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   13 (  11 usr;   1 prp; 0-3 aty)
%            Number of functors    :   19 (  19 usr;   6 con; 0-3 aty)
%            Number of variables   :  505 ( 451   !;   0   ?; 505   :)

% Comments : 
%------------------------------------------------------------------------------
tff(c_Groups_Oplus__class_Oplus_type,type,
    c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).

tff(v_na_____type,type,
    v_na____: $i ).

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

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

tff(c_Polynomial_Oorder_type,type,
    c_Polynomial_Oorder: ( $i * $i * $i ) > $i ).

tff(v_pa_____type,type,
    v_pa____: $i ).

tff(v_a_____type,type,
    v_a____: $i ).

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

tff(c_Polynomial_Odegree_type,type,
    c_Polynomial_Odegree: ( $i * $i ) > $i ).

tff(v_s_____type,type,
    v_s____: $i ).

tff(c_Groups_Ominus__class_Ominus_type,type,
    c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).

tff(c_Orderings_Oord__class_Oless__eq_type,type,
    c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).

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

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

tff(hAPP_type,type,
    hAPP: ( $i * $i ) > $i ).

tff(c_Polynomial_OpCons_type,type,
    c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).

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

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

tff(c_Groups_Ouminus__class_Ouminus_type,type,
    c_Groups_Ouminus__class_Ouminus: ( $i * $i ) > $i ).

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

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

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

tff(class_Rings_Oidom_type,type,
    class_Rings_Oidom: $i > $o ).

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

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

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

tff(1,plain,
    ^ [V_nb_2: $i,V_m_2: $i] :
      refl(( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_nb_2))
        <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) )
      <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_nb_2))
        <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ) )),
    inference(bind,[status(th)],[]) ).

tff(2,plain,
    ( ! [V_nb_2: $i,V_m_2: $i] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_nb_2))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) )
  <=> ! [V_nb_2: $i,V_m_2: $i] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_nb_2))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [V_nb_2: $i,V_m_2: $i] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_nb_2))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) )
  <=> ! [V_nb_2: $i,V_m_2: $i] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_nb_2))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(4,axiom,
    ! [V_nb_2: $i,V_m_2: $i] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_nb_2))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).

tff(5,plain,
    ! [V_nb_2: $i,V_m_2: $i] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_nb_2))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ! [V_nb_2: $i,V_m_2: $i] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_nb_2))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ),
    inference(skolemize,[status(sab)],[5]) ).

tff(7,plain,
    ! [V_nb_2: $i,V_m_2: $i] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_nb_2))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ),
    inference(modus_ponens,[status(thm)],[6,2]) ).

tff(8,plain,
    ( ~ ! [V_nb_2: $i,V_m_2: $i] :
          ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_nb_2))
        <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) )
    | ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_na____,c_Nat_OSuc(v_na____))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_na____,v_na____) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(9,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_na____,c_Nat_OSuc(v_na____))
  <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_na____,v_na____) ),
    inference(unit_resolution,[status(thm)],[8,7]) ).

tff(10,plain,
    ^ [V_n: $i] :
      refl(( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n))
      <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)) )),
    inference(bind,[status(th)],[]) ).

tff(11,plain,
    ( ! [V_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n))
  <=> ! [V_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)) ),
    inference(quant_intro,[status(thm)],[10]) ).

tff(12,plain,
    ( ! [V_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n))
  <=> ! [V_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)) ),
    inference(rewrite,[status(thm)],[]) ).

tff(13,axiom,
    ! [V_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessI) ).

tff(14,plain,
    ! [V_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)),
    inference(modus_ponens,[status(thm)],[13,12]) ).

tff(15,plain,
    ! [V_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)),
    inference(skolemize,[status(sab)],[14]) ).

tff(16,plain,
    ! [V_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)),
    inference(modus_ponens,[status(thm)],[15,11]) ).

tff(17,plain,
    ( ~ ! [V_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_na____,c_Nat_OSuc(v_na____)) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(18,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_na____,c_Nat_OSuc(v_na____)),
    inference(unit_resolution,[status(thm)],[17,16]) ).

tff(19,plain,
    ( ~ ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_na____,c_Nat_OSuc(v_na____))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_na____,v_na____) )
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_na____,c_Nat_OSuc(v_na____))
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_na____,v_na____) ),
    inference(tautology,[status(thm)],[]) ).

tff(20,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_na____,v_na____),
    inference(unit_resolution,[status(thm)],[19,18,9]) ).

tff(21,plain,
    ^ [V_n: $i,V_m: $i] :
      refl(( ( ~ 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) ) )
      <=> ( ~ 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) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(22,plain,
    ( ! [V_n: $i,V_m: $i] :
        ( ~ 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) ) )
  <=> ! [V_n: $i,V_m: $i] :
        ( ~ 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) ) ) ),
    inference(quant_intro,[status(thm)],[21]) ).

tff(23,plain,
    ( ! [V_n: $i,V_m: $i] :
        ( ~ 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) ) )
  <=> ! [V_n: $i,V_m: $i] :
        ( ~ 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) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(24,plain,
    ^ [V_n: $i,V_m: $i] :
      rewrite(( ( 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) ) )
      <=> ( ~ 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) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(25,plain,
    ( ! [V_n: $i,V_m: $i] :
        ( 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) ) )
  <=> ! [V_n: $i,V_m: $i] :
        ( ~ 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) ) ) ),
    inference(quant_intro,[status(thm)],[24]) ).

tff(26,axiom,
    ! [V_n: $i,V_m: $i] :
      ( 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('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__is__0__eq_H) ).

tff(27,plain,
    ! [V_n: $i,V_m: $i] :
      ( ~ 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) ) ),
    inference(modus_ponens,[status(thm)],[26,25]) ).

tff(28,plain,
    ! [V_n: $i,V_m: $i] :
      ( ~ 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) ) ),
    inference(modus_ponens,[status(thm)],[27,23]) ).

tff(29,plain,
    ! [V_n: $i,V_m: $i] :
      ( ~ 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) ) ),
    inference(skolemize,[status(sab)],[28]) ).

tff(30,plain,
    ! [V_n: $i,V_m: $i] :
      ( ~ 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) ) ),
    inference(modus_ponens,[status(thm)],[29,22]) ).

