% Mizar ND problem: t119_orders_1,orders_1,517,24 
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(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_ordinal1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A) ) ) ),
    file(ordinal1,cc1_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,cc1_ordinal1)]).

fof(cc2_ordinal1,theorem,(
    ! [A] : 
      ( ( v1_ordinal1(A)
        & v2_ordinal1(A) )
     => v3_ordinal1(A) ) ),
    file(ordinal1,cc2_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,cc2_ordinal1)]).

fof(cc3_ordinal1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(ordinal1,cc3_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,cc3_ordinal1)]).

fof(rc1_ordinal1,theorem,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc1_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,rc1_ordinal1)]).

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_ordinal1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc2_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,rc2_ordinal1)]).

fof(rc3_ordinal1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc3_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,rc3_ordinal1)]).

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_ordinal1,theorem,
    ( 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_xboole_0(k1_xboole_0)
    & v1_ordinal1(k1_xboole_0)
    & v2_ordinal1(k1_xboole_0)
    & v3_ordinal1(k1_xboole_0) ),
    file(ordinal1,fc2_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,fc2_ordinal1)]).

fof(d3_orders_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v1_orders_1(A)
      <=> ( v1_relat_2(A)
          & v8_relat_2(A) ) ) ) ),
    file(orders_1,d3_orders_1),
    [interesting(0.9),axiom,file(orders_1,d3_orders_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_k3_relat_1,axiom,(
    $true ),
    file(relat_1,k3_relat_1),
    [interesting(0.9),axiom,file(relat_1,k3_relat_1)]).

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

fof(dt_c1_35_2__orders_1,assumption,(
    $true ),
    introduced(assumption,[file(orders_1,c1_35_2__orders_1)]),
    [interesting(0.65),axiom,file(orders_1,c1_35_2__orders_1)]).

fof(d1_relat_2,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r1_relat_2(A,B)
        <=> ! [C] : 
              ( r2_hidden(C,B)
             => r2_hidden(k4_tarski(C,C),A) ) ) ) ),
    file(relat_2,d1_relat_2),
    [interesting(0.9),axiom,file(relat_2,d1_relat_2)]).

fof(d9_relat_2,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v1_relat_2(A)
      <=> r1_relat_2(A,k3_relat_1(A)) ) ) ),
    file(relat_2,d9_relat_2),
    [interesting(0.9),axiom,file(relat_2,d9_relat_2)]).

fof(dh_c1_35_2__orders_1,definition,
    ( ~ ( r2_hidden(c1_35_2__orders_1,k3_relat_1(k1_xboole_0))
        & ~ r2_hidden(k4_tarski(c1_35_2__orders_1,c1_35_2__orders_1),k1_xboole_0) )
   => ! [A] : 
        ~ ( r2_hidden(A,k3_relat_1(k1_xboole_0))
          & ~ r2_hidden(k4_tarski(A,A),k1_xboole_0) ) ),
    introduced(definition,[new_symbol(c1_35_2__orders_1),file(orders_1,c1_35_2__orders_1)]),
    [interesting(0.65),axiom,file(orders_1,c1_35_2__orders_1)]).

fof(e1_35_2__orders_1,assumption,(
    r2_hidden(c1_35_2__orders_1,k3_relat_1(k1_xboole_0)) ),
    introduced(assumption,[file(orders_1,e1_35_2__orders_1)]),
    [interesting(0.65),axiom,file(orders_1,e1_35_2__orders_1)]).

fof(fc9_finset_1,theorem,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_xboole_0(A,B)) ) ),
    file(finset_1,fc9_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc9_finset_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(commutativity_k2_xboole_0,theorem,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

fof(idempotence_k2_xboole_0,theorem,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

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_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    [interesting(0.9),axiom,file(relat_1,k1_relat_1)]).

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

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

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

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

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(fc2_finset_1,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(k2_tarski(A,B))
      & v1_finset_1(k2_tarski(A,B)) ) ),
    file(finset_1,fc2_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc2_finset_1)]).

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(t1_boole,theorem,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    [interesting(0.9),axiom,file(boole,t1_boole)]).

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(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(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(d6_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => k3_relat_1(A) = k2_xboole_0(k1_relat_1(A),k2_relat_1(A)) ) ),
    file(relat_1,d6_relat_1),
    [interesting(0.9),axiom,file(relat_1,d6_relat_1)]).

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(t60_relat_1,theorem,
    ( k1_relat_1(k1_xboole_0) = k1_xboole_0
    & k2_relat_1(k1_xboole_0) = k1_xboole_0 ),
    file(relat_1,t60_relat_1),
    [interesting(0.9),axiom,file(relat_1,t60_relat_1)]).

fof(e1_35_1__orders_1,plain,(
    k3_relat_1(k1_xboole_0) = k2_xboole_0(k1_xboole_0,k1_xboole_0) ),
    inference(mizar_by,[status(thm),assumptions([])],[existence_m1_subset_1,dt_m1_subset_1,t2_subset,antisymmetry_r2_hidden,fc9_finset_1,rc1_finset_1,t1_subset,cc1_finset_1,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,rc1_ordinal1,rc1_partfun1,rc2_ordinal1,rc3_ordinal1,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,dt_k1_relat_1,dt_k1_xboole_0,dt_k2_relat_1,dt_k2_xboole_0,dt_k3_relat_1,fc2_ordinal1,t1_boole,t6_boole,d6_relat_1,t60_relat_1]),
    [interesting(0.65),file(orders_1,e1_35_1__orders_1),[file(orders_1,e1_35_1__orders_1)]]).

fof(e2_35_1__orders_1,plain,(
    k2_xboole_0(k1_xboole_0,k1_xboole_0) = k1_xboole_0 ),
    inference(mizar_by,[status(thm),assumptions([])],[existence_m1_subset_1,dt_m1_subset_1,t2_subset,antisymmetry_r2_hidden,fc9_finset_1,rc1_finset_1,t1_subset,cc1_finset_1,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,rc1_ordinal1,rc1_partfun1,rc2_ordinal1,rc3_ordinal1,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,dt_k1_xboole_0,dt_k2_xboole_0,fc2_ordinal1,t1_boole,t6_boole]),
    [interesting(0.65),file(orders_1,e2_35_1__orders_1),[file(orders_1,e2_35_1__orders_1)]]).

fof(e1_35__orders_1,plain,(
    k3_relat_1(k1_xboole_0) = k1_xboole_0 ),
    inference(iterative_eq,[status(thm),assumptions([])],[e1_35_1__orders_1,e2_35_1__orders_1]),
    [interesting(0.8),file(orders_1,e1_35__orders_1),[file(orders_1,e1_35__orders_1)]]).

fof(e2_35_2__orders_1,plain,(
    r2_hidden(k4_tarski(c1_35_2__orders_1,c1_35_2__orders_1),k1_xboole_0) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_35_2__orders_1,e1_35_2__orders_1])],[fc9_finset_1,rc1_finset_1,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k1_tarski,dt_k2_relat_1,dt_k2_tarski,dt_k2_xboole_0,dt_m1_subset_1,cc1_finset_1,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,rc1_ordinal1,rc1_partfun1,rc2_ordinal1,rc3_ordinal1,t1_boole,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k3_relat_1,dt_k4_tarski,dt_c1_35_2__orders_1,fc2_ordinal1,t1_subset,t6_boole,t7_boole,d6_relat_1,d5_tarski,e1_35_2__orders_1,e1_35__orders_1]),
    [interesting(0.65),file(orders_1,e2_35_2__orders_1),[file(orders_1,e2_35_2__orders_1)]]).

