TSTP Solution File: ALG398-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : ALG398-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n007.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 : Tue Sep  6 16:10:05 EDT 2022

% Result   : Unsatisfiable 0.55s 0.70s
% Output   : Proof 0.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   58
% Syntax   : Number of formulae    :  116 (  41 unt;  16 typ;   0 def)
%            Number of atoms       :  345 ( 174 equ)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives :  406 ( 179   ~; 187   |;   0   &)
%                                         (  40 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of FOOLs       :   18 (  18 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   20 (  11   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-3 aty)
%            Number of functors    :   12 (  12 usr;   5 con; 0-3 aty)
%            Number of variables   :  207 ( 189   !;   0   ?; 207   :)

% Comments : 
%------------------------------------------------------------------------------
tff(c_HOL_Otimes__class_Otimes_type,type,
    c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).

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

tff(c_Polynomial_Opoly_type,type,
    c_Polynomial_Opoly: ( $i * $i * $i ) > $i ).

tff(v_c_____type,type,
    v_c____: $i ).

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

tff(v_x_type,type,
    v_x: $i ).

tff(c_Polynomial_Osmult_type,type,
    c_Polynomial_Osmult: ( $i * $i * $i ) > $i ).

tff(v_q_____type,type,
    v_q____: $i ).

tff(c_HOL_Oinverse__class_Oinverse_type,type,
    c_HOL_Oinverse__class_Oinverse: ( $i * $i ) > $i ).

tff(c_HOL_Ozero__class_Ozero_type,type,
    c_HOL_Ozero__class_Ozero: $i > $i ).

tff(c_HOL_Oinverse__class_Odivide_type,type,
    c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).

tff(c_HOL_Oone__class_Oone_type,type,
    c_HOL_Oone__class_Oone: $i > $i ).

tff(class_Ring__and__Field_Ocomm__semiring__0_type,type,
    class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).

tff(class_Ring__and__Field_Ofield_type,type,
    class_Ring__and__Field_Ofield: $i > $o ).

tff(class_Ring__and__Field_Ocomm__semiring__1_type,type,
    class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).

tff(class_Ring__and__Field_Odivision__by__zero_type,type,
    class_Ring__and__Field_Odivision__by__zero: $i > $o ).

tff(1,plain,
    ( ( c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) )
  <=> ( c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pqc0_0) ).

tff(3,plain,
    c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(modus_ponens,[status(thm)],[2,1]) ).

tff(4,plain,
    c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),
    inference(symmetry,[status(thm)],[3]) ).

tff(5,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
  <=> class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
    inference(rewrite,[status(thm)],]) ).

tff(6,axiom,
    class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).

tff(7,plain,
    class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
    inference(modus_ponens,[status(thm)],[6,5]) ).

tff(8,plain,
    ^ [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
      refl(
        ( ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
          | ( c_Polynomial_Opoly(c_Polynomial_Osmult(V_a,V_p,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Opoly(V_p,V_x,T_a),T_a) ) )
      <=> ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
          | ( c_Polynomial_Opoly(c_Polynomial_Osmult(V_a,V_p,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Opoly(V_p,V_x,T_a),T_a) ) ) )),
    inference(bind,[status(th)],]) ).

tff(9,plain,
    ( ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
        | ( c_Polynomial_Opoly(c_Polynomial_Osmult(V_a,V_p,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Opoly(V_p,V_x,T_a),T_a) ) )
  <=> ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
        | ( c_Polynomial_Opoly(c_Polynomial_Osmult(V_a,V_p,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Opoly(V_p,V_x,T_a),T_a) ) ) ),
    inference(quant_intro,[status(thm)],[8]) ).

tff(10,plain,
    ( ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
        | ( c_Polynomial_Opoly(c_Polynomial_Osmult(V_a,V_p,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Opoly(V_p,V_x,T_a),T_a) ) )
  <=> ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
        | ( c_Polynomial_Opoly(c_Polynomial_Osmult(V_a,V_p,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Opoly(V_p,V_x,T_a),T_a) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(11,axiom,
    ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
      | ( c_Polynomial_Opoly(c_Polynomial_Osmult(V_a,V_p,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Opoly(V_p,V_x,T_a),T_a) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__smult_0) ).

tff(12,plain,
    ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
      | ( c_Polynomial_Opoly(c_Polynomial_Osmult(V_a,V_p,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Opoly(V_p,V_x,T_a),T_a) ) ),
    inference(modus_ponens,[status(thm)],[11,10]) ).