tff(31,plain,
    ( ( ~ ! [V_n: $i,V_m: $i] :
            ( ~ 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) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_na____,v_na____)
      | ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,v_na____) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
  <=> ( ~ ! [V_n: $i,V_m: $i] :
            ( ~ 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) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_na____,v_na____)
      | ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,v_na____) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(32,plain,
    ( ~ ! [V_n: $i,V_m: $i] :
          ( ~ 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) ) )
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_na____,v_na____)
    | ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,v_na____) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(33,plain,
    ( ~ ! [V_n: $i,V_m: $i] :
          ( ~ 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) ) )
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_na____,v_na____)
    | ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,v_na____) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(modus_ponens,[status(thm)],[32,31]) ).

tff(34,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_na____,v_na____)
    | ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,v_na____) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(unit_resolution,[status(thm)],[33,30]) ).

tff(35,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,v_na____) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(unit_resolution,[status(thm)],[34,20]) ).

tff(36,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,v_na____),
    inference(symmetry,[status(thm)],[35]) ).

tff(37,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_na____) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,v_na____),v_na____),
    inference(monotonicity,[status(thm)],[36]) ).

tff(38,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,v_na____),v_na____) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_na____),
    inference(symmetry,[status(thm)],[37]) ).

tff(39,plain,
    ^ [V_m: $i,V_n: $i] :
      refl(( ( ~ 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 ) )
      <=> ( ~ 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 ) ) )),
    inference(bind,[status(th)],[]) ).

tff(40,plain,
    ( ! [V_m: $i,V_n: $i] :
        ( ~ 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 ) )
  <=> ! [V_m: $i,V_n: $i] :
        ( ~ 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 ) ) ),
    inference(quant_intro,[status(thm)],[39]) ).

tff(41,plain,
    ( ! [V_m: $i,V_n: $i] :
        ( ~ 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 ) )
  <=> ! [V_m: $i,V_n: $i] :
        ( ~ 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 ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(42,plain,
    ^ [V_m: $i,V_n: $i] :
      rewrite(( ( 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 ) )
      <=> ( ~ 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 ) ) )),
    inference(bind,[status(th)],[]) ).

tff(43,plain,
    ( ! [V_m: $i,V_n: $i] :
        ( 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 ) )
  <=> ! [V_m: $i,V_n: $i] :
        ( ~ 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 ) ) ),
    inference(quant_intro,[status(thm)],[42]) ).

tff(44,axiom,
    ! [V_m: $i,V_n: $i] :
      ( 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('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff__inverse2) ).

tff(45,plain,
    ! [V_m: $i,V_n: $i] :
      ( ~ 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 ) ),
    inference(modus_ponens,[status(thm)],[44,43]) ).

tff(46,plain,
    ! [V_m: $i,V_n: $i] :
      ( ~ 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 ) ),
    inference(modus_ponens,[status(thm)],[45,41]) ).

tff(47,plain,
    ! [V_m: $i,V_n: $i] :
      ( ~ 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 ) ),
    inference(skolemize,[status(sab)],[46]) ).

tff(48,plain,
    ! [V_m: $i,V_n: $i] :
      ( ~ 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 ) ),
    inference(modus_ponens,[status(thm)],[47,40]) ).

tff(49,plain,
    ( ( ~ ! [V_m: $i,V_n: $i] :
            ( ~ 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 ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_na____,v_na____)
      | ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,v_na____),v_na____) = v_na____ ) )
  <=> ( ~ ! [V_m: $i,V_n: $i] :
            ( ~ 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 ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_na____,v_na____)
      | ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,v_na____),v_na____) = v_na____ ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(50,plain,
    ( ~ ! [V_m: $i,V_n: $i] :
          ( ~ 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 ) )
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_na____,v_na____)
    | ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,v_na____),v_na____) = v_na____ ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(51,plain,
    ( ~ ! [V_m: $i,V_n: $i] :
          ( ~ 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 ) )
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_na____,v_na____)
    | ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,v_na____),v_na____) = v_na____ ) ),
    inference(modus_ponens,[status(thm)],[50,49]) ).

tff(52,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_na____,v_na____)
    | ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,v_na____),v_na____) = v_na____ ) ),
    inference(unit_resolution,[status(thm)],[51,48]) ).

tff(53,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,v_na____),v_na____) = v_na____,
    inference(unit_resolution,[status(thm)],[52,20]) ).

tff(54,plain,
    v_na____ = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,v_na____),v_na____),
    inference(symmetry,[status(thm)],[53]) ).

tff(55,plain,
    ( ( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____) = v_na____ )
  <=> ( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____) = v_na____ ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(56,axiom,
    c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____) = v_na____,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dpn) ).

tff(57,plain,
    c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____) = v_na____,
    inference(modus_ponens,[status(thm)],[56,55]) ).

tff(58,plain,
    ( ( v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____) )
  <=> ( v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(59,axiom,
    v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_s) ).

tff(60,plain,
    v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____),
    inference(modus_ponens,[status(thm)],[59,58]) ).

tff(61,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____) = v_pa____,
    inference(symmetry,[status(thm)],[60]) ).

tff(62,plain,
    c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____)) = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____),
    inference(monotonicity,[status(thm)],[61]) ).

tff(63,plain,
    ^ [T_1: $i] :
      refl(( ( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
          | ~ class_Rings_Oidom(T_1) )
      <=> ( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
          | ~ class_Rings_Oidom(T_1) ) )),
    inference(bind,[status(th)],[]) ).

tff(64,plain,
    ( ! [T_1: $i] :
        ( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
        | ~ class_Rings_Oidom(T_1) )
  <=> ! [T_1: $i] :
        ( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
        | ~ class_Rings_Oidom(T_1) ) ),
    inference(quant_intro,[status(thm)],[63]) ).

tff(65,plain,
    ( ! [T_1: $i] :
        ( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
        | ~ class_Rings_Oidom(T_1) )
  <=> ! [T_1: $i] :
        ( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
        | ~ class_Rings_Oidom(T_1) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(66,plain,
    ^ [T_1: $i] :
      rewrite(( ( class_Rings_Oidom(T_1)
         => class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)) )
      <=> ( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
          | ~ class_Rings_Oidom(T_1) ) )),
    inference(bind,[status(th)],[]) ).

tff(67,plain,
    ( ! [T_1: $i] :
        ( class_Rings_Oidom(T_1)
       => class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)) )
  <=> ! [T_1: $i] :
        ( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
        | ~ class_Rings_Oidom(T_1) ) ),
    inference(quant_intro,[status(thm)],[66]) ).

tff(68,axiom,
    ! [T_1: $i] :
      ( class_Rings_Oidom(T_1)
     => class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors) ).

tff(69,plain,
    ! [T_1: $i] :
      ( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Oidom(T_1) ),
    inference(modus_ponens,[status(thm)],[68,67]) ).

