SET007 Axioms: SET007+221.ax


%------------------------------------------------------------------------------
% File     : SET007+221 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : The Fundamental Logic Structure in Quantum Mechanics
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : qmax_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   85 (  28 unit)
%            Number of atoms       :  352 (  36 equality)
%            Maximal formula depth :   22 (   5 average)
%            Number of connectives :  281 (  14 ~  ;   0  |; 109  &)
%                                         (  14 <=>; 144 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   26 (   1 propositional; 0-3 arity)
%            Number of functors    :   36 (   4 constant; 0-4 arity)
%            Number of variables   :  163 (   0 singleton; 156 !;   7 ?)
%            Maximal term depth    :    5 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_qmax_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_prob_1(B,A) )
     => ~ v1_xboole_0(k1_qmax_1(A,B)) ) )).

fof(rc1_qmax_1,axiom,(
    ? [A] :
      ( l1_qmax_1(A)
      & v1_qmax_1(A) ) )).

fof(fc2_qmax_1,axiom,(
    ! [A] :
      ( l1_qmax_1(A)
     => ~ v1_xboole_0(k2_qmax_1(A)) ) )).

fof(fc3_qmax_1,axiom,(
    ! [A] :
      ( l1_qmax_1(A)
     => ~ v1_xboole_0(k3_qmax_1(A)) ) )).

fof(rc2_qmax_1,axiom,(
    ? [A] :
      ( l1_qmax_1(A)
      & v1_qmax_1(A)
      & v2_qmax_1(A) ) )).

fof(rc3_qmax_1,axiom,(
    ! [A] :
    ? [B] :
      ( l2_qmax_1(B,A)
      & v3_qmax_1(B,A) ) )).

fof(fc4_qmax_1,axiom,(
    ! [A] :
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ~ v1_xboole_0(k5_qmax_1(A)) ) )).

fof(d1_qmax_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_prob_1(B,A)
         => ! [C] :
              ( C = k1_qmax_1(A,B)
            <=> ! [D] :
                  ( r2_hidden(D,C)
                <=> m4_prob_1(D,A,B) ) ) ) ) )).

fof(d2_qmax_1,axiom,(
    ! [A] :
      ( l1_qmax_1(A)
     => k2_qmax_1(A) = u1_qmax_1(A) ) )).

fof(d3_qmax_1,axiom,(
    ! [A] :
      ( l1_qmax_1(A)
     => k3_qmax_1(A) = u2_qmax_1(A) ) )).

fof(d4_qmax_1,axiom,(
    ! [A] :
      ( l1_qmax_1(A)
     => ! [B] :
          ( m1_subset_1(B,k2_qmax_1(A))
         => ! [C] :
              ( m1_subset_1(C,k3_qmax_1(A))
             => k4_qmax_1(A,B,C) = k1_funct_1(u3_qmax_1(A),k1_domain_1(k2_qmax_1(A),k3_qmax_1(A),B,C)) ) ) ) )).

fof(d5_qmax_1,axiom,(
    ! [A] :
      ( l1_qmax_1(A)
     => ( v2_qmax_1(A)
      <=> ( ! [B] :
              ( m1_subset_1(B,k2_qmax_1(A))
             => ! [C] :
                  ( m1_subset_1(C,k2_qmax_1(A))
                 => ( ! [D] :
                        ( m1_subset_1(D,k3_qmax_1(A))
                       => k4_qmax_1(A,B,D) = k4_qmax_1(A,C,D) )
                   => B = C ) ) )
          & ! [B] :
              ( m1_subset_1(B,k3_qmax_1(A))
             => ! [C] :
                  ( m1_subset_1(C,k3_qmax_1(A))
                 => ( ! [D] :
                        ( m1_subset_1(D,k2_qmax_1(A))
                       => k4_qmax_1(A,D,B) = k4_qmax_1(A,D,C) )
                   => B = C ) ) )
          & ! [B] :
              ( m1_subset_1(B,k3_qmax_1(A))
             => ! [C] :
                  ( m1_subset_1(C,k3_qmax_1(A))
                 => ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( r1_xreal_0(np__0,D)
                          & r1_xreal_0(D,np__1)
                          & ! [E] :
                              ( m1_subset_1(E,k3_qmax_1(A))
                             => ~ ! [F] :
                                    ( m1_subset_1(F,k2_qmax_1(A))
                                   => ! [G] :
                                        ( m3_prob_1(G,k1_numbers,k14_prob_1)
                                       => k10_prob_1(k1_numbers,k14_prob_1,k4_qmax_1(A,F,E),G) = k2_xcmplx_0(k3_xcmplx_0(D,k10_prob_1(k1_numbers,k14_prob_1,k4_qmax_1(A,F,B),G)),k3_xcmplx_0(k6_xcmplx_0(np__1,D),k10_prob_1(k1_numbers,k14_prob_1,k4_qmax_1(A,F,C),G))) ) ) ) ) ) ) ) ) ) ) )).

