% Mizar ND problem: t5_funct_6,funct_6,124,58 
fof(dh_c1_5__funct_6,definition,
    ( ( ~ v1_xboole_0(c1_5__funct_6)
     => ! [A] : 
          ( ~ v1_xboole_0(A)
         => k4_card_3(k10_finseq_1(c1_5__funct_6,A)) = a_2_0_funct_6(c1_5__funct_6,A) ) )
   => ! [B] : 
        ( ~ v1_xboole_0(B)
       => ! [C] : 
            ( ~ v1_xboole_0(C)
           => k4_card_3(k10_finseq_1(B,C)) = a_2_0_funct_6(B,C) ) ) ),
    introduced(definition,[new_symbol(c1_5__funct_6),file(funct_6,c1_5__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,c1_5__funct_6)]).

fof(dh_c2_5__funct_6,definition,
    ( ( ~ v1_xboole_0(c2_5__funct_6)
     => k4_card_3(k10_finseq_1(c1_5__funct_6,c2_5__funct_6)) = a_2_0_funct_6(c1_5__funct_6,c2_5__funct_6) )
   => ! [A] : 
        ( ~ v1_xboole_0(A)
       => k4_card_3(k10_finseq_1(c1_5__funct_6,A)) = a_2_0_funct_6(c1_5__funct_6,A) ) ),
    introduced(definition,[new_symbol(c2_5__funct_6),file(funct_6,c2_5__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,c2_5__funct_6)]).

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_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(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(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_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_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(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(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_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(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(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(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

fof(dt_k10_finseq_1,axiom,(
    $true ),
    file(finseq_1,k10_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k10_finseq_1)]).

fof(dt_k4_card_3,axiom,(
    $true ),
    file(card_3,k4_card_3),
    [interesting(0.9),axiom,file(card_3,k4_card_3)]).

fof(dt_c1_5__funct_6,assumption,(
    ~ v1_xboole_0(c1_5__funct_6) ),
    introduced(assumption,[file(funct_6,c1_5__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,c1_5__funct_6)]).

fof(dt_c2_5__funct_6,assumption,(
    ~ v1_xboole_0(c2_5__funct_6) ),
    introduced(assumption,[file(funct_6,c2_5__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,c2_5__funct_6)]).

fof(fc5_finseq_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(k10_finseq_1(A,B))
      & v1_funct_1(k10_finseq_1(A,B)) ) ),
    file(finseq_1,fc5_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc5_finseq_1)]).

fof(fc7_finseq_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(k10_finseq_1(A,B))
      & v1_funct_1(k10_finseq_1(A,B))
      & v1_finset_1(k10_finseq_1(A,B))
      & v1_finseq_1(k10_finseq_1(A,B)) ) ),
    file(finseq_1,fc7_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc7_finseq_1)]).

fof(t2_tarski,theorem,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    [interesting(0.9),axiom,file(tarski,t2_tarski)]).

fof(fraenkel_a_2_0_funct_6,definition,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C) )
     => ( r2_hidden(A,a_2_0_funct_6(B,C))
      <=> ? [D,E] : 
            ( m1_subset_1(D,B)
            & m1_subset_1(E,C)
            & A = k10_finseq_1(D,E) ) ) ) ),
    file(funct_6,a_2_0_funct_6),
    [interesting(0.9),axiom,file(funct_6,a_2_0_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(dt_c1_5_1__funct_6,assumption,(
    $true ),
    introduced(assumption,[file(funct_6,c1_5_1__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,c1_5_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_5_1__funct_6,definition,
    ( ~ ( r2_hidden(c1_5_1__funct_6,k4_card_3(k10_finseq_1(c1_5__funct_6,c2_5__funct_6)))
        & ~ r2_hidden(c1_5_1__funct_6,a_2_0_funct_6(c1_5__funct_6,c2_5__funct_6)) )
   => ! [A] : 
        ~ ( r2_hidden(A,k4_card_3(k10_finseq_1(c1_5__funct_6,c2_5__funct_6)))
          & ~ r2_hidden(A,a_2_0_funct_6(c1_5__funct_6,c2_5__funct_6)) ) ),
    introduced(definition,[new_symbol(c1_5_1__funct_6),file(funct_6,c1_5_1__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,c1_5_1__funct_6)]).

fof(e1_5_1__funct_6,assumption,(
    r2_hidden(c1_5_1__funct_6,k4_card_3(k10_finseq_1(c1_5__funct_6,c2_5__funct_6))) ),
    introduced(assumption,[file(funct_6,e1_5_1__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,e1_5_1__funct_6)]).