tff(70,plain,
    ! [T_1: $i] :
      ( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Oidom(T_1) ),
    inference(modus_ponens,[status(thm)],[69,65]) ).

tff(71,plain,
    ! [T_1: $i] :
      ( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Oidom(T_1) ),
    inference(skolemize,[status(sab)],[70]) ).

tff(72,plain,
    ! [T_1: $i] :
      ( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Oidom(T_1) ),
    inference(modus_ponens,[status(thm)],[71,64]) ).

tff(73,plain,
    ( class_Rings_Oidom(tc_Complex_Ocomplex)
  <=> class_Rings_Oidom(tc_Complex_Ocomplex) ),
    inference(rewrite,[status(thm)],[]) ).

tff(74,axiom,
    class_Rings_Oidom(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).

tff(75,plain,
    class_Rings_Oidom(tc_Complex_Ocomplex),
    inference(modus_ponens,[status(thm)],[74,73]) ).

tff(76,plain,
    ( ( ~ ! [T_1: $i] :
            ( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
            | ~ class_Rings_Oidom(T_1) )
      | class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
      | ~ class_Rings_Oidom(tc_Complex_Ocomplex) )
  <=> ( ~ ! [T_1: $i] :
            ( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
            | ~ class_Rings_Oidom(T_1) )
      | class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
      | ~ class_Rings_Oidom(tc_Complex_Ocomplex) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(77,plain,
    ( ~ ! [T_1: $i] :
          ( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
          | ~ class_Rings_Oidom(T_1) )
    | class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ class_Rings_Oidom(tc_Complex_Ocomplex) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(78,plain,
    ( ~ ! [T_1: $i] :
          ( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
          | ~ class_Rings_Oidom(T_1) )
    | class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ class_Rings_Oidom(tc_Complex_Ocomplex) ),
    inference(modus_ponens,[status(thm)],[77,76]) ).

tff(79,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    inference(unit_resolution,[status(thm)],[78,75,72]) ).

tff(80,plain,
    ( class_Groups_Ozero(tc_Complex_Ocomplex)
  <=> class_Groups_Ozero(tc_Complex_Ocomplex) ),
    inference(rewrite,[status(thm)],[]) ).

tff(81,axiom,
    class_Groups_Ozero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).

tff(82,plain,
    class_Groups_Ozero(tc_Complex_Ocomplex),
    inference(modus_ponens,[status(thm)],[81,80]) ).

tff(83,plain,
    ^ [V_pb_2: $i,V_aa_2: $i,T_a: $i] :
      refl(( ( ~ class_Groups_Ozero(T_a)
          | ~ ( ( ( V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) )
                | ( V_pb_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
            <=> ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )
      <=> ( ~ class_Groups_Ozero(T_a)
          | ~ ( ( ( V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) )
                | ( V_pb_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
            <=> ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(84,plain,
    ( ! [V_pb_2: $i,V_aa_2: $i,T_a: $i] :
        ( ~ class_Groups_Ozero(T_a)
        | ~ ( ( ( V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) )
              | ( V_pb_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
          <=> ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )
  <=> ! [V_pb_2: $i,V_aa_2: $i,T_a: $i] :
        ( ~ class_Groups_Ozero(T_a)
        | ~ ( ( ( V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) )
              | ( V_pb_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
          <=> ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ) ),
    inference(quant_intro,[status(thm)],[83]) ).

tff(85,plain,
    ^ [V_pb_2: $i,V_aa_2: $i,T_a: $i] :
      rewrite(( ( ~ class_Groups_Ozero(T_a)
          | ( ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
          <=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
              & ( V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ) )
      <=> ( ~ class_Groups_Ozero(T_a)
          | ~ ( ( ( V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) )
                | ( V_pb_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
            <=> ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(86,plain,
    ( ! [V_pb_2: $i,V_aa_2: $i,T_a: $i] :
        ( ~ class_Groups_Ozero(T_a)
        | ( ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
        <=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
            & ( V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ) )
  <=> ! [V_pb_2: $i,V_aa_2: $i,T_a: $i] :
        ( ~ class_Groups_Ozero(T_a)
        | ~ ( ( ( V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) )
              | ( V_pb_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
          <=> ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ) ),
    inference(quant_intro,[status(thm)],[85]) ).

tff(87,plain,
    ( ! [V_pb_2: $i,V_aa_2: $i,T_a: $i] :
        ( ~ class_Groups_Ozero(T_a)
        | ( ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
        <=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
            & ( V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ) )
  <=> ! [V_pb_2: $i,V_aa_2: $i,T_a: $i] :
        ( ~ class_Groups_Ozero(T_a)
        | ( ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
        <=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
            & ( V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(88,plain,
    ^ [V_pb_2: $i,V_aa_2: $i,T_a: $i] :
      rewrite(( ( class_Groups_Ozero(T_a)
         => ( ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
          <=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
              & ( V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ) )
      <=> ( ~ class_Groups_Ozero(T_a)
          | ( ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
          <=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
              & ( V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(89,plain,
    ( ! [V_pb_2: $i,V_aa_2: $i,T_a: $i] :
        ( class_Groups_Ozero(T_a)
       => ( ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
        <=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
            & ( V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ) )
  <=> ! [V_pb_2: $i,V_aa_2: $i,T_a: $i] :
        ( ~ class_Groups_Ozero(T_a)
        | ( ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
        <=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
            & ( V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ) ) ),
    inference(quant_intro,[status(thm)],[88]) ).

tff(90,axiom,
    ! [V_pb_2: $i,V_aa_2: $i,T_a: $i] :
      ( class_Groups_Ozero(T_a)
     => ( ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
      <=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
          & ( V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__eq__0__iff) ).

tff(91,plain,
    ! [V_pb_2: $i,V_aa_2: $i,T_a: $i] :
      ( ~ class_Groups_Ozero(T_a)
      | ( ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
      <=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
          & ( V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ) ),
    inference(modus_ponens,[status(thm)],[90,89]) ).

tff(92,plain,
    ! [V_pb_2: $i,V_aa_2: $i,T_a: $i] :
      ( ~ class_Groups_Ozero(T_a)
      | ( ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
      <=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
          & ( V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ) ),
    inference(modus_ponens,[status(thm)],[91,87]) ).

tff(93,plain,
    ! [V_pb_2: $i,V_aa_2: $i,T_a: $i] :
      ( ~ class_Groups_Ozero(T_a)
      | ( ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
      <=> ( ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
          & ( V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ) ),
    inference(skolemize,[status(sab)],[92]) ).

