TSTP Solution File: SWV632-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SWV632-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n025.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 15:23:54 EDT 2022

% Result   : Unsatisfiable 63.36s 40.77s
% Output   : Proof 63.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   59
% Syntax   : Number of formulae    :  121 (  45 unt;  18 typ;   0 def)
%            Number of atoms       :  245 ( 142 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  240 ( 106   ~;  96   |;   0   &)
%                                         (  38 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of FOOLs       :    8 (   8 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   21 (  12   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :   16 (  16 usr;   6 con; 0-3 aty)
%            Number of variables   :  228 ( 207   !;   0   ?; 228   :)

% Comments : 
%------------------------------------------------------------------------------
tff(c_HOL_Oord__class_Oless_type,type,
    c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).

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

tff(c_HOL_Oplus__class_Oplus_type,type,
    c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).

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

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

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

tff(c_Suc_type,type,
    c_Suc: $i > $i ).

tff(c_Int_Onumber__class_Onumber__of_type,type,
    c_Int_Onumber__class_Onumber__of: ( $i * $i ) > $i ).

tff(c_Int_OBit0_type,type,
    c_Int_OBit0: $i > $i ).

tff(c_Int_OBit1_type,type,
    c_Int_OBit1: $i > $i ).

tff(c_Int_OPls_type,type,
    c_Int_OPls: $i ).

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

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

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

tff(v_j_type,type,
    v_j: $i ).

tff(v_i_type,type,
    v_i: $i ).

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

tff(v_m_type,type,
    v_m: $i ).

tff(1,plain,
    ( ( c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) )
  <=> ( c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Suc(c_HOL_Oone__class_Oone(tc_nat)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,plain,
    ( ( c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) )
  <=> ( c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(3,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__1__add__1_0) ).

tff(4,plain,
    c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),
    inference(modus_ponens,[status(thm)],[3,2]) ).

tff(5,plain,
    c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Suc(c_HOL_Oone__class_Oone(tc_nat)),
    inference(modus_ponens,[status(thm)],[4,1]) ).

tff(6,plain,
    ^ [V_z: $i] :
      refl(
        ( ( c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),V_z,tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) )
      <=> ( c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),V_z,tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) ) )),
    inference(bind,[status(th)],]) ).

tff(7,plain,
    ( ! [V_z: $i] : ( c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),V_z,tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) )
  <=> ! [V_z: $i] : ( c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),V_z,tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) ) ),
    inference(quant_intro,[status(thm)],[6]) ).

tff(8,plain,
    ^ [V_z: $i] :
      rewrite(
        ( ( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_z,tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) )
      <=> ( c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),V_z,tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) ) )),
    inference(bind,[status(th)],]) ).

tff(9,plain,
    ( ! [V_z: $i] : ( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_z,tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) )
  <=> ! [V_z: $i] : ( c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),V_z,tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) ) ),
    inference(quant_intro,[status(thm)],[8]) ).

tff(10,plain,
    ( ! [V_z: $i] : ( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_z,tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) )
  <=> ! [V_z: $i] : ( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_z,tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(11,axiom,
    ! [V_z: $i] : ( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_z,tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__2_0) ).

tff(12,plain,
    ! [V_z: $i] : ( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_z,tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) ),
    inference(modus_ponens,[status(thm)],[11,10]) ).

tff(13,plain,
    ! [V_z: $i] : ( c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),V_z,tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) ),
    inference(modus_ponens,[status(thm)],[12,9]) ).

tff(14,plain,
    ! [V_z: $i] : ( c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),V_z,tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) ),
    inference(skolemize,[status(sab)],[13]) ).

tff(15,plain,
    ! [V_z: $i] : ( c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),V_z,tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) ),
    inference(modus_ponens,[status(thm)],[14,7]) ).

tff(16,plain,
    ( ~ ! [V_z: $i] : ( c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),V_z,tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) )
    | ( c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(17,plain,
    c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    inference(unit_resolution,[status(thm)],[16,15]) ).

tff(18,plain,
    ^ [V_n: $i,V_m: $i] :
      refl(
        ( ( c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) )
      <=> ( c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ) )),
    inference(bind,[status(th)],]) ).

tff(19,plain,
    ( ! [V_n: $i,V_m: $i] : ( c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) )
  <=> ! [V_n: $i,V_m: $i] : ( c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ) ),
    inference(quant_intro,[status(thm)],[18]) ).

