% Mizar ND problem: t7_eqrel_1,eqrel_1,100,33 
fof(dh_c1_6__eqrel_1,definition,
    ( ( v3_relat_2(k1_eqrel_1(c1_6__eqrel_1))
      & v8_relat_2(k1_eqrel_1(c1_6__eqrel_1))
      & v1_partfun1(k1_eqrel_1(c1_6__eqrel_1),c1_6__eqrel_1,c1_6__eqrel_1)
      & m2_relset_1(k1_eqrel_1(c1_6__eqrel_1),c1_6__eqrel_1,c1_6__eqrel_1) )
   => ! [A] : 
        ( v3_relat_2(k1_eqrel_1(A))
        & v8_relat_2(k1_eqrel_1(A))
        & v1_partfun1(k1_eqrel_1(A),A,A)
        & m2_relset_1(k1_eqrel_1(A),A,A) ) ),
    introduced(definition,[new_symbol(c1_6__eqrel_1),file(eqrel_1,c1_6__eqrel_1)]),
    [interesting(0.8),axiom,file(eqrel_1,c1_6__eqrel_1)]).

fof(cc1_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) ) ) ),
    file(finseq_1,cc1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,cc1_finseq_1)]).

fof(rc1_finseq_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc1_finseq_1)]).

fof(rc1_partfun1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A) ) ),
    file(partfun1,rc1_partfun1),
    [interesting(0.9),axiom,file(partfun1,rc1_partfun1)]).

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(rc3_finseq_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc3_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc3_finseq_1)]).

fof(rc6_finseq_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc6_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc6_finseq_1)]).

fof(rc7_finseq_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc7_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc7_finseq_1)]).

fof(rc8_finseq_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc8_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc8_finseq_1)]).

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

fof(fc2_finseq_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & 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_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0) ),
    file(finseq_1,fc2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc2_finseq_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(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(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

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_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_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(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(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(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(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_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k2_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(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(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(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_eqrel_1,axiom,(
    ! [A] : m2_relset_1(k1_eqrel_1(A),A,A) ),
    file(eqrel_1,k1_eqrel_1),
    [interesting(0.9),axiom,file(eqrel_1,k1_eqrel_1)]).

fof(dt_k3_relat_1,axiom,(
    $true ),
    file(relat_1,k3_relat_1),
    [interesting(0.9),axiom,file(relat_1,k3_relat_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(dt_c1_6__eqrel_1,assumption,(
    $true ),
    introduced(assumption,[file(eqrel_1,c1_6__eqrel_1)]),
    [interesting(0.8),axiom,file(eqrel_1,c1_6__eqrel_1)]).

fof(cc1_partfun1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v3_relat_2(A)
        & v8_relat_2(A) )
     => ( v1_relat_1(A)
        & v1_relat_2(A) ) ) ),
    file(partfun1,cc1_partfun1),
    [interesting(0.9),axiom,file(partfun1,cc1_partfun1)]).

fof(fc1_eqrel_1,theorem,(
    ! [A] : 
      ( v1_relat_1(k1_eqrel_1(A))
      & v1_relat_2(k1_eqrel_1(A))
      & v1_partfun1(k1_eqrel_1(A),A,A) ) ),
    file(eqrel_1,fc1_eqrel_1),
    [interesting(0.9),axiom,file(eqrel_1,fc1_eqrel_1)]).

fof(d1_eqrel_1,definition,(
    ! [A] : k1_eqrel_1(A) = k2_zfmisc_1(A,A) ),
    file(eqrel_1,d1_eqrel_1),
    [interesting(0.9),axiom,file(eqrel_1,d1_eqrel_1)]).

fof(t97_orders_1,theorem,(
    ! [A,B] : 
      ( ( v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => k3_relat_1(B) = A ) ),
    file(orders_1,t97_orders_1),
    [interesting(0.9),axiom,file(orders_1,t97_orders_1)]).

