% Mizar problem: t53_margrel1,margrel1,764,36 
fof(t53_margrel1,conjecture,(
    ! [A] : 
      ( ( ~ r2_hidden(k7_margrel1,A)
       => k14_margrel1(A) = k8_margrel1 )
      & ~ ( k14_margrel1(A) = k8_margrel1
          & r2_hidden(k7_margrel1,A) )
      & ( r2_hidden(k7_margrel1,A)
       => k14_margrel1(A) = k7_margrel1 )
      & ( k14_margrel1(A) = k7_margrel1
       => r2_hidden(k7_margrel1,A) ) ) ),
    inference(mizar_bg_added,[status(thm)],[rc1_margrel1,commutativity_k2_tarski,dt_k1_xboole_0,dt_k2_tarski,fc1_margrel1,fc3_subset_1,fc1_xboole_0,existence_m1_subset_1,dt_k6_margrel1,dt_m1_subset_1,fc3_margrel1,rc2_margrel1,cc1_margrel1,rc1_xboole_0,rc2_xboole_0,spc0_boole,spc1_boole,t2_subset,t6_boole,t8_boole,d12_margrel1,spc0_boole,spc1_boole,antisymmetry_r2_hidden,redefinition_k14_margrel1,dt_k13_margrel1,dt_k14_margrel1,dt_k7_margrel1,dt_k8_margrel1,fc6_margrel1,t1_subset,t7_boole,d13_margrel1,d14_margrel1,d18_margrel1]),
    [file(margrel1,t53_margrel1)]).

fof(rc1_margrel1,axiom,(
    ? [A] : v1_margrel1(A) ),
    file(margrel1,rc1_margrel1),
    []).

fof(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

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

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

fof(fc1_margrel1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_margrel1(k1_xboole_0) ),
    file(margrel1,fc1_margrel1),
    []).

fof(fc3_subset_1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_1),
    []).

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

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

fof(dt_k6_margrel1,axiom,(
    $true ),
    file(margrel1,k6_margrel1),
    []).

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

fof(fc3_margrel1,axiom,(
    ~ v1_xboole_0(k6_margrel1) ),
    file(margrel1,fc3_margrel1),
    []).

fof(rc2_margrel1,axiom,(
    ? [A] : v2_margrel1(A) ),
    file(margrel1,rc2_margrel1),
    []).

fof(cc1_margrel1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k6_margrel1)
     => v2_margrel1(A) ) ),
    file(margrel1,cc1_margrel1),
    []).

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

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

fof(spc0_boole,axiom,(
    v1_xboole_0(0) ),
    file(boole,spc0_boole),
    []).

fof(spc1_boole,axiom,(
    ~ v1_xboole_0(1) ),
    file(boole,spc1_boole),
    []).

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

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

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

fof(d12_margrel1,axiom,(
    k6_margrel1 = k2_tarski(0,1) ),
    file(margrel1,d12_margrel1),
    []).

fof(spc0_boole,axiom,(
    v1_xboole_0(0) ),
    file(boole,spc0_boole),
    []).

fof(spc1_boole,axiom,(
    ~ v1_xboole_0(1) ),
    file(boole,spc1_boole),
    []).

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

fof(redefinition_k14_margrel1,axiom,(
    ! [A] : k14_margrel1(A) = k13_margrel1(A) ),
    file(margrel1,k14_margrel1),
    []).

fof(dt_k13_margrel1,axiom,(
    $true ),
    file(margrel1,k13_margrel1),
    []).

fof(dt_k14_margrel1,axiom,(
    ! [A] : m1_subset_1(k14_margrel1(A),k6_margrel1) ),
    file(margrel1,k14_margrel1),
    []).

fof(dt_k7_margrel1,axiom,(
    m1_subset_1(k7_margrel1,k6_margrel1) ),
    file(margrel1,k7_margrel1),
    []).

fof(dt_k8_margrel1,axiom,(
    m1_subset_1(k8_margrel1,k6_margrel1) ),
    file(margrel1,k8_margrel1),
    []).

fof(fc6_margrel1,axiom,(
    ! [A] : v2_margrel1(k13_margrel1(A)) ),
    file(margrel1,fc6_margrel1),
    []).

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

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

fof(d13_margrel1,axiom,(
    k7_margrel1 = 0 ),
    file(margrel1,d13_margrel1),
    []).

fof(d14_margrel1,axiom,(
    k8_margrel1 = 1 ),
    file(margrel1,d14_margrel1),
    []).

fof(d18_margrel1,axiom,(
    ! [A] : 
      ( ( ~ r2_hidden(k7_margrel1,A)
       => k13_margrel1(A) = k8_margrel1 )
      & ( r2_hidden(k7_margrel1,A)
       => k13_margrel1(A) = k7_margrel1 ) ) ),
    file(margrel1,d18_margrel1),
    []).