fof(i3_35_2__orders_1,theorem,(
    $true ),
    introduced(tautology,[file(orders_1,i3_35_2__orders_1)]),
    [interesting(0.65),trivial,file(orders_1,i3_35_2__orders_1)]).

fof(i2_35_2__orders_1,plain,(
    r2_hidden(k4_tarski(c1_35_2__orders_1,c1_35_2__orders_1),k1_xboole_0) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_35_2__orders_1,e1_35_2__orders_1])],[e2_35_2__orders_1,i3_35_2__orders_1]),
    [interesting(0.65),file(orders_1,i2_35_2__orders_1),[file(orders_1,i2_35_2__orders_1)]]).

fof(i1_35_2__orders_1,plain,(
    ~ ( r2_hidden(c1_35_2__orders_1,k3_relat_1(k1_xboole_0))
      & ~ r2_hidden(k4_tarski(c1_35_2__orders_1,c1_35_2__orders_1),k1_xboole_0) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_35_2__orders_1]),discharge_asm(discharge,[e1_35_2__orders_1])],[e1_35_2__orders_1,i2_35_2__orders_1]),
    [interesting(0.65),file(orders_1,i1_35_2__orders_1),[file(orders_1,i1_35_2__orders_1)]]).

fof(i1_35_2_tmp__orders_1,plain,(
    ~ ( r2_hidden(c1_35_2__orders_1,k3_relat_1(k1_xboole_0))
      & ~ r2_hidden(k4_tarski(c1_35_2__orders_1,c1_35_2__orders_1),k1_xboole_0) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_35_2__orders_1])],[dt_c1_35_2__orders_1,i1_35_2__orders_1]),
    [interesting(0.8),e2_35__orders_1]).

fof(e2_35__orders_1,plain,(
    v1_relat_2(k1_xboole_0) ),
    inference(let,[status(thm),assumptions([])],[i1_35_2_tmp__orders_1,rc1_finset_1,cc1_finset_1,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,rc1_ordinal1,rc1_partfun1,rc2_ordinal1,rc3_ordinal1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k3_relat_1,dt_k4_tarski,fc2_ordinal1,d1_relat_2,d9_relat_2,dh_c1_35_2__orders_1]),
    [interesting(0.8),file(orders_1,e2_35__orders_1),[file(orders_1,e2_35__orders_1)]]).

fof(dt_c1_35_3__orders_1,assumption,(
    $true ),
    introduced(assumption,[file(orders_1,c1_35_3__orders_1)]),
    [interesting(0.65),axiom,file(orders_1,c1_35_3__orders_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(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(dh_c1_35_3__orders_1,definition,
    ( ! [A,B] : 
        ~ ( r2_hidden(c1_35_3__orders_1,k3_relat_1(k1_xboole_0))
          & r2_hidden(A,k3_relat_1(k1_xboole_0))
          & r2_hidden(B,k3_relat_1(k1_xboole_0))
          & r2_hidden(k4_tarski(c1_35_3__orders_1,A),k1_xboole_0)
          & r2_hidden(k4_tarski(A,B),k1_xboole_0)
          & ~ r2_hidden(k4_tarski(c1_35_3__orders_1,B),k1_xboole_0) )
   => ! [C,D,E] : 
        ~ ( r2_hidden(C,k3_relat_1(k1_xboole_0))
          & r2_hidden(D,k3_relat_1(k1_xboole_0))
          & r2_hidden(E,k3_relat_1(k1_xboole_0))
          & r2_hidden(k4_tarski(C,D),k1_xboole_0)
          & r2_hidden(k4_tarski(D,E),k1_xboole_0)
          & ~ r2_hidden(k4_tarski(C,E),k1_xboole_0) ) ),
    introduced(definition,[new_symbol(c1_35_3__orders_1),file(orders_1,c1_35_3__orders_1)]),
    [interesting(0.65),axiom,file(orders_1,c1_35_3__orders_1)]).

fof(dh_c2_35_3__orders_1,definition,
    ( ! [A] : 
        ~ ( r2_hidden(c1_35_3__orders_1,k3_relat_1(k1_xboole_0))
          & r2_hidden(c2_35_3__orders_1,k3_relat_1(k1_xboole_0))
          & r2_hidden(A,k3_relat_1(k1_xboole_0))
          & r2_hidden(k4_tarski(c1_35_3__orders_1,c2_35_3__orders_1),k1_xboole_0)
          & r2_hidden(k4_tarski(c2_35_3__orders_1,A),k1_xboole_0)
          & ~ r2_hidden(k4_tarski(c1_35_3__orders_1,A),k1_xboole_0) )
   => ! [B,C] : 
        ~ ( r2_hidden(c1_35_3__orders_1,k3_relat_1(k1_xboole_0))
          & r2_hidden(B,k3_relat_1(k1_xboole_0))
          & r2_hidden(C,k3_relat_1(k1_xboole_0))
          & r2_hidden(k4_tarski(c1_35_3__orders_1,B),k1_xboole_0)
          & r2_hidden(k4_tarski(B,C),k1_xboole_0)
          & ~ r2_hidden(k4_tarski(c1_35_3__orders_1,C),k1_xboole_0) ) ),
    introduced(definition,[new_symbol(c2_35_3__orders_1),file(orders_1,c2_35_3__orders_1)]),
    [interesting(0.65),axiom,file(orders_1,c2_35_3__orders_1)]).

fof(dh_c3_35_3__orders_1,definition,
    ( ~ ( r2_hidden(c1_35_3__orders_1,k3_relat_1(k1_xboole_0))
        & r2_hidden(c2_35_3__orders_1,k3_relat_1(k1_xboole_0))
        & r2_hidden(c3_35_3__orders_1,k3_relat_1(k1_xboole_0))
        & r2_hidden(k4_tarski(c1_35_3__orders_1,c2_35_3__orders_1),k1_xboole_0)
        & r2_hidden(k4_tarski(c2_35_3__orders_1,c3_35_3__orders_1),k1_xboole_0)
        & ~ r2_hidden(k4_tarski(c1_35_3__orders_1,c3_35_3__orders_1),k1_xboole_0) )
   => ! [A] : 
        ~ ( r2_hidden(c1_35_3__orders_1,k3_relat_1(k1_xboole_0))
          & r2_hidden(c2_35_3__orders_1,k3_relat_1(k1_xboole_0))
          & r2_hidden(A,k3_relat_1(k1_xboole_0))
          & r2_hidden(k4_tarski(c1_35_3__orders_1,c2_35_3__orders_1),k1_xboole_0)
          & r2_hidden(k4_tarski(c2_35_3__orders_1,A),k1_xboole_0)
          & ~ r2_hidden(k4_tarski(c1_35_3__orders_1,A),k1_xboole_0) ) ),
    introduced(definition,[new_symbol(c3_35_3__orders_1),file(orders_1,c3_35_3__orders_1)]),
    [interesting(0.65),axiom,file(orders_1,c3_35_3__orders_1)]).

