Z3---4.15.1.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : Z3---4.15.1
% Problem  : SWW281+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_E %s %d THM

% Computer : n011.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 05:36:46 AM UTC 2025

% Result   : Theorem 39.06s 39.22s
% Output   : Proof 39.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   69
% Syntax   : Number of formulae    :  182 (  67 unt;   0 typ;   0 def)
%            Number of atoms       :  595 ( 220 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  690 ( 299   ~; 295   |;   0   &)
%                                         (  64 <=>;  32  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :   12 (   2 avg)
%            Number of FOOLs       :   22 (  22 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-3 aty)
%            Number of functors    :   20 (  20 usr;   8 con; 0-3 aty)
%            Number of variables   :  531 ( 477   !;   0   ?; 531   :)

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

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

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

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

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

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

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

tff(v_r_____type,type,
    v_r____: $i ).

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

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

tff(c_Groups_Ozero__class_Ozero_type,type,
    c_Groups_Ozero__class_Ozero: $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(v_u_____type,type,
    v_u____: $i ).

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

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

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

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

tff(class_Orderings_Opreorder_type,type,
    class_Orderings_Opreorder: $i > $o ).

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

tff(1,plain,
    ^ [T_1: $i] :
      refl(( ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
          | ~ class_Rings_Ocomm__semiring__1(T_1) )
      <=> ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
          | ~ class_Rings_Ocomm__semiring__1(T_1) ) )),
    inference(bind,[status(th)],[]) ).

tff(2,plain,
    ( ! [T_1: $i] :
        ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
        | ~ class_Rings_Ocomm__semiring__1(T_1) )
  <=> ! [T_1: $i] :
        ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
        | ~ class_Rings_Ocomm__semiring__1(T_1) ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [T_1: $i] :
        ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
        | ~ class_Rings_Ocomm__semiring__1(T_1) )
  <=> ! [T_1: $i] :
        ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
        | ~ class_Rings_Ocomm__semiring__1(T_1) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(4,plain,
    ^ [T_1: $i] :
      rewrite(( ( class_Rings_Ocomm__semiring__1(T_1)
         => class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)) )
      <=> ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
          | ~ class_Rings_Ocomm__semiring__1(T_1) ) )),
    inference(bind,[status(th)],[]) ).

tff(5,plain,
    ( ! [T_1: $i] :
        ( class_Rings_Ocomm__semiring__1(T_1)
       => class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)) )
  <=> ! [T_1: $i] :
        ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
        | ~ class_Rings_Ocomm__semiring__1(T_1) ) ),
    inference(quant_intro,[status(thm)],[4]) ).

tff(6,axiom,
    ! [T_1: $i] :
      ( class_Rings_Ocomm__semiring__1(T_1)
     => class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).

tff(7,plain,
    ! [T_1: $i] :
      ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Ocomm__semiring__1(T_1) ),
    inference(modus_ponens,[status(thm)],[6,5]) ).

tff(8,plain,
    ! [T_1: $i] :
      ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Ocomm__semiring__1(T_1) ),
    inference(modus_ponens,[status(thm)],[7,3]) ).

tff(9,plain,
    ! [T_1: $i] :
      ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Ocomm__semiring__1(T_1) ),
    inference(skolemize,[status(sab)],[8]) ).

tff(10,plain,
    ! [T_1: $i] :
      ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Ocomm__semiring__1(T_1) ),
    inference(modus_ponens,[status(thm)],[9,2]) ).

tff(11,plain,
    ( class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
  <=> class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
    inference(rewrite,[status(thm)],[]) ).

tff(12,axiom,
    class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).

tff(13,plain,
    class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    ( ( ~ ! [T_1: $i] :
            ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
            | ~ class_Rings_Ocomm__semiring__1(T_1) )
      | class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
      | ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) )
  <=> ( ~ ! [T_1: $i] :
            ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
            | ~ class_Rings_Ocomm__semiring__1(T_1) )
      | class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
      | ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(15,plain,
    ( ~ ! [T_1: $i] :
          ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
          | ~ class_Rings_Ocomm__semiring__1(T_1) )
    | class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(16,plain,
    ( ~ ! [T_1: $i] :
          ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
          | ~ class_Rings_Ocomm__semiring__1(T_1) )
    | class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
    inference(modus_ponens,[status(thm)],[15,14]) ).

tff(17,plain,
    class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    inference(unit_resolution,[status(thm)],[16,13,10]) ).