tff(13,plain,
    ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
      | ( c_Polynomial_Opoly(c_Polynomial_Osmult(V_a,V_p,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Opoly(V_p,V_x,T_a),T_a) ) ),
    inference(skolemize,[status(sab)],[12]) ).

tff(14,plain,
    ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
      | ( c_Polynomial_Opoly(c_Polynomial_Osmult(V_a,V_p,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Opoly(V_p,V_x,T_a),T_a) ) ),
    inference(modus_ponens,[status(thm)],[13,9]) ).

tff(15,plain,
    ( ( ~ ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
            ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
            | ( c_Polynomial_Opoly(c_Polynomial_Osmult(V_a,V_p,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Opoly(V_p,V_x,T_a),T_a) ) )
      | ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
      | ( c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
  <=> ( ~ ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
            ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
            | ( c_Polynomial_Opoly(c_Polynomial_Osmult(V_a,V_p,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Opoly(V_p,V_x,T_a),T_a) ) )
      | ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
      | ( c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(16,plain,
    ( ~ ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
          ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
          | ( c_Polynomial_Opoly(c_Polynomial_Osmult(V_a,V_p,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Opoly(V_p,V_x,T_a),T_a) ) )
    | ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
    | ( c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(17,plain,
    ( ~ ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
          ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
          | ( c_Polynomial_Opoly(c_Polynomial_Osmult(V_a,V_p,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Opoly(V_p,V_x,T_a),T_a) ) )
    | ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
    | ( c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
    inference(modus_ponens,[status(thm)],[16,15]) ).

tff(18,plain,
    c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(unit_resolution,[status(thm)],[17,14,7]) ).

tff(19,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),
    inference(symmetry,[status(thm)],[18]) ).

tff(20,plain,
    c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(monotonicity,[status(thm)],[3]) ).

tff(21,plain,
    c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(symmetry,[status(thm)],[20]) ).

tff(22,plain,
    ( class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
  <=> class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ),
    inference(rewrite,[status(thm)],]) ).

tff(23,axiom,
    class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).

tff(24,plain,
    class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
    inference(modus_ponens,[status(thm)],[23,22]) ).

tff(25,plain,
    ^ [V_a: $i,T_a: $i] :
      refl(
        ( ( ~ class_Ring__and__Field_Ofield(T_a)
          | ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) )
      <=> ( ~ class_Ring__and__Field_Ofield(T_a)
          | ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ) )),
    inference(bind,[status(th)],]) ).

tff(26,plain,
    ( ! [V_a: $i,T_a: $i] :
        ( ~ class_Ring__and__Field_Ofield(T_a)
        | ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) )
  <=> ! [V_a: $i,T_a: $i] :
        ( ~ class_Ring__and__Field_Ofield(T_a)
        | ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ) ),
    inference(quant_intro,[status(thm)],[25]) ).

tff(27,plain,
    ( ! [V_a: $i,T_a: $i] :
        ( ~ class_Ring__and__Field_Ofield(T_a)
        | ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) )
  <=> ! [V_a: $i,T_a: $i] :
        ( ~ class_Ring__and__Field_Ofield(T_a)
        | ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(28,axiom,
    ! [V_a: $i,T_a: $i] :
      ( ~ class_Ring__and__Field_Ofield(T_a)
      | ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__divide_0) ).

tff(29,plain,
    ! [V_a: $i,T_a: $i] :
      ( ~ class_Ring__and__Field_Ofield(T_a)
      | ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ),
    inference(modus_ponens,[status(thm)],[28,27]) ).

tff(30,plain,
    ! [V_a: $i,T_a: $i] :
      ( ~ class_Ring__and__Field_Ofield(T_a)
      | ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ),
    inference(skolemize,[status(sab)],[29]) ).

tff(31,plain,
    ! [V_a: $i,T_a: $i] :
      ( ~ class_Ring__and__Field_Ofield(T_a)
      | ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ),
    inference(modus_ponens,[status(thm)],[30,26]) ).

