% Mizar ND problem: t5_grcat_1,grcat_1,113,46 
fof(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

fof(cc1_funct_2,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(funct_2,cc1_funct_2)]).

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(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,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),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_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(cc1_relset_1,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(relset_1,cc1_relset_1)]).

fof(cc5_funct_2,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(funct_2,cc5_funct_2)]).

fof(cc6_funct_2,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(funct_2,cc6_funct_2)]).

fof(fc1_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc1_subset_1)]).

fof(rc1_funct_2,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(funct_2,rc1_funct_2)]).

fof(rc1_subset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc1_subset_1)]).

fof(rc2_partfun1,theorem,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C) ) ),
    file(partfun1,rc2_partfun1),
    [interesting(0.9),axiom,file(partfun1,rc2_partfun1)]).

fof(rc2_subset_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc2_subset_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(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(t3_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    [interesting(0.9),axiom,file(subset,t3_subset)]).

fof(t4_subset,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    [interesting(0.9),axiom,file(subset,t4_subset)]).

fof(t5_subset,theorem,(
    ! [A,B,C] : 
      ~ ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C))
        & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    [interesting(0.9),axiom,file(subset,t5_subset)]).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(redefinition_m2_relset_1,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    [interesting(0.9),axiom,file(tarski,k1_tarski)]).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_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),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(fc2_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc2_subset_1)]).

fof(fc4_subset_1,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc4_subset_1)]).

fof(rc1_xboole_0,theorem,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc1_xboole_0)]).

fof(rc2_xboole_0,theorem,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc2_xboole_0)]).

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_binop_1,axiom,(
    $true ),
    file(binop_1,k1_binop_1),
    [interesting(0.9),axiom,file(binop_1,k1_binop_1)]).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    [interesting(0.9),axiom,file(funct_1,k1_funct_1)]).

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_midsp_1,axiom,
    ( v1_funct_1(k2_midsp_1)
    & v1_funct_2(k2_midsp_1,k2_zfmisc_1(k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0)),k1_tarski(k1_xboole_0))
    & m2_relset_1(k2_midsp_1,k2_zfmisc_1(k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0)),k1_tarski(k1_xboole_0)) ),
    file(midsp_1,k2_midsp_1),
    [interesting(0.9),axiom,file(midsp_1,k2_midsp_1)]).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    [interesting(0.9),axiom,file(tarski,k4_tarski)]).

fof(fc1_xboole_0,theorem,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,fc1_xboole_0)]).

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(d1_binop_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : k1_binop_1(A,B,C) = k1_funct_1(A,k4_tarski(B,C)) ) ),
    file(binop_1,d1_binop_1),
    [interesting(0.9),axiom,file(binop_1,d1_binop_1)]).

fof(t34_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k1_tarski(C),k1_tarski(D)))
    <=> ( A = C
        & B = D ) ) ),
    file(zfmisc_1,t34_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,t34_zfmisc_1)]).

fof(e2_6__grcat_1,plain,(
    r2_hidden(k4_tarski(k1_xboole_0,k1_xboole_0),k2_zfmisc_1(k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0))) ),
    inference(mizar_by,[status(thm),assumptions([])],[existence_m1_subset_1,dt_m1_subset_1,fc4_subset_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_k4_tarski,fc1_xboole_0,fc2_subset_1,t1_subset,t6_boole,t7_boole,t34_zfmisc_1]),
    [interesting(0.8),file(grcat_1,e2_6__grcat_1),[file(grcat_1,e2_6__grcat_1)]]).

fof(t65_funct_2,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,k1_tarski(B))
        & m2_relset_1(D,A,k1_tarski(B)) )
     => ( r2_hidden(C,A)
       => k1_funct_1(D,C) = B ) ) ),
    file(funct_2,t65_funct_2),
    [interesting(0.9),axiom,file(funct_2,t65_funct_2)]).

fof(e3_6__grcat_1,plain,(
    k1_funct_1(k2_midsp_1,k4_tarski(k1_xboole_0,k1_xboole_0)) = k1_xboole_0 ),
    inference(mizar_by,[status(thm),assumptions([])],[reflexivity_r1_tarski,cc1_funct_2,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,cc1_relset_1,cc5_funct_2,cc6_funct_2,fc1_subset_1,fc4_subset_1,rc1_funct_2,rc1_subset_1,rc1_xboole_0,rc2_partfun1,rc2_subset_1,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_tarski,dt_k1_xboole_0,dt_k2_midsp_1,dt_k2_zfmisc_1,dt_k4_tarski,dt_m2_relset_1,fc1_xboole_0,fc2_subset_1,t1_subset,t6_boole,t7_boole,e2_6__grcat_1,t65_funct_2]),
    [interesting(0.8),file(grcat_1,e3_6__grcat_1),[file(grcat_1,e3_6__grcat_1)]]).