tff(18,plain,
    ^ [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
      refl(( ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ) )
      <=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(19,plain,
    ( ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
        ( ~ class_Rings_Ocomm__semiring__1(T_a)
        | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ) )
  <=> ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
        ( ~ class_Rings_Ocomm__semiring__1(T_a)
        | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ) ) ),
    inference(quant_intro,[status(thm)],[18]) ).

tff(20,plain,
    ( ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
        ( ~ class_Rings_Ocomm__semiring__1(T_a)
        | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ) )
  <=> ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
        ( ~ class_Rings_Ocomm__semiring__1(T_a)
        | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(21,plain,
    ^ [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
      rewrite(( ( class_Rings_Ocomm__semiring__1(T_a)
         => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ) )
      <=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(22,plain,
    ( ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
        ( class_Rings_Ocomm__semiring__1(T_a)
       => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ) )
  <=> ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
        ( ~ class_Rings_Ocomm__semiring__1(T_a)
        | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ) ) ),
    inference(quant_intro,[status(thm)],[21]) ).

tff(23,axiom,
    ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).

tff(24,plain,
    ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
      ( ~ class_Rings_Ocomm__semiring__1(T_a)
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ) ),
    inference(modus_ponens,[status(thm)],[23,22]) ).

tff(25,plain,
    ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
      ( ~ class_Rings_Ocomm__semiring__1(T_a)
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ) ),
    inference(modus_ponens,[status(thm)],[24,20]) ).

tff(26,plain,
    ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
      ( ~ class_Rings_Ocomm__semiring__1(T_a)
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ) ),
    inference(skolemize,[status(sab)],[25]) ).

tff(27,plain,
    ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
      ( ~ class_Rings_Ocomm__semiring__1(T_a)
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ) ),
    inference(modus_ponens,[status(thm)],[26,19]) ).

tff(28,plain,
    ( ( ~ ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
            ( ~ class_Rings_Ocomm__semiring__1(T_a)
            | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ) )
      | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(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____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) = 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____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))))) ) )
  <=> ( ~ ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
            ( ~ class_Rings_Ocomm__semiring__1(T_a)
            | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ) )
      | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(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____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) = 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____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))))) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(29,plain,
    ( ~ ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
          ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ) )
    | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(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____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) = 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____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(30,plain,
    ( ~ ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
          ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ) )
    | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(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____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) = 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____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))))) ) ),
    inference(modus_ponens,[status(thm)],[29,28]) ).

tff(31,plain,
    ( ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(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____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) = 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____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))))) ) ),
    inference(unit_resolution,[status(thm)],[30,27]) ).

tff(32,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(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____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) = 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____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))))),
    inference(unit_resolution,[status(thm)],[31,17]) ).

tff(33,plain,
    ^ [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
      refl(( ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) )
      <=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(34,plain,
    ( ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
        ( ~ class_Rings_Ocomm__semiring__1(T_a)
        | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) )
  <=> ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
        ( ~ class_Rings_Ocomm__semiring__1(T_a)
        | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) ) ),
    inference(quant_intro,[status(thm)],[33]) ).

tff(35,plain,
    ( ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
        ( ~ class_Rings_Ocomm__semiring__1(T_a)
        | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) )
  <=> ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
        ( ~ class_Rings_Ocomm__semiring__1(T_a)
        | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(36,plain,
    ^ [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
      rewrite(( ( class_Rings_Ocomm__semiring__1(T_a)
         => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) )
      <=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(37,plain,
    ( ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
        ( class_Rings_Ocomm__semiring__1(T_a)
       => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) )
  <=> ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
        ( ~ class_Rings_Ocomm__semiring__1(T_a)
        | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) ) ),
    inference(quant_intro,[status(thm)],[36]) ).

tff(38,axiom,
    ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).

tff(39,plain,
    ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
      ( ~ class_Rings_Ocomm__semiring__1(T_a)
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) ),
    inference(modus_ponens,[status(thm)],[38,37]) ).

tff(40,plain,
    ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
      ( ~ class_Rings_Ocomm__semiring__1(T_a)
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) ),
    inference(modus_ponens,[status(thm)],[39,35]) ).

tff(41,plain,
    ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
      ( ~ class_Rings_Ocomm__semiring__1(T_a)
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) ),
    inference(skolemize,[status(sab)],[40]) ).

tff(42,plain,
    ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
      ( ~ class_Rings_Ocomm__semiring__1(T_a)
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) ),
    inference(modus_ponens,[status(thm)],[41,34]) ).

