% Mizar problem: t7_yellow21,yellow21,1204,58 
fof(t7_yellow21,conjecture,(
    ! [A,B] : 
      ( v3_ordinal1(B)
     => ~ ( r2_wellord2(A,B)
          & ! [C] : 
              ( ( v1_relat_2(C)
                & v4_relat_2(C)
                & v8_relat_2(C)
                & v1_partfun1(C,A,A)
                & m2_relset_1(C,A,A) )
             => ~ ( r2_wellord1(C,A)
                  & k2_wellord2(C) = B ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_funct_1,cc1_ordinal1,cc1_realset1,cc1_relset_1,cc1_setfam_1,cc2_funct_1,cc2_ordinal1,cc3_ordinal1,cc3_yellow21,commutativity_k2_tarski,commutativity_k2_xboole_0,d12_relat_2,d14_relat_2,d16_relat_2,d1_wellord2,d2_wellord2,d4_partfun1,d4_wellord2,d5_funct_1,d5_tarski,d5_wellord1,d6_relat_1,d7_wellord1,d8_relat_1,d8_wellord1,d9_relat_2,dt_k1_funct_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_wellord2,dt_k1_xboole_0,dt_k1_yellow_1,dt_k1_zfmisc_1,dt_k2_funct_1,dt_k2_relat_1,dt_k2_tarski,dt_k2_wellord2,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_relat_1,dt_k4_relset_1,dt_k4_tarski,dt_k5_relat_1,dt_k5_relset_1,dt_k7_relset_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc1_funct_1,fc1_subset_1,fc2_ordinal1,fc2_setfam_1,fc2_subset_1,fc3_realset1,fc3_setfam_1,fc3_subset_1,fc3_yellow21,fc4_setfam_1,fc4_subset_1,fc4_yellow21,fc5_yellow21,idempotence_k2_xboole_0,rc1_funct_1,rc1_ordinal1,rc1_realset1,rc1_setfam_1,rc1_subset_1,rc2_funct_1,rc2_ordinal1,rc2_realset1,rc2_subset_1,rc3_funct_1,rc3_ordinal1,rc3_yellow21,rc4_funct_1,redefinition_k1_yellow_1,redefinition_k4_relset_1,redefinition_k5_relset_1,redefinition_k7_relset_1,redefinition_m2_relset_1,redefinition_r2_wellord2,reflexivity_r1_tarski,reflexivity_r2_wellord2,symmetry_r2_wellord2,t1_boole,t1_subset,t2_subset,t30_relat_1,t31_funct_2,t3_subset,t46_relat_1,t47_relat_1,t49_wellord1,t4_funct_2,t4_subset,t4_wellord2,t53_wellord1,t55_funct_1,t56_funct_1,t57_funct_1,t5_subset,t5_wellord1,t6_boole,t6_wellord2,t7_boole,t8_boole,t8_funct_1,t8_wellord1,t99_orders_1]),
    [file(yellow21,t7_yellow21)]).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

fof(cc1_funct_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    []).

fof(cc1_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A) ) ) ),
    file(ordinal1,cc1_ordinal1),
    []).

fof(cc1_realset1,axiom,(
    ! [A] : 
      ( ~ v1_realset1(A)
     => ~ v1_xboole_0(A) ) ),
    file(realset1,cc1_realset1),
    []).

fof(cc1_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    []).

fof(cc1_setfam_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_setfam_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ~ v1_xboole_0(B) ) ) ),
    file(setfam_1,cc1_setfam_1),
    []).

fof(cc2_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    []).

fof(cc2_ordinal1,axiom,(
    ! [A] : 
      ( ( v1_ordinal1(A)
        & v2_ordinal1(A) )
     => v3_ordinal1(A) ) ),
    file(ordinal1,cc2_ordinal1),
    []).

fof(cc3_ordinal1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(ordinal1,cc3_ordinal1),
    []).

