TSTP Solution File: SWV616-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SWV616-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n006.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 : Thu Sep 29 15:23:47 EDT 2022

% Result   : Unsatisfiable 0.65s 0.73s
% Output   : Proof 0.72s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   30
% Syntax   : Number of formulae    :   54 (  18 unt;  12 typ;   0 def)
%            Number of atoms       :  112 (  57 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  128 (  60   ~;  56   |;   0   &)
%                                         (  12 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of FOOLs       :    2 (   2 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   16 (   8   >;   8   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   4 con; 0-3 aty)
%            Number of variables   :  107 ( 100   !;   0   ?; 107   :)

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

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

tff(c_HOL_Ominus__class_Ominus_type,type,
    c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).

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

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

tff(v_k_type,type,
    v_k: $i ).

tff(c_FFT__Mirabelle_Oroot_type,type,
    c_FFT__Mirabelle_Oroot: $i > $i ).

tff(v_n_type,type,
    v_n: $i ).

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

tff(tc_nat_type,type,
    tc_nat: $i ).

tff(class_OrderedGroup_Omonoid__mult_type,type,
    class_OrderedGroup_Omonoid__mult: $i > $o ).

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

tff(1,plain,
    ( class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
  <=> class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).

tff(3,plain,
    class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
    inference(modus_ponens,[status(thm)],[2,1]) ).

tff(4,plain,
    ^ [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
      refl(
        ( ( ~ class_OrderedGroup_Omonoid__mult(T_a)
          | ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) )
      <=> ( ~ class_OrderedGroup_Omonoid__mult(T_a)
          | ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) ) )),
    inference(bind,[status(th)],]) ).

tff(5,plain,
    ( ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
        ( ~ class_OrderedGroup_Omonoid__mult(T_a)
        | ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) )
  <=> ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
        ( ~ class_OrderedGroup_Omonoid__mult(T_a)
        | ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) ) ),
    inference(quant_intro,[status(thm)],[4]) ).

tff(6,plain,
    ( ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
        ( ~ class_OrderedGroup_Omonoid__mult(T_a)
        | ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) )
  <=> ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
        ( ~ class_OrderedGroup_Omonoid__mult(T_a)
        | ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(7,axiom,
    ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
      ( ~ class_OrderedGroup_Omonoid__mult(T_a)
      | ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mult_0) ).

tff(8,plain,
    ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
      ( ~ class_OrderedGroup_Omonoid__mult(T_a)
      | ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) ),
    inference(modus_ponens,[status(thm)],[7,6]) ).

tff(9,plain,
    ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
      ( ~ class_OrderedGroup_Omonoid__mult(T_a)
      | ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) ),
    inference(skolemize,[status(sab)],[8]) ).

tff(10,plain,
    ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
      ( ~ class_OrderedGroup_Omonoid__mult(T_a)
      | ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) ),
    inference(modus_ponens,[status(thm)],[9,5]) ).

tff(11,plain,
    ( ( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
            ( ~ class_OrderedGroup_Omonoid__mult(T_a)
            | ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) )
      | ~ class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
      | ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),c_HOL_Otimes__class_Otimes(v_n,v_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex) ) )
  <=> ( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
            ( ~ class_OrderedGroup_Omonoid__mult(T_a)
            | ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) )
      | ~ class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
      | ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),c_HOL_Otimes__class_Otimes(v_n,v_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(12,plain,
    ( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
          ( ~ class_OrderedGroup_Omonoid__mult(T_a)
          | ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) )
    | ~ class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
    | ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),c_HOL_Otimes__class_Otimes(v_n,v_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(13,plain,
    ( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
          ( ~ class_OrderedGroup_Omonoid__mult(T_a)
          | ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) )
    | ~ class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
    | ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),c_HOL_Otimes__class_Otimes(v_n,v_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex) ) ),
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),c_HOL_Otimes__class_Otimes(v_n,v_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),
    inference(unit_resolution,[status(thm)],[13,10,3]) ).

tff(15,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
  <=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
    inference(rewrite,[status(thm)],]) ).

tff(16,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).

tff(17,plain,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    inference(modus_ponens,[status(thm)],[16,15]) ).

tff(18,plain,
    ^ [V_b: $i,V_a: $i,T_a: $i] :
      refl(
        ( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
          | ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
      <=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
          | ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ) )),
    inference(bind,[status(th)],]) ).

tff(19,plain,
    ( ! [V_b: $i,V_a: $i,T_a: $i] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
        | ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
  <=> ! [V_b: $i,V_a: $i,T_a: $i] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
        | ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ) ),
    inference(quant_intro,[status(thm)],[18]) ).

tff(20,plain,
    ( ! [V_b: $i,V_a: $i,T_a: $i] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
        | ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
  <=> ! [V_b: $i,V_a: $i,T_a: $i] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
        | ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(21,axiom,
    ! [V_b: $i,V_a: $i,T_a: $i] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
      | ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).

tff(22,plain,
    ! [V_b: $i,V_a: $i,T_a: $i] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
      | ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ),
    inference(modus_ponens,[status(thm)],[21,20]) ).