tff(43,plain,
    ( ( ~ ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
            ( ~ class_Rings_Ocomm__semiring__1(T_a)
            | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) )
      | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(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____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(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____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) ) )
  <=> ( ~ ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
            ( ~ class_Rings_Ocomm__semiring__1(T_a)
            | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) )
      | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(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____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(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____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(44,plain,
    ( ~ ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
          ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) )
    | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(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____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(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____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(45,plain,
    ( ~ ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
          ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) )
    | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(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____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(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____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) ) ),
    inference(modus_ponens,[status(thm)],[44,43]) ).

tff(46,plain,
    ( ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(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____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(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____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) ) ),
    inference(unit_resolution,[status(thm)],[45,42]) ).

tff(47,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(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____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(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____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))),
    inference(unit_resolution,[status(thm)],[46,17]) ).

tff(48,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(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____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(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____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))),
    inference(symmetry,[status(thm)],[47]) ).

tff(49,plain,
    ^ [V_ry: $i,V_rx: $i,V_lx: $i,T_a: $i] :
      refl(( ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) )
      <=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(50,plain,
    ( ! [V_ry: $i,V_rx: $i,V_lx: $i,T_a: $i] :
        ( ~ class_Rings_Ocomm__semiring__1(T_a)
        | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) )
  <=> ! [V_ry: $i,V_rx: $i,V_lx: $i,T_a: $i] :
        ( ~ class_Rings_Ocomm__semiring__1(T_a)
        | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) ) ),
    inference(quant_intro,[status(thm)],[49]) ).

tff(51,plain,
    ( ! [V_ry: $i,V_rx: $i,V_lx: $i,T_a: $i] :
        ( ~ class_Rings_Ocomm__semiring__1(T_a)
        | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) )
  <=> ! [V_ry: $i,V_rx: $i,V_lx: $i,T_a: $i] :
        ( ~ class_Rings_Ocomm__semiring__1(T_a)
        | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(52,plain,
    ^ [V_ry: $i,V_rx: $i,V_lx: $i,T_a: $i] :
      rewrite(( ( class_Rings_Ocomm__semiring__1(T_a)
         => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) )
      <=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(53,plain,
    ( ! [V_ry: $i,V_rx: $i,V_lx: $i,T_a: $i] :
        ( class_Rings_Ocomm__semiring__1(T_a)
       => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) )
  <=> ! [V_ry: $i,V_rx: $i,V_lx: $i,T_a: $i] :
        ( ~ class_Rings_Ocomm__semiring__1(T_a)
        | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) ) ),
    inference(quant_intro,[status(thm)],[52]) ).

tff(54,axiom,
    ! [V_ry: $i,V_rx: $i,V_lx: $i,T_a: $i] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).

tff(55,plain,
    ! [V_ry: $i,V_rx: $i,V_lx: $i,T_a: $i] :
      ( ~ class_Rings_Ocomm__semiring__1(T_a)
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) ),
    inference(modus_ponens,[status(thm)],[54,53]) ).

tff(56,plain,
    ! [V_ry: $i,V_rx: $i,V_lx: $i,T_a: $i] :
      ( ~ class_Rings_Ocomm__semiring__1(T_a)
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) ),
    inference(modus_ponens,[status(thm)],[55,51]) ).

tff(57,plain,
    ! [V_ry: $i,V_rx: $i,V_lx: $i,T_a: $i] :
      ( ~ class_Rings_Ocomm__semiring__1(T_a)
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) ),
    inference(skolemize,[status(sab)],[56]) ).

tff(58,plain,
    ! [V_ry: $i,V_rx: $i,V_lx: $i,T_a: $i] :
      ( ~ class_Rings_Ocomm__semiring__1(T_a)
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) ),
    inference(modus_ponens,[status(thm)],[57,50]) ).

tff(59,plain,
    ( ( ~ ! [V_ry: $i,V_rx: $i,V_lx: $i,T_a: $i] :
            ( ~ class_Rings_Ocomm__semiring__1(T_a)
            | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) )
      | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(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____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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____))),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))) ) )
  <=> ( ~ ! [V_ry: $i,V_rx: $i,V_lx: $i,T_a: $i] :
            ( ~ class_Rings_Ocomm__semiring__1(T_a)
            | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) )
      | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(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____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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____))),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(60,plain,
    ( ~ ! [V_ry: $i,V_rx: $i,V_lx: $i,T_a: $i] :
          ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) )
    | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(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____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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____))),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(61,plain,
    ( ~ ! [V_ry: $i,V_rx: $i,V_lx: $i,T_a: $i] :
          ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) )
    | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(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____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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____))),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))) ) ),
    inference(modus_ponens,[status(thm)],[60,59]) ).