fof(e1_35_3__orders_1,assumption,(
    r2_hidden(c1_35_3__orders_1,k3_relat_1(k1_xboole_0)) ),
    introduced(assumption,[file(orders_1,e1_35_3__orders_1)]),
    [interesting(0.65),axiom,file(orders_1,e1_35_3__orders_1)]).

fof(dt_c2_35_3__orders_1,assumption,(
    $true ),
    introduced(assumption,[file(orders_1,c2_35_3__orders_1)]),
    [interesting(0.65),axiom,file(orders_1,c2_35_3__orders_1)]).

fof(dt_c3_35_3__orders_1,assumption,(
    $true ),
    introduced(assumption,[file(orders_1,c3_35_3__orders_1)]),
    [interesting(0.65),axiom,file(orders_1,c3_35_3__orders_1)]).

fof(e2_35_3__orders_1,plain,(
    ~ ( r2_hidden(c2_35_3__orders_1,k3_relat_1(k1_xboole_0))
      & r2_hidden(c3_35_3__orders_1,k3_relat_1(k1_xboole_0))
      & r2_hidden(k4_tarski(c1_35_3__orders_1,c2_35_3__orders_1),k1_xboole_0)
      & r2_hidden(k4_tarski(c2_35_3__orders_1,c3_35_3__orders_1),k1_xboole_0)
      & ~ r2_hidden(k4_tarski(c1_35_3__orders_1,c3_35_3__orders_1),k1_xboole_0) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_35_3__orders_1,dt_c2_35_3__orders_1,dt_c3_35_3__orders_1])],[fc9_finset_1,rc1_finset_1,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k1_tarski,dt_k2_relat_1,dt_k2_tarski,dt_k2_xboole_0,dt_m1_subset_1,cc1_finset_1,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,rc1_ordinal1,rc1_partfun1,rc2_ordinal1,rc3_ordinal1,t1_boole,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k3_relat_1,dt_k4_tarski,dt_c1_35_3__orders_1,dt_c2_35_3__orders_1,dt_c3_35_3__orders_1,fc2_ordinal1,t1_subset,t6_boole,t7_boole,d6_relat_1,d5_tarski]),
    [interesting(0.65),file(orders_1,e2_35_3__orders_1),[file(orders_1,e2_35_3__orders_1)]]).

fof(i5_35_3__orders_1,theorem,(
    $true ),
    introduced(tautology,[file(orders_1,i5_35_3__orders_1)]),
    [interesting(0.65),trivial,file(orders_1,i5_35_3__orders_1)]).

fof(i4_35_3__orders_1,plain,(
    ~ ( r2_hidden(c2_35_3__orders_1,k3_relat_1(k1_xboole_0))
      & r2_hidden(c3_35_3__orders_1,k3_relat_1(k1_xboole_0))
      & r2_hidden(k4_tarski(c1_35_3__orders_1,c2_35_3__orders_1),k1_xboole_0)
      & r2_hidden(k4_tarski(c2_35_3__orders_1,c3_35_3__orders_1),k1_xboole_0)
      & ~ r2_hidden(k4_tarski(c1_35_3__orders_1,c3_35_3__orders_1),k1_xboole_0) ) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_35_3__orders_1,dt_c2_35_3__orders_1,dt_c3_35_3__orders_1])],[e2_35_3__orders_1,i5_35_3__orders_1]),
    [interesting(0.65),file(orders_1,i4_35_3__orders_1),[file(orders_1,i4_35_3__orders_1)]]).

fof(i3_35_3__orders_1,plain,(
    ~ ( r2_hidden(c1_35_3__orders_1,k3_relat_1(k1_xboole_0))
      & r2_hidden(c2_35_3__orders_1,k3_relat_1(k1_xboole_0))
      & r2_hidden(c3_35_3__orders_1,k3_relat_1(k1_xboole_0))
      & r2_hidden(k4_tarski(c1_35_3__orders_1,c2_35_3__orders_1),k1_xboole_0)
      & r2_hidden(k4_tarski(c2_35_3__orders_1,c3_35_3__orders_1),k1_xboole_0)
      & ~ r2_hidden(k4_tarski(c1_35_3__orders_1,c3_35_3__orders_1),k1_xboole_0) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_35_3__orders_1,dt_c2_35_3__orders_1,dt_c3_35_3__orders_1]),discharge_asm(discharge,[e1_35_3__orders_1])],[e1_35_3__orders_1,i4_35_3__orders_1]),
    [interesting(0.65),file(orders_1,i3_35_3__orders_1),[file(orders_1,i3_35_3__orders_1)]]).

fof(i3_35_3_tmp__orders_1,plain,(
    ~ ( r2_hidden(c1_35_3__orders_1,k3_relat_1(k1_xboole_0))
      & r2_hidden(c2_35_3__orders_1,k3_relat_1(k1_xboole_0))
      & r2_hidden(c3_35_3__orders_1,k3_relat_1(k1_xboole_0))
      & r2_hidden(k4_tarski(c1_35_3__orders_1,c2_35_3__orders_1),k1_xboole_0)
      & r2_hidden(k4_tarski(c2_35_3__orders_1,c3_35_3__orders_1),k1_xboole_0)
      & ~ r2_hidden(k4_tarski(c1_35_3__orders_1,c3_35_3__orders_1),k1_xboole_0) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_35_3__orders_1,dt_c2_35_3__orders_1]),discharge_asm(discharge,[dt_c3_35_3__orders_1])],[dt_c3_35_3__orders_1,i3_35_3__orders_1]),
    [interesting(0.65),i2_35_3__orders_1]).

fof(i2_35_3__orders_1,plain,(
    ! [A] : 
      ~ ( r2_hidden(c1_35_3__orders_1,k3_relat_1(k1_xboole_0))
        & r2_hidden(c2_35_3__orders_1,k3_relat_1(k1_xboole_0))
        & r2_hidden(A,k3_relat_1(k1_xboole_0))
        & r2_hidden(k4_tarski(c1_35_3__orders_1,c2_35_3__orders_1),k1_xboole_0)
        & r2_hidden(k4_tarski(c2_35_3__orders_1,A),k1_xboole_0)
        & ~ r2_hidden(k4_tarski(c1_35_3__orders_1,A),k1_xboole_0) ) ),
    inference(let,[status(thm),assumptions([dt_c1_35_3__orders_1,dt_c2_35_3__orders_1])],[i3_35_3_tmp__orders_1,dh_c3_35_3__orders_1]),
    [interesting(0.65),file(orders_1,i2_35_3__orders_1),[file(orders_1,i2_35_3__orders_1)]]).

fof(i2_35_3_tmp__orders_1,plain,(
    ! [A] : 
      ~ ( r2_hidden(c1_35_3__orders_1,k3_relat_1(k1_xboole_0))
        & r2_hidden(c2_35_3__orders_1,k3_relat_1(k1_xboole_0))
        & r2_hidden(A,k3_relat_1(k1_xboole_0))
        & r2_hidden(k4_tarski(c1_35_3__orders_1,c2_35_3__orders_1),k1_xboole_0)
        & r2_hidden(k4_tarski(c2_35_3__orders_1,A),k1_xboole_0)
        & ~ r2_hidden(k4_tarski(c1_35_3__orders_1,A),k1_xboole_0) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_35_3__orders_1]),discharge_asm(discharge,[dt_c2_35_3__orders_1])],[dt_c2_35_3__orders_1,i2_35_3__orders_1]),
    [interesting(0.65),i1_35_3__orders_1]).

