% Mizar problem: t12_waybel10,waybel10,544,23 
fof(t12_waybel10,conjecture,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l1_orders_2(B) )
     => ! [C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,u1_struct_0(B))
            & m2_relset_1(C,A,u1_struct_0(B)) )
         => ! [D] : 
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,u1_struct_0(B))
                & m2_relset_1(D,A,u1_struct_0(B)) )
             => ! [E] : 
                  ( m1_subset_1(E,u1_struct_0(k6_yellow_1(A,B)))
                 => ! [F] : 
                      ( m1_subset_1(F,u1_struct_0(k6_yellow_1(A,B)))
                     => ( ( E = C
                          & F = D )
                       => ( r1_orders_2(k6_yellow_1(A,B),E,F)
                        <=> r1_yellow_2(A,B,C,D) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_orders_2,antisymmetry_r2_hidden,cc1_funct_2,cc1_relset_1,cc1_yellow_1,cc5_funct_2,cc6_funct_2,d1_yellow_2,d4_yellow_1,d5_yellow_1,dt_g1_orders_2,dt_k12_pralg_1,dt_k1_funct_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_funcop_1,dt_k2_pre_circ,dt_k2_zfmisc_1,dt_k4_card_3,dt_k5_yellow_1,dt_k6_yellow_1,dt_l1_orders_2,dt_l1_struct_0,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_orders_2,dt_u1_struct_0,existence_l1_orders_2,existence_l1_struct_0,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc10_yellow_1,fc11_yellow_1,fc13_yellow_1,fc1_struct_0,fc1_subset_1,fc1_waybel10,fc1_xboole_0,fc4_subset_1,fc7_waybel_3,fc8_waybel_3,free_g1_orders_2,rc1_funct_2,rc1_subset_1,rc1_xboole_0,rc1_yellow_1,rc2_partfun1,rc2_subset_1,rc2_xboole_0,rc3_struct_0,rc5_struct_0,redefinition_k2_pre_circ,redefinition_m2_relset_1,reflexivity_r1_tarski,t13_funcop_1,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(waybel10,t12_waybel10)]).

fof(abstractness_v1_orders_2,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v1_orders_2(A)
       => A = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) ) ) ),
    file(orders_2,v1_orders_2),
    []).

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

fof(cc1_funct_2,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_partfun1(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc1_funct_2),
    []).

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_yellow_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_yellow_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_pralg_1(A) ) ) ),
    file(yellow_1,cc1_yellow_1),
    []).

fof(cc5_funct_2,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc5_funct_2),
    []).

fof(cc6_funct_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & ~ v1_xboole_0(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc6_funct_2),
    []).

fof(d1_yellow_2,axiom,(
    ! [A,B] : 
      ( l1_orders_2(B)
     => ! [C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,u1_struct_0(B))
            & m2_relset_1(C,A,u1_struct_0(B)) )
         => ! [D] : 
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,u1_struct_0(B))
                & m2_relset_1(D,A,u1_struct_0(B)) )
             => ( r1_yellow_2(A,B,C,D)
              <=> ! [E] : ~ ( r2_hidden(E,A)
                    & ! [F] : 
                        ( m1_subset_1(F,u1_struct_0(B))
                       => ! [G] : 
                            ( m1_subset_1(G,u1_struct_0(B))
                           => ~ ( F = k1_funct_1(C,E)
                                & G = k1_funct_1(D,E)
                                & r1_orders_2(B,F,G) ) ) ) ) ) ) ) ) ),
    file(yellow_2,d1_yellow_2),
    []).

fof(d4_yellow_1,axiom,(
    ! [A,B] : 
      ( ( v1_yellow_1(B)
        & m1_pboole(B,A) )
     => ! [C] : 
          ( ( v1_orders_2(C)
            & l1_orders_2(C) )
         => ( C = k5_yellow_1(A,B)
          <=> ( u1_struct_0(C) = k4_card_3(k12_pralg_1(A,B))
              & ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(C))
                     => ( r2_hidden(D,k4_card_3(k12_pralg_1(A,B)))
                       => ( r1_orders_2(C,D,E)
                        <=> ? [F] : 
                              ( v1_relat_1(F)
                              & v1_funct_1(F)
                              & ? [G] : 
                                  ( v1_relat_1(G)
                                  & v1_funct_1(G)
                                  & F = D
                                  & G = E
                                  & ! [H] : ~ ( r2_hidden(H,A)
                                      & ! [I] : 
                                          ( l1_orders_2(I)
                                         => ! [J] : 
                                              ( m1_subset_1(J,u1_struct_0(I))
                                             => ! [K] : 
                                                  ( m1_subset_1(K,u1_struct_0(I))
                                                 => ~ ( I = k1_funct_1(B,H)
                                                      & J = k1_funct_1(F,H)
                                                      & K = k1_funct_1(G,H)
                                                      & r1_orders_2(I,J,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(yellow_1,d4_yellow_1),
    []).

fof(d5_yellow_1,axiom,(
    ! [A,B] : 
      ( l1_orders_2(B)
     => k6_yellow_1(A,B) = k5_yellow_1(A,k2_pre_circ(A,B)) ) ),
    file(yellow_1,d5_yellow_1),
    []).

fof(dt_g1_orders_2,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,A,A)
     => ( v1_orders_2(g1_orders_2(A,B))
        & l1_orders_2(g1_orders_2(A,B)) ) ) ),
    file(orders_2,g1_orders_2),
    []).

fof(dt_k12_pralg_1,axiom,(
    ! [A,B] : 
      ( ( v2_pralg_1(B)
        & m1_pboole(B,A) )
     => m1_pboole(k12_pralg_1(A,B),A) ) ),
    file(pralg_1,k12_pralg_1),
    []).