fof(e3_6__eqrel_1,plain,(
    k3_relat_1(k1_eqrel_1(c1_6__eqrel_1)) = c1_6__eqrel_1 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__eqrel_1])],[cc1_finseq_1,rc1_finseq_1,rc1_partfun1,rc2_partfun1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,fc2_finseq_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,fc4_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,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,fc1_subset_1,t3_subset,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_eqrel_1,dt_k3_relat_1,dt_m2_relset_1,dt_c1_6__eqrel_1,fc1_eqrel_1,d1_eqrel_1,t97_orders_1]),
    [interesting(0.8),file(eqrel_1,e3_6__eqrel_1),[file(eqrel_1,e3_6__eqrel_1)]]).

fof(commutativity_k2_tarski,theorem,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_tarski)]).

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

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_tarski)]).

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(fc3_subset_1,theorem,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc3_subset_1)]).

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

fof(d5_tarski,definition,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    [interesting(0.9),axiom,file(tarski,d5_tarski)]).

fof(t107_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D))
     => r2_hidden(k4_tarski(B,A),k2_zfmisc_1(D,C)) ) ),
    file(zfmisc_1,t107_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,t107_zfmisc_1)]).

fof(e1_6_1__eqrel_1,plain,(
    ! [A,B] : 
      ( ( r2_hidden(A,c1_6__eqrel_1)
        & r2_hidden(B,c1_6__eqrel_1)
        & r2_hidden(k4_tarski(A,B),k1_eqrel_1(c1_6__eqrel_1)) )
     => r2_hidden(k4_tarski(B,A),k1_eqrel_1(c1_6__eqrel_1)) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__eqrel_1])],[reflexivity_r1_tarski,cc1_finseq_1,rc1_finseq_1,rc1_partfun1,rc2_partfun1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,existence_m1_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc1_subset_1,fc2_finseq_1,rc1_subset_1,rc2_subset_1,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,dt_m2_relset_1,fc2_subset_1,fc3_subset_1,fc4_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_eqrel_1,dt_k2_zfmisc_1,dt_k4_tarski,dt_c1_6__eqrel_1,fc1_eqrel_1,t1_subset,t7_boole,d1_eqrel_1,d5_tarski,t107_zfmisc_1]),
    [interesting(0.65),file(eqrel_1,e1_6_1__eqrel_1),[file(eqrel_1,e1_6_1__eqrel_1)]]).

fof(d3_relat_2,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r3_relat_2(A,B)
        <=> ! [C,D] : 
              ( ( r2_hidden(C,B)
                & r2_hidden(D,B)
                & r2_hidden(k4_tarski(C,D),A) )
             => r2_hidden(k4_tarski(D,C),A) ) ) ) ),
    file(relat_2,d3_relat_2),
    [interesting(0.9),axiom,file(relat_2,d3_relat_2)]).

fof(e2_6_1__eqrel_1,plain,(
    r3_relat_2(k1_eqrel_1(c1_6__eqrel_1),c1_6__eqrel_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__eqrel_1])],[reflexivity_r1_tarski,cc1_finseq_1,rc1_finseq_1,rc1_partfun1,rc2_partfun1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,existence_m1_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc1_subset_1,fc2_finseq_1,rc1_subset_1,rc2_subset_1,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k2_tarski,dt_k2_zfmisc_1,dt_m1_subset_1,dt_m2_relset_1,fc2_subset_1,fc3_subset_1,fc4_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_eqrel_1,dt_k4_tarski,dt_c1_6__eqrel_1,fc1_eqrel_1,t1_subset,t7_boole,d1_eqrel_1,d5_tarski,e1_6_1__eqrel_1,d3_relat_2]),
    [interesting(0.65),file(eqrel_1,e2_6_1__eqrel_1),[file(eqrel_1,e2_6_1__eqrel_1)]]).

fof(i1_6_1__eqrel_1,theorem,(
    $true ),
    introduced(tautology,[file(eqrel_1,i1_6_1__eqrel_1)]),
    [interesting(0.65),trivial,file(eqrel_1,i1_6_1__eqrel_1)]).

