% Mizar problem: t51_cat_4,cat_4,1437,50 
fof(t51_cat_4,conjecture,(
    ! [A,B,C] : 
      ( m1_subset_1(C,u2_cat_1(k23_cat_4(A,B)))
     => ! [D] : 
          ( m1_subset_1(D,u2_cat_1(k23_cat_4(A,B)))
         => C = D ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v5_cat_4,antisymmetry_r2_hidden,cc1_finset_1,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc2_finset_1,cc2_funct_1,d1_cat_1,d26_cat_4,d2_cqc_lang,dt_g2_cat_4,dt_k10_pboole,dt_k1_algstr_1,dt_k1_cat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k23_cat_4,dt_k2_funcop_1,dt_k2_zfmisc_1,dt_k3_cqc_lang,dt_k4_tarski,dt_k9_funct_2,dt_l1_cat_1,dt_l2_cat_4,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_cat_1,dt_u2_cat_1,dt_u3_cat_1,dt_u4_cat_1,dt_u5_cat_1,dt_u5_cat_4,dt_u6_cat_1,dt_u6_cat_4,dt_u7_cat_4,dt_u8_cat_4,existence_l1_cat_1,existence_l2_cat_4,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc12_relat_1,fc14_finset_1,fc1_cqc_lang,fc1_finset_1,fc1_subset_1,fc2_cat_4,fc2_subset_1,fc4_relat_1,fc4_subset_1,free_g2_cat_4,rc1_finset_1,rc1_funct_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,rc3_finset_1,rc3_funct_1,rc3_relat_1,rc4_cat_4,rc4_finset_1,rc4_funct_1,rc5_cat_4,redefinition_k10_pboole,redefinition_m2_relset_1,reflexivity_r1_tarski,t1_subset,t2_subset,t3_subset,t4_subset,t50_cat_4,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(cat_4,t51_cat_4)]).

fof(abstractness_v5_cat_4,axiom,(
    ! [A] : 
      ( l2_cat_4(A)
     => ( v5_cat_4(A)
       => A = g2_cat_4(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A),u5_cat_4(A),u6_cat_4(A),u7_cat_4(A),u8_cat_4(A)) ) ) ),
    file(cat_4,v5_cat_4),
    []).

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

fof(cc1_finset_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_1),
    []).

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

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

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(cc2_finset_1,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_finset_1(B) ) ) ),
    file(finset_1,cc2_finset_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(d1_cat_1,axiom,(
    ! [A,B,C] : k1_cat_1(A,B,C) = k3_cqc_lang(k4_tarski(A,B),C) ),
    file(cat_1,d1_cat_1),
    []).

fof(d26_cat_4,axiom,(
    ! [A,B] : k23_cat_4(A,B) = g2_cat_4(k1_tarski(A),k1_tarski(B),k10_pboole(k1_tarski(B),A),k10_pboole(k1_tarski(B),A),k1_cat_1(B,B,B),k10_pboole(k1_tarski(A),B),k1_algstr_1(A),k9_funct_2(A,A,A),k9_funct_2(A,A,B),k9_funct_2(A,A,B)) ),
    file(cat_4,d26_cat_4),
    []).

fof(d2_cqc_lang,axiom,(
    ! [A,B] : k3_cqc_lang(A,B) = k2_funcop_1(k1_tarski(A),B) ),
    file(cqc_lang,d2_cqc_lang),
    []).

fof(dt_g2_cat_4,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,B,A)
        & m1_relset_1(C,B,A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A)
        & v1_funct_1(E)
        & m1_relset_1(E,k2_zfmisc_1(B,B),B)
        & v1_funct_1(F)
        & v1_funct_2(F,A,B)
        & m1_relset_1(F,A,B)
        & m1_subset_1(G,A)
        & v1_funct_1(H)
        & v1_funct_2(H,k2_zfmisc_1(A,A),A)
        & m1_relset_1(H,k2_zfmisc_1(A,A),A)
        & v1_funct_1(I)
        & v1_funct_2(I,k2_zfmisc_1(A,A),B)
        & m1_relset_1(I,k2_zfmisc_1(A,A),B)
        & v1_funct_1(J)
        & v1_funct_2(J,k2_zfmisc_1(A,A),B)
        & m1_relset_1(J,k2_zfmisc_1(A,A),B) )
     => ( v5_cat_4(g2_cat_4(A,B,C,D,E,F,G,H,I,J))
        & l2_cat_4(g2_cat_4(A,B,C,D,E,F,G,H,I,J)) ) ) ),
    file(cat_4,g2_cat_4),
    []).

