% Mizar ND problem: t90_funct_6,funct_6,2541,58 
fof(dh_c1_99__funct_6,definition,
    ( ( ( v1_relat_1(c1_99__funct_6)
        & v1_funct_1(c1_99__funct_6)
        & v1_funcop_1(c1_99__funct_6) )
     => k1_relat_1(k3_funct_6(c1_99__funct_6)) = k1_relat_1(c1_99__funct_6) )
   => ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A)
          & v1_funcop_1(A) )
       => k1_relat_1(k3_funct_6(A)) = k1_relat_1(A) ) ),
    introduced(definition,[new_symbol(c1_99__funct_6),file(funct_6,c1_99__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,c1_99__funct_6)]).

fof(rc1_funcop_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_funcop_1(A) ) ),
    file(funcop_1,rc1_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,rc1_funcop_1)]).

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(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    [interesting(0.9),axiom,file(relat_1,k1_relat_1)]).

fof(dt_k3_funct_6,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k3_funct_6(A))
        & v1_funct_1(k3_funct_6(A)) ) ) ),
    file(funct_6,k3_funct_6),
    [interesting(0.9),axiom,file(funct_6,k3_funct_6)]).

fof(dt_c1_99__funct_6,assumption,
    ( v1_relat_1(c1_99__funct_6)
    & v1_funct_1(c1_99__funct_6)
    & v1_funcop_1(c1_99__funct_6) ),
    introduced(assumption,[file(funct_6,c1_99__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,c1_99__funct_6)]).

fof(d10_xboole_0,definition,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,d10_xboole_0)]).

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_c1_99_1__funct_6,assumption,(
    $true ),
    introduced(assumption,[file(funct_6,c1_99_1__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,c1_99_1__funct_6)]).

fof(d3_tarski,definition,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    [interesting(0.9),axiom,file(tarski,d3_tarski)]).

fof(dh_c1_99_1__funct_6,definition,
    ( ~ ( r2_hidden(c1_99_1__funct_6,k1_relat_1(k3_funct_6(c1_99__funct_6)))
        & ~ r2_hidden(c1_99_1__funct_6,k1_relat_1(c1_99__funct_6)) )
   => ! [A] : 
        ~ ( r2_hidden(A,k1_relat_1(k3_funct_6(c1_99__funct_6)))
          & ~ r2_hidden(A,k1_relat_1(c1_99__funct_6)) ) ),
    introduced(definition,[new_symbol(c1_99_1__funct_6),file(funct_6,c1_99_1__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,c1_99_1__funct_6)]).

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(fc11_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k2_relat_1(A)) ) ),
    file(finseq_1,fc11_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc11_finseq_1)]).

fof(fc17_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k1_relat_1(A)) ) ),
    file(finseq_1,fc17_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc17_finseq_1)]).

fof(fc18_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k10_relat_1(A,B)) ) ),
    file(finseq_1,fc18_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc18_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(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(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(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(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

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(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(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(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(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(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_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(fc5_relat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k1_relat_1(A)) ) ),
    file(relat_1,fc5_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc5_relat_1)]).

fof(fc6_relat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k2_relat_1(A)) ) ),
    file(relat_1,fc6_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc6_relat_1)]).

fof(fc7_funcop_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => ( v1_relat_1(k1_funct_1(A,B))
        & v1_funct_1(k1_funct_1(A,B)) ) ) ),
    file(funcop_1,fc7_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,fc7_funcop_1)]).

fof(fc7_relat_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k1_relat_1(A))
        & v1_relat_1(k1_relat_1(A)) ) ) ),
    file(relat_1,fc7_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc7_relat_1)]).

fof(fc8_relat_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k2_relat_1(A))
        & v1_relat_1(k2_relat_1(A)) ) ) ),
    file(relat_1,fc8_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc8_relat_1)]).