tff(62,plain,
    ( ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(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____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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____))),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))) ) ),
    inference(unit_resolution,[status(thm)],[61,58]) ).

tff(63,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____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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____))),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))),
    inference(unit_resolution,[status(thm)],[62,17]) ).

tff(64,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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____))),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,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____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))),
    inference(symmetry,[status(thm)],[63]) ).

tff(65,plain,
    ^ [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
      refl(( ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) )
      <=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(66,plain,
    ( ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
        ( ~ class_Rings_Ocomm__semiring__1(T_a)
        | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) )
  <=> ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
        ( ~ class_Rings_Ocomm__semiring__1(T_a)
        | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) ) ),
    inference(quant_intro,[status(thm)],[65]) ).

tff(67,plain,
    ( ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
        ( ~ class_Rings_Ocomm__semiring__1(T_a)
        | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) )
  <=> ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
        ( ~ class_Rings_Ocomm__semiring__1(T_a)
        | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(68,plain,
    ^ [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
      rewrite(( ( class_Rings_Ocomm__semiring__1(T_a)
         => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) )
      <=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(69,plain,
    ( ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
        ( class_Rings_Ocomm__semiring__1(T_a)
       => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) )
  <=> ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
        ( ~ class_Rings_Ocomm__semiring__1(T_a)
        | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) ) ),
    inference(quant_intro,[status(thm)],[68]) ).

tff(70,axiom,
    ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).

tff(71,plain,
    ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
      ( ~ class_Rings_Ocomm__semiring__1(T_a)
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) ),
    inference(modus_ponens,[status(thm)],[70,69]) ).

tff(72,plain,
    ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
      ( ~ class_Rings_Ocomm__semiring__1(T_a)
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) ),
    inference(modus_ponens,[status(thm)],[71,67]) ).

tff(73,plain,
    ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
      ( ~ class_Rings_Ocomm__semiring__1(T_a)
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) ),
    inference(skolemize,[status(sab)],[72]) ).

tff(74,plain,
    ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
      ( ~ class_Rings_Ocomm__semiring__1(T_a)
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) ),
    inference(modus_ponens,[status(thm)],[73,66]) ).

tff(75,plain,
    ( ( ~ ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
            ( ~ class_Rings_Ocomm__semiring__1(T_a)
            | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) )
      | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(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____))),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))) = 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_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))) ) )
  <=> ( ~ ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
            ( ~ class_Rings_Ocomm__semiring__1(T_a)
            | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) )
      | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(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____))),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))) = 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_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(76,plain,
    ( ~ ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
          ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) )
    | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(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____))),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))) = 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_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(77,plain,
    ( ~ ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
          ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) )
    | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(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____))),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))) = 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_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))) ) ),
    inference(modus_ponens,[status(thm)],[76,75]) ).

tff(78,plain,
    ( ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(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____))),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))) = 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_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))) ) ),
    inference(unit_resolution,[status(thm)],[77,74]) ).

tff(79,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____))),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))) = 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_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))),
    inference(unit_resolution,[status(thm)],[78,17]) ).

tff(80,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_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,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____))),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))),
    inference(symmetry,[status(thm)],[79]) ).

tff(81,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,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) )
      <=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
          | ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ) )),
    inference(bind,[status(th)],[]) ).

tff(82,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,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,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,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ) ),
    inference(quant_intro,[status(thm)],[81]) ).

tff(83,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,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,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,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(84,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,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) )
      <=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
          | ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ) )),
    inference(bind,[status(th)],[]) ).

tff(85,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,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,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,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ) ),
    inference(quant_intro,[status(thm)],[84]) ).

tff(86,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,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff__inverse) ).

tff(87,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,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ),
    inference(modus_ponens,[status(thm)],[86,85]) ).

tff(88,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,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ),
    inference(modus_ponens,[status(thm)],[87,83]) ).

tff(89,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,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ),
    inference(skolemize,[status(sab)],[88]) ).

tff(90,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,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ),
    inference(modus_ponens,[status(thm)],[89,82]) ).