fof(d6_qmax_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & m2_relset_1(B,A,A) )
     => ( r1_qmax_1(A,B)
      <=> ! [C] :
            ( m1_subset_1(C,A)
           => k1_funct_1(B,k1_funct_1(B,C)) = C ) ) ) )).

fof(d7_qmax_1,axiom,(
    ! [A,B] :
      ( l2_qmax_1(B,A)
     => ( r2_qmax_1(A,B)
      <=> ? [C] :
            ( m2_relset_1(C,A,A)
            & ? [D] :
                ( v1_funct_1(D)
                & v1_funct_2(D,A,A)
                & m2_relset_1(D,A,A)
                & B = g2_qmax_1(A,C,D)
                & r2_orders_1(C,A)
                & r1_qmax_1(A,D)
                & ! [E] :
                    ( m1_subset_1(E,A)
                   => ! [F] :
                        ( m1_subset_1(F,A)
                       => ( r2_hidden(k4_tarski(E,F),C)
                         => r2_hidden(k4_tarski(k1_funct_1(D,F),k1_funct_1(D,E)),C) ) ) ) ) ) ) ) )).

fof(d8_qmax_1,axiom,(
    ! [A] :
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => k5_qmax_1(A) = k2_zfmisc_1(k2_qmax_1(A),k14_prob_1) ) )).

fof(t1_qmax_1,axiom,(
    $true )).

fof(t2_qmax_1,axiom,(
    $true )).

fof(t3_qmax_1,axiom,(
    $true )).

fof(t4_qmax_1,axiom,(
    $true )).

fof(t5_qmax_1,axiom,(
    $true )).

fof(t6_qmax_1,axiom,(
    $true )).

fof(t7_qmax_1,axiom,(
    $true )).

fof(t8_qmax_1,axiom,(
    $true )).

fof(t9_qmax_1,axiom,(
    $true )).

fof(t10_qmax_1,axiom,(
    $true )).

fof(t11_qmax_1,axiom,(
    $true )).

fof(t12_qmax_1,axiom,(
    $true )).

fof(t13_qmax_1,axiom,(
    $true )).

fof(t14_qmax_1,axiom,(
    ! [A] :
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k5_qmax_1(A))
         => B = k1_domain_1(k2_qmax_1(A),k1_zfmisc_1(k1_numbers),k6_qmax_1(A,B),k7_qmax_1(A,B)) ) ) )).

fof(t15_qmax_1,axiom,(
    $true )).

fof(t16_qmax_1,axiom,(
    ! [A] :
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k3_qmax_1(A))
         => ! [C] :
              ( m1_subset_1(C,k5_qmax_1(A))
             => ! [D] :
                  ( m3_prob_1(D,k1_numbers,k14_prob_1)
                 => ( D = k3_subset_1(k1_numbers,k7_qmax_1(A,C))
                   => k10_prob_1(k1_numbers,k14_prob_1,k4_qmax_1(A,k6_qmax_1(A,C),B),k7_qmax_1(A,C)) = k6_xcmplx_0(np__1,k10_prob_1(k1_numbers,k14_prob_1,k4_qmax_1(A,k6_qmax_1(A,C),B),D)) ) ) ) ) ) )).

fof(d9_qmax_1,axiom,(
    ! [A] :
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k5_qmax_1(A))
         => k8_qmax_1(A,B) = k1_domain_1(k2_qmax_1(A),k1_zfmisc_1(k1_numbers),k6_qmax_1(A,B),k3_subset_1(k1_numbers,k7_qmax_1(A,B))) ) ) )).