tff(20,plain,
    ( ! [V_n: $i,V_m: $i] : ( c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) )
  <=> ! [V_n: $i,V_m: $i] : ( c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(21,axiom,
    ! [V_n: $i,V_m: $i] : ( c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__Suc_0) ).

tff(22,plain,
    ! [V_n: $i,V_m: $i] : ( c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ),
    inference(modus_ponens,[status(thm)],[21,20]) ).

tff(23,plain,
    ! [V_n: $i,V_m: $i] : ( c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ),
    inference(skolemize,[status(sab)],[22]) ).

tff(24,plain,
    ! [V_n: $i,V_m: $i] : ( c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ),
    inference(modus_ponens,[status(thm)],[23,19]) ).

tff(25,plain,
    ( ~ ! [V_n: $i,V_m: $i] : ( c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) )
    | ( c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(26,plain,
    c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(unit_resolution,[status(thm)],[25,24]) ).

tff(27,plain,
    c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    inference(symmetry,[status(thm)],[26]) ).

tff(28,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
  <=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
    inference(rewrite,[status(thm)],]) ).

tff(29,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).

tff(30,plain,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    inference(modus_ponens,[status(thm)],[29,28]) ).

tff(31,plain,
    ^ [V_a: $i,T_a: $i,V_m: $i] :
      refl(
        ( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
          | ( c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) )
      <=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
          | ( c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) ) )),
    inference(bind,[status(th)],]) ).

tff(32,plain,
    ( ! [V_a: $i,T_a: $i,V_m: $i] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
        | ( c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) )
  <=> ! [V_a: $i,T_a: $i,V_m: $i] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
        | ( c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) ) ),
    inference(quant_intro,[status(thm)],[31]) ).

tff(33,plain,
    ( ! [V_a: $i,T_a: $i,V_m: $i] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
        | ( c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) )
  <=> ! [V_a: $i,T_a: $i,V_m: $i] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
        | ( c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(34,axiom,
    ! [V_a: $i,T_a: $i,V_m: $i] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
      | ( c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).

tff(35,plain,
    ! [V_a: $i,T_a: $i,V_m: $i] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
      | ( c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) ),
    inference(modus_ponens,[status(thm)],[34,33]) ).

tff(36,plain,
    ! [V_a: $i,T_a: $i,V_m: $i] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
      | ( c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) ),
    inference(skolemize,[status(sab)],[35]) ).

tff(37,plain,
    ! [V_a: $i,T_a: $i,V_m: $i] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
      | ( c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) ),
    inference(modus_ponens,[status(thm)],[36,32]) ).

tff(38,plain,
    ( ( ~ ! [V_a: $i,T_a: $i,V_m: $i] :
            ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
            | ( c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) )
      | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
      | ( c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) )
  <=> ( ~ ! [V_a: $i,T_a: $i,V_m: $i] :
            ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
            | ( c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) )
      | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
      | ( c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(39,plain,
    ( ~ ! [V_a: $i,T_a: $i,V_m: $i] :
          ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
          | ( c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) )
    | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
    | ( c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(40,plain,
    ( ~ ! [V_a: $i,T_a: $i,V_m: $i] :
          ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
          | ( c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) )
    | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
    | ( c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
    inference(modus_ponens,[status(thm)],[39,38]) ).

tff(41,plain,
    c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    inference(unit_resolution,[status(thm)],[40,37,30]) ).

tff(42,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(symmetry,[status(thm)],[41]) ).

tff(43,plain,
    ^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
      refl(
        ( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
          | ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) )
      <=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
          | ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ) )),
    inference(bind,[status(th)],]) ).

tff(44,plain,
    ( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
        | ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) )
  <=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
        | ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ) ),
    inference(quant_intro,[status(thm)],[43]) ).

tff(45,plain,
    ( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
        | ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) )
  <=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
        | ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(46,axiom,
    ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).

tff(47,plain,
    ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ),
    inference(modus_ponens,[status(thm)],[46,45]) ).

tff(48,plain,
    ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ),
    inference(skolemize,[status(sab)],[47]) ).

tff(49,plain,
    ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ),
    inference(modus_ponens,[status(thm)],[48,44]) ).

tff(50,plain,
    ( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
            ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
            | ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) )
      | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) )
  <=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
            ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
            | ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) )
      | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
      | ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(51,plain,
    ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
          ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
          | ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) )
    | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
    | ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(52,plain,
    ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
          ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
          | ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) )
    | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
    | ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
    inference(modus_ponens,[status(thm)],[51,50]) ).

tff(53,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(unit_resolution,[status(thm)],[52,49,30]) ).