tff(91,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),v_na____)
  <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),v_na____) ),
    inference(rewrite,[status(thm)],[]) ).

tff(92,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),v_na____),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096order_Aa_Ap_A_060_061_An_096) ).

tff(93,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),v_na____),
    inference(modus_ponens,[status(thm)],[92,91]) ).

tff(94,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,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),v_na____)
      | ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))) = 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,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),v_na____)
      | ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))) = v_na____ ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(95,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,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) )
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),v_na____)
    | ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))) = v_na____ ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(96,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,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) )
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),v_na____)
    | ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))) = v_na____ ) ),
    inference(modus_ponens,[status(thm)],[95,94]) ).

tff(97,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))) = v_na____,
    inference(unit_resolution,[status(thm)],[96,93,90]) ).

tff(98,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_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))) = 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))))),v_na____),
    inference(monotonicity,[status(thm)],[97]) ).

tff(99,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))))),v_na____) = 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_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))),
    inference(symmetry,[status(thm)],[98]) ).

tff(100,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))))),v_na____) = 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____))),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))),
    inference(transitivity,[status(thm)],[99,80]) ).

tff(101,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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))))),v_na____)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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____))),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))),
    inference(monotonicity,[status(thm)],[100]) ).

tff(102,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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))))),v_na____)) = 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____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))),
    inference(transitivity,[status(thm)],[101,64]) ).

tff(103,plain,
    hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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))))),v_na____))) = hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(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____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))))),
    inference(monotonicity,[status(thm)],[102]) ).

tff(104,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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))))),v_na____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(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____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))),
    inference(monotonicity,[status(thm)],[103]) ).

tff(105,plain,
    ( ( ~ ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
            ( ~ class_Rings_Ocomm__semiring__1(T_a)
            | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) )
      | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),v_s____)),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))))),v_na____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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))))),v_na____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) ) )
  <=> ( ~ ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
            ( ~ class_Rings_Ocomm__semiring__1(T_a)
            | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) )
      | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),v_s____)),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))))),v_na____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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))))),v_na____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(106,plain,
    ( ~ ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
          ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) )
    | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),v_s____)),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))))),v_na____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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))))),v_na____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(107,plain,
    ( ~ ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
          ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) )
    | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),v_s____)),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))))),v_na____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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))))),v_na____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) ) ),
    inference(modus_ponens,[status(thm)],[106,105]) ).

tff(108,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),v_s____)),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))))),v_na____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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))))),v_na____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))),
    inference(unit_resolution,[status(thm)],[107,42,17]) ).

tff(109,plain,
    ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____) )
  <=> ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(110,axiom,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_u) ).

tff(111,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____),
    inference(modus_ponens,[status(thm)],[110,109]) ).

tff(112,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)),
    inference(symmetry,[status(thm)],[111]) ).

tff(113,plain,
    ^ [V_b: $i,V_a: $i,T_a: $i] :
      refl(( ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
      <=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(114,plain,
    ( ! [V_b: $i,V_a: $i,T_a: $i] :
        ( ~ class_Rings_Ocomm__semiring__1(T_a)
        | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
  <=> ! [V_b: $i,V_a: $i,T_a: $i] :
        ( ~ class_Rings_Ocomm__semiring__1(T_a)
        | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ) ),
    inference(quant_intro,[status(thm)],[113]) ).

tff(115,plain,
    ( ! [V_b: $i,V_a: $i,T_a: $i] :
        ( ~ class_Rings_Ocomm__semiring__1(T_a)
        | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
  <=> ! [V_b: $i,V_a: $i,T_a: $i] :
        ( ~ class_Rings_Ocomm__semiring__1(T_a)
        | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(116,plain,
    ^ [V_b: $i,V_a: $i,T_a: $i] :
      rewrite(( ( class_Rings_Ocomm__semiring__1(T_a)
         => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
      <=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(117,plain,
    ( ! [V_b: $i,V_a: $i,T_a: $i] :
        ( class_Rings_Ocomm__semiring__1(T_a)
       => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
  <=> ! [V_b: $i,V_a: $i,T_a: $i] :
        ( ~ class_Rings_Ocomm__semiring__1(T_a)
        | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ) ),
    inference(quant_intro,[status(thm)],[116]) ).

tff(118,axiom,
    ! [V_b: $i,V_a: $i,T_a: $i] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).

tff(119,plain,
    ! [V_b: $i,V_a: $i,T_a: $i] :
      ( ~ class_Rings_Ocomm__semiring__1(T_a)
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ),
    inference(modus_ponens,[status(thm)],[118,117]) ).