fof(d10_qmax_1,axiom,(
    ! [A] :
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k5_qmax_1(A))
         => ! [C] :
              ( m1_subset_1(C,k5_qmax_1(A))
             => ( r3_qmax_1(A,B,C)
              <=> ! [D] :
                    ( m1_subset_1(D,k3_qmax_1(A))
                   => r1_xreal_0(k10_prob_1(k1_numbers,k14_prob_1,k4_qmax_1(A,k6_qmax_1(A,B),D),k7_qmax_1(A,B)),k10_prob_1(k1_numbers,k14_prob_1,k4_qmax_1(A,k6_qmax_1(A,C),D),k7_qmax_1(A,C))) ) ) ) ) ) )).

fof(d11_qmax_1,axiom,(
    ! [A] :
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k5_qmax_1(A))
         => ! [C] :
              ( m1_subset_1(C,k5_qmax_1(A))
             => ( r4_qmax_1(A,B,C)
              <=> ( r3_qmax_1(A,B,C)
                  & r3_qmax_1(A,C,B) ) ) ) ) ) )).

fof(t17_qmax_1,axiom,(
    $true )).

fof(t18_qmax_1,axiom,(
    $true )).

fof(t19_qmax_1,axiom,(
    $true )).

fof(t20_qmax_1,axiom,(
    ! [A] :
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k5_qmax_1(A))
         => ! [C] :
              ( m1_subset_1(C,k5_qmax_1(A))
             => ( r4_qmax_1(A,B,C)
              <=> ! [D] :
                    ( m1_subset_1(D,k3_qmax_1(A))
                   => k10_prob_1(k1_numbers,k14_prob_1,k4_qmax_1(A,k6_qmax_1(A,B),D),k7_qmax_1(A,B)) = k10_prob_1(k1_numbers,k14_prob_1,k4_qmax_1(A,k6_qmax_1(A,C),D),k7_qmax_1(A,C)) ) ) ) ) ) )).

fof(t21_qmax_1,axiom,(
    ! [A] :
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k5_qmax_1(A))
         => r3_qmax_1(A,B,B) ) ) )).

fof(t22_qmax_1,axiom,(
    ! [A] :
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k5_qmax_1(A))
         => ! [C] :
              ( m1_subset_1(C,k5_qmax_1(A))
             => ! [D] :
                  ( m1_subset_1(D,k5_qmax_1(A))
                 => ( ( r3_qmax_1(A,B,C)
                      & r3_qmax_1(A,C,D) )
                   => r3_qmax_1(A,B,D) ) ) ) ) ) )).

fof(t23_qmax_1,axiom,(
    ! [A] :
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k5_qmax_1(A))
         => r4_qmax_1(A,B,B) ) ) )).

fof(t24_qmax_1,axiom,(
    ! [A] :
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k5_qmax_1(A))
         => ! [C] :
              ( m1_subset_1(C,k5_qmax_1(A))
             => ( r4_qmax_1(A,B,C)
               => r4_qmax_1(A,C,B) ) ) ) ) )).

fof(t25_qmax_1,axiom,(
    ! [A] :
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k5_qmax_1(A))
         => ! [C] :
              ( m1_subset_1(C,k5_qmax_1(A))
             => ! [D] :
                  ( m1_subset_1(D,k5_qmax_1(A))
                 => ( ( r4_qmax_1(A,B,C)
                      & r4_qmax_1(A,C,D) )
                   => r4_qmax_1(A,B,D) ) ) ) ) ) )).

fof(t26_qmax_1,axiom,(
    ! [A] :
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k5_qmax_1(A))
         => ( k6_qmax_1(A,k8_qmax_1(A,B)) = k6_qmax_1(A,B)
            & k7_qmax_1(A,k8_qmax_1(A,B)) = k3_subset_1(k1_numbers,k7_qmax_1(A,B)) ) ) ) )).

fof(t27_qmax_1,axiom,(
    ! [A] :
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k5_qmax_1(A))
         => k8_qmax_1(A,k8_qmax_1(A,B)) = B ) ) )).