tff(54,plain,
    c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    inference(symmetry,[status(thm)],[53]) ).

tff(55,plain,
    c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_Suc(c_HOL_Oone__class_Oone(tc_nat)),
    inference(transitivity,[status(thm)],[54,42,27,17,5]) ).

tff(56,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat)
  <=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(monotonicity,[status(thm)],[55]) ).

tff(57,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
  <=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat) ),
    inference(symmetry,[status(thm)],[56]) ).

tff(58,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
  <=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(rewrite,[status(thm)],]) ).

tff(59,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
  <=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) ),
    inference(rewrite,[status(thm)],]) ).

tff(60,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos2_0) ).

tff(61,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),
    inference(modus_ponens,[status(thm)],[60,59]) ).

tff(62,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
    inference(modus_ponens,[status(thm)],[61,58]) ).

tff(63,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat),
    inference(modus_ponens,[status(thm)],[62,57]) ).

tff(64,plain,
    ^ [V_rx: $i,T_a: $i,V_ry: $i,V_lx: $i] :
      refl(
        ( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
          | ( c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) ) )
      <=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
          | ( c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) ) ) )),
    inference(bind,[status(th)],]) ).

tff(65,plain,
    ( ! [V_rx: $i,T_a: $i,V_ry: $i,V_lx: $i] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
        | ( c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) ) )
  <=> ! [V_rx: $i,T_a: $i,V_ry: $i,V_lx: $i] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
        | ( c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) ) ) ),
    inference(quant_intro,[status(thm)],[64]) ).

tff(66,plain,
    ( ! [V_rx: $i,T_a: $i,V_ry: $i,V_lx: $i] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
        | ( c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) ) )
  <=> ! [V_rx: $i,T_a: $i,V_ry: $i,V_lx: $i] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
        | ( c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(67,axiom,
    ! [V_rx: $i,T_a: $i,V_ry: $i,V_lx: $i] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
      | ( c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).

tff(68,plain,
    ! [V_rx: $i,T_a: $i,V_ry: $i,V_lx: $i] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
      | ( c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) ) ),
    inference(modus_ponens,[status(thm)],[67,66]) ).

tff(69,plain,
    ! [V_rx: $i,T_a: $i,V_ry: $i,V_lx: $i] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
      | ( c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) ) ),
    inference(skolemize,[status(sab)],[68]) ).

tff(70,plain,
    ! [V_rx: $i,T_a: $i,V_ry: $i,V_lx: $i] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
      | ( c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) ) ),
    inference(modus_ponens,[status(thm)],[69,65]) ).

tff(71,plain,
    ( ( ~ ! [V_rx: $i,T_a: $i,V_ry: $i,V_lx: $i] :
            ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
            | ( c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) ) )
      | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
      | ( c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_j,tc_nat),tc_nat) ) )
  <=> ( ~ ! [V_rx: $i,T_a: $i,V_ry: $i,V_lx: $i] :
            ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
            | ( c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) ) )
      | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
      | ( c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_j,tc_nat),tc_nat) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(72,plain,
    ( ~ ! [V_rx: $i,T_a: $i,V_ry: $i,V_lx: $i] :
          ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
          | ( c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) ) )
    | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
    | ( c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_j,tc_nat),tc_nat) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(73,plain,
    ( ~ ! [V_rx: $i,T_a: $i,V_ry: $i,V_lx: $i] :
          ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
          | ( c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) ) )
    | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
    | ( c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_j,tc_nat),tc_nat) ) ),
    inference(modus_ponens,[status(thm)],[72,71]) ).

tff(74,plain,
    c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_j,tc_nat),tc_nat),
    inference(unit_resolution,[status(thm)],[73,70,30]) ).

tff(75,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),
    inference(monotonicity,[status(thm)],[55]) ).

tff(76,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_j,tc_nat),tc_nat),
    inference(transitivity,[status(thm)],[75,74]) ).

tff(77,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),v_m,tc_nat) = c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_m,tc_nat),
    inference(monotonicity,[status(thm)],[55]) ).

tff(78,plain,
    c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),v_m,tc_nat)) = c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_m,tc_nat)),
    inference(monotonicity,[status(thm)],[77]) ).

tff(79,plain,
    c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),
    inference(monotonicity,[status(thm)],[78,76]) ).

tff(80,plain,
    ( ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex) )
  <=> ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex) ) ),
    inference(monotonicity,[status(thm)],[79]) ).

tff(81,plain,
    ( ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex) )
  <=> ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex) ) ),
    inference(symmetry,[status(thm)],[80]) ).