fof(e1_6__eqrel_1,plain,(
    r3_relat_2(k1_eqrel_1(c1_6__eqrel_1),c1_6__eqrel_1) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_6__eqrel_1])],[e2_6_1__eqrel_1,i1_6_1__eqrel_1]),
    [interesting(0.8),file(eqrel_1,e1_6__eqrel_1),[file(eqrel_1,e1_6__eqrel_1)]]).

fof(t106_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D))
    <=> ( r2_hidden(A,C)
        & r2_hidden(B,D) ) ) ),
    file(zfmisc_1,t106_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,t106_zfmisc_1)]).

fof(e1_6_2__eqrel_1,plain,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,c1_6__eqrel_1)
        & r2_hidden(B,c1_6__eqrel_1)
        & r2_hidden(C,c1_6__eqrel_1)
        & r2_hidden(k4_tarski(A,B),k1_eqrel_1(c1_6__eqrel_1))
        & r2_hidden(k4_tarski(B,C),k1_eqrel_1(c1_6__eqrel_1)) )
     => r2_hidden(k4_tarski(A,C),k1_eqrel_1(c1_6__eqrel_1)) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__eqrel_1])],[reflexivity_r1_tarski,cc1_finseq_1,rc1_finseq_1,rc1_partfun1,rc2_partfun1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,existence_m1_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc1_subset_1,fc2_finseq_1,rc1_subset_1,rc2_subset_1,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,dt_m2_relset_1,fc2_subset_1,fc3_subset_1,fc4_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_eqrel_1,dt_k2_zfmisc_1,dt_k4_tarski,dt_c1_6__eqrel_1,fc1_eqrel_1,t1_subset,t7_boole,d1_eqrel_1,d5_tarski,t106_zfmisc_1]),
    [interesting(0.65),file(eqrel_1,e1_6_2__eqrel_1),[file(eqrel_1,e1_6_2__eqrel_1)]]).

fof(d8_relat_2,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r8_relat_2(A,B)
        <=> ! [C,D,E] : 
              ( ( r2_hidden(C,B)
                & r2_hidden(D,B)
                & r2_hidden(E,B)
                & r2_hidden(k4_tarski(C,D),A)
                & r2_hidden(k4_tarski(D,E),A) )
             => r2_hidden(k4_tarski(C,E),A) ) ) ) ),
    file(relat_2,d8_relat_2),
    [interesting(0.9),axiom,file(relat_2,d8_relat_2)]).

fof(e2_6_2__eqrel_1,plain,(
    r8_relat_2(k1_eqrel_1(c1_6__eqrel_1),c1_6__eqrel_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__eqrel_1])],[reflexivity_r1_tarski,cc1_finseq_1,rc1_finseq_1,rc1_partfun1,rc2_partfun1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,existence_m1_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc1_subset_1,fc2_finseq_1,rc1_subset_1,rc2_subset_1,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k2_tarski,dt_k2_zfmisc_1,dt_m1_subset_1,dt_m2_relset_1,fc2_subset_1,fc3_subset_1,fc4_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_eqrel_1,dt_k4_tarski,dt_c1_6__eqrel_1,fc1_eqrel_1,t1_subset,t7_boole,d1_eqrel_1,d5_tarski,e1_6_2__eqrel_1,d8_relat_2]),
    [interesting(0.65),file(eqrel_1,e2_6_2__eqrel_1),[file(eqrel_1,e2_6_2__eqrel_1)]]).

fof(i1_6_2__eqrel_1,theorem,(
    $true ),
    introduced(tautology,[file(eqrel_1,i1_6_2__eqrel_1)]),
    [interesting(0.65),trivial,file(eqrel_1,i1_6_2__eqrel_1)]).

fof(e2_6__eqrel_1,plain,(
    r8_relat_2(k1_eqrel_1(c1_6__eqrel_1),c1_6__eqrel_1) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_6__eqrel_1])],[e2_6_2__eqrel_1,i1_6_2__eqrel_1]),
    [interesting(0.8),file(eqrel_1,e2_6__eqrel_1),[file(eqrel_1,e2_6__eqrel_1)]]).