fof(e4_6__grcat_1,plain,(
    k1_binop_1(k2_midsp_1,k1_xboole_0,k1_xboole_0) = k1_xboole_0 ),
    inference(mizar_by,[status(thm),assumptions([])],[reflexivity_r1_tarski,cc1_funct_2,antisymmetry_r2_hidden,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,cc1_relset_1,cc5_funct_2,cc6_funct_2,fc1_subset_1,rc1_funct_2,rc1_subset_1,rc2_partfun1,rc2_subset_1,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k2_zfmisc_1,dt_m2_relset_1,fc2_subset_1,fc4_subset_1,rc1_xboole_0,rc2_xboole_0,t7_boole,t8_boole,dt_k1_binop_1,dt_k1_funct_1,dt_k1_xboole_0,dt_k2_midsp_1,dt_k4_tarski,fc1_xboole_0,t6_boole,d1_binop_1,e3_6__grcat_1]),
    [interesting(0.8),file(grcat_1,e4_6__grcat_1),[file(grcat_1,e4_6__grcat_1)]]).

fof(dt_k7_vectsp_2,axiom,
    ( v1_funct_1(k7_vectsp_2)
    & v1_funct_2(k7_vectsp_2,k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0))
    & m2_relset_1(k7_vectsp_2,k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0)) ),
    file(vectsp_2,k7_vectsp_2),
    [interesting(0.9),axiom,file(vectsp_2,k7_vectsp_2)]).

fof(d1_tarski,definition,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    [interesting(0.9),axiom,file(tarski,d1_tarski)]).

fof(e1_6__grcat_1,plain,(
    r2_hidden(k1_xboole_0,k1_tarski(k1_xboole_0)) ),
    inference(mizar_by,[status(thm),assumptions([])],[existence_m1_subset_1,dt_m1_subset_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_tarski,dt_k1_xboole_0,fc1_xboole_0,fc2_subset_1,t1_subset,t6_boole,t7_boole,d1_tarski]),
    [interesting(0.8),file(grcat_1,e1_6__grcat_1),[file(grcat_1,e1_6__grcat_1)]]).

fof(e5_6__grcat_1,plain,(
    k1_funct_1(k7_vectsp_2,k1_xboole_0) = k1_xboole_0 ),
    inference(mizar_by,[status(thm),assumptions([])],[reflexivity_r1_tarski,cc1_funct_2,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,cc1_relset_1,cc5_funct_2,cc6_funct_2,fc1_subset_1,fc4_subset_1,rc1_funct_2,rc1_subset_1,rc1_xboole_0,rc2_partfun1,rc2_subset_1,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_tarski,dt_k1_xboole_0,dt_k7_vectsp_2,dt_m2_relset_1,fc1_xboole_0,fc2_subset_1,t1_subset,t6_boole,t7_boole,e1_6__grcat_1,t65_funct_2]),
    [interesting(0.8),file(grcat_1,e5_6__grcat_1),[file(grcat_1,e5_6__grcat_1)]]).

fof(dt_k8_vectsp_2,axiom,(
    m1_subset_1(k8_vectsp_2,k1_tarski(k1_xboole_0)) ),
    file(vectsp_2,k8_vectsp_2),
    [interesting(0.9),axiom,file(vectsp_2,k8_vectsp_2)]).

fof(e6_6__grcat_1,plain,(
    k8_vectsp_2 = k1_xboole_0 ),
    inference(mizar_by,[status(thm),assumptions([])],[existence_m1_subset_1,dt_m1_subset_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_tarski,dt_k1_xboole_0,dt_k8_vectsp_2,fc1_xboole_0,fc2_subset_1,t1_subset,t6_boole,t7_boole,d1_tarski]),
    [interesting(0.8),file(grcat_1,e6_6__grcat_1),[file(grcat_1,e6_6__grcat_1)]]).

fof(i3_6__grcat_1,theorem,(
    $true ),
    introduced(tautology,[file(grcat_1,i3_6__grcat_1)]),
    [interesting(0.8),trivial,file(grcat_1,i3_6__grcat_1)]).

fof(i2_6__grcat_1,plain,(
    k8_vectsp_2 = k1_xboole_0 ),
    inference(conclusion,[status(thm),assumptions([])],[e6_6__grcat_1,i3_6__grcat_1]),
    [interesting(0.8),file(grcat_1,i2_6__grcat_1),[file(grcat_1,i2_6__grcat_1)]]).

fof(i1_6__grcat_1,plain,
    ( k1_funct_1(k7_vectsp_2,k1_xboole_0) = k1_xboole_0
    & k8_vectsp_2 = k1_xboole_0 ),
    inference(conclusion,[status(thm),assumptions([])],[e5_6__grcat_1,i2_6__grcat_1]),
    [interesting(0.8),file(grcat_1,i1_6__grcat_1),[file(grcat_1,i1_6__grcat_1)]]).

fof(t5_grcat_1,theorem,
    ( k1_binop_1(k2_midsp_1,k1_xboole_0,k1_xboole_0) = k1_xboole_0
    & k1_funct_1(k7_vectsp_2,k1_xboole_0) = k1_xboole_0
    & k8_vectsp_2 = k1_xboole_0 ),
    inference(conclusion,[status(thm),assumptions([])],[e4_6__grcat_1,i1_6__grcat_1]),
    [interesting(1),file(grcat_1,t5_grcat_1),[file(grcat_1,t5_grcat_1)]]).