fof(t28_qmax_1,axiom,(
    ! [A] :
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k5_qmax_1(A))
         => ! [C] :
              ( m1_subset_1(C,k5_qmax_1(A))
             => ( r3_qmax_1(A,B,C)
               => r3_qmax_1(A,k8_qmax_1(A,C),k8_qmax_1(A,B)) ) ) ) ) )).

fof(d12_qmax_1,axiom,(
    ! [A] :
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ! [B] :
          ( ( v3_relat_2(B)
            & v8_relat_2(B)
            & v1_partfun1(B,k5_qmax_1(A),k5_qmax_1(A))
            & m2_relset_1(B,k5_qmax_1(A),k5_qmax_1(A)) )
         => ( B = k9_qmax_1(A)
          <=> ! [C] :
                ( m1_subset_1(C,k5_qmax_1(A))
               => ! [D] :
                    ( m1_subset_1(D,k5_qmax_1(A))
                   => ( r2_hidden(k1_domain_1(k5_qmax_1(A),k5_qmax_1(A),C,D),B)
                    <=> r4_qmax_1(A,C,D) ) ) ) ) ) ) )).

fof(t29_qmax_1,axiom,(
    $true )).

fof(t30_qmax_1,axiom,(
    ! [A] :
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k5_qmax_1(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k5_qmax_1(A)))
             => ( ( r2_hidden(B,k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)))
                  & r2_hidden(C,k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A))) )
               => ! [D] :
                    ( m1_subset_1(D,k5_qmax_1(A))
                   => ! [E] :
                        ( m1_subset_1(E,k5_qmax_1(A))
                       => ! [F] :
                            ( m1_subset_1(F,k5_qmax_1(A))
                           => ! [G] :
                                ( m1_subset_1(G,k5_qmax_1(A))
                               => ( ( r2_hidden(D,B)
                                    & r2_hidden(E,B)
                                    & r2_hidden(F,C)
                                    & r2_hidden(G,C)
                                    & r3_qmax_1(A,D,F) )
                                 => r3_qmax_1(A,E,G) ) ) ) ) ) ) ) ) ) )).

fof(d13_qmax_1,axiom,(
    ! [A] :
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ! [B] :
          ( m2_relset_1(B,k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)),k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)))
         => ( B = k10_qmax_1(A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(k5_qmax_1(A)))
               => ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(k5_qmax_1(A)))
                   => ( r2_hidden(k1_domain_1(k1_zfmisc_1(k5_qmax_1(A)),k1_zfmisc_1(k5_qmax_1(A)),C,D),B)
                    <=> ( r2_hidden(C,k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)))
                        & r2_hidden(D,k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)))
                        & ! [E] :
                            ( m1_subset_1(E,k5_qmax_1(A))
                           => ! [F] :
                                ( m1_subset_1(F,k5_qmax_1(A))
                               => ( ( r2_hidden(E,C)
                                    & r2_hidden(F,D) )
                                 => r3_qmax_1(A,E,F) ) ) ) ) ) ) ) ) ) ) )).

fof(t31_qmax_1,axiom,(
    $true )).

fof(t32_qmax_1,axiom,(
    ! [A] :
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k5_qmax_1(A))
         => ! [C] :
              ( m1_subset_1(C,k5_qmax_1(A))
             => ( r3_qmax_1(A,B,C)
              <=> r2_hidden(k1_domain_1(k1_zfmisc_1(k5_qmax_1(A)),k1_zfmisc_1(k5_qmax_1(A)),k6_eqrel_1(k5_qmax_1(A),k9_qmax_1(A),B),k6_eqrel_1(k5_qmax_1(A),k9_qmax_1(A),C)),k10_qmax_1(A)) ) ) ) ) )).

fof(t33_qmax_1,axiom,(
    ! [A] :
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k5_qmax_1(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k5_qmax_1(A)))
             => ( ( r2_hidden(B,k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)))
                  & r2_hidden(C,k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A))) )
               => ! [D] :
                    ( m1_subset_1(D,k5_qmax_1(A))
                   => ! [E] :
                        ( m1_subset_1(E,k5_qmax_1(A))
                       => ( ( r2_hidden(D,B)
                            & r2_hidden(E,B)
                            & r2_hidden(k8_qmax_1(A,D),C) )
                         => r2_hidden(k8_qmax_1(A,E),C) ) ) ) ) ) ) ) )).

