% Mizar ND problem: t2_rfinseq,rfinseq,84,33 
fof(dh_c1_4__rfinseq,definition,
    ( ( ( v1_relat_1(c1_4__rfinseq)
        & v1_funct_1(c1_4__rfinseq) )
     => ! [A] : 
          ( ( v1_relat_1(A)
            & v1_funct_1(A) )
         => ! [B] : 
              ( ( v1_relat_1(B)
                & v1_funct_1(B) )
             => ( ( r1_rfinseq(c1_4__rfinseq,A)
                  & r1_rfinseq(c1_4__rfinseq,B) )
               => r1_rfinseq(A,B) ) ) ) )
   => ! [C] : 
        ( ( v1_relat_1(C)
          & v1_funct_1(C) )
       => ! [D] : 
            ( ( v1_relat_1(D)
              & v1_funct_1(D) )
           => ! [E] : 
                ( ( v1_relat_1(E)
                  & v1_funct_1(E) )
               => ( ( r1_rfinseq(C,D)
                    & r1_rfinseq(C,E) )
                 => r1_rfinseq(D,E) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_4__rfinseq),file(rfinseq,c1_4__rfinseq)]),
    [interesting(0.8),axiom,file(rfinseq,c1_4__rfinseq)]).

fof(dh_c2_4__rfinseq,definition,
    ( ( ( v1_relat_1(c2_4__rfinseq)
        & v1_funct_1(c2_4__rfinseq) )
     => ! [A] : 
          ( ( v1_relat_1(A)
            & v1_funct_1(A) )
         => ( ( r1_rfinseq(c1_4__rfinseq,c2_4__rfinseq)
              & r1_rfinseq(c1_4__rfinseq,A) )
           => r1_rfinseq(c2_4__rfinseq,A) ) ) )
   => ! [B] : 
        ( ( v1_relat_1(B)
          & v1_funct_1(B) )
       => ! [C] : 
            ( ( v1_relat_1(C)
              & v1_funct_1(C) )
           => ( ( r1_rfinseq(c1_4__rfinseq,B)
                & r1_rfinseq(c1_4__rfinseq,C) )
             => r1_rfinseq(B,C) ) ) ) ),
    introduced(definition,[new_symbol(c2_4__rfinseq),file(rfinseq,c2_4__rfinseq)]),
    [interesting(0.8),axiom,file(rfinseq,c2_4__rfinseq)]).

fof(dh_c3_4__rfinseq,definition,
    ( ( ( v1_relat_1(c3_4__rfinseq)
        & v1_funct_1(c3_4__rfinseq) )
     => ( ( r1_rfinseq(c1_4__rfinseq,c2_4__rfinseq)
          & r1_rfinseq(c1_4__rfinseq,c3_4__rfinseq) )
       => r1_rfinseq(c2_4__rfinseq,c3_4__rfinseq) ) )
   => ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A) )
       => ( ( r1_rfinseq(c1_4__rfinseq,c2_4__rfinseq)
            & r1_rfinseq(c1_4__rfinseq,A) )
         => r1_rfinseq(c2_4__rfinseq,A) ) ) ),
    introduced(definition,[new_symbol(c3_4__rfinseq),file(rfinseq,c3_4__rfinseq)]),
    [interesting(0.8),axiom,file(rfinseq,c3_4__rfinseq)]).

fof(e1_4__rfinseq,assumption,
    ( r1_rfinseq(c1_4__rfinseq,c2_4__rfinseq)
    & r1_rfinseq(c1_4__rfinseq,c3_4__rfinseq) ),
    introduced(assumption,[file(rfinseq,e1_4__rfinseq)]),
    [interesting(0.8),axiom,file(rfinseq,e1_4__rfinseq)]).

fof(cc1_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    [interesting(0.9),axiom,file(membered,cc1_membered)]).

fof(cc2_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    [interesting(0.9),axiom,file(membered,cc2_membered)]).

fof(cc3_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    [interesting(0.9),axiom,file(membered,cc3_membered)]).

fof(cc4_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    [interesting(0.9),axiom,file(membered,cc4_membered)]).

fof(rc1_membered,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    [interesting(0.9),axiom,file(membered,rc1_membered)]).