fof(i1_35_3__orders_1,plain,(
    ! [A,B] : 
      ~ ( r2_hidden(c1_35_3__orders_1,k3_relat_1(k1_xboole_0))
        & r2_hidden(A,k3_relat_1(k1_xboole_0))
        & r2_hidden(B,k3_relat_1(k1_xboole_0))
        & r2_hidden(k4_tarski(c1_35_3__orders_1,A),k1_xboole_0)
        & r2_hidden(k4_tarski(A,B),k1_xboole_0)
        & ~ r2_hidden(k4_tarski(c1_35_3__orders_1,B),k1_xboole_0) ) ),
    inference(let,[status(thm),assumptions([dt_c1_35_3__orders_1])],[i2_35_3_tmp__orders_1,dh_c2_35_3__orders_1]),
    [interesting(0.65),file(orders_1,i1_35_3__orders_1),[file(orders_1,i1_35_3__orders_1)]]).

fof(i1_35_3_tmp__orders_1,plain,(
    ! [A,B] : 
      ~ ( r2_hidden(c1_35_3__orders_1,k3_relat_1(k1_xboole_0))
        & r2_hidden(A,k3_relat_1(k1_xboole_0))
        & r2_hidden(B,k3_relat_1(k1_xboole_0))
        & r2_hidden(k4_tarski(c1_35_3__orders_1,A),k1_xboole_0)
        & r2_hidden(k4_tarski(A,B),k1_xboole_0)
        & ~ r2_hidden(k4_tarski(c1_35_3__orders_1,B),k1_xboole_0) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_35_3__orders_1])],[dt_c1_35_3__orders_1,i1_35_3__orders_1]),
    [interesting(0.8),e3_35__orders_1]).

fof(e3_35__orders_1,plain,(
    v8_relat_2(k1_xboole_0) ),
    inference(let,[status(thm),assumptions([])],[i1_35_3_tmp__orders_1,rc1_finset_1,cc1_finset_1,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,rc1_ordinal1,rc1_partfun1,rc2_ordinal1,rc3_ordinal1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k3_relat_1,dt_k4_tarski,fc2_ordinal1,d8_relat_2,d16_relat_2,dh_c1_35_3__orders_1]),
    [interesting(0.8),file(orders_1,e3_35__orders_1),[file(orders_1,e3_35__orders_1)]]).

fof(d4_orders_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v2_orders_1(A)
      <=> ( v1_relat_2(A)
          & v8_relat_2(A)
          & v4_relat_2(A) ) ) ) ),
    file(orders_1,d4_orders_1),
    [interesting(0.9),axiom,file(orders_1,d4_orders_1)]).

fof(e4_35__orders_1,plain,
    ( v1_relat_2(k1_xboole_0)
    & v8_relat_2(k1_xboole_0) ),
    inference(mizar_by,[status(thm),assumptions([])],[existence_m1_subset_1,dt_m1_subset_1,t2_subset,antisymmetry_r2_hidden,rc1_finset_1,t1_subset,cc1_finset_1,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,rc1_ordinal1,rc1_partfun1,rc2_ordinal1,rc3_ordinal1,t7_boole,t8_boole,dt_k1_xboole_0,fc2_ordinal1,t6_boole,e3_35__orders_1,e2_35__orders_1]),
    [interesting(0.8),file(orders_1,e4_35__orders_1),[file(orders_1,e4_35__orders_1)]]).

fof(dt_c1_35_4__orders_1,assumption,(
    $true ),
    introduced(assumption,[file(orders_1,c1_35_4__orders_1)]),
    [interesting(0.65),axiom,file(orders_1,c1_35_4__orders_1)]).

fof(d4_relat_2,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r4_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) )
             => C = D ) ) ) ),
    file(relat_2,d4_relat_2),
    [interesting(0.9),axiom,file(relat_2,d4_relat_2)]).

fof(d12_relat_2,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v4_relat_2(A)
      <=> r4_relat_2(A,k3_relat_1(A)) ) ) ),
    file(relat_2,d12_relat_2),
    [interesting(0.9),axiom,file(relat_2,d12_relat_2)]).

fof(dh_c1_35_4__orders_1,definition,
    ( ! [A] : 
        ~ ( r2_hidden(c1_35_4__orders_1,k3_relat_1(k1_xboole_0))
          & r2_hidden(A,k3_relat_1(k1_xboole_0))
          & r2_hidden(k4_tarski(c1_35_4__orders_1,A),k1_xboole_0)
          & r2_hidden(k4_tarski(A,c1_35_4__orders_1),k1_xboole_0)
          & c1_35_4__orders_1 != A )
   => ! [B,C] : 
        ~ ( r2_hidden(B,k3_relat_1(k1_xboole_0))
          & r2_hidden(C,k3_relat_1(k1_xboole_0))
          & r2_hidden(k4_tarski(B,C),k1_xboole_0)
          & r2_hidden(k4_tarski(C,B),k1_xboole_0)
          & B != C ) ),
    introduced(definition,[new_symbol(c1_35_4__orders_1),file(orders_1,c1_35_4__orders_1)]),
    [interesting(0.65),axiom,file(orders_1,c1_35_4__orders_1)]).

fof(dh_c2_35_4__orders_1,definition,
    ( ~ ( r2_hidden(c1_35_4__orders_1,k3_relat_1(k1_xboole_0))
        & r2_hidden(c2_35_4__orders_1,k3_relat_1(k1_xboole_0))
        & r2_hidden(k4_tarski(c1_35_4__orders_1,c2_35_4__orders_1),k1_xboole_0)
        & r2_hidden(k4_tarski(c2_35_4__orders_1,c1_35_4__orders_1),k1_xboole_0)
        & c1_35_4__orders_1 != c2_35_4__orders_1 )
   => ! [A] : 
        ~ ( r2_hidden(c1_35_4__orders_1,k3_relat_1(k1_xboole_0))
          & r2_hidden(A,k3_relat_1(k1_xboole_0))
          & r2_hidden(k4_tarski(c1_35_4__orders_1,A),k1_xboole_0)
          & r2_hidden(k4_tarski(A,c1_35_4__orders_1),k1_xboole_0)
          & c1_35_4__orders_1 != A ) ),
    introduced(definition,[new_symbol(c2_35_4__orders_1),file(orders_1,c2_35_4__orders_1)]),
    [interesting(0.65),axiom,file(orders_1,c2_35_4__orders_1)]).

fof(e1_35_4__orders_1,assumption,(
    r2_hidden(c1_35_4__orders_1,k3_relat_1(k1_xboole_0)) ),
    introduced(assumption,[file(orders_1,e1_35_4__orders_1)]),
    [interesting(0.65),axiom,file(orders_1,e1_35_4__orders_1)]).

fof(dt_c2_35_4__orders_1,assumption,(
    $true ),
    introduced(assumption,[file(orders_1,c2_35_4__orders_1)]),
    [interesting(0.65),axiom,file(orders_1,c2_35_4__orders_1)]).

