% Mizar problem: t37_e_siec,e_siec,922,44 
fof(t37_e_siec,conjecture,(
    ! [A] : 
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => ( k5_relat_1(k16_e_siec(A),k16_e_siec(A)) = k16_e_siec(A)
        & k5_relat_1(k16_e_siec(A),k17_e_siec(A)) = k16_e_siec(A)
        & k5_relat_1(k17_e_siec(A),k16_e_siec(A)) = k17_e_siec(A)
        & k5_relat_1(k17_e_siec(A),k17_e_siec(A)) = k17_e_siec(A) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_relat_1,commutativity_k2_xboole_0,d21_e_siec,d22_e_siec,dt_k16_e_siec,dt_k17_e_siec,dt_k1_relat_1,dt_k1_sysrel,dt_k1_xboole_0,dt_k2_relat_1,dt_k2_xboole_0,dt_k4_relat_1,dt_k4_xboole_0,dt_k5_relat_1,dt_k6_relat_1,dt_l1_e_siec,dt_l1_struct_0,dt_m1_subset_1,dt_u1_e_siec,dt_u1_struct_0,dt_u2_e_siec,existence_l1_e_siec,existence_l1_struct_0,existence_m1_subset_1,fc10_relat_1,fc11_relat_1,fc12_relat_1,fc2_relat_1,fc3_relat_1,fc4_relat_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,fc9_relat_1,idempotence_k2_xboole_0,involutiveness_k4_relat_1,rc1_relat_1,rc2_e_siec,rc2_relat_1,rc3_e_siec,rc3_relat_1,t18_e_siec,t1_boole,t1_subset,t20_sysrel,t29_sysrel,t2_subset,t31_e_siec,t32_e_siec,t35_e_siec,t3_boole,t4_boole,t54_relat_1,t6_boole,t72_relat_1,t7_boole,t8_boole]),
    [file(e_siec,t37_e_siec)]).

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

fof(cc1_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_1),
    []).

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(d21_e_siec,axiom,(
    ! [A] : 
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => k16_e_siec(A) = k2_xboole_0(k4_relat_1(k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A)))),k6_relat_1(k4_xboole_0(u1_struct_0(A),k2_relat_1(u2_e_siec(A))))) ) ),
    file(e_siec,d21_e_siec),
    []).

fof(d22_e_siec,axiom,(
    ! [A] : 
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => k17_e_siec(A) = k2_xboole_0(k4_relat_1(k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A)))),k6_relat_1(k4_xboole_0(u1_struct_0(A),k2_relat_1(u1_e_siec(A))))) ) ),
    file(e_siec,d22_e_siec),
    []).

fof(dt_k16_e_siec,axiom,(
    ! [A] : 
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => v1_relat_1(k16_e_siec(A)) ) ),
    file(e_siec,k16_e_siec),
    []).

fof(dt_k17_e_siec,axiom,(
    ! [A] : 
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => v1_relat_1(k17_e_siec(A)) ) ),
    file(e_siec,k17_e_siec),
    []).

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

fof(dt_k1_sysrel,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => v1_relat_1(k1_sysrel(A)) ) ),
    file(sysrel,k1_sysrel),
    []).

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

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

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

fof(dt_k4_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => v1_relat_1(k4_relat_1(A)) ) ),
    file(relat_1,k4_relat_1),
    []).

fof(dt_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    []).

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_k6_relat_1,axiom,(
    ! [A] : v1_relat_1(k6_relat_1(A)) ),
    file(relat_1,k6_relat_1),
    []).

fof(dt_l1_e_siec,axiom,(
    ! [A] : 
      ( l1_e_siec(A)
     => l1_struct_0(A) ) ),
    file(e_siec,l1_e_siec),
    []).

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

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

fof(dt_u1_e_siec,axiom,(
    ! [A] : 
      ( l1_e_siec(A)
     => v1_relat_1(u1_e_siec(A)) ) ),
    file(e_siec,u1_e_siec),
    []).

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

fof(dt_u2_e_siec,axiom,(
    ! [A] : 
      ( l1_e_siec(A)
     => v1_relat_1(u2_e_siec(A)) ) ),
    file(e_siec,u2_e_siec),
    []).

fof(existence_l1_e_siec,axiom,(
    ? [A] : l1_e_siec(A) ),
    file(e_siec,l1_e_siec),
    []).

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

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

fof(fc10_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_xboole_0(A)
        & v1_relat_1(B) )
     => ( v1_xboole_0(k5_relat_1(B,A))
        & v1_relat_1(k5_relat_1(B,A)) ) ) ),
    file(relat_1,fc10_relat_1),
    []).

fof(fc11_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k4_relat_1(A))
        & v1_relat_1(k4_relat_1(A)) ) ) ),
    file(relat_1,fc11_relat_1),
    []).

fof(fc12_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0) ),
    file(relat_1,fc12_relat_1),
    []).

fof(fc2_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k2_xboole_0(A,B)) ) ),
    file(relat_1,fc2_relat_1),
    []).

fof(fc3_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k4_xboole_0(A,B)) ) ),
    file(relat_1,fc3_relat_1),
    []).