tff(120,plain,
    ! [V_b: $i,V_a: $i,T_a: $i] :
      ( ~ class_Rings_Ocomm__semiring__1(T_a)
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ),
    inference(modus_ponens,[status(thm)],[119,115]) ).

tff(121,plain,
    ! [V_b: $i,V_a: $i,T_a: $i] :
      ( ~ class_Rings_Ocomm__semiring__1(T_a)
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ),
    inference(skolemize,[status(sab)],[120]) ).

tff(122,plain,
    ! [V_b: $i,V_a: $i,T_a: $i] :
      ( ~ class_Rings_Ocomm__semiring__1(T_a)
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ),
    inference(modus_ponens,[status(thm)],[121,114]) ).

tff(123,plain,
    ( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
            ( ~ class_Rings_Ocomm__semiring__1(T_a)
            | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
      | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),v_s____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____) ) )
  <=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
            ( ~ class_Rings_Ocomm__semiring__1(T_a)
            | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
      | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),v_s____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(124,plain,
    ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
          ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
    | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),v_s____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(125,plain,
    ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
          ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
    | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),v_s____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____) ) ),
    inference(modus_ponens,[status(thm)],[124,123]) ).

tff(126,plain,
    ( ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),v_s____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____) ) ),
    inference(unit_resolution,[status(thm)],[125,122]) ).

tff(127,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),v_s____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____),
    inference(unit_resolution,[status(thm)],[126,17]) ).

tff(128,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),v_s____) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)),
    inference(transitivity,[status(thm)],[127,112]) ).

tff(129,plain,
    hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),v_s____)) = 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)),v_r____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))),
    inference(monotonicity,[status(thm)],[128]) ).

tff(130,plain,
    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)),v_r____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))) = hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),v_s____)),
    inference(symmetry,[status(thm)],[129]) ).

tff(131,plain,
    hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____)) = 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)),v_r____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))),
    inference(monotonicity,[status(thm)],[112]) ).

tff(132,plain,
    hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),v_s____)),
    inference(transitivity,[status(thm)],[131,130]) ).

tff(133,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____)),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))))),v_na____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),v_s____)),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))))),v_na____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))),
    inference(monotonicity,[status(thm)],[132]) ).

tff(134,plain,
    ( ( ~ ! [V_ry: $i,V_rx: $i,V_lx: $i,T_a: $i] :
            ( ~ class_Rings_Ocomm__semiring__1(T_a)
            | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) )
      | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____)),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))))),v_na____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) = 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))))),v_na____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) ) )
  <=> ( ~ ! [V_ry: $i,V_rx: $i,V_lx: $i,T_a: $i] :
            ( ~ class_Rings_Ocomm__semiring__1(T_a)
            | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) )
      | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
      | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____)),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))))),v_na____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) = 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))))),v_na____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(135,plain,
    ( ~ ! [V_ry: $i,V_rx: $i,V_lx: $i,T_a: $i] :
          ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) )
    | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____)),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))))),v_na____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) = 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))))),v_na____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(136,plain,
    ( ~ ! [V_ry: $i,V_rx: $i,V_lx: $i,T_a: $i] :
          ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) )
    | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____)),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))))),v_na____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) = 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))))),v_na____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) ) ),
    inference(modus_ponens,[status(thm)],[135,134]) ).

tff(137,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____)),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))))),v_na____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) = 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))))),v_na____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))),
    inference(unit_resolution,[status(thm)],[136,58,17]) ).

tff(138,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))))),v_na____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____)),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))))),v_na____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))),
    inference(symmetry,[status(thm)],[137]) ).

tff(139,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))) = 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)),v_r____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))),
    inference(monotonicity,[status(thm)],[131]) ).

tff(140,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)),v_r____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))),
    inference(symmetry,[status(thm)],[139]) ).

tff(141,plain,
    ( ( ~ ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
            ( ~ class_Rings_Ocomm__semiring__1(T_a)
            | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) )
      | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(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)),v_r____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))) ) )
  <=> ( ~ ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
            ( ~ class_Rings_Ocomm__semiring__1(T_a)
            | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) )
      | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(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)),v_r____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(142,plain,
    ( ~ ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
          ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) )
    | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(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)),v_r____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(143,plain,
    ( ~ ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
          ( ~ class_Rings_Ocomm__semiring__1(T_a)
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) )
    | ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(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)),v_r____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))) ) ),
    inference(modus_ponens,[status(thm)],[142,141]) ).