fof(cc3_yellow21,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v2_wellord1(A) )
     => ( v1_relat_1(A)
        & v1_wellord1(A)
        & v1_relat_2(A)
        & v4_relat_2(A)
        & v6_relat_2(A)
        & v8_relat_2(A) ) ) ),
    file(yellow21,cc3_yellow21),
    []).

fof(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

fof(commutativity_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    []).

fof(d12_relat_2,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v4_relat_2(A)
      <=> r4_relat_2(A,k3_relat_1(A)) ) ) ),
    file(relat_2,d12_relat_2),
    []).

fof(d14_relat_2,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v6_relat_2(A)
      <=> r6_relat_2(A,k3_relat_1(A)) ) ) ),
    file(relat_2,d14_relat_2),
    []).

fof(d16_relat_2,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v8_relat_2(A)
      <=> r8_relat_2(A,k3_relat_1(A)) ) ) ),
    file(relat_2,d16_relat_2),
    []).

fof(d1_wellord2,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( B = k1_wellord2(A)
      <=> ( k3_relat_1(B) = A
          & ! [C,D] : 
              ( ( r2_hidden(C,A)
                & r2_hidden(D,A) )
             => ( r2_hidden(k4_tarski(C,D),B)
              <=> r1_tarski(C,D) ) ) ) ) ) ),
    file(wellord2,d1_wellord2),
    []).

fof(d2_wellord2,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v2_wellord1(A)
       => ! [B] : 
            ( v3_ordinal1(B)
           => ( B = k2_wellord2(A)
            <=> r4_wellord1(A,k1_wellord2(B)) ) ) ) ) ),
    file(wellord2,d2_wellord2),
    []).

fof(d4_partfun1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( v1_partfun1(C,A,B)
      <=> k4_relset_1(A,B,C) = A ) ) ),
    file(partfun1,d4_partfun1),
    []).

fof(d4_wellord2,axiom,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
    <=> ? [C] : 
          ( v1_relat_1(C)
          & v1_funct_1(C)
          & v2_funct_1(C)
          & k1_relat_1(C) = A
          & k2_relat_1(C) = B ) ) ),
    file(wellord2,d4_wellord2),
    []).

fof(d5_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( r2_hidden(D,k1_relat_1(A))
                  & C = k1_funct_1(A,D) ) ) ) ) ),
    file(funct_1,d5_funct_1),
    []).

fof(d5_tarski,axiom,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    []).

fof(d5_wellord1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r2_wellord1(A,B)
        <=> ( r1_relat_2(A,B)
            & r8_relat_2(A,B)
            & r4_relat_2(A,B)
            & r6_relat_2(A,B)
            & r1_wellord1(A,B) ) ) ) ),
    file(wellord1,d5_wellord1),
    []).

fof(d6_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => k3_relat_1(A) = k2_xboole_0(k1_relat_1(A),k2_relat_1(A)) ) ),
    file(relat_1,d6_relat_1),
    []).

fof(d7_wellord1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r3_wellord1(A,B,C)
              <=> ( k1_relat_1(C) = k3_relat_1(A)
                  & k2_relat_1(C) = k3_relat_1(B)
                  & v2_funct_1(C)
                  & ! [D,E] : 
                      ( r2_hidden(k4_tarski(D,E),A)
                    <=> ( r2_hidden(D,k3_relat_1(A))
                        & r2_hidden(E,k3_relat_1(A))
                        & r2_hidden(k4_tarski(k1_funct_1(C,D),k1_funct_1(C,E)),B) ) ) ) ) ) ) ) ),
    file(wellord1,d7_wellord1),
    []).

fof(d8_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ! [C] : 
              ( v1_relat_1(C)
             => ( C = k5_relat_1(A,B)
              <=> ! [D,E] : 
                    ( r2_hidden(k4_tarski(D,E),C)
                  <=> ? [F] : 
                        ( r2_hidden(k4_tarski(D,F),A)
                        & r2_hidden(k4_tarski(F,E),B) ) ) ) ) ) ) ),
    file(relat_1,d8_relat_1),
    []).