fof(e2_35_4__orders_1,plain,(
    ~ ( r2_hidden(c2_35_4__orders_1,k3_relat_1(k1_xboole_0))
      & r2_hidden(k4_tarski(c1_35_4__orders_1,c2_35_4__orders_1),k1_xboole_0)
      & r2_hidden(k4_tarski(c2_35_4__orders_1,c1_35_4__orders_1),k1_xboole_0)
      & c1_35_4__orders_1 != c2_35_4__orders_1 ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_35_4__orders_1,dt_c2_35_4__orders_1])],[fc9_finset_1,rc1_finset_1,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k1_tarski,dt_k2_relat_1,dt_k2_tarski,dt_k2_xboole_0,dt_m1_subset_1,cc1_finset_1,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,rc1_ordinal1,rc1_partfun1,rc2_ordinal1,rc3_ordinal1,t1_boole,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k3_relat_1,dt_k4_tarski,dt_c1_35_4__orders_1,dt_c2_35_4__orders_1,fc2_ordinal1,t1_subset,t6_boole,t7_boole,d6_relat_1,d5_tarski]),
    [interesting(0.65),file(orders_1,e2_35_4__orders_1),[file(orders_1,e2_35_4__orders_1)]]).

fof(i4_35_4__orders_1,theorem,(
    $true ),
    introduced(tautology,[file(orders_1,i4_35_4__orders_1)]),
    [interesting(0.65),trivial,file(orders_1,i4_35_4__orders_1)]).

fof(i3_35_4__orders_1,plain,(
    ~ ( r2_hidden(c2_35_4__orders_1,k3_relat_1(k1_xboole_0))
      & r2_hidden(k4_tarski(c1_35_4__orders_1,c2_35_4__orders_1),k1_xboole_0)
      & r2_hidden(k4_tarski(c2_35_4__orders_1,c1_35_4__orders_1),k1_xboole_0)
      & c1_35_4__orders_1 != c2_35_4__orders_1 ) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_35_4__orders_1,dt_c2_35_4__orders_1])],[e2_35_4__orders_1,i4_35_4__orders_1]),
    [interesting(0.65),file(orders_1,i3_35_4__orders_1),[file(orders_1,i3_35_4__orders_1)]]).

fof(i2_35_4__orders_1,plain,(
    ~ ( r2_hidden(c1_35_4__orders_1,k3_relat_1(k1_xboole_0))
      & r2_hidden(c2_35_4__orders_1,k3_relat_1(k1_xboole_0))
      & r2_hidden(k4_tarski(c1_35_4__orders_1,c2_35_4__orders_1),k1_xboole_0)
      & r2_hidden(k4_tarski(c2_35_4__orders_1,c1_35_4__orders_1),k1_xboole_0)
      & c1_35_4__orders_1 != c2_35_4__orders_1 ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_35_4__orders_1,dt_c2_35_4__orders_1]),discharge_asm(discharge,[e1_35_4__orders_1])],[e1_35_4__orders_1,i3_35_4__orders_1]),
    [interesting(0.65),file(orders_1,i2_35_4__orders_1),[file(orders_1,i2_35_4__orders_1)]]).

fof(i2_35_4_tmp__orders_1,plain,(
    ~ ( r2_hidden(c1_35_4__orders_1,k3_relat_1(k1_xboole_0))
      & r2_hidden(c2_35_4__orders_1,k3_relat_1(k1_xboole_0))
      & r2_hidden(k4_tarski(c1_35_4__orders_1,c2_35_4__orders_1),k1_xboole_0)
      & r2_hidden(k4_tarski(c2_35_4__orders_1,c1_35_4__orders_1),k1_xboole_0)
      & c1_35_4__orders_1 != c2_35_4__orders_1 ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_35_4__orders_1]),discharge_asm(discharge,[dt_c2_35_4__orders_1])],[dt_c2_35_4__orders_1,i2_35_4__orders_1]),
    [interesting(0.65),i1_35_4__orders_1]).

fof(i1_35_4__orders_1,plain,(
    ! [A] : 
      ~ ( r2_hidden(c1_35_4__orders_1,k3_relat_1(k1_xboole_0))
        & r2_hidden(A,k3_relat_1(k1_xboole_0))
        & r2_hidden(k4_tarski(c1_35_4__orders_1,A),k1_xboole_0)
        & r2_hidden(k4_tarski(A,c1_35_4__orders_1),k1_xboole_0)
        & c1_35_4__orders_1 != A ) ),
    inference(let,[status(thm),assumptions([dt_c1_35_4__orders_1])],[i2_35_4_tmp__orders_1,dh_c2_35_4__orders_1]),
    [interesting(0.65),file(orders_1,i1_35_4__orders_1),[file(orders_1,i1_35_4__orders_1)]]).

fof(i1_35_4_tmp__orders_1,plain,(
    ! [A] : 
      ~ ( r2_hidden(c1_35_4__orders_1,k3_relat_1(k1_xboole_0))
        & r2_hidden(A,k3_relat_1(k1_xboole_0))
        & r2_hidden(k4_tarski(c1_35_4__orders_1,A),k1_xboole_0)
        & r2_hidden(k4_tarski(A,c1_35_4__orders_1),k1_xboole_0)
        & c1_35_4__orders_1 != A ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_35_4__orders_1])],[dt_c1_35_4__orders_1,i1_35_4__orders_1]),
    [interesting(0.8),e5_35__orders_1]).

fof(e5_35__orders_1,plain,(
    v4_relat_2(k1_xboole_0) ),
    inference(let,[status(thm),assumptions([])],[i1_35_4_tmp__orders_1,rc1_finset_1,cc1_finset_1,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,rc1_ordinal1,rc1_partfun1,rc2_ordinal1,rc3_ordinal1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k3_relat_1,dt_k4_tarski,fc2_ordinal1,d4_relat_2,d12_relat_2,dh_c1_35_4__orders_1]),
    [interesting(0.8),file(orders_1,e5_35__orders_1),[file(orders_1,e5_35__orders_1)]]).

fof(d5_orders_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v3_orders_1(A)
      <=> ( v1_relat_2(A)
          & v8_relat_2(A)
          & v4_relat_2(A)
          & v6_relat_2(A) ) ) ) ),
    file(orders_1,d5_orders_1),
    [interesting(0.9),axiom,file(orders_1,d5_orders_1)]).

fof(e6_35__orders_1,plain,
    ( v1_relat_2(k1_xboole_0)
    & v8_relat_2(k1_xboole_0)
    & v4_relat_2(k1_xboole_0) ),
    inference(mizar_by,[status(thm),assumptions([])],[existence_m1_subset_1,dt_m1_subset_1,t2_subset,antisymmetry_r2_hidden,rc1_finset_1,t1_subset,cc1_finset_1,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,rc1_ordinal1,rc1_partfun1,rc2_ordinal1,rc3_ordinal1,t7_boole,t8_boole,dt_k1_xboole_0,fc2_ordinal1,t6_boole,e5_35__orders_1,e2_35__orders_1,e3_35__orders_1]),
    [interesting(0.8),file(orders_1,e6_35__orders_1),[file(orders_1,e6_35__orders_1)]]).