fof(dt_k10_pboole,axiom,(
    ! [A,B] : 
      ( v1_funct_1(k10_pboole(A,B))
      & v1_funct_2(k10_pboole(A,B),A,k1_tarski(B))
      & m2_relset_1(k10_pboole(A,B),A,k1_tarski(B)) ) ),
    file(pboole,k10_pboole),
    []).

fof(dt_k1_algstr_1,axiom,(
    ! [A] : m1_subset_1(k1_algstr_1(A),k1_tarski(A)) ),
    file(algstr_1,k1_algstr_1),
    []).

fof(dt_k1_cat_1,axiom,(
    ! [A,B,C] : 
      ( v1_funct_1(k1_cat_1(A,B,C))
      & m2_relset_1(k1_cat_1(A,B,C),k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) ) ),
    file(cat_1,k1_cat_1),
    []).

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

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_k23_cat_4,axiom,(
    ! [A,B] : 
      ( v5_cat_4(k23_cat_4(A,B))
      & l2_cat_4(k23_cat_4(A,B)) ) ),
    file(cat_4,k23_cat_4),
    []).

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

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

fof(dt_k3_cqc_lang,axiom,(
    $true ),
    file(cqc_lang,k3_cqc_lang),
    []).

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

fof(dt_k9_funct_2,axiom,(
    ! [A,B,C] : 
      ( v1_funct_1(k9_funct_2(A,B,C))
      & v1_funct_2(k9_funct_2(A,B,C),k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C))
      & m2_relset_1(k9_funct_2(A,B,C),k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) ) ),
    file(funct_2,k9_funct_2),
    []).

fof(dt_l1_cat_1,axiom,(
    $true ),
    file(cat_1,l1_cat_1),
    []).

fof(dt_l2_cat_4,axiom,(
    ! [A] : 
      ( l2_cat_4(A)
     => l1_cat_1(A) ) ),
    file(cat_4,l2_cat_4),
    []).

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_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ~ v1_xboole_0(u1_cat_1(A)) ) ),
    file(cat_1,u1_cat_1),
    []).

fof(dt_u2_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ~ v1_xboole_0(u2_cat_1(A)) ) ),
    file(cat_1,u2_cat_1),
    []).

fof(dt_u3_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ( v1_funct_1(u3_cat_1(A))
        & v1_funct_2(u3_cat_1(A),u2_cat_1(A),u1_cat_1(A))
        & m2_relset_1(u3_cat_1(A),u2_cat_1(A),u1_cat_1(A)) ) ) ),
    file(cat_1,u3_cat_1),
    []).

fof(dt_u4_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ( v1_funct_1(u4_cat_1(A))
        & v1_funct_2(u4_cat_1(A),u2_cat_1(A),u1_cat_1(A))
        & m2_relset_1(u4_cat_1(A),u2_cat_1(A),u1_cat_1(A)) ) ) ),
    file(cat_1,u4_cat_1),
    []).

fof(dt_u5_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ( v1_funct_1(u5_cat_1(A))
        & m2_relset_1(u5_cat_1(A),k2_zfmisc_1(u2_cat_1(A),u2_cat_1(A)),u2_cat_1(A)) ) ) ),
    file(cat_1,u5_cat_1),
    []).

fof(dt_u5_cat_4,axiom,(
    ! [A] : 
      ( l2_cat_4(A)
     => m1_subset_1(u5_cat_4(A),u1_cat_1(A)) ) ),
    file(cat_4,u5_cat_4),
    []).

fof(dt_u6_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ( v1_funct_1(u6_cat_1(A))
        & v1_funct_2(u6_cat_1(A),u1_cat_1(A),u2_cat_1(A))
        & m2_relset_1(u6_cat_1(A),u1_cat_1(A),u2_cat_1(A)) ) ) ),
    file(cat_1,u6_cat_1),
    []).

fof(dt_u6_cat_4,axiom,(
    ! [A] : 
      ( l2_cat_4(A)
     => ( v1_funct_1(u6_cat_4(A))
        & v1_funct_2(u6_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u1_cat_1(A))
        & m2_relset_1(u6_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u1_cat_1(A)) ) ) ),
    file(cat_4,u6_cat_4),
    []).