tff(23,plain,
    ! [V_b: $i,V_a: $i,T_a: $i] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
      | ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ),
    inference(skolemize,[status(sab)],[22]) ).

tff(24,plain,
    ! [V_b: $i,V_a: $i,T_a: $i] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
      | ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ),
    inference(modus_ponens,[status(thm)],[23,19]) ).

tff(25,plain,
    ( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
            ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
            | ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
      | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
      | ( c_HOL_Otimes__class_Otimes(v_n,v_k,tc_nat) = c_HOL_Otimes__class_Otimes(v_k,v_n,tc_nat) ) )
  <=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
            ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
            | ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
      | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
      | ( c_HOL_Otimes__class_Otimes(v_n,v_k,tc_nat) = c_HOL_Otimes__class_Otimes(v_k,v_n,tc_nat) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(26,plain,
    ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
          ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
          | ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
    | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
    | ( c_HOL_Otimes__class_Otimes(v_n,v_k,tc_nat) = c_HOL_Otimes__class_Otimes(v_k,v_n,tc_nat) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(27,plain,
    ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
          ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
          | ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) )
    | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
    | ( c_HOL_Otimes__class_Otimes(v_n,v_k,tc_nat) = c_HOL_Otimes__class_Otimes(v_k,v_n,tc_nat) ) ),
    inference(modus_ponens,[status(thm)],[26,25]) ).

tff(28,plain,
    c_HOL_Otimes__class_Otimes(v_n,v_k,tc_nat) = c_HOL_Otimes__class_Otimes(v_k,v_n,tc_nat),
    inference(unit_resolution,[status(thm)],[27,24,17]) ).

tff(29,plain,
    c_HOL_Otimes__class_Otimes(v_k,v_n,tc_nat) = c_HOL_Otimes__class_Otimes(v_n,v_k,tc_nat),
    inference(symmetry,[status(thm)],[28]) ).

tff(30,plain,
    c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),c_HOL_Otimes__class_Otimes(v_k,v_n,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),c_HOL_Otimes__class_Otimes(v_n,v_k,tc_nat),tc_Complex_Ocomplex),
    inference(monotonicity,[status(thm)],[29]) ).

tff(31,plain,
    ( ( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
            ( ~ class_OrderedGroup_Omonoid__mult(T_a)
            | ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) )
      | ~ class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
      | ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),c_HOL_Otimes__class_Otimes(v_k,v_n,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex) ) )
  <=> ( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
            ( ~ class_OrderedGroup_Omonoid__mult(T_a)
            | ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) )
      | ~ class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
      | ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),c_HOL_Otimes__class_Otimes(v_k,v_n,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(32,plain,
    ( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
          ( ~ class_OrderedGroup_Omonoid__mult(T_a)
          | ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) )
    | ~ class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
    | ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),c_HOL_Otimes__class_Otimes(v_k,v_n,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(33,plain,
    ( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
          ( ~ class_OrderedGroup_Omonoid__mult(T_a)
          | ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) )
    | ~ class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
    | ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),c_HOL_Otimes__class_Otimes(v_k,v_n,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex) ) ),
    inference(modus_ponens,[status(thm)],[32,31]) ).

tff(34,plain,
    c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),c_HOL_Otimes__class_Otimes(v_k,v_n,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),
    inference(unit_resolution,[status(thm)],[33,10,3]) ).

tff(35,plain,
    c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),c_HOL_Otimes__class_Otimes(v_k,v_n,tc_nat),tc_Complex_Ocomplex),
    inference(symmetry,[status(thm)],[34]) ).

tff(36,plain,
    c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),
    inference(transitivity,[status(thm)],[35,30,14]) ).

tff(37,plain,
    c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(monotonicity,[status(thm)],[36]) ).

tff(38,plain,
    c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(monotonicity,[status(thm)],[37]) ).

tff(39,plain,
    ( ( c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) )
  <=> ( c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(40,axiom,
    c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

tff(41,plain,
    c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(modus_ponens,[status(thm)],[40,39]) ).

tff(42,plain,
    $false,
    inference(unit_resolution,[status(thm)],[41,38]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWV616-1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35  % Computer : n006.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Sun Sep  4 06:22:23 EDT 2022
% 0.20/0.35  % CPUTime  : 
% 0.20/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.20/0.35  Usage: tptp [options] [-file:]file
% 0.20/0.35    -h, -?       prints this message.
% 0.20/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.20/0.35    -m, -model   generate model.
% 0.20/0.35    -p, -proof   generate proof.
% 0.20/0.35    -c, -core    generate unsat core of named formulas.
% 0.20/0.35    -st, -statistics display statistics.
% 0.20/0.35    -t:timeout   set timeout (in second).
% 0.20/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.20/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.20/0.35    -<param>:<value> configuration parameter and value.
% 0.20/0.35    -o:<output-file> file to place output in.
% 0.65/0.73  % SZS status Unsatisfiable
% 0.65/0.73  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------