tff(94,plain,
    ! [V_pb_2: $i,V_aa_2: $i,T_a: $i] :
      ( ~ class_Groups_Ozero(T_a)
      | ~ ( ( ( V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) )
            | ( V_pb_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
        <=> ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
    inference(modus_ponens,[status(thm)],[93,86]) ).

tff(95,plain,
    ! [V_pb_2: $i,V_aa_2: $i,T_a: $i] :
      ( ~ class_Groups_Ozero(T_a)
      | ~ ( ( ( V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) )
            | ( V_pb_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
        <=> ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
    inference(modus_ponens,[status(thm)],[94,84]) ).

tff(96,plain,
    ( ( ~ ! [V_pb_2: $i,V_aa_2: $i,T_a: $i] :
            ( ~ class_Groups_Ozero(T_a)
            | ~ ( ( ( V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) )
                  | ( V_pb_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
              <=> ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )
      | ~ class_Groups_Ozero(tc_Complex_Ocomplex)
      | ~ ( ( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
            | ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) )
        <=> ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) )
  <=> ( ~ ! [V_pb_2: $i,V_aa_2: $i,T_a: $i] :
            ( ~ class_Groups_Ozero(T_a)
            | ~ ( ( ( V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) )
                  | ( V_pb_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
              <=> ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )
      | ~ class_Groups_Ozero(tc_Complex_Ocomplex)
      | ~ ( ( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
            | ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) )
        <=> ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(97,plain,
    ( ~ ! [V_pb_2: $i,V_aa_2: $i,T_a: $i] :
          ( ~ class_Groups_Ozero(T_a)
          | ~ ( ( ( V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) )
                | ( V_pb_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
            <=> ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )
    | ~ class_Groups_Ozero(tc_Complex_Ocomplex)
    | ~ ( ( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
          | ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) )
      <=> ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(98,plain,
    ( ~ ! [V_pb_2: $i,V_aa_2: $i,T_a: $i] :
          ( ~ class_Groups_Ozero(T_a)
          | ~ ( ( ( V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) )
                | ( V_pb_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
            <=> ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )
    | ~ class_Groups_Ozero(tc_Complex_Ocomplex)
    | ~ ( ( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
          | ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) )
      <=> ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ),
    inference(modus_ponens,[status(thm)],[97,96]) ).

tff(99,plain,
    ~ ( ( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
        | ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) )
    <=> ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
    inference(unit_resolution,[status(thm)],[98,95,82]) ).

tff(100,plain,
    ( ( ~ ! [V_pb_2: $i,V_aa_2: $i,T_a: $i] :
            ( ~ class_Groups_Ozero(T_a)
            | ~ ( ( ( V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) )
                  | ( V_pb_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
              <=> ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )
      | ~ class_Groups_Ozero(tc_Complex_Ocomplex)
      | ( ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
      <=> ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) )
  <=> ( ~ ! [V_pb_2: $i,V_aa_2: $i,T_a: $i] :
            ( ~ class_Groups_Ozero(T_a)
            | ~ ( ( ( V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) )
                  | ( V_pb_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
              <=> ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )
      | ~ class_Groups_Ozero(tc_Complex_Ocomplex)
      | ( ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
      <=> ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(101,plain,
    ( ( ~ class_Groups_Ozero(tc_Complex_Ocomplex)
      | ~ ( ( ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
            | ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) )
        <=> ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) )
  <=> ( ~ class_Groups_Ozero(tc_Complex_Ocomplex)
      | ( ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
      <=> ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(102,plain,
    ( ( ~ ! [V_pb_2: $i,V_aa_2: $i,T_a: $i] :
            ( ~ class_Groups_Ozero(T_a)
            | ~ ( ( ( V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) )
                  | ( V_pb_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
              <=> ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )
      | ~ class_Groups_Ozero(tc_Complex_Ocomplex)
      | ~ ( ( ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
            | ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) )
        <=> ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) )
  <=> ( ~ ! [V_pb_2: $i,V_aa_2: $i,T_a: $i] :
            ( ~ class_Groups_Ozero(T_a)
            | ~ ( ( ( V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) )
                  | ( V_pb_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
              <=> ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )
      | ~ class_Groups_Ozero(tc_Complex_Ocomplex)
      | ( ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
      <=> ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ) ),
    inference(monotonicity,[status(thm)],[101]) ).

tff(103,plain,
    ( ( ~ ! [V_pb_2: $i,V_aa_2: $i,T_a: $i] :
            ( ~ class_Groups_Ozero(T_a)
            | ~ ( ( ( V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) )
                  | ( V_pb_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
              <=> ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )
      | ~ class_Groups_Ozero(tc_Complex_Ocomplex)
      | ~ ( ( ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
            | ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) )
        <=> ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) )
  <=> ( ~ ! [V_pb_2: $i,V_aa_2: $i,T_a: $i] :
            ( ~ class_Groups_Ozero(T_a)
            | ~ ( ( ( V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) )
                  | ( V_pb_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
              <=> ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )
      | ~ class_Groups_Ozero(tc_Complex_Ocomplex)
      | ( ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
      <=> ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ) ),
    inference(transitivity,[status(thm)],[102,100]) ).

tff(104,plain,
    ( ~ ! [V_pb_2: $i,V_aa_2: $i,T_a: $i] :
          ( ~ class_Groups_Ozero(T_a)
          | ~ ( ( ( V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) )
                | ( V_pb_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
            <=> ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )
    | ~ class_Groups_Ozero(tc_Complex_Ocomplex)
    | ~ ( ( ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
          | ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) )
      <=> ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(105,plain,
    ( ~ ! [V_pb_2: $i,V_aa_2: $i,T_a: $i] :
          ( ~ class_Groups_Ozero(T_a)
          | ~ ( ( ( V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) )
                | ( V_pb_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
            <=> ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )
    | ~ class_Groups_Ozero(tc_Complex_Ocomplex)
    | ( ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
    <=> ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ),
    inference(modus_ponens,[status(thm)],[104,103]) ).

tff(106,plain,
    ( ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
  <=> ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
    inference(unit_resolution,[status(thm)],[105,95,82]) ).

tff(107,plain,
    ( class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)
  <=> class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) ),
    inference(rewrite,[status(thm)],[]) ).

tff(108,axiom,
    class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).

tff(109,plain,
    class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
    inference(modus_ponens,[status(thm)],[108,107]) ).