fof(dt_u7_cat_4,axiom,(
    ! [A] : 
      ( l2_cat_4(A)
     => ( v1_funct_1(u7_cat_4(A))
        & v1_funct_2(u7_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A))
        & m2_relset_1(u7_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A)) ) ) ),
    file(cat_4,u7_cat_4),
    []).

fof(dt_u8_cat_4,axiom,(
    ! [A] : 
      ( l2_cat_4(A)
     => ( v1_funct_1(u8_cat_4(A))
        & v1_funct_2(u8_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A))
        & m2_relset_1(u8_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A)) ) ) ),
    file(cat_4,u8_cat_4),
    []).

fof(existence_l1_cat_1,axiom,(
    ? [A] : l1_cat_1(A) ),
    file(cat_1,l1_cat_1),
    []).

fof(existence_l2_cat_4,axiom,(
    ? [A] : l2_cat_4(A) ),
    file(cat_4,l2_cat_4),
    []).

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(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(fc14_finset_1,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_zfmisc_1(A,B)) ) ),
    file(finset_1,fc14_finset_1),
    []).

fof(fc1_cqc_lang,axiom,(
    ! [A,B] : 
      ( v1_relat_1(k3_cqc_lang(A,B))
      & v1_funct_1(k3_cqc_lang(A,B)) ) ),
    file(cqc_lang,fc1_cqc_lang),
    []).

fof(fc1_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A)) ) ),
    file(finset_1,fc1_finset_1),
    []).

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

fof(fc2_cat_4,axiom,(
    ! [A,B] : 
      ( v2_cat_1(k23_cat_4(A,B))
      & v5_cat_4(k23_cat_4(A,B)) ) ),
    file(cat_4,fc2_cat_4),
    []).

fof(fc2_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_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(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(free_g2_cat_4,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,B,A)
        & m1_relset_1(C,B,A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A)
        & v1_funct_1(E)
        & m1_relset_1(E,k2_zfmisc_1(B,B),B)
        & v1_funct_1(F)
        & v1_funct_2(F,A,B)
        & m1_relset_1(F,A,B)
        & m1_subset_1(G,A)
        & v1_funct_1(H)
        & v1_funct_2(H,k2_zfmisc_1(A,A),A)
        & m1_relset_1(H,k2_zfmisc_1(A,A),A)
        & v1_funct_1(I)
        & v1_funct_2(I,k2_zfmisc_1(A,A),B)
        & m1_relset_1(I,k2_zfmisc_1(A,A),B)
        & v1_funct_1(J)
        & v1_funct_2(J,k2_zfmisc_1(A,A),B)
        & m1_relset_1(J,k2_zfmisc_1(A,A),B) )
     => ! [K,L,M,N,O,P,Q,R,S,T] : 
          ( g2_cat_4(A,B,C,D,E,F,G,H,I,J) = g2_cat_4(K,L,M,N,O,P,Q,R,S,T)
         => ( A = K
            & B = L
            & C = M
            & D = N
            & E = O
            & F = P
            & G = Q
            & H = R
            & I = S
            & J = T ) ) ) ),
    file(cat_4,g2_cat_4),
    []).

fof(rc1_finset_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A) ) ),
    file(finset_1,rc1_finset_1),
    []).

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

fof(rc1_relat_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_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_relat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_1),
    []).

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_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc3_finset_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_relat_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_1),
    []).

fof(rc4_cat_4,axiom,(
    ? [A] : 
      ( l2_cat_4(A)
      & v5_cat_4(A) ) ),
    file(cat_4,rc4_cat_4),
    []).

fof(rc4_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc4_finset_1),
    []).

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(rc5_cat_4,axiom,(
    ? [A] : 
      ( l2_cat_4(A)
      & v2_cat_1(A)
      & v5_cat_4(A) ) ),
    file(cat_4,rc5_cat_4),
    []).

fof(redefinition_k10_pboole,axiom,(
    ! [A,B] : k10_pboole(A,B) = k2_funcop_1(A,B) ),
    file(pboole,k10_pboole),
    []).

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(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(t50_cat_4,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,u2_cat_1(k23_cat_4(A,B)))
     => C = B ) ),
    file(cat_4,t50_cat_4),
    []).

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),
    []).