fof(dt_c1_35_5__orders_1,assumption,(
    $true ),
    introduced(assumption,[file(orders_1,c1_35_5__orders_1)]),
    [interesting(0.65),axiom,file(orders_1,c1_35_5__orders_1)]).

fof(d6_relat_2,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r6_relat_2(A,B)
        <=> ! [C,D] : 
              ~ ( r2_hidden(C,B)
                & r2_hidden(D,B)
                & C != D
                & ~ r2_hidden(k4_tarski(C,D),A)
                & ~ r2_hidden(k4_tarski(D,C),A) ) ) ) ),
    file(relat_2,d6_relat_2),
    [interesting(0.9),axiom,file(relat_2,d6_relat_2)]).

fof(d14_relat_2,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v6_relat_2(A)
      <=> r6_relat_2(A,k3_relat_1(A)) ) ) ),
    file(relat_2,d14_relat_2),
    [interesting(0.9),axiom,file(relat_2,d14_relat_2)]).

fof(dh_c1_35_5__orders_1,definition,
    ( ! [A] : 
        ~ ( r2_hidden(c1_35_5__orders_1,k3_relat_1(k1_xboole_0))
          & r2_hidden(A,k3_relat_1(k1_xboole_0))
          & c1_35_5__orders_1 != A
          & ~ r2_hidden(k4_tarski(c1_35_5__orders_1,A),k1_xboole_0)
          & ~ r2_hidden(k4_tarski(A,c1_35_5__orders_1),k1_xboole_0) )
   => ! [B,C] : 
        ~ ( r2_hidden(B,k3_relat_1(k1_xboole_0))
          & r2_hidden(C,k3_relat_1(k1_xboole_0))
          & B != C
          & ~ r2_hidden(k4_tarski(B,C),k1_xboole_0)
          & ~ r2_hidden(k4_tarski(C,B),k1_xboole_0) ) ),
    introduced(definition,[new_symbol(c1_35_5__orders_1),file(orders_1,c1_35_5__orders_1)]),
    [interesting(0.65),axiom,file(orders_1,c1_35_5__orders_1)]).

fof(dh_c2_35_5__orders_1,definition,
    ( ~ ( r2_hidden(c1_35_5__orders_1,k3_relat_1(k1_xboole_0))
        & r2_hidden(c2_35_5__orders_1,k3_relat_1(k1_xboole_0))
        & c1_35_5__orders_1 != c2_35_5__orders_1
        & ~ r2_hidden(k4_tarski(c1_35_5__orders_1,c2_35_5__orders_1),k1_xboole_0)
        & ~ r2_hidden(k4_tarski(c2_35_5__orders_1,c1_35_5__orders_1),k1_xboole_0) )
   => ! [A] : 
        ~ ( r2_hidden(c1_35_5__orders_1,k3_relat_1(k1_xboole_0))
          & r2_hidden(A,k3_relat_1(k1_xboole_0))
          & c1_35_5__orders_1 != A
          & ~ r2_hidden(k4_tarski(c1_35_5__orders_1,A),k1_xboole_0)
          & ~ r2_hidden(k4_tarski(A,c1_35_5__orders_1),k1_xboole_0) ) ),
    introduced(definition,[new_symbol(c2_35_5__orders_1),file(orders_1,c2_35_5__orders_1)]),
    [interesting(0.65),axiom,file(orders_1,c2_35_5__orders_1)]).

fof(e1_35_5__orders_1,assumption,(
    r2_hidden(c1_35_5__orders_1,k3_relat_1(k1_xboole_0)) ),
    introduced(assumption,[file(orders_1,e1_35_5__orders_1)]),
    [interesting(0.65),axiom,file(orders_1,e1_35_5__orders_1)]).

fof(dt_c2_35_5__orders_1,assumption,(
    $true ),
    introduced(assumption,[file(orders_1,c2_35_5__orders_1)]),
    [interesting(0.65),axiom,file(orders_1,c2_35_5__orders_1)]).

fof(e2_35_5__orders_1,plain,(
    ~ ( r2_hidden(c2_35_5__orders_1,k3_relat_1(k1_xboole_0))
      & c1_35_5__orders_1 != c2_35_5__orders_1
      & ~ r2_hidden(k4_tarski(c1_35_5__orders_1,c2_35_5__orders_1),k1_xboole_0)
      & ~ r2_hidden(k4_tarski(c2_35_5__orders_1,c1_35_5__orders_1),k1_xboole_0) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_35_5__orders_1,dt_c2_35_5__orders_1])],[fc9_finset_1,rc1_finset_1,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k1_tarski,dt_k2_relat_1,dt_k2_tarski,dt_k2_xboole_0,dt_m1_subset_1,cc1_finset_1,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,rc1_ordinal1,rc1_partfun1,rc2_ordinal1,rc3_ordinal1,t1_boole,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k3_relat_1,dt_k4_tarski,dt_c1_35_5__orders_1,dt_c2_35_5__orders_1,fc2_ordinal1,t1_subset,t6_boole,t7_boole,d6_relat_1,d5_tarski,e1_35__orders_1]),
    [interesting(0.65),file(orders_1,e2_35_5__orders_1),[file(orders_1,e2_35_5__orders_1)]]).

fof(i4_35_5__orders_1,theorem,(
    $true ),
    introduced(tautology,[file(orders_1,i4_35_5__orders_1)]),
    [interesting(0.65),trivial,file(orders_1,i4_35_5__orders_1)]).

fof(i3_35_5__orders_1,plain,(
    ~ ( r2_hidden(c2_35_5__orders_1,k3_relat_1(k1_xboole_0))
      & c1_35_5__orders_1 != c2_35_5__orders_1
      & ~ r2_hidden(k4_tarski(c1_35_5__orders_1,c2_35_5__orders_1),k1_xboole_0)
      & ~ r2_hidden(k4_tarski(c2_35_5__orders_1,c1_35_5__orders_1),k1_xboole_0) ) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_35_5__orders_1,dt_c2_35_5__orders_1])],[e2_35_5__orders_1,i4_35_5__orders_1]),
    [interesting(0.65),file(orders_1,i3_35_5__orders_1),[file(orders_1,i3_35_5__orders_1)]]).

fof(i2_35_5__orders_1,plain,(
    ~ ( r2_hidden(c1_35_5__orders_1,k3_relat_1(k1_xboole_0))
      & r2_hidden(c2_35_5__orders_1,k3_relat_1(k1_xboole_0))
      & c1_35_5__orders_1 != c2_35_5__orders_1
      & ~ r2_hidden(k4_tarski(c1_35_5__orders_1,c2_35_5__orders_1),k1_xboole_0)
      & ~ r2_hidden(k4_tarski(c2_35_5__orders_1,c1_35_5__orders_1),k1_xboole_0) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_35_5__orders_1,dt_c2_35_5__orders_1]),discharge_asm(discharge,[e1_35_5__orders_1])],[e1_35_5__orders_1,i3_35_5__orders_1]),
    [interesting(0.65),file(orders_1,i2_35_5__orders_1),[file(orders_1,i2_35_5__orders_1)]]).