tff(110,plain,
    ^ [T_a: $i] :
      refl(( ( ~ class_Rings_Ozero__neq__one(T_a)
          | ( c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) )
      <=> ( ~ class_Rings_Ozero__neq__one(T_a)
          | ( c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(111,plain,
    ( ! [T_a: $i] :
        ( ~ class_Rings_Ozero__neq__one(T_a)
        | ( c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) )
  <=> ! [T_a: $i] :
        ( ~ class_Rings_Ozero__neq__one(T_a)
        | ( c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    inference(quant_intro,[status(thm)],[110]) ).

tff(112,plain,
    ( ! [T_a: $i] :
        ( ~ class_Rings_Ozero__neq__one(T_a)
        | ( c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) )
  <=> ! [T_a: $i] :
        ( ~ class_Rings_Ozero__neq__one(T_a)
        | ( c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(113,plain,
    ^ [T_a: $i] :
      rewrite(( ( class_Rings_Ozero__neq__one(T_a)
         => ( c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) )
      <=> ( ~ class_Rings_Ozero__neq__one(T_a)
          | ( c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(114,plain,
    ( ! [T_a: $i] :
        ( class_Rings_Ozero__neq__one(T_a)
       => ( c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) )
  <=> ! [T_a: $i] :
        ( ~ class_Rings_Ozero__neq__one(T_a)
        | ( c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    inference(quant_intro,[status(thm)],[113]) ).

tff(115,axiom,
    ! [T_a: $i] :
      ( class_Rings_Ozero__neq__one(T_a)
     => ( c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__neq__zero) ).

tff(116,plain,
    ! [T_a: $i] :
      ( ~ class_Rings_Ozero__neq__one(T_a)
      | ( c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ),
    inference(modus_ponens,[status(thm)],[115,114]) ).

tff(117,plain,
    ! [T_a: $i] :
      ( ~ class_Rings_Ozero__neq__one(T_a)
      | ( c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ),
    inference(modus_ponens,[status(thm)],[116,112]) ).

tff(118,plain,
    ! [T_a: $i] :
      ( ~ class_Rings_Ozero__neq__one(T_a)
      | ( c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ),
    inference(skolemize,[status(sab)],[117]) ).

tff(119,plain,
    ! [T_a: $i] :
      ( ~ class_Rings_Ozero__neq__one(T_a)
      | ( c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ),
    inference(modus_ponens,[status(thm)],[118,111]) ).

tff(120,plain,
    ( ( ~ ! [T_a: $i] :
            ( ~ class_Rings_Ozero__neq__one(T_a)
            | ( c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) )
      | ~ class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)
      | ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) )
  <=> ( ~ ! [T_a: $i] :
            ( ~ class_Rings_Ozero__neq__one(T_a)
            | ( c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) )
      | ~ class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)
      | ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(121,plain,
    ( ~ ! [T_a: $i] :
          ( ~ class_Rings_Ozero__neq__one(T_a)
          | ( c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) )
    | ~ class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)
    | ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(122,plain,
    ( ~ ! [T_a: $i] :
          ( ~ class_Rings_Ozero__neq__one(T_a)
          | ( c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) )
    | ~ class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)
    | ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
    inference(modus_ponens,[status(thm)],[121,120]) ).

tff(123,plain,
    c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(unit_resolution,[status(thm)],[122,119,109]) ).

tff(124,plain,
    ( ~ ( ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
      <=> ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) )
    | ( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
    | ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
    inference(tautology,[status(thm)],[]) ).

tff(125,plain,
    c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    inference(unit_resolution,[status(thm)],[124,123,106]) ).

tff(126,plain,
    ( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
    | ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
    | ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
    inference(tautology,[status(thm)],[]) ).

tff(127,plain,
    ( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
    | ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
    inference(unit_resolution,[status(thm)],[126,125]) ).

tff(128,plain,
    ( ( ( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
        | ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) )
    <=> ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) )
    | ~ ( ( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
        | ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) )
    | ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
    inference(tautology,[status(thm)],[]) ).

tff(129,plain,
    c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    inference(unit_resolution,[status(thm)],[128,127,99]) ).

tff(130,plain,
    ^ [V_n: $i,V_a: $i,T_a: $i] :
      refl(( ( ( 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) )
      <=> ( ( 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(bind,[status(th)],[]) ).

tff(131,plain,
    ( ! [V_n: $i,V_a: $i,T_a: $i] :
        ( ( 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) )
  <=> ! [V_n: $i,V_a: $i,T_a: $i] :
        ( ( 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(quant_intro,[status(thm)],[130]) ).

tff(132,plain,
    ( ! [V_n: $i,V_a: $i,T_a: $i] :
        ( ( 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) )
  <=> ! [V_n: $i,V_a: $i,T_a: $i] :
        ( ( 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(rewrite,[status(thm)],[]) ).

tff(133,plain,
    ^ [V_n: $i,V_a: $i,T_a: $i] :
      trans(monotonicity(rewrite(( ( ( 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) ) )
          <=> ( ( 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)
           => ( ( 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) ) ) )
        <=> ( class_Rings_Oring__1__no__zero__divisors(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) ) ) ) )),
        rewrite(( ( class_Rings_Oring__1__no__zero__divisors(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) ) ) )
        <=> ( ( 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) ) )),
        ( ( 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) ) ) )
      <=> ( ( 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(bind,[status(th)],[]) ).

tff(134,plain,
    ( ! [V_n: $i,V_a: $i,T_a: $i] :
        ( 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) ) ) )
  <=> ! [V_n: $i,V_a: $i,T_a: $i] :
        ( ( 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(quant_intro,[status(thm)],[133]) ).

tff(135,axiom,
    ! [V_n: $i,V_a: $i,T_a: $i] :
      ( 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('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__power__not__zero) ).

tff(136,plain,
    ! [V_n: $i,V_a: $i,T_a: $i] :
      ( ( 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(modus_ponens,[status(thm)],[135,134]) ).

tff(137,plain,
    ! [V_n: $i,V_a: $i,T_a: $i] :
      ( ( 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(modus_ponens,[status(thm)],[136,132]) ).

tff(138,plain,
    ! [V_n: $i,V_a: $i,T_a: $i] :
      ( ( 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(skolemize,[status(sab)],[137]) ).

tff(139,plain,
    ! [V_n: $i,V_a: $i,T_a: $i] :
      ( ( 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(modus_ponens,[status(thm)],[138,131]) ).