fof(t34_qmax_1,axiom,(
    ! [A] :
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k5_qmax_1(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k5_qmax_1(A)))
             => ( ( r2_hidden(B,k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)))
                  & r2_hidden(C,k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A))) )
               => ! [D] :
                    ( m1_subset_1(D,k5_qmax_1(A))
                   => ! [E] :
                        ( m1_subset_1(E,k5_qmax_1(A))
                       => ( ( r2_hidden(k8_qmax_1(A,D),C)
                            & r2_hidden(k8_qmax_1(A,E),C)
                            & r2_hidden(D,B) )
                         => r2_hidden(E,B) ) ) ) ) ) ) ) )).

fof(d14_qmax_1,axiom,(
    ! [A] :
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)),k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)))
            & m2_relset_1(B,k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)),k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A))) )
         => ( B = k11_qmax_1(A)
          <=> ! [C] :
                ( m1_subset_1(C,k5_qmax_1(A))
               => k1_funct_1(B,k6_eqrel_1(k5_qmax_1(A),k9_qmax_1(A),C)) = k6_eqrel_1(k5_qmax_1(A),k9_qmax_1(A),k8_qmax_1(A,C)) ) ) ) ) )).

fof(t35_qmax_1,axiom,(
    $true )).

fof(t36_qmax_1,axiom,(
    ! [A] :
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => r2_qmax_1(k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)),g2_qmax_1(k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)),k10_qmax_1(A),k11_qmax_1(A))) ) )).

fof(dt_l1_qmax_1,axiom,(
    $true )).

fof(existence_l1_qmax_1,axiom,(
    ? [A] : l1_qmax_1(A) )).

fof(dt_l2_qmax_1,axiom,(
    $true )).

fof(existence_l2_qmax_1,axiom,(
    ! [A] :
    ? [B] : l2_qmax_1(B,A) )).

fof(abstractness_v1_qmax_1,axiom,(
    ! [A] :
      ( l1_qmax_1(A)
     => ( v1_qmax_1(A)
       => A = g1_qmax_1(u1_qmax_1(A),u2_qmax_1(A),u3_qmax_1(A)) ) ) )).

fof(abstractness_v3_qmax_1,axiom,(
    ! [A,B] :
      ( l2_qmax_1(B,A)
     => ( v3_qmax_1(B,A)
       => B = g2_qmax_1(A,u4_qmax_1(A,B),u5_qmax_1(A,B)) ) ) )).

fof(dt_k1_qmax_1,axiom,(
    $true )).

fof(dt_k2_qmax_1,axiom,(
    $true )).

fof(dt_k3_qmax_1,axiom,(
    $true )).

fof(dt_k4_qmax_1,axiom,(
    ! [A,B,C] :
      ( ( l1_qmax_1(A)
        & m1_subset_1(B,k2_qmax_1(A))
        & m1_subset_1(C,k3_qmax_1(A)) )
     => m4_prob_1(k4_qmax_1(A,B,C),k1_numbers,k14_prob_1) ) )).

fof(dt_k5_qmax_1,axiom,(
    $true )).

fof(dt_k6_qmax_1,axiom,(
    ! [A,B] :
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A)
        & m1_subset_1(B,k5_qmax_1(A)) )
     => m1_subset_1(k6_qmax_1(A,B),k2_qmax_1(A)) ) )).

fof(redefinition_k6_qmax_1,axiom,(
    ! [A,B] :
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A)
        & m1_subset_1(B,k5_qmax_1(A)) )
     => k6_qmax_1(A,B) = k1_mcart_1(B) ) )).

fof(dt_k7_qmax_1,axiom,(
    ! [A,B] :
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A)
        & m1_subset_1(B,k5_qmax_1(A)) )
     => m3_prob_1(k7_qmax_1(A,B),k1_numbers,k14_prob_1) ) )).

fof(redefinition_k7_qmax_1,axiom,(
    ! [A,B] :
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A)
        & m1_subset_1(B,k5_qmax_1(A)) )
     => k7_qmax_1(A,B) = k2_mcart_1(B) ) )).

