% Mizar ND problem: t3_card_3,card_3,95,28 
fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(t2_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    [interesting(0.9),axiom,file(subset,t2_subset)]).

fof(antisymmetry_r2_hidden,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    [interesting(0.9),axiom,file(hidden,r2_hidden)]).

fof(rc1_finset_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A) ) ),
    file(finset_1,rc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc1_finset_1)]).

fof(rc2_card_1,theorem,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v1_finset_1(A)
      & v1_card_1(A) ) ),
    file(card_1,rc2_card_1),
    [interesting(0.9),axiom,file(card_1,rc2_card_1)]).

fof(rc5_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v2_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc5_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc5_funct_1)]).

fof(t1_subset,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    [interesting(0.9),axiom,file(subset,t1_subset)]).

fof(cc1_card_1,theorem,(
    ! [A] : 
      ( v1_card_1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(card_1,cc1_card_1),
    [interesting(0.9),axiom,file(card_1,cc1_card_1)]).

fof(cc1_finset_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,cc1_finset_1)]).

fof(cc1_funct_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc1_funct_1)]).

fof(cc1_ordinal1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A) ) ) ),
    file(ordinal1,cc1_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,cc1_ordinal1)]).

fof(cc1_relat_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_1),
    [interesting(0.9),axiom,file(relat_1,cc1_relat_1)]).

fof(cc2_funct_1,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(funct_1,cc2_funct_1)]).

fof(cc2_ordinal1,theorem,(
    ! [A] : 
      ( ( v1_ordinal1(A)
        & v2_ordinal1(A) )
     => v3_ordinal1(A) ) ),
    file(ordinal1,cc2_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,cc2_ordinal1)]).

fof(cc3_ordinal1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(ordinal1,cc3_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,cc3_ordinal1)]).

fof(fc2_card_3,theorem,(
    ! [A,B] : 
      ( v1_card_1(B)
     => ( v1_relat_1(k2_funcop_1(A,B))
        & v1_funct_1(k2_funcop_1(A,B))
        & v1_ordinal2(k2_funcop_1(A,B))
        & v1_card_3(k2_funcop_1(A,B)) ) ) ),
    file(card_3,fc2_card_3),
    [interesting(0.9),axiom,file(card_3,fc2_card_3)]).

fof(fc3_funcop_1,theorem,(
    ! [A,B] : 
      ( v1_xboole_0(B)
     => ( v1_xboole_0(k2_funcop_1(B,A))
        & v1_relat_1(k2_funcop_1(B,A))
        & v1_funct_1(k2_funcop_1(B,A))
        & v2_funct_1(k2_funcop_1(B,A)) ) ) ),
    file(funcop_1,fc3_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,fc3_funcop_1)]).

fof(fc4_ordinal2,theorem,(
    ! [A,B] : 
      ( v3_ordinal1(B)
     => ( v1_relat_1(k2_funcop_1(A,B))
        & v1_funct_1(k2_funcop_1(A,B))
        & v1_ordinal2(k2_funcop_1(A,B)) ) ) ),
    file(ordinal2,fc4_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,fc4_ordinal2)]).

fof(fc9_funcop_1,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ( v1_relat_1(k2_funcop_1(A,B))
        & v2_relat_1(k2_funcop_1(A,B))
        & v1_funct_1(k2_funcop_1(A,B)) ) ) ),
    file(funcop_1,fc9_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,fc9_funcop_1)]).

fof(rc1_card_1,theorem,(
    ? [A] : v1_card_1(A) ),
    file(card_1,rc1_card_1),
    [interesting(0.9),axiom,file(card_1,rc1_card_1)]).

fof(rc1_ordinal1,theorem,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc1_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,rc1_ordinal1)]).

fof(rc1_relat_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc1_relat_1)]).

fof(rc2_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc2_funct_1)]).

fof(rc2_ordinal1,theorem,(
    ? [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),
    [interesting(0.9),axiom,file(ordinal1,rc2_ordinal1)]).

fof(rc2_relat_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc2_relat_1)]).

fof(rc3_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc3_funct_1)]).

fof(rc3_ordinal1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc3_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,rc3_ordinal1)]).

fof(rc3_relat_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc3_relat_1)]).

fof(rc4_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc4_funct_1)]).

fof(t7_boole,theorem,(
    ! [A,B] : 
      ~ ( r2_hidden(A,B)
        & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    [interesting(0.9),axiom,file(boole,t7_boole)]).

fof(t8_boole,theorem,(
    ! [A,B] : 
      ~ ( v1_xboole_0(A)
        & A != B
        & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    [interesting(0.9),axiom,file(boole,t8_boole)]).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

fof(dt_k2_funcop_1,axiom,(
    $true ),
    file(funcop_1,k2_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,k2_funcop_1)]).

fof(dh_c1_6__card_3,definition,
    ( ? [A] : v1_card_1(A)
   => v1_card_1(c1_6__card_3) ),
    introduced(definition,[new_symbol(c1_6__card_3),file(card_3,c1_6__card_3)]),
    [interesting(0.8),axiom,file(card_3,c1_6__card_3)]).