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_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(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(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_k10_relat_1,axiom,(
    $true ),
    file(relat_1,k10_relat_1),
    [interesting(0.9),axiom,file(relat_1,k10_relat_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_funct_6,axiom,(
    $true ),
    file(funct_6,k1_funct_6),
    [interesting(0.9),axiom,file(funct_6,k1_funct_6)]).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    [interesting(0.9),axiom,file(relat_1,k2_relat_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(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(dt_k2_funct_5,axiom,(
    $true ),
    file(funct_5,k2_funct_5),
    [interesting(0.9),axiom,file(funct_5,k2_funct_5)]).

fof(d3_funct_6,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( B = k3_funct_6(A)
          <=> ( k1_relat_1(B) = k10_relat_1(A,k1_funct_6(k2_relat_1(A)))
              & ! [C] : 
                  ( r2_hidden(C,k10_relat_1(A,k1_funct_6(k2_relat_1(A))))
                 => k1_funct_1(B,C) = k2_funct_5(k1_funct_1(A,C)) ) ) ) ) ) ),
    file(funct_6,d3_funct_6),
    [interesting(0.9),axiom,file(funct_6,d3_funct_6)]).

fof(e1_99_1__funct_6,plain,(
    k1_relat_1(k3_funct_6(c1_99__funct_6)) = k10_relat_1(c1_99__funct_6,k1_funct_6(k2_relat_1(c1_99__funct_6))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_99__funct_6])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,fc18_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc6_relat_1,fc7_funcop_1,fc7_relat_1,fc8_relat_1,rc1_funcop_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k10_relat_1,dt_k1_funct_1,dt_k1_funct_6,dt_k1_relat_1,dt_k2_funct_5,dt_k2_relat_1,dt_k3_funct_6,dt_c1_99__funct_6,rc1_funct_1,t1_subset,t7_boole,d3_funct_6]),
    [interesting(0.65),file(funct_6,e1_99_1__funct_6),[file(funct_6,e1_99_1__funct_6)]]).

fof(t28_funct_6,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r2_hidden(A,k10_relat_1(B,k1_funct_6(k2_relat_1(B))))
      <=> ( r2_hidden(A,k1_relat_1(B))
          & v1_relat_1(k1_funct_1(B,A))
          & v1_funct_1(k1_funct_1(B,A)) ) ) ) ),
    file(funct_6,t28_funct_6),
    [interesting(0.9),axiom,file(funct_6,t28_funct_6)]).

fof(e2_99_1__funct_6,plain,
    ( r2_hidden(c1_99_1__funct_6,k1_relat_1(k3_funct_6(c1_99__funct_6)))
   => r2_hidden(c1_99_1__funct_6,k1_relat_1(c1_99__funct_6)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_99_1__funct_6,dt_c1_99__funct_6])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,fc18_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc6_relat_1,fc7_funcop_1,fc7_relat_1,fc8_relat_1,rc1_funcop_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k10_relat_1,dt_k1_funct_1,dt_k1_funct_6,dt_k1_relat_1,dt_k2_relat_1,dt_k3_funct_6,dt_c1_99__funct_6,dt_c1_99_1__funct_6,rc1_funct_1,t1_subset,t7_boole,e1_99_1__funct_6,t28_funct_6]),
    [interesting(0.65),file(funct_6,e2_99_1__funct_6),[file(funct_6,e2_99_1__funct_6)]]).

fof(i2_99_1__funct_6,theorem,(
    $true ),
    introduced(tautology,[file(funct_6,i2_99_1__funct_6)]),
    [interesting(0.65),trivial,file(funct_6,i2_99_1__funct_6)]).

fof(i1_99_1__funct_6,plain,(
    ~ ( r2_hidden(c1_99_1__funct_6,k1_relat_1(k3_funct_6(c1_99__funct_6)))
      & ~ r2_hidden(c1_99_1__funct_6,k1_relat_1(c1_99__funct_6)) ) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_99_1__funct_6,dt_c1_99__funct_6])],[e2_99_1__funct_6,i2_99_1__funct_6]),
    [interesting(0.65),file(funct_6,i1_99_1__funct_6),[file(funct_6,i1_99_1__funct_6)]]).

fof(i1_99_1_tmp__funct_6,plain,(
    ~ ( r2_hidden(c1_99_1__funct_6,k1_relat_1(k3_funct_6(c1_99__funct_6)))
      & ~ r2_hidden(c1_99_1__funct_6,k1_relat_1(c1_99__funct_6)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_99__funct_6]),discharge_asm(discharge,[dt_c1_99_1__funct_6])],[dt_c1_99_1__funct_6,i1_99_1__funct_6]),
    [interesting(0.8),e1_99__funct_6]).