tff(140,plain,
    ( ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
            ( ( 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) )
      | ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
      | ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
      | ~ class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
  <=> ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
            ( ( 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) )
      | ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
      | ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
      | ~ class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(141,plain,
    ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
      | ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
      | ~ class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
  <=> ( ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
      | ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
      | ~ class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(142,plain,
    ( ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
            ( ( 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) )
      | ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
      | ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
      | ~ class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
  <=> ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
            ( ( 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) )
      | ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
      | ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
      | ~ class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
    inference(monotonicity,[status(thm)],[141]) ).

tff(143,plain,
    ( ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
            ( ( 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) )
      | ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
      | ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
      | ~ class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
  <=> ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
            ( ( 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) )
      | ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
      | ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
      | ~ class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
    inference(transitivity,[status(thm)],[142,140]) ).

tff(144,plain,
    ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
          ( ( 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) )
    | ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
    | ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
    | ~ class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(145,plain,
    ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
          ( ( 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) )
    | ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
    | ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
    | ~ class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    inference(modus_ponens,[status(thm)],[144,143]) ).

tff(146,plain,
    ( ( c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
    | ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
    | ~ class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    inference(unit_resolution,[status(thm)],[145,139]) ).

tff(147,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    inference(unit_resolution,[status(thm)],[146,129,79]) ).

tff(148,plain,
    ^ [V_q: $i,V_p: $i,T_a: $i] :
      refl(( ( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
          | ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
          | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
          | ~ class_Rings_Oidom(T_a) )
      <=> ( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
          | ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
          | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
          | ~ class_Rings_Oidom(T_a) ) )),
    inference(bind,[status(th)],[]) ).

tff(149,plain,
    ( ! [V_q: $i,V_p: $i,T_a: $i] :
        ( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
        | ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
        | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
        | ~ class_Rings_Oidom(T_a) )
  <=> ! [V_q: $i,V_p: $i,T_a: $i] :
        ( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
        | ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
        | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
        | ~ class_Rings_Oidom(T_a) ) ),
    inference(quant_intro,[status(thm)],[148]) ).

tff(150,plain,
    ( ! [V_q: $i,V_p: $i,T_a: $i] :
        ( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
        | ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
        | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
        | ~ class_Rings_Oidom(T_a) )
  <=> ! [V_q: $i,V_p: $i,T_a: $i] :
        ( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
        | ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
        | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
        | ~ class_Rings_Oidom(T_a) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(151,plain,
    ^ [V_q: $i,V_p: $i,T_a: $i] :
      trans(monotonicity(trans(monotonicity(rewrite(( ( ( V_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
                 => ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) ) )
              <=> ( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
                  | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) ) ) )),
              ( ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
               => ( ( V_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
                 => ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) ) ) )
            <=> ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
               => ( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
                  | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) ) ) ) )),
            rewrite(( ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
               => ( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
                  | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) ) ) )
            <=> ( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
                | ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
                | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) ) ) )),
            ( ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
             => ( ( V_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
               => ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) ) ) )
          <=> ( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
              | ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
              | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) ) ) )),
          ( ( class_Rings_Oidom(T_a)
           => ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
             => ( ( V_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
               => ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) ) ) ) )
        <=> ( class_Rings_Oidom(T_a)
           => ( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
              | ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
              | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) ) ) ) )),
        rewrite(( ( class_Rings_Oidom(T_a)
           => ( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
              | ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
              | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) ) ) )
        <=> ( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
            | ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
            | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
            | ~ class_Rings_Oidom(T_a) ) )),
        ( ( class_Rings_Oidom(T_a)
         => ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
           => ( ( V_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
             => ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) ) ) ) )
      <=> ( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
          | ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
          | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
          | ~ class_Rings_Oidom(T_a) ) )),
    inference(bind,[status(th)],[]) ).

tff(152,plain,
    ( ! [V_q: $i,V_p: $i,T_a: $i] :
        ( class_Rings_Oidom(T_a)
       => ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
         => ( ( V_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
           => ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) ) ) ) )
  <=> ! [V_q: $i,V_p: $i,T_a: $i] :
        ( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
        | ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
        | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
        | ~ class_Rings_Oidom(T_a) ) ),
    inference(quant_intro,[status(thm)],[151]) ).

tff(153,axiom,
    ! [V_q: $i,V_p: $i,T_a: $i] :
      ( class_Rings_Oidom(T_a)
     => ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
       => ( ( V_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
         => ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__mult__eq) ).

tff(154,plain,
    ! [V_q: $i,V_p: $i,T_a: $i] :
      ( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
      | ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
      | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
      | ~ class_Rings_Oidom(T_a) ),
    inference(modus_ponens,[status(thm)],[153,152]) ).

tff(155,plain,
    ! [V_q: $i,V_p: $i,T_a: $i] :
      ( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
      | ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
      | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
      | ~ class_Rings_Oidom(T_a) ),
    inference(modus_ponens,[status(thm)],[154,150]) ).

tff(156,plain,
    ! [V_q: $i,V_p: $i,T_a: $i] :
      ( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
      | ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
      | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
      | ~ class_Rings_Oidom(T_a) ),
    inference(skolemize,[status(sab)],[155]) ).

tff(157,plain,
    ! [V_q: $i,V_p: $i,T_a: $i] :
      ( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
      | ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
      | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
      | ~ class_Rings_Oidom(T_a) ),
    inference(modus_ponens,[status(thm)],[156,149]) ).

tff(158,plain,
    ( ( v_s____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
  <=> ( v_s____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(159,axiom,
    v_s____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sne) ).

tff(160,plain,
    v_s____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    inference(modus_ponens,[status(thm)],[159,158]) ).

tff(161,plain,
    ( ( ~ ! [V_q: $i,V_p: $i,T_a: $i] :
            ( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
            | ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
            | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
            | ~ class_Rings_Oidom(T_a) )
      | ( v_s____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
      | ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
      | ( c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)) )
      | ~ class_Rings_Oidom(tc_Complex_Ocomplex) )
  <=> ( ~ ! [V_q: $i,V_p: $i,T_a: $i] :
            ( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
            | ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
            | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
            | ~ class_Rings_Oidom(T_a) )
      | ( v_s____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
      | ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
      | ( c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)) )
      | ~ class_Rings_Oidom(tc_Complex_Ocomplex) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(162,plain,
    ( ~ ! [V_q: $i,V_p: $i,T_a: $i] :
          ( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
          | ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
          | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
          | ~ class_Rings_Oidom(T_a) )
    | ( v_s____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
    | ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
    | ( c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)) )
    | ~ class_Rings_Oidom(tc_Complex_Ocomplex) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(163,plain,
    ( ~ ! [V_q: $i,V_p: $i,T_a: $i] :
          ( ( V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
          | ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
          | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) )
          | ~ class_Rings_Oidom(T_a) )
    | ( v_s____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
    | ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
    | ( c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)) )
    | ~ class_Rings_Oidom(tc_Complex_Ocomplex) ),
    inference(modus_ponens,[status(thm)],[162,161]) ).