tff(32,plain,
    ( ( ~ ! [V_a: $i,T_a: $i] :
            ( ~ class_Ring__and__Field_Ofield(T_a)
            | ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) )
      | ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
      | ( c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
  <=> ( ~ ! [V_a: $i,T_a: $i] :
            ( ~ class_Ring__and__Field_Ofield(T_a)
            | ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) )
      | ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
      | ( c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(33,plain,
    ( ~ ! [V_a: $i,T_a: $i] :
          ( ~ class_Ring__and__Field_Ofield(T_a)
          | ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) )
    | ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
    | ( c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(34,plain,
    ( ~ ! [V_a: $i,T_a: $i] :
          ( ~ class_Ring__and__Field_Ofield(T_a)
          | ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) )
    | ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
    | ( c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
    inference(modus_ponens,[status(thm)],[33,32]) ).

tff(35,plain,
    c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(unit_resolution,[status(thm)],[34,31,24]) ).

tff(36,plain,
    c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(symmetry,[status(thm)],[35]) ).

tff(37,plain,
    c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(transitivity,[status(thm)],[36,21]) ).

tff(38,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(monotonicity,[status(thm)],[37]) ).

tff(39,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),
    inference(transitivity,[status(thm)],[38,19]) ).

tff(40,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(monotonicity,[status(thm)],[39,4]) ).

tff(41,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
  <=> class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
    inference(rewrite,[status(thm)],]) ).

tff(42,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).

tff(43,plain,
    class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
    inference(modus_ponens,[status(thm)],[42,41]) ).

tff(44,plain,
    ^ [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
      refl(
        ( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
          | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) )
      <=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
          | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) ) )),
    inference(bind,[status(th)],]) ).

tff(45,plain,
    ( ! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
        | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) )
  <=> ! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
        | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) ) ),
    inference(quant_intro,[status(thm)],[44]) ).

tff(46,plain,
    ( ! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
        | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) )
  <=> ! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
        | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(47,axiom,
    ! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).

tff(48,plain,
    ! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) ),
    inference(modus_ponens,[status(thm)],[47,46]) ).

tff(49,plain,
    ! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) ),
    inference(skolemize,[status(sab)],[48]) ).

tff(50,plain,
    ! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) ),
    inference(modus_ponens,[status(thm)],[49,45]) ).

tff(51,plain,
    ( ( ~ ! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
            ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
            | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) )
      | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
  <=> ( ~ ! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
            ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
            | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) )
      | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(52,plain,
    ( ~ ! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
          ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
          | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) )
    | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
    | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(53,plain,
    ( ~ ! [V_rx: $i,V_ly: $i,T_a: $i,V_lx: $i] :
          ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
          | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) )
    | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
    | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
    inference(modus_ponens,[status(thm)],[52,51]) ).

tff(54,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(unit_resolution,[status(thm)],[53,50,43]) ).

tff(55,plain,
    ( ( c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
  <=> ( c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
    inference(monotonicity,[status(thm)],[4]) ).

tff(56,plain,
    ( ( c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
  <=> ( c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
    inference(symmetry,[status(thm)],[55]) ).

tff(57,plain,
    ( ( c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
  <=> ( c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
    inference(monotonicity,[status(thm)],[56]) ).

tff(58,plain,
    ( ( c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
  <=> ( c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(59,plain,
    ( ( c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
  <=> ( c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(60,axiom,
    c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_a00_0) ).

tff(61,plain,
    c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(modus_ponens,[status(thm)],[60,59]) ).

tff(62,plain,
    c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(modus_ponens,[status(thm)],[61,58]) ).

tff(63,plain,
    c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(modus_ponens,[status(thm)],[62,57]) ).

tff(64,plain,
    ( class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
  <=> class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) ),
    inference(rewrite,[status(thm)],]) ).

tff(65,axiom,
    class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).

tff(66,plain,
    class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
    inference(modus_ponens,[status(thm)],[65,64]) ).

tff(67,plain,
    ^ [V_c: $i,V_b: $i,T_a: $i] :
      refl(
        ( ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
          | ~ class_Ring__and__Field_Ofield(T_a)
          | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
          | ( V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) ) )
      <=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
          | ~ class_Ring__and__Field_Ofield(T_a)
          | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
          | ( V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) ) ) )),
    inference(bind,[status(th)],]) ).

tff(68,plain,
    ( ! [V_c: $i,V_b: $i,T_a: $i] :
        ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
        | ~ class_Ring__and__Field_Ofield(T_a)
        | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
        | ( V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) ) )
  <=> ! [V_c: $i,V_b: $i,T_a: $i] :
        ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
        | ~ class_Ring__and__Field_Ofield(T_a)
        | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
        | ( V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) ) ) ),
    inference(quant_intro,[status(thm)],[67]) ).