fof(e1_99__funct_6,plain,(
    r1_tarski(k1_relat_1(k3_funct_6(c1_99__funct_6)),k1_relat_1(c1_99__funct_6)) ),
    inference(let,[status(thm),assumptions([dt_c1_99__funct_6])],[i1_99_1_tmp__funct_6,rc1_funcop_1,rc1_funct_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_relat_1,dt_k3_funct_6,dt_c1_99__funct_6,d3_tarski,dh_c1_99_1__funct_6]),
    [interesting(0.8),file(funct_6,e1_99__funct_6),[file(funct_6,e1_99__funct_6)]]).

fof(dt_c1_99_2__funct_6,assumption,(
    $true ),
    introduced(assumption,[file(funct_6,c1_99_2__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,c1_99_2__funct_6)]).

fof(dh_c1_99_2__funct_6,definition,
    ( ~ ( r2_hidden(c1_99_2__funct_6,k1_relat_1(c1_99__funct_6))
        & ~ r2_hidden(c1_99_2__funct_6,k1_relat_1(k3_funct_6(c1_99__funct_6))) )
   => ! [A] : 
        ~ ( r2_hidden(A,k1_relat_1(c1_99__funct_6))
          & ~ r2_hidden(A,k1_relat_1(k3_funct_6(c1_99__funct_6))) ) ),
    introduced(definition,[new_symbol(c1_99_2__funct_6),file(funct_6,c1_99_2__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,c1_99_2__funct_6)]).

fof(e1_99_2__funct_6,assumption,(
    r2_hidden(c1_99_2__funct_6,k1_relat_1(c1_99__funct_6)) ),
    introduced(assumption,[file(funct_6,e1_99_2__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,e1_99_2__funct_6)]).

fof(e3_99_2__funct_6,plain,(
    k1_relat_1(k3_funct_6(c1_99__funct_6)) = k10_relat_1(c1_99__funct_6,k1_funct_6(k2_relat_1(c1_99__funct_6))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_99__funct_6])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,fc18_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc6_relat_1,fc7_funcop_1,fc7_relat_1,fc8_relat_1,rc1_funcop_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k10_relat_1,dt_k1_funct_1,dt_k1_funct_6,dt_k1_relat_1,dt_k2_funct_5,dt_k2_relat_1,dt_k3_funct_6,dt_c1_99__funct_6,rc1_funct_1,t1_subset,t7_boole,d3_funct_6]),
    [interesting(0.65),file(funct_6,e3_99_2__funct_6),[file(funct_6,e3_99_2__funct_6)]]).

fof(e2_99_2__funct_6,plain,
    ( v1_relat_1(k1_funct_1(c1_99__funct_6,c1_99_2__funct_6))
    & v1_funct_1(k1_funct_1(c1_99__funct_6,c1_99_2__funct_6)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_99__funct_6,dt_c1_99_2__funct_6])],[fc7_funcop_1,rc1_funcop_1,dt_k1_funct_1,dt_c1_99__funct_6,dt_c1_99_2__funct_6,rc1_funct_1]),
    [interesting(0.65),file(funct_6,e2_99_2__funct_6),[file(funct_6,e2_99_2__funct_6)]]).

fof(e4_99_2__funct_6,plain,(
    r2_hidden(c1_99_2__funct_6,k1_relat_1(k3_funct_6(c1_99__funct_6))) ),
    inference(mizar_by,[status(thm),assumptions([e1_99_2__funct_6,dt_c1_99__funct_6,dt_c1_99_2__funct_6])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,fc18_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc6_relat_1,fc7_funcop_1,fc7_relat_1,fc8_relat_1,rc1_funcop_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k10_relat_1,dt_k1_funct_1,dt_k1_funct_6,dt_k1_relat_1,dt_k2_relat_1,dt_k3_funct_6,dt_c1_99__funct_6,dt_c1_99_2__funct_6,rc1_funct_1,t1_subset,t7_boole,e3_99_2__funct_6,e1_99_2__funct_6,e2_99_2__funct_6,t28_funct_6]),
    [interesting(0.65),file(funct_6,e4_99_2__funct_6),[file(funct_6,e4_99_2__funct_6)]]).

fof(i3_99_2__funct_6,theorem,(
    $true ),
    introduced(tautology,[file(funct_6,i3_99_2__funct_6)]),
    [interesting(0.65),trivial,file(funct_6,i3_99_2__funct_6)]).