tff(144,plain,
    ( ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(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)),v_r____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))) ) ),
    inference(unit_resolution,[status(thm)],[143,74]) ).

tff(145,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)),v_r____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))),
    inference(unit_resolution,[status(thm)],[144,17]) ).

tff(146,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))) = 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)),v_r____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))),
    inference(symmetry,[status(thm)],[145]) ).

tff(147,plain,
    ( class_Orderings_Opreorder(tc_Nat_Onat)
  <=> class_Orderings_Opreorder(tc_Nat_Onat) ),
    inference(rewrite,[status(thm)],[]) ).

tff(148,axiom,
    class_Orderings_Opreorder(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).

tff(149,plain,
    class_Orderings_Opreorder(tc_Nat_Onat),
    inference(modus_ponens,[status(thm)],[148,147]) ).

tff(150,plain,
    ^ [V_y: $i,V_x: $i,T_a: $i] :
      refl(( ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
          | ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
          | ~ class_Orderings_Opreorder(T_a) )
      <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
          | ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
          | ~ class_Orderings_Opreorder(T_a) ) )),
    inference(bind,[status(th)],[]) ).

tff(151,plain,
    ( ! [V_y: $i,V_x: $i,T_a: $i] :
        ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
        | ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
        | ~ class_Orderings_Opreorder(T_a) )
  <=> ! [V_y: $i,V_x: $i,T_a: $i] :
        ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
        | ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
        | ~ class_Orderings_Opreorder(T_a) ) ),
    inference(quant_intro,[status(thm)],[150]) ).

tff(152,plain,
    ( ! [V_y: $i,V_x: $i,T_a: $i] :
        ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
        | ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
        | ~ class_Orderings_Opreorder(T_a) )
  <=> ! [V_y: $i,V_x: $i,T_a: $i] :
        ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
        | ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
        | ~ class_Orderings_Opreorder(T_a) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(153,plain,
    ^ [V_y: $i,V_x: $i,T_a: $i] :
      trans(monotonicity(rewrite(( ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
             => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) )
          <=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
              | c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) )),
          ( ( class_Orderings_Opreorder(T_a)
           => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
             => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) )
        <=> ( class_Orderings_Opreorder(T_a)
           => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
              | c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) )),
        rewrite(( ( class_Orderings_Opreorder(T_a)
           => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
              | c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) )
        <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
            | ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
            | ~ class_Orderings_Opreorder(T_a) ) )),
        ( ( class_Orderings_Opreorder(T_a)
         => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
           => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) )
      <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
          | ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
          | ~ class_Orderings_Opreorder(T_a) ) )),
    inference(bind,[status(th)],[]) ).

tff(154,plain,
    ( ! [V_y: $i,V_x: $i,T_a: $i] :
        ( class_Orderings_Opreorder(T_a)
       => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
         => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) )
  <=> ! [V_y: $i,V_x: $i,T_a: $i] :
        ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
        | ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
        | ~ class_Orderings_Opreorder(T_a) ) ),
    inference(quant_intro,[status(thm)],[153]) ).

tff(155,axiom,
    ! [V_y: $i,V_x: $i,T_a: $i] :
      ( class_Orderings_Opreorder(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
       => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__le) ).

tff(156,plain,
    ! [V_y: $i,V_x: $i,T_a: $i] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
      | ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(modus_ponens,[status(thm)],[155,154]) ).

tff(157,plain,
    ! [V_y: $i,V_x: $i,T_a: $i] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
      | ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(modus_ponens,[status(thm)],[156,152]) ).

tff(158,plain,
    ! [V_y: $i,V_x: $i,T_a: $i] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
      | ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(skolemize,[status(sab)],[157]) ).

tff(159,plain,
    ! [V_y: $i,V_x: $i,T_a: $i] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
      | ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(modus_ponens,[status(thm)],[158,151]) ).

tff(160,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____),v_na____) ),
    inference(rewrite,[status(thm)],[]) ).

tff(161,axiom,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),v_na____),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dsn) ).

tff(162,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),v_na____),
    inference(modus_ponens,[status(thm)],[161,160]) ).