tff(69,plain,
    ( ! [V_c: $i,V_b: $i,T_a: $i] :
        ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
        | ~ class_Ring__and__Field_Ofield(T_a)
        | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
        | ( V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) ) )
  <=> ! [V_c: $i,V_b: $i,T_a: $i] :
        ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
        | ~ class_Ring__and__Field_Ofield(T_a)
        | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
        | ( V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(70,plain,
    ^ [V_c: $i,V_b: $i,T_a: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              rewrite(
                ( ( ~ class_Ring__and__Field_Ofield(T_a)
                  | ~ class_Ring__and__Field_Odivision__by__zero(T_a) )
              <=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
                  | ~ class_Ring__and__Field_Ofield(T_a) ) )),
              ( ( ~ class_Ring__and__Field_Ofield(T_a)
                | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
                | ( V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) ) )
            <=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
                | ~ class_Ring__and__Field_Ofield(T_a)
                | ( V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) ) ) )),
            rewrite(
              ( ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
                | ~ class_Ring__and__Field_Ofield(T_a)
                | ( V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) ) )
            <=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
                | ~ class_Ring__and__Field_Ofield(T_a)
                | ( V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) ) ) )),
            ( ( ~ class_Ring__and__Field_Ofield(T_a)
              | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
              | ( V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) ) )
          <=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
              | ~ class_Ring__and__Field_Ofield(T_a)
              | ( V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) ) ) )),
          ( ( ~ class_Ring__and__Field_Ofield(T_a)
            | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
            | ( V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) )
            | ( V_c = c_HOL_Ozero__class_Ozero(T_a) ) )
        <=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
            | ~ class_Ring__and__Field_Ofield(T_a)
            | ( V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) )
            | ( V_c = c_HOL_Ozero__class_Ozero(T_a) ) ) )),
        rewrite(
          ( ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
            | ~ class_Ring__and__Field_Ofield(T_a)
            | ( V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) )
            | ( V_c = c_HOL_Ozero__class_Ozero(T_a) ) )
        <=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
            | ~ class_Ring__and__Field_Ofield(T_a)
            | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
            | ( V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) ) ) )),
        ( ( ~ class_Ring__and__Field_Ofield(T_a)
          | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
          | ( V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) )
          | ( V_c = c_HOL_Ozero__class_Ozero(T_a) ) )
      <=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
          | ~ class_Ring__and__Field_Ofield(T_a)
          | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
          | ( V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) ) ) )),
    inference(bind,[status(th)],]) ).

tff(71,plain,
    ( ! [V_c: $i,V_b: $i,T_a: $i] :
        ( ~ class_Ring__and__Field_Ofield(T_a)
        | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
        | ( V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) )
        | ( V_c = c_HOL_Ozero__class_Ozero(T_a) ) )
  <=> ! [V_c: $i,V_b: $i,T_a: $i] :
        ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
        | ~ class_Ring__and__Field_Ofield(T_a)
        | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
        | ( V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) ) ) ),
    inference(quant_intro,[status(thm)],[70]) ).

tff(72,axiom,
    ! [V_c: $i,V_b: $i,T_a: $i] :
      ( ~ class_Ring__and__Field_Ofield(T_a)
      | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
      | ( V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) )
      | ( V_c = c_HOL_Ozero__class_Ozero(T_a) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_0) ).

tff(73,plain,
    ! [V_c: $i,V_b: $i,T_a: $i] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
      | ~ class_Ring__and__Field_Ofield(T_a)
      | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
      | ( V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) ) ),
    inference(modus_ponens,[status(thm)],[72,71]) ).

tff(74,plain,
    ! [V_c: $i,V_b: $i,T_a: $i] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
      | ~ class_Ring__and__Field_Ofield(T_a)
      | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
      | ( V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) ) ),
    inference(modus_ponens,[status(thm)],[73,69]) ).

tff(75,plain,
    ! [V_c: $i,V_b: $i,T_a: $i] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
      | ~ class_Ring__and__Field_Ofield(T_a)
      | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
      | ( V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) ) ),
    inference(skolemize,[status(sab)],[74]) ).

tff(76,plain,
    ! [V_c: $i,V_b: $i,T_a: $i] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
      | ~ class_Ring__and__Field_Ofield(T_a)
      | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
      | ( V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) ) ),
    inference(modus_ponens,[status(thm)],[75,68]) ).