fof(i2_99_2__funct_6,plain,(
    r2_hidden(c1_99_2__funct_6,k1_relat_1(k3_funct_6(c1_99__funct_6))) ),
    inference(conclusion,[status(thm),assumptions([e1_99_2__funct_6,dt_c1_99__funct_6,dt_c1_99_2__funct_6])],[e4_99_2__funct_6,i3_99_2__funct_6]),
    [interesting(0.65),file(funct_6,i2_99_2__funct_6),[file(funct_6,i2_99_2__funct_6)]]).

fof(i1_99_2__funct_6,plain,(
    ~ ( r2_hidden(c1_99_2__funct_6,k1_relat_1(c1_99__funct_6))
      & ~ r2_hidden(c1_99_2__funct_6,k1_relat_1(k3_funct_6(c1_99__funct_6))) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_99__funct_6,dt_c1_99_2__funct_6]),discharge_asm(discharge,[e1_99_2__funct_6])],[e1_99_2__funct_6,i2_99_2__funct_6]),
    [interesting(0.65),file(funct_6,i1_99_2__funct_6),[file(funct_6,i1_99_2__funct_6)]]).

fof(i1_99_2_tmp__funct_6,plain,(
    ~ ( r2_hidden(c1_99_2__funct_6,k1_relat_1(c1_99__funct_6))
      & ~ r2_hidden(c1_99_2__funct_6,k1_relat_1(k3_funct_6(c1_99__funct_6))) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_99__funct_6]),discharge_asm(discharge,[dt_c1_99_2__funct_6])],[dt_c1_99_2__funct_6,i1_99_2__funct_6]),
    [interesting(0.8),e2_99__funct_6]).

fof(e2_99__funct_6,plain,(
    r1_tarski(k1_relat_1(c1_99__funct_6),k1_relat_1(k3_funct_6(c1_99__funct_6))) ),
    inference(let,[status(thm),assumptions([dt_c1_99__funct_6])],[i1_99_2_tmp__funct_6,rc1_funcop_1,rc1_funct_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_relat_1,dt_k3_funct_6,dt_c1_99__funct_6,d3_tarski,dh_c1_99_2__funct_6]),
    [interesting(0.8),file(funct_6,e2_99__funct_6),[file(funct_6,e2_99__funct_6)]]).

fof(i3_99__funct_6,theorem,(
    $true ),
    introduced(tautology,[file(funct_6,i3_99__funct_6)]),
    [interesting(0.8),trivial,file(funct_6,i3_99__funct_6)]).

fof(i2_99__funct_6,plain,(
    r1_tarski(k1_relat_1(c1_99__funct_6),k1_relat_1(k3_funct_6(c1_99__funct_6))) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_99__funct_6])],[e2_99__funct_6,i3_99__funct_6]),
    [interesting(0.8),file(funct_6,i2_99__funct_6),[file(funct_6,i2_99__funct_6)]]).

fof(i1_99__funct_6,plain,(
    k1_relat_1(k3_funct_6(c1_99__funct_6)) = k1_relat_1(c1_99__funct_6) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_99__funct_6])],[rc1_funcop_1,rc1_funct_1,reflexivity_r1_tarski,dt_k1_relat_1,dt_k3_funct_6,dt_c1_99__funct_6,d10_xboole_0,e1_99__funct_6,i2_99__funct_6]),
    [interesting(0.8),file(funct_6,i1_99__funct_6),[file(funct_6,i1_99__funct_6)]]).

fof(i1_99_tmp__funct_6,plain,
    ( ( v1_relat_1(c1_99__funct_6)
      & v1_funct_1(c1_99__funct_6)
      & v1_funcop_1(c1_99__funct_6) )
   => k1_relat_1(k3_funct_6(c1_99__funct_6)) = k1_relat_1(c1_99__funct_6) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_99__funct_6])],[dt_c1_99__funct_6,i1_99__funct_6]),
    [interesting(1),t90_funct_6]).

fof(t90_funct_6,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => k1_relat_1(k3_funct_6(A)) = k1_relat_1(A) ) ),
    inference(let,[status(thm),assumptions([])],[i1_99_tmp__funct_6,dh_c1_99__funct_6]),
    [interesting(1),file(funct_6,t90_funct_6),[file(funct_6,t90_funct_6)]]).