tff(163,plain,
    ( ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
            ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
            | ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
            | ~ class_Orderings_Opreorder(T_a) )
      | ~ class_Orderings_Opreorder(tc_Nat_Onat)
      | c_Orderings_Oord__class_Oless__eq(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____),v_na____) )
  <=> ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
            ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
            | ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
            | ~ class_Orderings_Opreorder(T_a) )
      | ~ class_Orderings_Opreorder(tc_Nat_Onat)
      | c_Orderings_Oord__class_Oless__eq(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____),v_na____) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(164,plain,
    ( ( c_Orderings_Oord__class_Oless__eq(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____),v_na____)
      | ~ class_Orderings_Opreorder(tc_Nat_Onat) )
  <=> ( ~ class_Orderings_Opreorder(tc_Nat_Onat)
      | c_Orderings_Oord__class_Oless__eq(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____),v_na____) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(165,plain,
    ( ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
            ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
            | ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
            | ~ class_Orderings_Opreorder(T_a) )
      | c_Orderings_Oord__class_Oless__eq(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____),v_na____)
      | ~ class_Orderings_Opreorder(tc_Nat_Onat) )
  <=> ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
            ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
            | ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
            | ~ class_Orderings_Opreorder(T_a) )
      | ~ class_Orderings_Opreorder(tc_Nat_Onat)
      | c_Orderings_Oord__class_Oless__eq(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____),v_na____) ) ),
    inference(monotonicity,[status(thm)],[164]) ).

tff(166,plain,
    ( ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
            ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
            | ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
            | ~ class_Orderings_Opreorder(T_a) )
      | c_Orderings_Oord__class_Oless__eq(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____),v_na____)
      | ~ class_Orderings_Opreorder(tc_Nat_Onat) )
  <=> ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
            ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
            | ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
            | ~ class_Orderings_Opreorder(T_a) )
      | ~ class_Orderings_Opreorder(tc_Nat_Onat)
      | c_Orderings_Oord__class_Oless__eq(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____),v_na____) ) ),
    inference(transitivity,[status(thm)],[165,163]) ).

tff(167,plain,
    ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
          ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
          | ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
          | ~ class_Orderings_Opreorder(T_a) )
    | c_Orderings_Oord__class_Oless__eq(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____),v_na____)
    | ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(168,plain,
    ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
          ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
          | ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
          | ~ class_Orderings_Opreorder(T_a) )
    | ~ class_Orderings_Opreorder(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless__eq(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____),v_na____) ),
    inference(modus_ponens,[status(thm)],[167,166]) ).

tff(169,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),v_na____),
    inference(unit_resolution,[status(thm)],[168,162,159,149]) ).

tff(170,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,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))) = 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,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))) = v_na____ ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(171,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,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) )
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))) = v_na____ ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(172,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,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) )
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))) = v_na____ ) ),
    inference(modus_ponens,[status(thm)],[171,170]) ).

tff(173,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))) = v_na____,
    inference(unit_resolution,[status(thm)],[172,90,169]) ).

tff(174,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),v_na____),
    inference(monotonicity,[status(thm)],[173]) ).

tff(175,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),v_na____) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))),
    inference(symmetry,[status(thm)],[174]) ).

tff(176,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),v_na____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))),
    inference(transitivity,[status(thm)],[175,146,140]) ).

tff(177,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))))),v_na____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),v_na____)) = 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))))),v_na____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))),
    inference(monotonicity,[status(thm)],[176]) ).

tff(178,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))))),v_na____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),v_na____)) = 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____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))))),
    inference(transitivity,[status(thm)],[177,138,133,108,104,48,32]) ).

tff(179,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))))),v_na____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),v_na____)) != 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____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))))) )
  <=> ( 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))))),v_na____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),v_na____)) != 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____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))))) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(180,axiom,
    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))))),v_na____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),v_na____)) != 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____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

tff(181,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))))),v_na____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),v_na____)) != 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____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),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_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))))),
    inference(modus_ponens,[status(thm)],[180,179]) ).

tff(182,plain,
    $false,
    inference(unit_resolution,[status(thm)],[181,178]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SWW281+1 : TPTP v9.0.0. Released v5.2.0.
% 0.06/0.12  % Command    : run_E %s %d THM
% 0.12/0.33  % Computer : n011.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Fri Jun 20 11:22:41 EDT 2025
% 0.12/0.33  % CPUTime    : 
% 39.06/39.22  % SZS status Theorem
% 39.06/39.22  % SZS output start Proof
% See solution above
% 39.15/39.39  % E exiting
%------------------------------------------------------------------------------