fof(d8_wellord1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r4_wellord1(A,B)
          <=> ? [C] : 
                ( v1_relat_1(C)
                & v1_funct_1(C)
                & r3_wellord1(A,B,C) ) ) ) ) ),
    file(wellord1,d8_wellord1),
    []).

fof(d9_relat_2,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v1_relat_2(A)
      <=> r1_relat_2(A,k3_relat_1(A)) ) ) ),
    file(relat_2,d9_relat_2),
    []).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    []).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    []).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

fof(dt_k1_wellord2,axiom,(
    ! [A] : v1_relat_1(k1_wellord2(A)) ),
    file(wellord2,k1_wellord2),
    []).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

fof(dt_k1_yellow_1,axiom,(
    ! [A] : 
      ( v1_relat_2(k1_yellow_1(A))
      & v4_relat_2(k1_yellow_1(A))
      & v8_relat_2(k1_yellow_1(A))
      & v1_partfun1(k1_yellow_1(A),A,A)
      & m2_relset_1(k1_yellow_1(A),A,A) ) ),
    file(yellow_1,k1_yellow_1),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

fof(dt_k2_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k2_funct_1(A))
        & v1_funct_1(k2_funct_1(A)) ) ) ),
    file(funct_1,k2_funct_1),
    []).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    []).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

fof(dt_k2_wellord2,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => v3_ordinal1(k2_wellord2(A)) ) ),
    file(wellord2,k2_wellord2),
    []).

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_k3_relat_1,axiom,(
    $true ),
    file(relat_1,k3_relat_1),
    []).

fof(dt_k4_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(relset_1,k4_relset_1),
    []).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

fof(dt_k5_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k5_relat_1(A,B)) ) ),
    file(relat_1,k5_relat_1),
    []).

fof(dt_k5_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k5_relset_1(A,B,C),k1_zfmisc_1(B)) ) ),
    file(relset_1,k5_relset_1),
    []).

fof(dt_k7_relset_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( m1_relset_1(E,A,B)
        & m1_relset_1(F,C,D) )
     => m2_relset_1(k7_relset_1(A,B,C,D,E,F),A,D) ) ),
    file(relset_1,k7_relset_1),
    []).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    []).

fof(fc1_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k5_relat_1(A,B))
        & v1_funct_1(k5_relat_1(A,B)) ) ) ),
    file(funct_1,fc1_funct_1),
    []).

fof(fc1_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    []).

fof(fc2_ordinal1,axiom,
    ( v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_xboole_0(k1_xboole_0)
    & v1_ordinal1(k1_xboole_0)
    & v2_ordinal1(k1_xboole_0)
    & v3_ordinal1(k1_xboole_0) ),
    file(ordinal1,fc2_ordinal1),
    []).

fof(fc2_setfam_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( ~ v1_xboole_0(k1_tarski(A))
        & v1_setfam_1(k1_tarski(A)) ) ) ),
    file(setfam_1,fc2_setfam_1),
    []).

fof(fc2_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    []).

fof(fc3_realset1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A))
      & v1_realset1(k1_tarski(A)) ) ),
    file(realset1,fc3_realset1),
    []).

fof(fc3_setfam_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ( ~ v1_xboole_0(k2_tarski(A,B))
        & v1_setfam_1(k2_tarski(A,B)) ) ) ),
    file(setfam_1,fc3_setfam_1),
    []).

fof(fc3_subset_1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_1),
    []).

fof(fc3_yellow21,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A)
        & v1_relat_1(B)
        & v1_relat_2(B) )
     => ( v1_relat_1(k5_relat_1(k5_relat_1(A,B),k2_funct_1(A)))
        & v1_relat_2(k5_relat_1(k5_relat_1(A,B),k2_funct_1(A))) ) ) ),
    file(yellow21,fc3_yellow21),
    []).

fof(fc4_setfam_1,axiom,(
    ! [A,B] : 
      ( ( v1_setfam_1(A)
        & v1_setfam_1(B) )
     => v1_setfam_1(k2_xboole_0(A,B)) ) ),
    file(setfam_1,fc4_setfam_1),
    []).