fof(dt_k8_qmax_1,axiom,(
    ! [A,B] :
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A)
        & m1_subset_1(B,k5_qmax_1(A)) )
     => m1_subset_1(k8_qmax_1(A,B),k5_qmax_1(A)) ) )).

fof(dt_k9_qmax_1,axiom,(
    ! [A] :
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ( v3_relat_2(k9_qmax_1(A))
        & v8_relat_2(k9_qmax_1(A))
        & v1_partfun1(k9_qmax_1(A),k5_qmax_1(A),k5_qmax_1(A))
        & m2_relset_1(k9_qmax_1(A),k5_qmax_1(A),k5_qmax_1(A)) ) ) )).

fof(dt_k10_qmax_1,axiom,(
    ! [A] :
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => m2_relset_1(k10_qmax_1(A),k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)),k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A))) ) )).

fof(dt_k11_qmax_1,axiom,(
    ! [A] :
      ( ( v2_qmax_1(A)
        & l1_qmax_1(A) )
     => ( v1_funct_1(k11_qmax_1(A))
        & v1_funct_2(k11_qmax_1(A),k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)),k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)))
        & m2_relset_1(k11_qmax_1(A),k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)),k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A))) ) ) )).

fof(dt_u1_qmax_1,axiom,(
    ! [A] :
      ( l1_qmax_1(A)
     => ~ v1_xboole_0(u1_qmax_1(A)) ) )).

fof(dt_u2_qmax_1,axiom,(
    ! [A] :
      ( l1_qmax_1(A)
     => ~ v1_xboole_0(u2_qmax_1(A)) ) )).

fof(dt_u3_qmax_1,axiom,(
    ! [A] :
      ( l1_qmax_1(A)
     => ( v1_funct_1(u3_qmax_1(A))
        & v1_funct_2(u3_qmax_1(A),k2_zfmisc_1(u1_qmax_1(A),u2_qmax_1(A)),k1_qmax_1(k1_numbers,k14_prob_1))
        & m2_relset_1(u3_qmax_1(A),k2_zfmisc_1(u1_qmax_1(A),u2_qmax_1(A)),k1_qmax_1(k1_numbers,k14_prob_1)) ) ) )).

fof(dt_u4_qmax_1,axiom,(
    ! [A,B] :
      ( l2_qmax_1(B,A)
     => m2_relset_1(u4_qmax_1(A,B),A,A) ) )).

fof(dt_u5_qmax_1,axiom,(
    ! [A,B] :
      ( l2_qmax_1(B,A)
     => ( v1_funct_1(u5_qmax_1(A,B))
        & v1_funct_2(u5_qmax_1(A,B),A,A)
        & m2_relset_1(u5_qmax_1(A,B),A,A) ) ) )).

fof(dt_g1_qmax_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,B),k1_qmax_1(k1_numbers,k14_prob_1))
        & m1_relset_1(C,k2_zfmisc_1(A,B),k1_qmax_1(k1_numbers,k14_prob_1)) )
     => ( v1_qmax_1(g1_qmax_1(A,B,C))
        & l1_qmax_1(g1_qmax_1(A,B,C)) ) ) )).

fof(free_g1_qmax_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,B),k1_qmax_1(k1_numbers,k14_prob_1))
        & m1_relset_1(C,k2_zfmisc_1(A,B),k1_qmax_1(k1_numbers,k14_prob_1)) )
     => ! [D,E,F] :
          ( g1_qmax_1(A,B,C) = g1_qmax_1(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) )).

fof(dt_g2_qmax_1,axiom,(
    ! [A,B,C] :
      ( ( m1_relset_1(B,A,A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,A)
        & m1_relset_1(C,A,A) )
     => ( v3_qmax_1(g2_qmax_1(A,B,C),A)
        & l2_qmax_1(g2_qmax_1(A,B,C),A) ) ) )).

fof(free_g2_qmax_1,axiom,(
    ! [A,B,C] :
      ( ( m1_relset_1(B,A,A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,A)
        & m1_relset_1(C,A,A) )
     => ! [D,E,F] :
          ( g2_qmax_1(A,B,C) = g2_qmax_1(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) )).
%------------------------------------------------------------------------------