fof(fc4_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_1),
    []).

fof(fc5_relat_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k1_relat_1(A)) ) ),
    file(relat_1,fc5_relat_1),
    []).

fof(fc6_relat_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k2_relat_1(A)) ) ),
    file(relat_1,fc6_relat_1),
    []).

fof(fc7_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k1_relat_1(A))
        & v1_relat_1(k1_relat_1(A)) ) ) ),
    file(relat_1,fc7_relat_1),
    []).

fof(fc8_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k2_relat_1(A))
        & v1_relat_1(k2_relat_1(A)) ) ) ),
    file(relat_1,fc8_relat_1),
    []).

fof(fc9_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_xboole_0(A)
        & v1_relat_1(B) )
     => ( v1_xboole_0(k5_relat_1(A,B))
        & v1_relat_1(k5_relat_1(A,B)) ) ) ),
    file(relat_1,fc9_relat_1),
    []).

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

fof(involutiveness_k4_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => k4_relat_1(k4_relat_1(A)) = A ) ),
    file(relat_1,k4_relat_1),
    []).

fof(rc1_relat_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_1),
    []).

fof(rc2_e_siec,axiom,(
    ? [A] : 
      ( l1_e_siec(A)
      & v2_e_siec(A) ) ),
    file(e_siec,rc2_e_siec),
    []).

fof(rc2_relat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_1),
    []).

fof(rc3_e_siec,axiom,(
    ? [A] : 
      ( l1_e_siec(A)
      & v3_e_siec(A) ) ),
    file(e_siec,rc3_e_siec),
    []).

fof(rc3_relat_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_1),
    []).

fof(t18_e_siec,axiom,(
    ! [A] : 
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => ( k2_relat_1(u1_e_siec(A)) = k2_relat_1(k1_sysrel(u1_e_siec(A)))
        & k2_relat_1(u1_e_siec(A)) = k1_relat_1(k1_sysrel(u1_e_siec(A)))
        & k2_relat_1(u2_e_siec(A)) = k2_relat_1(k1_sysrel(u2_e_siec(A)))
        & k2_relat_1(u2_e_siec(A)) = k1_relat_1(k1_sysrel(u2_e_siec(A)))
        & k2_relat_1(u1_e_siec(A)) = k2_relat_1(u2_e_siec(A)) ) ) ),
    file(e_siec,t18_e_siec),
    []).

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(t20_sysrel,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ! [C] : 
              ( v1_relat_1(C)
             => ( k5_relat_1(k2_xboole_0(A,B),C) = k2_xboole_0(k5_relat_1(A,C),k5_relat_1(B,C))
                & k5_relat_1(A,k2_xboole_0(B,C)) = k2_xboole_0(k5_relat_1(A,B),k5_relat_1(A,C)) ) ) ) ) ),
    file(sysrel,t20_sysrel),
    []).

fof(t29_sysrel,axiom,(
    ! [A] : k5_relat_1(k6_relat_1(A),k6_relat_1(A)) = k6_relat_1(A) ),
    file(sysrel,t29_sysrel),
    []).

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

fof(t31_e_siec,axiom,(
    ! [A] : 
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => ( k5_relat_1(k6_relat_1(k4_xboole_0(u1_struct_0(A),k2_relat_1(u2_e_siec(A)))),k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A)))) = k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A)))
        & k5_relat_1(k6_relat_1(k4_xboole_0(u1_struct_0(A),k2_relat_1(u1_e_siec(A)))),k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A)))) = k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A))) ) ) ),
    file(e_siec,t31_e_siec),
    []).

fof(t32_e_siec,axiom,(
    ! [A] : 
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => ( k5_relat_1(k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A))),k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A)))) = k1_xboole_0
        & k5_relat_1(k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A))),k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A)))) = k1_xboole_0
        & k5_relat_1(k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A))),k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A)))) = k1_xboole_0
        & k5_relat_1(k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A))),k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A)))) = k1_xboole_0 ) ) ),
    file(e_siec,t32_e_siec),
    []).

fof(t35_e_siec,axiom,(
    ! [A] : 
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => ( k5_relat_1(k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A))),k6_relat_1(k4_xboole_0(u1_struct_0(A),k2_relat_1(u2_e_siec(A))))) = k1_xboole_0
        & k5_relat_1(k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A))),k6_relat_1(k4_xboole_0(u1_struct_0(A),k2_relat_1(u1_e_siec(A))))) = k1_xboole_0 ) ) ),
    file(e_siec,t35_e_siec),
    []).

fof(t3_boole,axiom,(
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t3_boole),
    []).

fof(t4_boole,axiom,(
    ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ),
    file(boole,t4_boole),
    []).

fof(t54_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => k4_relat_1(k5_relat_1(A,B)) = k5_relat_1(k4_relat_1(B),k4_relat_1(A)) ) ) ),
    file(relat_1,t54_relat_1),
    []).

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

fof(t72_relat_1,axiom,(
    ! [A] : k4_relat_1(k6_relat_1(A)) = k6_relat_1(A) ),
    file(relat_1,t72_relat_1),
    []).

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),
    []).