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(cc15_membered,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    [interesting(0.9),axiom,file(membered,cc15_membered)]).

fof(cc1_finset_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,cc1_finset_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(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(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_finset_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A) ) ),
    file(finset_1,rc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc1_finset_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(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(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(symmetry_r1_rfinseq,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => ( r1_rfinseq(A,B)
       => r1_rfinseq(B,A) ) ) ),
    file(rfinseq,r1_rfinseq),
    [interesting(0.9),axiom,file(rfinseq,r1_rfinseq)]).

fof(reflexivity_r1_rfinseq,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => r1_rfinseq(A,A) ) ),
    file(rfinseq,r1_rfinseq),
    [interesting(0.9),axiom,file(rfinseq,r1_rfinseq)]).

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_card_1,axiom,(
    ! [A] : v1_card_1(k1_card_1(A)) ),
    file(card_1,k1_card_1),
    [interesting(0.9),axiom,file(card_1,k1_card_1)]).

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

fof(dt_c2_4__rfinseq,assumption,
    ( v1_relat_1(c2_4__rfinseq)
    & v1_funct_1(c2_4__rfinseq) ),
    introduced(assumption,[file(rfinseq,c2_4__rfinseq)]),
    [interesting(0.8),axiom,file(rfinseq,c2_4__rfinseq)]).

fof(dt_c3_4__rfinseq,assumption,
    ( v1_relat_1(c3_4__rfinseq)
    & v1_funct_1(c3_4__rfinseq) ),
    introduced(assumption,[file(rfinseq,c3_4__rfinseq)]),
    [interesting(0.8),axiom,file(rfinseq,c3_4__rfinseq)]).

fof(dt_c4_4__rfinseq,assumption,(
    $true ),
    introduced(assumption,[file(rfinseq,c4_4__rfinseq)]),
    [interesting(0.8),axiom,file(rfinseq,c4_4__rfinseq)]).

fof(fc1_finset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A)) ) ),
    file(finset_1,fc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc1_finset_1)]).

fof(d1_rfinseq,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_rfinseq(A,B)
          <=> ! [C] : k1_card_1(k10_relat_1(A,k1_tarski(C))) = k1_card_1(k10_relat_1(B,k1_tarski(C))) ) ) ) ),
    file(rfinseq,d1_rfinseq),
    [interesting(0.9),axiom,file(rfinseq,d1_rfinseq)]).

fof(dh_c4_4__rfinseq,definition,
    ( k1_card_1(k10_relat_1(c2_4__rfinseq,k1_tarski(c4_4__rfinseq))) = k1_card_1(k10_relat_1(c3_4__rfinseq,k1_tarski(c4_4__rfinseq)))
   => ! [A] : k1_card_1(k10_relat_1(c2_4__rfinseq,k1_tarski(A))) = k1_card_1(k10_relat_1(c3_4__rfinseq,k1_tarski(A))) ),
    introduced(definition,[new_symbol(c4_4__rfinseq),file(rfinseq,c4_4__rfinseq)]),
    [interesting(0.8),axiom,file(rfinseq,c4_4__rfinseq)]).

fof(cc3_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc3_nat_1),
    [interesting(0.9),axiom,file(nat_1,cc3_nat_1)]).

fof(fc10_membered,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A))
        & v4_membered(k1_tarski(A)) ) ) ),
    file(membered,fc10_membered),
    [interesting(0.9),axiom,file(membered,fc10_membered)]).

fof(fc11_membered,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A))
        & v4_membered(k1_tarski(A))
        & v5_membered(k1_tarski(A)) ) ) ),
    file(membered,fc11_membered),
    [interesting(0.9),axiom,file(membered,fc11_membered)]).

fof(fc7_membered,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => v1_membered(k1_tarski(A)) ) ),
    file(membered,fc7_membered),
    [interesting(0.9),axiom,file(membered,fc7_membered)]).

fof(fc8_membered,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A)) ) ) ),
    file(membered,fc8_membered),
    [interesting(0.9),axiom,file(membered,fc8_membered)]).

fof(fc9_membered,theorem,(
    ! [A] : 
      ( v1_rat_1(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A)) ) ) ),
    file(membered,fc9_membered),
    [interesting(0.9),axiom,file(membered,fc9_membered)]).

fof(rc1_nat_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc1_nat_1),
    [interesting(0.9),axiom,file(nat_1,rc1_nat_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(cc10_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    [interesting(0.9),axiom,file(membered,cc10_membered)]).

fof(cc11_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    [interesting(0.9),axiom,file(membered,cc11_membered)]).

fof(cc12_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc12_membered),
    [interesting(0.9),axiom,file(membered,cc12_membered)]).

fof(cc13_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc13_membered),
    [interesting(0.9),axiom,file(membered,cc13_membered)]).

fof(cc14_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v4_ordinal2(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc14_membered),
    [interesting(0.9),axiom,file(membered,cc14_membered)]).