fof(i2_35_5_tmp__orders_1,plain,(
    ~ ( r2_hidden(c1_35_5__orders_1,k3_relat_1(k1_xboole_0))
      & r2_hidden(c2_35_5__orders_1,k3_relat_1(k1_xboole_0))
      & c1_35_5__orders_1 != c2_35_5__orders_1
      & ~ r2_hidden(k4_tarski(c1_35_5__orders_1,c2_35_5__orders_1),k1_xboole_0)
      & ~ r2_hidden(k4_tarski(c2_35_5__orders_1,c1_35_5__orders_1),k1_xboole_0) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_35_5__orders_1]),discharge_asm(discharge,[dt_c2_35_5__orders_1])],[dt_c2_35_5__orders_1,i2_35_5__orders_1]),
    [interesting(0.65),i1_35_5__orders_1]).

fof(i1_35_5__orders_1,plain,(
    ! [A] : 
      ~ ( r2_hidden(c1_35_5__orders_1,k3_relat_1(k1_xboole_0))
        & r2_hidden(A,k3_relat_1(k1_xboole_0))
        & c1_35_5__orders_1 != A
        & ~ r2_hidden(k4_tarski(c1_35_5__orders_1,A),k1_xboole_0)
        & ~ r2_hidden(k4_tarski(A,c1_35_5__orders_1),k1_xboole_0) ) ),
    inference(let,[status(thm),assumptions([dt_c1_35_5__orders_1])],[i2_35_5_tmp__orders_1,dh_c2_35_5__orders_1]),
    [interesting(0.65),file(orders_1,i1_35_5__orders_1),[file(orders_1,i1_35_5__orders_1)]]).

fof(i1_35_5_tmp__orders_1,plain,(
    ! [A] : 
      ~ ( r2_hidden(c1_35_5__orders_1,k3_relat_1(k1_xboole_0))
        & r2_hidden(A,k3_relat_1(k1_xboole_0))
        & c1_35_5__orders_1 != A
        & ~ r2_hidden(k4_tarski(c1_35_5__orders_1,A),k1_xboole_0)
        & ~ r2_hidden(k4_tarski(A,c1_35_5__orders_1),k1_xboole_0) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_35_5__orders_1])],[dt_c1_35_5__orders_1,i1_35_5__orders_1]),
    [interesting(0.8),e7_35__orders_1]).

fof(e7_35__orders_1,plain,(
    v6_relat_2(k1_xboole_0) ),
    inference(let,[status(thm),assumptions([])],[i1_35_5_tmp__orders_1,rc1_finset_1,cc1_finset_1,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,rc1_ordinal1,rc1_partfun1,rc2_ordinal1,rc3_ordinal1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k3_relat_1,dt_k4_tarski,fc2_ordinal1,d6_relat_2,d14_relat_2,dh_c1_35_5__orders_1]),
    [interesting(0.8),file(orders_1,e7_35__orders_1),[file(orders_1,e7_35__orders_1)]]).

fof(d4_wellord1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v2_wellord1(A)
      <=> ( v1_relat_2(A)
          & v8_relat_2(A)
          & v4_relat_2(A)
          & v6_relat_2(A)
          & v1_wellord1(A) ) ) ) ),
    file(wellord1,d4_wellord1),
    [interesting(0.9),axiom,file(wellord1,d4_wellord1)]).

fof(e8_35__orders_1,plain,
    ( v1_relat_2(k1_xboole_0)
    & v8_relat_2(k1_xboole_0)
    & v4_relat_2(k1_xboole_0)
    & v6_relat_2(k1_xboole_0) ),
    inference(mizar_by,[status(thm),assumptions([])],[existence_m1_subset_1,dt_m1_subset_1,t2_subset,antisymmetry_r2_hidden,rc1_finset_1,t1_subset,cc1_finset_1,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,rc1_ordinal1,rc1_partfun1,rc2_ordinal1,rc3_ordinal1,t7_boole,t8_boole,dt_k1_xboole_0,fc2_ordinal1,t6_boole,e7_35__orders_1,e2_35__orders_1,e3_35__orders_1,e5_35__orders_1]),
    [interesting(0.8),file(orders_1,e8_35__orders_1),[file(orders_1,e8_35__orders_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(symmetry_r1_xboole_0,theorem,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
     => r1_xboole_0(B,A) ) ),
    file(xboole_0,r1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,r1_xboole_0)]).

fof(dt_k1_wellord1,axiom,(
    $true ),
    file(wellord1,k1_wellord1),
    [interesting(0.9),axiom,file(wellord1,k1_wellord1)]).

fof(dt_c1_35__orders_1,assumption,(
    $true ),
    introduced(assumption,[file(orders_1,c1_35__orders_1)]),
    [interesting(0.8),axiom,file(orders_1,c1_35__orders_1)]).

fof(d2_wellord1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v1_wellord1(A)
      <=> ! [B] : 
            ~ ( r1_tarski(B,k3_relat_1(A))
              & B != k1_xboole_0
              & ! [C] : 
                  ~ ( r2_hidden(C,B)
                    & r1_xboole_0(k1_wellord1(A,C),B) ) ) ) ) ),
    file(wellord1,d2_wellord1),
    [interesting(0.9),axiom,file(wellord1,d2_wellord1)]).

fof(dh_c1_35__orders_1,definition,
    ( ~ ( r1_tarski(c1_35__orders_1,k3_relat_1(k1_xboole_0))
        & c1_35__orders_1 != k1_xboole_0
        & ! [A] : 
            ~ ( r2_hidden(A,c1_35__orders_1)
              & r1_xboole_0(k1_wellord1(k1_xboole_0,A),c1_35__orders_1) ) )
   => ! [B] : 
        ~ ( r1_tarski(B,k3_relat_1(k1_xboole_0))
          & B != k1_xboole_0
          & ! [C] : 
              ~ ( r2_hidden(C,B)
                & r1_xboole_0(k1_wellord1(k1_xboole_0,C),B) ) ) ),
    introduced(definition,[new_symbol(c1_35__orders_1),file(orders_1,c1_35__orders_1)]),
    [interesting(0.8),axiom,file(orders_1,c1_35__orders_1)]).

fof(e9_35__orders_1,assumption,
    ( r1_tarski(c1_35__orders_1,k3_relat_1(k1_xboole_0))
    & c1_35__orders_1 != k1_xboole_0 ),
    introduced(assumption,[file(orders_1,e9_35__orders_1)]),
    [interesting(0.8),axiom,file(orders_1,e9_35__orders_1)]).

fof(cc2_finset_1,theorem,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_finset_1(B) ) ) ),
    file(finset_1,cc2_finset_1),
    [interesting(0.9),axiom,file(finset_1,cc2_finset_1)]).

fof(rc3_finset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc3_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc3_finset_1)]).

fof(rc4_finset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc4_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc4_finset_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(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(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(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(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(t3_xboole_1,theorem,(
    ! [A] : 
      ( r1_tarski(A,k1_xboole_0)
     => A = k1_xboole_0 ) ),
    file(xboole_1,t3_xboole_1),
    [interesting(0.9),axiom,file(xboole_1,t3_xboole_1)]).