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(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(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(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(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(t2_funct_6,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(A,k4_card_3(k10_finseq_1(B,C)))
    <=> ? [D,E] : 
          ( r2_hidden(D,B)
          & r2_hidden(E,C)
          & A = k10_finseq_1(D,E) ) ) ),
    file(funct_6,t2_funct_6),
    [interesting(0.9),axiom,file(funct_6,t2_funct_6)]).

fof(e2_5_1__funct_6,plain,(
    ? [A,B] : 
      ( r2_hidden(A,c1_5__funct_6)
      & r2_hidden(B,c2_5__funct_6)
      & c1_5_1__funct_6 = k10_finseq_1(A,B) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__funct_6,dt_c1_5_1__funct_6,dt_c2_5__funct_6,e1_5_1__funct_6])],[rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc3_finseq_1,rc3_funct_1,rc6_finseq_1,existence_m1_subset_1,dt_m1_subset_1,cc1_finseq_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,rc1_finseq_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k10_finseq_1,dt_k4_card_3,dt_c1_5__funct_6,dt_c1_5_1__funct_6,dt_c2_5__funct_6,fc5_finseq_1,fc7_finseq_1,t1_subset,t7_boole,e1_5_1__funct_6,t2_funct_6]),
    [interesting(0.65),file(funct_6,e2_5_1__funct_6),[file(funct_6,e2_5_1__funct_6)]]).

fof(e3_5_1__funct_6,plain,(
    r2_hidden(c1_5_1__funct_6,a_2_0_funct_6(c1_5__funct_6,c2_5__funct_6)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__funct_6,dt_c1_5_1__funct_6,dt_c2_5__funct_6,e1_5_1__funct_6])],[rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc3_finseq_1,rc3_funct_1,rc6_finseq_1,existence_m1_subset_1,dt_m1_subset_1,cc1_finseq_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,rc1_finseq_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k10_finseq_1,dt_c1_5__funct_6,dt_c1_5_1__funct_6,dt_c2_5__funct_6,fc5_finseq_1,fc7_finseq_1,t1_subset,t7_boole,t2_tarski,fraenkel_a_2_0_funct_6,e2_5_1__funct_6]),
    [interesting(0.65),file(funct_6,e3_5_1__funct_6),[file(funct_6,e3_5_1__funct_6)]]).

fof(i3_5_1__funct_6,theorem,(
    $true ),
    introduced(tautology,[file(funct_6,i3_5_1__funct_6)]),
    [interesting(0.65),trivial,file(funct_6,i3_5_1__funct_6)]).

fof(i2_5_1__funct_6,plain,(
    r2_hidden(c1_5_1__funct_6,a_2_0_funct_6(c1_5__funct_6,c2_5__funct_6)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_5__funct_6,dt_c1_5_1__funct_6,dt_c2_5__funct_6,e1_5_1__funct_6])],[e3_5_1__funct_6,i3_5_1__funct_6]),
    [interesting(0.65),file(funct_6,i2_5_1__funct_6),[file(funct_6,i2_5_1__funct_6)]]).

fof(i1_5_1__funct_6,plain,(
    ~ ( r2_hidden(c1_5_1__funct_6,k4_card_3(k10_finseq_1(c1_5__funct_6,c2_5__funct_6)))
      & ~ r2_hidden(c1_5_1__funct_6,a_2_0_funct_6(c1_5__funct_6,c2_5__funct_6)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__funct_6,dt_c1_5_1__funct_6,dt_c2_5__funct_6]),discharge_asm(discharge,[e1_5_1__funct_6])],[e1_5_1__funct_6,i2_5_1__funct_6]),
    [interesting(0.65),file(funct_6,i1_5_1__funct_6),[file(funct_6,i1_5_1__funct_6)]]).

fof(i1_5_1_tmp__funct_6,plain,(
    ~ ( r2_hidden(c1_5_1__funct_6,k4_card_3(k10_finseq_1(c1_5__funct_6,c2_5__funct_6)))
      & ~ r2_hidden(c1_5_1__funct_6,a_2_0_funct_6(c1_5__funct_6,c2_5__funct_6)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__funct_6,dt_c2_5__funct_6]),discharge_asm(discharge,[dt_c1_5_1__funct_6])],[dt_c1_5_1__funct_6,i1_5_1__funct_6]),
    [interesting(0.8),e1_5__funct_6]).