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

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

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

fof(dt_k2_funcop_1,axiom,(
    $true ),
    file(funcop_1,k2_funcop_1),
    []).

fof(dt_k2_pre_circ,axiom,(
    ! [A,B] : m1_pboole(k2_pre_circ(A,B),A) ),
    file(pre_circ,k2_pre_circ),
    []).

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

fof(dt_k4_card_3,axiom,(
    $true ),
    file(card_3,k4_card_3),
    []).

fof(dt_k5_yellow_1,axiom,(
    ! [A,B] : 
      ( ( v1_yellow_1(B)
        & m1_pboole(B,A) )
     => ( v1_orders_2(k5_yellow_1(A,B))
        & l1_orders_2(k5_yellow_1(A,B)) ) ) ),
    file(yellow_1,k5_yellow_1),
    []).

fof(dt_k6_yellow_1,axiom,(
    ! [A,B] : 
      ( l1_orders_2(B)
     => ( v1_orders_2(k6_yellow_1(A,B))
        & l1_orders_2(k6_yellow_1(A,B)) ) ) ),
    file(yellow_1,k6_yellow_1),
    []).

fof(dt_l1_orders_2,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => l1_struct_0(A) ) ),
    file(orders_2,l1_orders_2),
    []).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    []).

fof(dt_m1_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B) ) ) ),
    file(pboole,m1_pboole),
    []).

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(dt_u1_orders_2,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => m2_relset_1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) ) ),
    file(orders_2,u1_orders_2),
    []).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    []).

fof(existence_l1_orders_2,axiom,(
    ? [A] : l1_orders_2(A) ),
    file(orders_2,l1_orders_2),
    []).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    []).

fof(existence_m1_pboole,axiom,(
    ! [A] : 
    ? [B] : m1_pboole(B,A) ),
    file(pboole,m1_pboole),
    []).

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(fc10_yellow_1,axiom,(
    ! [A,B] : 
      ( l1_orders_2(B)
     => ( v1_relat_1(k2_funcop_1(A,B))
        & v1_funct_1(k2_funcop_1(A,B))
        & v2_pralg_1(k2_funcop_1(A,B))
        & v1_yellow_1(k2_funcop_1(A,B)) ) ) ),
    file(yellow_1,fc10_yellow_1),
    []).

fof(fc11_yellow_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l1_orders_2(B) )
     => ( ~ v3_struct_0(k6_yellow_1(A,B))
        & v1_orders_2(k6_yellow_1(A,B)) ) ) ),
    file(yellow_1,fc11_yellow_1),
    []).

fof(fc13_yellow_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k6_yellow_1(k1_xboole_0,A))
        & v1_orders_2(k6_yellow_1(k1_xboole_0,A))
        & v3_realset2(k6_yellow_1(k1_xboole_0,A)) ) ) ),
    file(yellow_1,fc13_yellow_1),
    []).

fof(fc1_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    []).

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

fof(fc1_waybel10,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l1_orders_2(B) )
     => ( v1_relat_1(k2_funcop_1(A,B))
        & v1_funct_1(k2_funcop_1(A,B))
        & v1_yellow_1(k2_funcop_1(A,B))
        & v4_waybel_3(k2_funcop_1(A,B))
        & v2_pralg_1(k2_funcop_1(A,B)) ) ) ),
    file(waybel10,fc1_waybel10),
    []).

fof(fc1_xboole_0,axiom,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    []).

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(fc7_waybel_3,axiom,(
    ! [A,B] : 
      ( ( v1_yellow_1(B)
        & v4_waybel_3(B)
        & m1_pboole(B,A) )
     => ( ~ v3_struct_0(k5_yellow_1(A,B))
        & v1_orders_2(k5_yellow_1(A,B)) ) ) ),
    file(waybel_3,fc7_waybel_3),
    []).

fof(fc8_waybel_3,axiom,(
    ! [A,B] : 
      ( ( v1_yellow_1(B)
        & v4_waybel_3(B)
        & m1_pboole(B,A) )
     => ( ~ v3_struct_0(k5_yellow_1(A,B))
        & v1_orders_2(k5_yellow_1(A,B))
        & v1_monoid_0(k5_yellow_1(A,B)) ) ) ),
    file(waybel_3,fc8_waybel_3),
    []).

fof(free_g1_orders_2,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,A,A)
     => ! [C,D] : 
          ( g1_orders_2(A,B) = g1_orders_2(C,D)
         => ( A = C
            & B = D ) ) ) ),
    file(orders_2,g1_orders_2),
    []).

fof(rc1_funct_2,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C)
      & v1_funct_2(C,A,B) ) ),
    file(funct_2,rc1_funct_2),
    []).

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(rc1_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    []).

fof(rc1_yellow_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_pralg_1(B)
      & v1_yellow_1(B) ) ),
    file(yellow_1,rc1_yellow_1),
    []).

fof(rc2_partfun1,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C) ) ),
    file(partfun1,rc2_partfun1),
    []).

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(rc2_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

fof(rc3_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

fof(rc5_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(struct_0,rc5_struct_0),
    []).

fof(redefinition_k2_pre_circ,axiom,(
    ! [A,B] : k2_pre_circ(A,B) = k2_funcop_1(A,B) ),
    file(pre_circ,k2_pre_circ),
    []).

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

fof(t13_funcop_1,axiom,(
    ! [A,B,C] : 
      ( r2_hidden(B,A)
     => k1_funct_1(k2_funcop_1(A,C),B) = C ) ),
    file(funcop_1,t13_funcop_1),
    []).

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

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

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),
    []).