tff(77,plain,
    ( ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
            ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
            | ~ class_Ring__and__Field_Ofield(T_a)
            | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
            | ( V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) ) )
      | ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
      | ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
      | ( c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
      | ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
  <=> ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
            ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
            | ~ class_Ring__and__Field_Ofield(T_a)
            | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
            | ( V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) ) )
      | ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
      | ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
      | ( c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
      | ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(78,plain,
    ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
          ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
          | ~ class_Ring__and__Field_Ofield(T_a)
          | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
          | ( V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) ) )
    | ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
    | ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
    | ( c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
    | ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(79,plain,
    ( ~ ! [V_c: $i,V_b: $i,T_a: $i] :
          ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
          | ~ class_Ring__and__Field_Ofield(T_a)
          | ( V_c = c_HOL_Ozero__class_Ozero(T_a) )
          | ( V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) ) )
    | ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
    | ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
    | ( c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
    | ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
    inference(modus_ponens,[status(thm)],[78,77]) ).

tff(80,plain,
    c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(unit_resolution,[status(thm)],[79,76,66,24,63]) ).

tff(81,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(monotonicity,[status(thm)],[80]) ).

tff(82,plain,
    ^ [V_a: $i,T_a: $i] :
      refl(
        ( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
          | ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) )
      <=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
          | ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ) )),
    inference(bind,[status(th)],]) ).

tff(83,plain,
    ( ! [V_a: $i,T_a: $i] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
        | ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) )
  <=> ! [V_a: $i,T_a: $i] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
        | ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ) ),
    inference(quant_intro,[status(thm)],[82]) ).

tff(84,plain,
    ( ! [V_a: $i,T_a: $i] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
        | ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) )
  <=> ! [V_a: $i,T_a: $i] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
        | ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(85,axiom,
    ! [V_a: $i,T_a: $i] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).

tff(86,plain,
    ! [V_a: $i,T_a: $i] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ),
    inference(modus_ponens,[status(thm)],[85,84]) ).

tff(87,plain,
    ! [V_a: $i,T_a: $i] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ),
    inference(skolemize,[status(sab)],[86]) ).

tff(88,plain,
    ! [V_a: $i,T_a: $i] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ),
    inference(modus_ponens,[status(thm)],[87,83]) ).

tff(89,plain,
    ( ( ~ ! [V_a: $i,T_a: $i] :
            ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
            | ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) )
      | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) ) )
  <=> ( ~ ! [V_a: $i,T_a: $i] :
            ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
            | ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) )
      | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(90,plain,
    ( ~ ! [V_a: $i,T_a: $i] :
          ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
          | ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) )
    | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
    | ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(91,plain,
    ( ~ ! [V_a: $i,T_a: $i] :
          ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
          | ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) )
    | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
    | ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) ) ),
    inference(modus_ponens,[status(thm)],[90,89]) ).

tff(92,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),
    inference(unit_resolution,[status(thm)],[91,88,43]) ).

tff(93,plain,
    c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(symmetry,[status(thm)],[92]) ).

tff(94,plain,
    c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(transitivity,[status(thm)],[93,81,54,40]) ).

tff(95,plain,
    ( ( c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) )
  <=> ( c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(96,plain,
    ( ( c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) )
  <=> ( c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(97,axiom,
    c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

tff(98,plain,
    c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(modus_ponens,[status(thm)],[97,96]) ).

tff(99,plain,
    c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(modus_ponens,[status(thm)],[98,95]) ).

tff(100,plain,
    $false,
    inference(unit_resolution,[status(thm)],[99,94]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : ALG398-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33  % Computer : n007.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 : Mon Aug 29 16:27:30 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34  Usage: tptp [options] [-file:]file
% 0.12/0.34    -h, -?       prints this message.
% 0.12/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.34    -m, -model   generate model.
% 0.12/0.34    -p, -proof   generate proof.
% 0.12/0.34    -c, -core    generate unsat core of named formulas.
% 0.12/0.34    -st, -statistics display statistics.
% 0.12/0.34    -t:timeout   set timeout (in second).
% 0.12/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34    -<param>:<value> configuration parameter and value.
% 0.12/0.34    -o:<output-file> file to place output in.
% 0.55/0.70  % SZS status Unsatisfiable
% 0.55/0.70  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------