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(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(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(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(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(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(fc6_membered,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0) ),
    file(membered,fc6_membered),
    [interesting(0.9),axiom,file(membered,fc6_membered)]).

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(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(dt_c1_4__rfinseq,assumption,
    ( v1_relat_1(c1_4__rfinseq)
    & v1_funct_1(c1_4__rfinseq) ),
    introduced(assumption,[file(rfinseq,c1_4__rfinseq)]),
    [interesting(0.8),axiom,file(rfinseq,c1_4__rfinseq)]).

fof(e1_4_1__rfinseq,plain,(
    k1_card_1(k10_relat_1(c2_4__rfinseq,k1_tarski(c4_4__rfinseq))) = k1_card_1(k10_relat_1(c1_4__rfinseq,k1_tarski(c4_4__rfinseq))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__rfinseq,dt_c2_4__rfinseq,dt_c3_4__rfinseq,dt_c4_4__rfinseq,e1_4__rfinseq])],[cc3_nat_1,fc10_membered,fc11_membered,fc7_membered,fc8_membered,fc9_membered,rc1_nat_1,existence_m1_subset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_finseq_1,rc1_finseq_1,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,t2_subset,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc2_finseq_1,fc6_membered,rc1_membered,rc3_funct_1,rc6_finseq_1,t1_subset,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_funct_1,fc18_finseq_1,rc1_finset_1,rc1_funct_1,rc2_funct_1,rc7_finseq_1,t6_boole,t7_boole,t8_boole,symmetry_r1_rfinseq,reflexivity_r1_rfinseq,dt_k10_relat_1,dt_k1_card_1,dt_k1_tarski,dt_c1_4__rfinseq,dt_c2_4__rfinseq,dt_c3_4__rfinseq,dt_c4_4__rfinseq,fc1_finset_1,e1_4__rfinseq,d1_rfinseq]),
    [interesting(0.65),file(rfinseq,e1_4_1__rfinseq),[file(rfinseq,e1_4_1__rfinseq)]]).

fof(e2_4_1__rfinseq,plain,(
    k1_card_1(k10_relat_1(c1_4__rfinseq,k1_tarski(c4_4__rfinseq))) = k1_card_1(k10_relat_1(c3_4__rfinseq,k1_tarski(c4_4__rfinseq))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__rfinseq,dt_c2_4__rfinseq,dt_c3_4__rfinseq,dt_c4_4__rfinseq,e1_4__rfinseq])],[cc3_nat_1,fc10_membered,fc11_membered,fc7_membered,fc8_membered,fc9_membered,rc1_nat_1,existence_m1_subset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_finseq_1,rc1_finseq_1,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,t2_subset,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc2_finseq_1,fc6_membered,rc1_membered,rc3_funct_1,rc6_finseq_1,t1_subset,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_funct_1,fc18_finseq_1,rc1_finset_1,rc1_funct_1,rc2_funct_1,rc7_finseq_1,t6_boole,t7_boole,t8_boole,symmetry_r1_rfinseq,reflexivity_r1_rfinseq,dt_k10_relat_1,dt_k1_card_1,dt_k1_tarski,dt_c1_4__rfinseq,dt_c2_4__rfinseq,dt_c3_4__rfinseq,dt_c4_4__rfinseq,fc1_finset_1,e1_4__rfinseq,d1_rfinseq]),
    [interesting(0.65),file(rfinseq,e2_4_1__rfinseq),[file(rfinseq,e2_4_1__rfinseq)]]).

fof(e2_4__rfinseq,plain,(
    k1_card_1(k10_relat_1(c2_4__rfinseq,k1_tarski(c4_4__rfinseq))) = k1_card_1(k10_relat_1(c3_4__rfinseq,k1_tarski(c4_4__rfinseq))) ),
    inference(iterative_eq,[status(thm),assumptions([dt_c1_4__rfinseq,dt_c2_4__rfinseq,dt_c3_4__rfinseq,dt_c4_4__rfinseq,e1_4__rfinseq])],[e1_4_1__rfinseq,e2_4_1__rfinseq]),
    [interesting(0.8),file(rfinseq,e2_4__rfinseq),[file(rfinseq,e2_4__rfinseq)]]).