tff(164,plain,
    ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
    | ( c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)) ) ),
    inference(unit_resolution,[status(thm)],[163,160,157,75]) ).

tff(165,plain,
    c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)),
    inference(unit_resolution,[status(thm)],[164,147]) ).

tff(166,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)) = c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____)),
    inference(symmetry,[status(thm)],[165]) ).

tff(167,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))
  <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)) ),
    inference(rewrite,[status(thm)],[]) ).

tff(168,axiom,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

tff(169,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)),
    inference(modus_ponens,[status(thm)],[168,167]) ).

tff(170,plain,
    ^ [V_n: $i] :
      refl(( ( ~ 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))) ) )
      <=> ( ~ 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))) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(171,plain,
    ( ! [V_n: $i] :
        ( ~ 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))) ) )
  <=> ! [V_n: $i] :
        ( ~ 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))) ) ) ),
    inference(quant_intro,[status(thm)],[170]) ).

tff(172,plain,
    ( ! [V_n: $i] :
        ( ~ 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))) ) )
  <=> ! [V_n: $i] :
        ( ~ 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))) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(173,plain,
    ^ [V_n: $i] :
      rewrite(( ( 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))) ) )
      <=> ( ~ 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))) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(174,plain,
    ( ! [V_n: $i] :
        ( 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))) ) )
  <=> ! [V_n: $i] :
        ( ~ 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))) ) ) ),
    inference(quant_intro,[status(thm)],[173]) ).

tff(175,axiom,
    ! [V_n: $i] :
      ( 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('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__pred_H) ).

tff(176,plain,
    ! [V_n: $i] :
      ( ~ 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))) ) ),
    inference(modus_ponens,[status(thm)],[175,174]) ).

tff(177,plain,
    ! [V_n: $i] :
      ( ~ 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))) ) ),
    inference(modus_ponens,[status(thm)],[176,172]) ).

tff(178,plain,
    ! [V_n: $i] :
      ( ~ 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))) ) ),
    inference(skolemize,[status(sab)],[177]) ).

tff(179,plain,
    ! [V_n: $i] :
      ( ~ 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))) ) ),
    inference(modus_ponens,[status(thm)],[178,171]) ).

tff(180,plain,
    ( ( ~ ! [V_n: $i] :
            ( ~ 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))) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))
      | ( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) )
  <=> ( ~ ! [V_n: $i] :
            ( ~ 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))) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))
      | ( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(181,plain,
    ( ~ ! [V_n: $i] :
          ( ~ 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))) ) )
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))
    | ( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(182,plain,
    ( ~ ! [V_n: $i] :
          ( ~ 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))) ) )
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))
    | ( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
    inference(modus_ponens,[status(thm)],[181,180]) ).

tff(183,plain,
    c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
    inference(unit_resolution,[status(thm)],[182,179,169]) ).

tff(184,plain,
    c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),
    inference(symmetry,[status(thm)],[183]) ).

tff(185,plain,
    ( class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
  <=> class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
    inference(rewrite,[status(thm)],[]) ).

tff(186,axiom,
    class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).

tff(187,plain,
    class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
    inference(modus_ponens,[status(thm)],[186,185]) ).

tff(188,plain,
    ^ [V_n: $i,V_a: $i,T_a: $i] :
      refl(( ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) )
      <=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) ) )),
    inference(bind,[status(th)],[]) ).

tff(189,plain,
    ( ! [V_n: $i,V_a: $i,T_a: $i] :
        ( ~ class_Rings_Ocomm__semiring__1(T_a)
        | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) )
  <=> ! [V_n: $i,V_a: $i,T_a: $i] :
        ( ~ class_Rings_Ocomm__semiring__1(T_a)
        | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) ) ),
    inference(quant_intro,[status(thm)],[188]) ).

tff(190,plain,
    ( ! [V_n: $i,V_a: $i,T_a: $i] :
        ( ~ class_Rings_Ocomm__semiring__1(T_a)
        | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) )
  <=> ! [V_n: $i,V_a: $i,T_a: $i] :
        ( ~ class_Rings_Ocomm__semiring__1(T_a)
        | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(191,plain,
    ^ [V_n: $i,V_a: $i,T_a: $i] :
      rewrite(( ( class_Rings_Ocomm__semiring__1(T_a)
         => ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) )
      <=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) ) )),
    inference(bind,[status(th)],[]) ).

tff(192,plain,
    ( ! [V_n: $i,V_a: $i,T_a: $i] :
        ( class_Rings_Ocomm__semiring__1(T_a)
       => ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) )
  <=> ! [V_n: $i,V_a: $i,T_a: $i] :
        ( ~ class_Rings_Ocomm__semiring__1(T_a)
        | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) ) ),
    inference(quant_intro,[status(thm)],[191]) ).

tff(193,axiom,
    ! [V_n: $i,V_a: $i,T_a: $i] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__linear__power) ).

tff(194,plain,
    ! [V_n: $i,V_a: $i,T_a: $i] :
      ( ~ class_Rings_Ocomm__semiring__1(T_a)
      | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) ),
    inference(modus_ponens,[status(thm)],[193,192]) ).

tff(195,plain,
    ! [V_n: $i,V_a: $i,T_a: $i] :
      ( ~ class_Rings_Ocomm__semiring__1(T_a)
      | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) ),
    inference(modus_ponens,[status(thm)],[194,190]) ).

tff(196,plain,
    ! [V_n: $i,V_a: $i,T_a: $i] :
      ( ~ class_Rings_Ocomm__semiring__1(T_a)
      | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) ),
    inference(skolemize,[status(sab)],[195]) ).

tff(197,plain,
    ! [V_n: $i,V_a: $i,T_a: $i] :
      ( ~ class_Rings_Ocomm__semiring__1(T_a)
      | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) ),
    inference(modus_ponens,[status(thm)],[196,189]) ).

tff(198,plain,
    ( ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
            ( ~ class_Rings_Ocomm__semiring__1(T_a)
            | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) )
      | ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
      | ( c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))) = c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____) ) )
  <=> ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
            ( ~ class_Rings_Ocomm__semiring__1(T_a)
            | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) )
      | ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
      | ( c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))) = c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(199,plain,
    ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
          ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) )
    | ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
    | ( c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))) = c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(200,plain,
    ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
          ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ) )
    | ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
    | ( c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))) = c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____) ) ),
    inference(modus_ponens,[status(thm)],[199,198]) ).