fof(fc4_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    []).

fof(fc4_yellow21,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A)
        & v1_relat_1(B)
        & v4_relat_2(B) )
     => ( v1_relat_1(k5_relat_1(k5_relat_1(A,B),k2_funct_1(A)))
        & v4_relat_2(k5_relat_1(k5_relat_1(A,B),k2_funct_1(A))) ) ) ),
    file(yellow21,fc4_yellow21),
    []).

fof(fc5_yellow21,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A)
        & v1_relat_1(B)
        & v8_relat_2(B) )
     => ( v1_relat_1(k5_relat_1(k5_relat_1(A,B),k2_funct_1(A)))
        & v8_relat_2(k5_relat_1(k5_relat_1(A,B),k2_funct_1(A))) ) ) ),
    file(yellow21,fc5_yellow21),
    []).

fof(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

fof(rc1_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    []).

fof(rc1_ordinal1,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc1_ordinal1),
    []).

fof(rc1_realset1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_realset1(A) ) ),
    file(realset1,rc1_realset1),
    []).

fof(rc1_setfam_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_setfam_1(A) ) ),
    file(setfam_1,rc1_setfam_1),
    []).

fof(rc1_subset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    []).

fof(rc2_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    []).

fof(rc2_ordinal1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc2_ordinal1),
    []).

fof(rc2_realset1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & ~ v1_realset1(A) ) ),
    file(realset1,rc2_realset1),
    []).

fof(rc2_subset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    []).

fof(rc3_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    []).

fof(rc3_ordinal1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc3_ordinal1),
    []).

fof(rc3_yellow21,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_wellord1(A)
      & v2_wellord1(A)
      & v1_relat_2(A)
      & v4_relat_2(A)
      & v6_relat_2(A)
      & v8_relat_2(A) ) ),
    file(yellow21,rc3_yellow21),
    []).

fof(rc4_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    []).

fof(redefinition_k1_yellow_1,axiom,(
    ! [A] : k1_yellow_1(A) = k1_wellord2(A) ),
    file(yellow_1,k1_yellow_1),
    []).

fof(redefinition_k4_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k4_relset_1(A,B,C) = k1_relat_1(C) ) ),
    file(relset_1,k4_relset_1),
    []).

fof(redefinition_k5_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k5_relset_1(A,B,C) = k2_relat_1(C) ) ),
    file(relset_1,k5_relset_1),
    []).

fof(redefinition_k7_relset_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( m1_relset_1(E,A,B)
        & m1_relset_1(F,C,D) )
     => k7_relset_1(A,B,C,D,E,F) = k5_relat_1(E,F) ) ),
    file(relset_1,k7_relset_1),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(redefinition_r2_wellord2,axiom,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
    <=> r2_tarski(A,B) ) ),
    file(wellord2,r2_wellord2),
    []).

fof(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(reflexivity_r2_wellord2,axiom,(
    ! [A,B] : r2_wellord2(A,A) ),
    file(wellord2,r2_wellord2),
    []).

fof(symmetry_r2_wellord2,axiom,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
     => r2_wellord2(B,A) ) ),
    file(wellord2,r2_wellord2),
    []).

fof(t1_boole,axiom,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    []).

fof(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

fof(t2_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    []).

fof(t30_relat_1,axiom,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( r2_hidden(k4_tarski(A,B),C)
       => ( r2_hidden(A,k3_relat_1(C))
          & r2_hidden(B,k3_relat_1(C)) ) ) ) ),
    file(relat_1,t30_relat_1),
    []).

fof(t31_funct_2,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ( ( v2_funct_1(C)
          & k2_relat_1(C) = B )
       => ( v1_funct_1(k2_funct_1(C))
          & v1_funct_2(k2_funct_1(C),B,A)
          & m2_relset_1(k2_funct_1(C),B,A) ) ) ) ),
    file(funct_2,t31_funct_2),
    []).

fof(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).