fof(e1_5__funct_6,plain,(
    r1_tarski(k4_card_3(k10_finseq_1(c1_5__funct_6,c2_5__funct_6)),a_2_0_funct_6(c1_5__funct_6,c2_5__funct_6)) ),
    inference(let,[status(thm),assumptions([dt_c1_5__funct_6,dt_c2_5__funct_6])],[i1_5_1_tmp__funct_6,rc3_finseq_1,rc3_funct_1,rc6_finseq_1,dt_m1_subset_1,cc1_finseq_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,rc1_finseq_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc7_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k10_finseq_1,dt_k4_card_3,dt_c1_5__funct_6,dt_c2_5__funct_6,fc5_finseq_1,fc7_finseq_1,t2_tarski,fraenkel_a_2_0_funct_6,d3_tarski,dh_c1_5_1__funct_6]),
    [interesting(0.8),file(funct_6,e1_5__funct_6),[file(funct_6,e1_5__funct_6)]]).

fof(dt_c3_5__funct_6,assumption,(
    $true ),
    introduced(assumption,[file(funct_6,c3_5__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,c3_5__funct_6)]).

fof(dh_c3_5__funct_6,definition,
    ( ~ ( r2_hidden(c3_5__funct_6,a_2_0_funct_6(c1_5__funct_6,c2_5__funct_6))
        & ~ r2_hidden(c3_5__funct_6,k4_card_3(k10_finseq_1(c1_5__funct_6,c2_5__funct_6))) )
   => ! [A] : 
        ~ ( r2_hidden(A,a_2_0_funct_6(c1_5__funct_6,c2_5__funct_6))
          & ~ r2_hidden(A,k4_card_3(k10_finseq_1(c1_5__funct_6,c2_5__funct_6))) ) ),
    introduced(definition,[new_symbol(c3_5__funct_6),file(funct_6,c3_5__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,c3_5__funct_6)]).

fof(e2_5__funct_6,assumption,(
    r2_hidden(c3_5__funct_6,a_2_0_funct_6(c1_5__funct_6,c2_5__funct_6)) ),
    introduced(assumption,[file(funct_6,e2_5__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,e2_5__funct_6)]).

fof(e3_5__funct_6,plain,(
    ? [A] : 
      ( m1_subset_1(A,c1_5__funct_6)
      & ? [B] : 
          ( m1_subset_1(B,c2_5__funct_6)
          & c3_5__funct_6 = k10_finseq_1(A,B) ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__funct_6,dt_c2_5__funct_6,dt_c3_5__funct_6,e2_5__funct_6])],[rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc3_finseq_1,rc3_funct_1,rc6_finseq_1,cc1_finseq_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,rc1_finseq_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k10_finseq_1,dt_m1_subset_1,dt_c1_5__funct_6,dt_c2_5__funct_6,dt_c3_5__funct_6,fc5_finseq_1,fc7_finseq_1,t1_subset,t7_boole,t2_tarski,fraenkel_a_2_0_funct_6,e2_5__funct_6]),
    [interesting(0.8),file(funct_6,e3_5__funct_6),[file(funct_6,e3_5__funct_6)]]).

fof(e4_5__funct_6,plain,(
    r2_hidden(c3_5__funct_6,k4_card_3(k10_finseq_1(c1_5__funct_6,c2_5__funct_6))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__funct_6,dt_c2_5__funct_6,dt_c3_5__funct_6,e2_5__funct_6])],[rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc3_finseq_1,rc3_funct_1,rc6_finseq_1,cc1_finseq_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,rc1_finseq_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k10_finseq_1,dt_k4_card_3,dt_m1_subset_1,dt_c1_5__funct_6,dt_c2_5__funct_6,dt_c3_5__funct_6,fc5_finseq_1,fc7_finseq_1,t1_subset,t7_boole,e3_5__funct_6,t2_funct_6]),
    [interesting(0.8),file(funct_6,e4_5__funct_6),[file(funct_6,e4_5__funct_6)]]).

fof(i6_5__funct_6,theorem,(
    $true ),
    introduced(tautology,[file(funct_6,i6_5__funct_6)]),
    [interesting(0.8),trivial,file(funct_6,i6_5__funct_6)]).

fof(i5_5__funct_6,plain,(
    r2_hidden(c3_5__funct_6,k4_card_3(k10_finseq_1(c1_5__funct_6,c2_5__funct_6))) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_5__funct_6,dt_c2_5__funct_6,dt_c3_5__funct_6,e2_5__funct_6])],[e4_5__funct_6,i6_5__funct_6]),
    [interesting(0.8),file(funct_6,i5_5__funct_6),[file(funct_6,i5_5__funct_6)]]).