tff(201,plain,
    c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))) = c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),
    inference(unit_resolution,[status(thm)],[200,197,187]) ).

tff(202,plain,
    c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____) = c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),
    inference(symmetry,[status(thm)],[201]) ).

tff(203,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)),
    inference(monotonicity,[status(thm)],[202,184]) ).

tff(204,plain,
    ^ [V_n: $i,V_m: $i] :
      refl(( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,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(bind,[status(th)],[]) ).

tff(205,plain,
    ( ! [V_n: $i,V_m: $i] : ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m) )
  <=> ! [V_n: $i,V_m: $i] : ( 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(quant_intro,[status(thm)],[204]) ).

tff(206,plain,
    ( ! [V_n: $i,V_m: $i] : ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m) )
  <=> ! [V_n: $i,V_m: $i] : ( 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(rewrite,[status(thm)],[]) ).

tff(207,axiom,
    ! [V_n: $i,V_m: $i] : ( 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('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).

tff(208,plain,
    ! [V_n: $i,V_m: $i] : ( 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(modus_ponens,[status(thm)],[207,206]) ).

tff(209,plain,
    ! [V_n: $i,V_m: $i] : ( 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(skolemize,[status(sab)],[208]) ).

tff(210,plain,
    ! [V_n: $i,V_m: $i] : ( 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(modus_ponens,[status(thm)],[209,205]) ).

tff(211,plain,
    ( ~ ! [V_n: $i,V_m: $i] : ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m) )
    | ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(212,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
    inference(unit_resolution,[status(thm)],[211,210]) ).

tff(213,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)),
    inference(monotonicity,[status(thm)],[183]) ).

tff(214,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_na____),
    inference(transitivity,[status(thm)],[213,212,203,166,62,57,54,38]) ).

tff(215,plain,
    v_na____ = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____),
    inference(symmetry,[status(thm)],[57]) ).

tff(216,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),v_na____)
  <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____)) ),
    inference(monotonicity,[status(thm)],[215]) ).

tff(217,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____))
  <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),v_na____) ),
    inference(symmetry,[status(thm)],[216]) ).

tff(218,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____))
  <=> ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),v_na____) ),
    inference(monotonicity,[status(thm)],[217]) ).

tff(219,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____))
  <=> ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____)) ),
    inference(rewrite,[status(thm)],[]) ).

tff(220,axiom,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).

tff(221,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____)),
    inference(modus_ponens,[status(thm)],[220,219]) ).

tff(222,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),v_na____),
    inference(modus_ponens,[status(thm)],[221,218]) ).

tff(223,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))
  <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) ),
    inference(rewrite,[status(thm)],[]) ).

tff(224,axiom,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).

tff(225,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)),
    inference(modus_ponens,[status(thm)],[224,223]) ).

tff(226,plain,
    ^ [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
      refl(( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
          | ~ 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)
          | ~ 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) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(227,plain,
    ( ! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
        | ~ 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) ) )
  <=> ! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
        | ~ 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) ) ) ),
    inference(quant_intro,[status(thm)],[226]) ).

tff(228,plain,
    ( ! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
        | ~ 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) ) )
  <=> ! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
        | ~ 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) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(229,plain,
    ^ [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
      trans(monotonicity(rewrite(( ( ( 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) )
          <=> ( ( 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) ) )),
          ( ( 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) ) )
        <=> ( 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) ) ) )),
        rewrite(( ( 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) ) )
        <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
            | ~ 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_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) ) )
      <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
          | ~ 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) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(230,plain,
    ( ! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
        ( 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) ) )
  <=> ! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
        | ~ 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) ) ) ),
    inference(quant_intro,[status(thm)],[229]) ).

tff(231,axiom,
    ! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
      ( 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('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__eq__less) ).

tff(232,plain,
    ! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
      | ~ 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) ) ),
    inference(modus_ponens,[status(thm)],[231,230]) ).

tff(233,plain,
    ! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
      | ~ 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) ) ),
    inference(modus_ponens,[status(thm)],[232,228]) ).

tff(234,plain,
    ! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
      | ~ 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) ) ),
    inference(skolemize,[status(sab)],[233]) ).

tff(235,plain,
    ! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
      | ~ 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) ) ),
    inference(modus_ponens,[status(thm)],[234,227]) ).

tff(236,plain,
    ( ( ~ ! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
            ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
            | ~ 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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),v_na____)
      | ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_na____) ) )
  <=> ( ~ ! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
            ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
            | ~ 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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),v_na____)
      | ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_na____) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(237,plain,
    ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),v_na____)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))
      | ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_na____) ) )
  <=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),v_na____)
      | ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_na____) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(238,plain,
    ( ( ~ ! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
            ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
            | ~ 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,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),v_na____)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))
      | ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_na____) ) )
  <=> ( ~ ! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
            ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
            | ~ 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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),v_na____)
      | ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_na____) ) ) ),
    inference(monotonicity,[status(thm)],[237]) ).

tff(239,plain,
    ( ( ~ ! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
            ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
            | ~ 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,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),v_na____)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))
      | ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_na____) ) )
  <=> ( ~ ! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
            ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
            | ~ 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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),v_na____)
      | ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_na____) ) ) ),
    inference(transitivity,[status(thm)],[238,236]) ).

tff(240,plain,
    ( ~ ! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
          ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
          | ~ 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,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),v_na____)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))
    | ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_na____) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(241,plain,
    ( ~ ! [V_n: $i,V_m: $i,V_l: $i,V_k: $i] :
          ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
          | ~ 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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),v_na____)
    | ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_na____) ) ),
    inference(modus_ponens,[status(thm)],[240,239]) ).

tff(242,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),v_na____)
    | ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_na____) ) ),
    inference(unit_resolution,[status(thm)],[241,235,225]) ).

tff(243,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_na____),
    inference(unit_resolution,[status(thm)],[242,222]) ).

tff(244,plain,
    $false,
    inference(unit_resolution,[status(thm)],[243,214]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : SWW276+1 : TPTP v9.0.0. Released v5.2.0.
% 0.12/0.12  % Command    : run_E %s %d THM
% 0.12/0.34  % Computer : n015.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Fri Jun 20 11:23:10 EDT 2025
% 0.12/0.34  % CPUTime    : 
% 1.15/1.36  % SZS status Theorem
% 1.15/1.36  % SZS output start Proof
% See solution above
% 1.22/1.44  % E exiting
%------------------------------------------------------------------------------