fof(d11_relat_2,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v3_relat_2(A)
      <=> r3_relat_2(A,k3_relat_1(A)) ) ) ),
    file(relat_2,d11_relat_2),
    [interesting(0.9),axiom,file(relat_2,d11_relat_2)]).

fof(d16_relat_2,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v8_relat_2(A)
      <=> r8_relat_2(A,k3_relat_1(A)) ) ) ),
    file(relat_2,d16_relat_2),
    [interesting(0.9),axiom,file(relat_2,d16_relat_2)]).

fof(e4_6__eqrel_1,plain,
    ( v3_relat_2(k1_eqrel_1(c1_6__eqrel_1))
    & v8_relat_2(k1_eqrel_1(c1_6__eqrel_1))
    & v1_partfun1(k1_eqrel_1(c1_6__eqrel_1),c1_6__eqrel_1,c1_6__eqrel_1)
    & m2_relset_1(k1_eqrel_1(c1_6__eqrel_1),c1_6__eqrel_1,c1_6__eqrel_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__eqrel_1])],[cc1_finseq_1,rc1_finseq_1,rc1_partfun1,rc2_partfun1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,fc2_finseq_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,fc4_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,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,fc1_subset_1,t3_subset,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_eqrel_1,dt_k3_relat_1,dt_m2_relset_1,dt_c1_6__eqrel_1,cc1_partfun1,fc1_eqrel_1,d1_eqrel_1,e3_6__eqrel_1,e1_6__eqrel_1,e2_6__eqrel_1,d11_relat_2,d16_relat_2]),
    [interesting(0.8),file(eqrel_1,e4_6__eqrel_1),[file(eqrel_1,e4_6__eqrel_1)]]).

fof(i2_6__eqrel_1,theorem,(
    $true ),
    introduced(tautology,[file(eqrel_1,i2_6__eqrel_1)]),
    [interesting(0.8),trivial,file(eqrel_1,i2_6__eqrel_1)]).

fof(i1_6__eqrel_1,plain,
    ( v3_relat_2(k1_eqrel_1(c1_6__eqrel_1))
    & v8_relat_2(k1_eqrel_1(c1_6__eqrel_1))
    & v1_partfun1(k1_eqrel_1(c1_6__eqrel_1),c1_6__eqrel_1,c1_6__eqrel_1)
    & m2_relset_1(k1_eqrel_1(c1_6__eqrel_1),c1_6__eqrel_1,c1_6__eqrel_1) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_6__eqrel_1])],[e4_6__eqrel_1,i2_6__eqrel_1]),
    [interesting(0.8),file(eqrel_1,i1_6__eqrel_1),[file(eqrel_1,i1_6__eqrel_1)]]).

fof(i1_6_tmp__eqrel_1,plain,
    ( v3_relat_2(k1_eqrel_1(c1_6__eqrel_1))
    & v8_relat_2(k1_eqrel_1(c1_6__eqrel_1))
    & v1_partfun1(k1_eqrel_1(c1_6__eqrel_1),c1_6__eqrel_1,c1_6__eqrel_1)
    & m2_relset_1(k1_eqrel_1(c1_6__eqrel_1),c1_6__eqrel_1,c1_6__eqrel_1) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_6__eqrel_1])],[dt_c1_6__eqrel_1,i1_6__eqrel_1]),
    [interesting(1),t7_eqrel_1]).

fof(t7_eqrel_1,theorem,(
    ! [A] : 
      ( v3_relat_2(k1_eqrel_1(A))
      & v8_relat_2(k1_eqrel_1(A))
      & v1_partfun1(k1_eqrel_1(A),A,A)
      & m2_relset_1(k1_eqrel_1(A),A,A) ) ),
    inference(let,[status(thm),assumptions([])],[i1_6_tmp__eqrel_1,dh_c1_6__eqrel_1]),
    [interesting(1),file(eqrel_1,t7_eqrel_1),[file(eqrel_1,t7_eqrel_1)]]).