fof(i4_5__funct_6,plain,(
    ~ ( r2_hidden(c3_5__funct_6,a_2_0_funct_6(c1_5__funct_6,c2_5__funct_6))
      & ~ r2_hidden(c3_5__funct_6,k4_card_3(k10_finseq_1(c1_5__funct_6,c2_5__funct_6))) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__funct_6,dt_c2_5__funct_6,dt_c3_5__funct_6]),discharge_asm(discharge,[e2_5__funct_6])],[e2_5__funct_6,i5_5__funct_6]),
    [interesting(0.8),file(funct_6,i4_5__funct_6),[file(funct_6,i4_5__funct_6)]]).

fof(i4_5_tmp__funct_6,plain,(
    ~ ( r2_hidden(c3_5__funct_6,a_2_0_funct_6(c1_5__funct_6,c2_5__funct_6))
      & ~ r2_hidden(c3_5__funct_6,k4_card_3(k10_finseq_1(c1_5__funct_6,c2_5__funct_6))) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__funct_6,dt_c2_5__funct_6]),discharge_asm(discharge,[dt_c3_5__funct_6])],[dt_c3_5__funct_6,i4_5__funct_6]),
    [interesting(0.8),i3_5__funct_6]).

fof(i3_5__funct_6,plain,(
    r1_tarski(a_2_0_funct_6(c1_5__funct_6,c2_5__funct_6),k4_card_3(k10_finseq_1(c1_5__funct_6,c2_5__funct_6))) ),
    inference(let,[status(thm),assumptions([dt_c1_5__funct_6,dt_c2_5__funct_6])],[i4_5_tmp__funct_6,rc3_finseq_1,rc3_funct_1,rc6_finseq_1,dt_m1_subset_1,cc1_finseq_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,rc1_finseq_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc7_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k10_finseq_1,dt_k4_card_3,dt_c1_5__funct_6,dt_c2_5__funct_6,fc5_finseq_1,fc7_finseq_1,t2_tarski,fraenkel_a_2_0_funct_6,d3_tarski,dh_c3_5__funct_6]),
    [interesting(0.8),file(funct_6,i3_5__funct_6),[file(funct_6,i3_5__funct_6)]]).

fof(i2_5__funct_6,plain,(
    k4_card_3(k10_finseq_1(c1_5__funct_6,c2_5__funct_6)) = a_2_0_funct_6(c1_5__funct_6,c2_5__funct_6) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_5__funct_6,dt_c2_5__funct_6])],[rc3_finseq_1,rc3_funct_1,rc6_finseq_1,antisymmetry_r2_hidden,dt_m1_subset_1,cc1_finseq_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,rc1_finseq_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc7_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,dt_k10_finseq_1,dt_k4_card_3,dt_c1_5__funct_6,dt_c2_5__funct_6,fc5_finseq_1,fc7_finseq_1,t2_tarski,fraenkel_a_2_0_funct_6,d10_xboole_0,e1_5__funct_6,i3_5__funct_6]),
    [interesting(0.8),file(funct_6,i2_5__funct_6),[file(funct_6,i2_5__funct_6)]]).

fof(i2_5_tmp__funct_6,plain,
    ( ~ v1_xboole_0(c2_5__funct_6)
   => k4_card_3(k10_finseq_1(c1_5__funct_6,c2_5__funct_6)) = a_2_0_funct_6(c1_5__funct_6,c2_5__funct_6) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__funct_6]),discharge_asm(discharge,[dt_c2_5__funct_6])],[dt_c2_5__funct_6,i2_5__funct_6]),
    [interesting(0.8),i1_5__funct_6]).

fof(i1_5__funct_6,plain,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => k4_card_3(k10_finseq_1(c1_5__funct_6,A)) = a_2_0_funct_6(c1_5__funct_6,A) ) ),
    inference(let,[status(thm),assumptions([dt_c1_5__funct_6])],[i2_5_tmp__funct_6,dh_c2_5__funct_6]),
    [interesting(0.8),file(funct_6,i1_5__funct_6),[file(funct_6,i1_5__funct_6)]]).

fof(i1_5_tmp__funct_6,plain,
    ( ~ v1_xboole_0(c1_5__funct_6)
   => ! [A] : 
        ( ~ v1_xboole_0(A)
       => k4_card_3(k10_finseq_1(c1_5__funct_6,A)) = a_2_0_funct_6(c1_5__funct_6,A) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_5__funct_6])],[dt_c1_5__funct_6,i1_5__funct_6]),
    [interesting(1),t5_funct_6]).

fof(t5_funct_6,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => k4_card_3(k10_finseq_1(A,B)) = a_2_0_funct_6(A,B) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_5_tmp__funct_6,dh_c1_5__funct_6]),
    [interesting(1),file(funct_6,t5_funct_6),[file(funct_6,t5_funct_6)]]).