fof(i4_4__rfinseq,theorem,(
    $true ),
    introduced(tautology,[file(rfinseq,i4_4__rfinseq)]),
    [interesting(0.8),trivial,file(rfinseq,i4_4__rfinseq)]).

fof(i3_4__rfinseq,plain,(
    k1_card_1(k10_relat_1(c2_4__rfinseq,k1_tarski(c4_4__rfinseq))) = k1_card_1(k10_relat_1(c3_4__rfinseq,k1_tarski(c4_4__rfinseq))) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_4__rfinseq,dt_c2_4__rfinseq,dt_c3_4__rfinseq,dt_c4_4__rfinseq,e1_4__rfinseq])],[e2_4__rfinseq,i4_4__rfinseq]),
    [interesting(0.8),file(rfinseq,i3_4__rfinseq),[file(rfinseq,i3_4__rfinseq)]]).

fof(i3_4_tmp__rfinseq,plain,(
    k1_card_1(k10_relat_1(c2_4__rfinseq,k1_tarski(c4_4__rfinseq))) = k1_card_1(k10_relat_1(c3_4__rfinseq,k1_tarski(c4_4__rfinseq))) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_4__rfinseq,dt_c2_4__rfinseq,dt_c3_4__rfinseq,e1_4__rfinseq]),discharge_asm(discharge,[dt_c4_4__rfinseq])],[dt_c4_4__rfinseq,i3_4__rfinseq]),
    [interesting(0.8),i2_4__rfinseq]).

fof(i2_4__rfinseq,plain,(
    r1_rfinseq(c2_4__rfinseq,c3_4__rfinseq) ),
    inference(let,[status(thm),assumptions([dt_c1_4__rfinseq,dt_c2_4__rfinseq,dt_c3_4__rfinseq,e1_4__rfinseq])],[i3_4_tmp__rfinseq,cc1_membered,cc2_membered,cc3_membered,cc4_membered,rc1_membered,rc3_funct_1,rc6_finseq_1,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_funct_1,fc18_finseq_1,rc1_finset_1,rc1_funct_1,rc2_funct_1,rc7_finseq_1,symmetry_r1_rfinseq,reflexivity_r1_rfinseq,dt_k10_relat_1,dt_k1_card_1,dt_k1_tarski,dt_c2_4__rfinseq,dt_c3_4__rfinseq,fc1_finset_1,d1_rfinseq,dh_c4_4__rfinseq]),
    [interesting(0.8),file(rfinseq,i2_4__rfinseq),[file(rfinseq,i2_4__rfinseq)]]).

fof(i1_4__rfinseq,plain,
    ( ( r1_rfinseq(c1_4__rfinseq,c2_4__rfinseq)
      & r1_rfinseq(c1_4__rfinseq,c3_4__rfinseq) )
   => r1_rfinseq(c2_4__rfinseq,c3_4__rfinseq) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_4__rfinseq,dt_c2_4__rfinseq,dt_c3_4__rfinseq]),discharge_asm(discharge,[e1_4__rfinseq])],[e1_4__rfinseq,i2_4__rfinseq]),
    [interesting(0.8),file(rfinseq,i1_4__rfinseq),[file(rfinseq,i1_4__rfinseq)]]).

fof(i1_4_tmp__rfinseq,plain,
    ( ( v1_relat_1(c1_4__rfinseq)
      & v1_funct_1(c1_4__rfinseq)
      & v1_relat_1(c2_4__rfinseq)
      & v1_funct_1(c2_4__rfinseq)
      & v1_relat_1(c3_4__rfinseq)
      & v1_funct_1(c3_4__rfinseq) )
   => ( ( r1_rfinseq(c1_4__rfinseq,c2_4__rfinseq)
        & r1_rfinseq(c1_4__rfinseq,c3_4__rfinseq) )
     => r1_rfinseq(c2_4__rfinseq,c3_4__rfinseq) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_4__rfinseq,dt_c2_4__rfinseq,dt_c3_4__rfinseq])],[dt_c1_4__rfinseq,dt_c2_4__rfinseq,dt_c3_4__rfinseq,i1_4__rfinseq]),
    [interesting(1),t2_rfinseq]).

fof(t2_rfinseq,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( ( r1_rfinseq(A,B)
                  & r1_rfinseq(A,C) )
               => r1_rfinseq(B,C) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_4_tmp__rfinseq,dh_c1_4__rfinseq,dh_c2_4__rfinseq,dh_c3_4__rfinseq]),
    [interesting(1),file(rfinseq,t2_rfinseq),[file(rfinseq,t2_rfinseq)]]).