fof(e1_6__card_3,plain,(
    ? [A] : v1_card_1(A) ),
    inference(mizar_by,[status(thm),assumptions([])],[cc1_ordinal1,cc2_ordinal1,rc1_ordinal1,cc1_card_1,rc1_card_1]),
    [interesting(0.8),file(card_3,e1_6__card_3),[file(card_3,e1_6__card_3)]]).

fof(dt_c1_6__card_3,plain,(
    v1_card_1(c1_6__card_3) ),
    inference(consider,[status(thm),assumptions([])],[dh_c1_6__card_3,e1_6__card_3]),
    [interesting(0.8),file(card_3,c1_6__card_3),[file(card_3,c1_6__card_3)]]).

fof(fc12_relat_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0) ),
    file(relat_1,fc12_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc12_relat_1)]).

fof(fc1_funcop_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(k2_funcop_1(A,B))
      & v1_funct_1(k2_funcop_1(A,B)) ) ),
    file(funcop_1,fc1_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,fc1_funcop_1)]).

fof(fc2_funcop_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(k2_funcop_1(k1_xboole_0,A))
      & v1_relat_1(k2_funcop_1(k1_xboole_0,A))
      & v1_funct_1(k2_funcop_1(k1_xboole_0,A))
      & v2_funct_1(k2_funcop_1(k1_xboole_0,A)) ) ),
    file(funcop_1,fc2_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,fc2_funcop_1)]).

fof(fc2_ordinal1,theorem,
    ( 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),
    [interesting(0.9),axiom,file(ordinal1,fc2_ordinal1)]).

fof(fc4_relat_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc4_relat_1)]).

fof(rc1_card_3,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_card_3(A) ) ),
    file(card_3,rc1_card_3),
    [interesting(0.9),axiom,file(card_3,rc1_card_3)]).

fof(rc1_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc1_funct_1)]).

fof(t6_boole,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    [interesting(0.9),axiom,file(boole,t6_boole)]).

fof(e2_6__card_3,plain,(
    k1_xboole_0 = k2_funcop_1(k1_xboole_0,c1_6__card_3) ),
    inference(mizar_by,[status(thm),assumptions([])],[existence_m1_subset_1,dt_m1_subset_1,t2_subset,antisymmetry_r2_hidden,rc1_card_3,rc1_finset_1,rc2_card_1,rc5_funct_1,t1_subset,cc1_card_1,cc1_finset_1,cc1_funct_1,cc1_ordinal1,cc1_relat_1,cc2_funct_1,cc2_ordinal1,cc3_ordinal1,fc2_card_3,fc3_funcop_1,fc4_ordinal2,fc9_funcop_1,rc1_card_1,rc1_funct_1,rc1_ordinal1,rc1_relat_1,rc2_funct_1,rc2_ordinal1,rc2_relat_1,rc3_funct_1,rc3_ordinal1,rc3_relat_1,rc4_funct_1,t7_boole,t8_boole,dt_k1_xboole_0,dt_k2_funcop_1,dt_c1_6__card_3,fc12_relat_1,fc1_funcop_1,fc2_funcop_1,fc2_ordinal1,fc4_relat_1,t6_boole]),
    [interesting(0.8),file(card_3,e2_6__card_3),[file(card_3,e2_6__card_3)]]).

fof(e3_6__card_3,plain,
    ( v1_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v1_card_3(k1_xboole_0) ),
    inference(mizar_by,[status(thm),assumptions([])],[existence_m1_subset_1,dt_m1_subset_1,t2_subset,antisymmetry_r2_hidden,rc1_finset_1,rc2_card_1,rc5_funct_1,t1_subset,cc1_card_1,cc1_finset_1,cc1_funct_1,cc1_ordinal1,cc1_relat_1,cc2_funct_1,cc2_ordinal1,cc3_ordinal1,fc2_card_3,fc3_funcop_1,fc4_ordinal2,fc9_funcop_1,rc1_card_1,rc1_ordinal1,rc1_relat_1,rc2_funct_1,rc2_ordinal1,rc2_relat_1,rc3_funct_1,rc3_ordinal1,rc3_relat_1,rc4_funct_1,t7_boole,t8_boole,dt_k1_xboole_0,dt_k2_funcop_1,dt_c1_6__card_3,fc12_relat_1,fc1_funcop_1,fc2_funcop_1,fc2_ordinal1,fc4_relat_1,rc1_card_3,rc1_funct_1,t6_boole,e2_6__card_3]),
    [interesting(0.8),file(card_3,e3_6__card_3),[file(card_3,e3_6__card_3)]]).

fof(i1_6__card_3,theorem,(
    $true ),
    introduced(tautology,[file(card_3,i1_6__card_3)]),
    [interesting(0.8),trivial,file(card_3,i1_6__card_3)]).

fof(t3_card_3,theorem,
    ( v1_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v1_card_3(k1_xboole_0) ),
    inference(conclusion,[status(thm),assumptions([])],[e3_6__card_3,i1_6__card_3]),
    [interesting(1),file(card_3,t3_card_3),[file(card_3,t3_card_3)]]).