tff(82,plain,
    ( ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex) )
  <=> ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex) ) ),
    inference(monotonicity,[status(thm)],[81]) ).

tff(83,plain,
    ( ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex) )
  <=> ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(84,plain,
    ( ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex) )
  <=> ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(85,axiom,
    c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

tff(86,plain,
    c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex),
    inference(modus_ponens,[status(thm)],[85,84]) ).

tff(87,plain,
    c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex),
    inference(modus_ponens,[status(thm)],[86,83]) ).

tff(88,plain,
    c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex),
    inference(modus_ponens,[status(thm)],[87,82]) ).

tff(89,plain,
    ^ [V_n: $i,V_d: $i,V_k: $i] :
      refl(
        ( ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat)
          | ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) ) )
      <=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat)
          | ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) ) ) )),
    inference(bind,[status(th)],]) ).

tff(90,plain,
    ( ! [V_n: $i,V_d: $i,V_k: $i] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat)
        | ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) ) )
  <=> ! [V_n: $i,V_d: $i,V_k: $i] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat)
        | ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) ) ) ),
    inference(quant_intro,[status(thm)],[89]) ).

tff(91,plain,
    ( ! [V_n: $i,V_d: $i,V_k: $i] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat)
        | ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) ) )
  <=> ! [V_n: $i,V_d: $i,V_k: $i] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat)
        | ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(92,plain,
    ^ [V_n: $i,V_d: $i,V_k: $i] :
      rewrite(
        ( ( ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) )
          | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat) )
      <=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat)
          | ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) ) ) )),
    inference(bind,[status(th)],]) ).

tff(93,plain,
    ( ! [V_n: $i,V_d: $i,V_k: $i] :
        ( ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) )
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat) )
  <=> ! [V_n: $i,V_d: $i,V_k: $i] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat)
        | ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) ) ) ),
    inference(quant_intro,[status(thm)],[92]) ).

tff(94,axiom,
    ! [V_n: $i,V_d: $i,V_k: $i] :
      ( ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) )
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_root__cancel_0) ).

tff(95,plain,
    ! [V_n: $i,V_d: $i,V_k: $i] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat)
      | ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) ) ),
    inference(modus_ponens,[status(thm)],[94,93]) ).

tff(96,plain,
    ! [V_n: $i,V_d: $i,V_k: $i] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat)
      | ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) ) ),
    inference(modus_ponens,[status(thm)],[95,91]) ).

tff(97,plain,
    ! [V_n: $i,V_d: $i,V_k: $i] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat)
      | ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) ) ),
    inference(skolemize,[status(sab)],[96]) ).

tff(98,plain,
    ! [V_n: $i,V_d: $i,V_k: $i] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat)
      | ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) ) ),
    inference(modus_ponens,[status(thm)],[97,90]) ).

tff(99,plain,
    ( ( ~ ! [V_n: $i,V_d: $i,V_k: $i] :
            ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat)
            | ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) ) )
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat)
      | ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex) ) )
  <=> ( ~ ! [V_n: $i,V_d: $i,V_k: $i] :
            ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat)
            | ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) ) )
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat)
      | ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(100,plain,
    ( ~ ! [V_n: $i,V_d: $i,V_k: $i] :
          ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat)
          | ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) ) )
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat)
    | ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(101,plain,
    ( ~ ! [V_n: $i,V_d: $i,V_k: $i] :
          ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat)
          | ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) ) )
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat)
    | ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex) ) ),
    inference(modus_ponens,[status(thm)],[100,99]) ).

tff(102,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat)
    | ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex) ) ),
    inference(unit_resolution,[status(thm)],[101,98]) ).

tff(103,plain,
    $false,
    inference(unit_resolution,[status(thm)],[102,88,63]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWV632-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35  % Computer : n025.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 06:39:48 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35  Usage: tptp [options] [-file:]file
% 0.13/0.35    -h, -?       prints this message.
% 0.13/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.35    -m, -model   generate model.
% 0.13/0.35    -p, -proof   generate proof.
% 0.13/0.35    -c, -core    generate unsat core of named formulas.
% 0.13/0.35    -st, -statistics display statistics.
% 0.13/0.35    -t:timeout   set timeout (in second).
% 0.13/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35    -<param>:<value> configuration parameter and value.
% 0.13/0.35    -o:<output-file> file to place output in.
% 63.36/40.77  % SZS status Unsatisfiable
% 63.36/40.77  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------