fof(t46_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(k2_relat_1(A),k1_relat_1(B))
           => k1_relat_1(k5_relat_1(A,B)) = k1_relat_1(A) ) ) ) ),
    file(relat_1,t46_relat_1),
    []).

fof(t47_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(k1_relat_1(A),k2_relat_1(B))
           => k2_relat_1(k5_relat_1(B,A)) = k2_relat_1(A) ) ) ) ),
    file(relat_1,t47_relat_1),
    []).

fof(t49_wellord1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r3_wellord1(A,B,C)
               => r3_wellord1(B,A,k2_funct_1(C)) ) ) ) ) ),
    file(wellord1,t49_wellord1),
    []).

fof(t4_funct_2,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r1_tarski(k2_relat_1(B),A)
       => ( v1_funct_1(B)
          & v1_funct_2(B,k1_relat_1(B),A)
          & m2_relset_1(B,k1_relat_1(B),A) ) ) ) ),
    file(funct_2,t4_funct_2),
    []).

fof(t4_subset,axiom,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    []).

fof(t4_wellord2,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => v6_relat_2(k1_wellord2(A)) ) ),
    file(wellord2,t4_wellord2),
    []).

fof(t53_wellord1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r3_wellord1(A,B,C)
               => ( ( v1_relat_2(A)
                   => v1_relat_2(B) )
                  & ( v8_relat_2(A)
                   => v8_relat_2(B) )
                  & ( v6_relat_2(A)
                   => v6_relat_2(B) )
                  & ( v4_relat_2(A)
                   => v4_relat_2(B) )
                  & ( v1_wellord1(A)
                   => v1_wellord1(B) ) ) ) ) ) ) ),
    file(wellord1,t53_wellord1),
    []).

fof(t55_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
       => ( k2_relat_1(A) = k1_relat_1(k2_funct_1(A))
          & k1_relat_1(A) = k2_relat_1(k2_funct_1(A)) ) ) ) ),
    file(funct_1,t55_funct_1),
    []).

fof(t56_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( ( v2_funct_1(B)
          & r2_hidden(A,k1_relat_1(B)) )
       => ( A = k1_funct_1(k2_funct_1(B),k1_funct_1(B,A))
          & A = k1_funct_1(k5_relat_1(B,k2_funct_1(B)),A) ) ) ) ),
    file(funct_1,t56_funct_1),
    []).

fof(t57_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( ( v2_funct_1(B)
          & r2_hidden(A,k2_relat_1(B)) )
       => ( A = k1_funct_1(B,k1_funct_1(k2_funct_1(B),A))
          & A = k1_funct_1(k5_relat_1(k2_funct_1(B),B),A) ) ) ) ),
    file(funct_1,t57_funct_1),
    []).

fof(t5_subset,axiom,(
    ! [A,B,C] : ~ ( r2_hidden(A,B)
      & m1_subset_1(B,k1_zfmisc_1(C))
      & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    []).

fof(t5_wellord1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v1_wellord1(A)
      <=> r1_wellord1(A,k3_relat_1(A)) ) ) ),
    file(wellord1,t5_wellord1),
    []).

fof(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

fof(t6_wellord2,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => v1_wellord1(k1_wellord2(A)) ) ),
    file(wellord2,t6_wellord2),
    []).

fof(t7_boole,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    []).

fof(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).

fof(t8_funct_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(k4_tarski(A,B),C)
      <=> ( r2_hidden(A,k1_relat_1(C))
          & B = k1_funct_1(C,A) ) ) ) ),
    file(funct_1,t8_funct_1),
    []).

fof(t8_wellord1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( r2_wellord1(A,k3_relat_1(A))
      <=> v2_wellord1(A) ) ) ),
    file(wellord1,t8_wellord1),
    []).

fof(t99_orders_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_2(B)
        & v4_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => ( k4_relset_1(A,A,B) = A
        & k5_relset_1(A,A,B) = A ) ) ),
    file(orders_1,t99_orders_1),
    []).