fof(e10_35__orders_1,plain,(
    ? [A] : 
      ( r2_hidden(A,c1_35__orders_1)
      & r1_xboole_0(k1_wellord1(k1_xboole_0,A),c1_35__orders_1) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_35__orders_1,e9_35__orders_1])],[cc2_finset_1,fc9_finset_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_xboole_0,dt_m1_subset_1,cc1_finset_1,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,fc1_subset_1,rc1_ordinal1,rc1_partfun1,rc1_subset_1,rc2_ordinal1,rc2_subset_1,rc3_ordinal1,t1_boole,t2_subset,t4_subset,t5_subset,t8_boole,reflexivity_r1_tarski,symmetry_r1_xboole_0,antisymmetry_r2_hidden,dt_k1_wellord1,dt_k1_xboole_0,dt_k3_relat_1,dt_c1_35__orders_1,fc2_ordinal1,t1_subset,t3_subset,t6_boole,t7_boole,d6_relat_1,e9_35__orders_1,e1_35__orders_1,t3_xboole_1]),
    [interesting(0.8),file(orders_1,e10_35__orders_1),[file(orders_1,e10_35__orders_1)]]).

fof(i10_35__orders_1,theorem,(
    $true ),
    introduced(tautology,[file(orders_1,i10_35__orders_1)]),
    [interesting(0.8),trivial,file(orders_1,i10_35__orders_1)]).

fof(i9_35__orders_1,plain,(
    ? [A] : 
      ( r2_hidden(A,c1_35__orders_1)
      & r1_xboole_0(k1_wellord1(k1_xboole_0,A),c1_35__orders_1) ) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_35__orders_1,e9_35__orders_1])],[e10_35__orders_1,i10_35__orders_1]),
    [interesting(0.8),file(orders_1,i9_35__orders_1),[file(orders_1,i9_35__orders_1)]]).

fof(i8_35__orders_1,plain,(
    ~ ( r1_tarski(c1_35__orders_1,k3_relat_1(k1_xboole_0))
      & c1_35__orders_1 != k1_xboole_0
      & ! [A] : 
          ~ ( r2_hidden(A,c1_35__orders_1)
            & r1_xboole_0(k1_wellord1(k1_xboole_0,A),c1_35__orders_1) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_35__orders_1]),discharge_asm(discharge,[e9_35__orders_1])],[e9_35__orders_1,i9_35__orders_1]),
    [interesting(0.8),file(orders_1,i8_35__orders_1),[file(orders_1,i8_35__orders_1)]]).

fof(i8_35_tmp__orders_1,plain,(
    ~ ( r1_tarski(c1_35__orders_1,k3_relat_1(k1_xboole_0))
      & c1_35__orders_1 != k1_xboole_0
      & ! [A] : 
          ~ ( r2_hidden(A,c1_35__orders_1)
            & r1_xboole_0(k1_wellord1(k1_xboole_0,A),c1_35__orders_1) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_35__orders_1])],[dt_c1_35__orders_1,i8_35__orders_1]),
    [interesting(0.8),i7_35__orders_1]).

fof(i7_35__orders_1,plain,(
    v1_wellord1(k1_xboole_0) ),
    inference(let,[status(thm),assumptions([])],[i8_35_tmp__orders_1,rc1_finset_1,cc1_finset_1,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,rc1_ordinal1,rc1_partfun1,rc2_ordinal1,rc3_ordinal1,reflexivity_r1_tarski,symmetry_r1_xboole_0,antisymmetry_r2_hidden,dt_k1_wellord1,dt_k1_xboole_0,dt_k3_relat_1,fc2_ordinal1,d2_wellord1,dh_c1_35__orders_1]),
    [interesting(0.8),file(orders_1,i7_35__orders_1),[file(orders_1,i7_35__orders_1)]]).

fof(i6_35__orders_1,plain,(
    v2_wellord1(k1_xboole_0) ),
    inference(conclusion,[status(thm),assumptions([])],[rc1_finset_1,cc1_finset_1,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,rc1_ordinal1,rc1_partfun1,rc2_ordinal1,rc3_ordinal1,dt_k1_xboole_0,fc2_ordinal1,d4_wellord1,e8_35__orders_1,i7_35__orders_1]),
    [interesting(0.8),file(orders_1,i6_35__orders_1),[file(orders_1,i6_35__orders_1)]]).

fof(i5_35__orders_1,plain,
    ( v6_relat_2(k1_xboole_0)
    & v2_wellord1(k1_xboole_0) ),
    inference(conclusion,[status(thm),assumptions([])],[e7_35__orders_1,i6_35__orders_1]),
    [interesting(0.8),file(orders_1,i5_35__orders_1),[file(orders_1,i5_35__orders_1)]]).

fof(i4_35__orders_1,plain,
    ( v3_orders_1(k1_xboole_0)
    & v2_wellord1(k1_xboole_0) ),
    inference(conclusion,[status(thm),assumptions([])],[rc1_finset_1,cc1_finset_1,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,rc1_ordinal1,rc1_partfun1,rc2_ordinal1,rc3_ordinal1,dt_k1_xboole_0,fc2_ordinal1,d5_orders_1,e6_35__orders_1,i5_35__orders_1]),
    [interesting(0.8),file(orders_1,i4_35__orders_1),[file(orders_1,i4_35__orders_1)]]).

fof(i3_35__orders_1,plain,
    ( v4_relat_2(k1_xboole_0)
    & v3_orders_1(k1_xboole_0)
    & v2_wellord1(k1_xboole_0) ),
    inference(conclusion,[status(thm),assumptions([])],[e5_35__orders_1,i4_35__orders_1]),
    [interesting(0.8),file(orders_1,i3_35__orders_1),[file(orders_1,i3_35__orders_1)]]).

fof(i2_35__orders_1,plain,
    ( v2_orders_1(k1_xboole_0)
    & v3_orders_1(k1_xboole_0)
    & v2_wellord1(k1_xboole_0) ),
    inference(conclusion,[status(thm),assumptions([])],[rc1_finset_1,cc1_finset_1,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,rc1_ordinal1,rc1_partfun1,rc2_ordinal1,rc3_ordinal1,dt_k1_xboole_0,fc2_ordinal1,d4_orders_1,e4_35__orders_1,i3_35__orders_1]),
    [interesting(0.8),file(orders_1,i2_35__orders_1),[file(orders_1,i2_35__orders_1)]]).

fof(i1_35__orders_1,plain,
    ( v8_relat_2(k1_xboole_0)
    & v2_orders_1(k1_xboole_0)
    & v3_orders_1(k1_xboole_0)
    & v2_wellord1(k1_xboole_0) ),
    inference(conclusion,[status(thm),assumptions([])],[e3_35__orders_1,i2_35__orders_1]),
    [interesting(0.8),file(orders_1,i1_35__orders_1),[file(orders_1,i1_35__orders_1)]]).

fof(t119_orders_1,theorem,
    ( v1_orders_1(k1_xboole_0)
    & v2_orders_1(k1_xboole_0)
    & v3_orders_1(k1_xboole_0)
    & v2_wellord1(k1_xboole_0) ),
    inference(conclusion,[status(thm),assumptions([])],[rc1_finset_1,cc1_finset_1,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,rc1_ordinal1,rc1_partfun1,rc2_ordinal1,rc3_ordinal1,dt_k1_xboole_0,fc2_ordinal1,d3_orders_1,e2_35__orders_1,i1_35__orders_1]),
    [interesting(1),file(orders_1,t119_orders_1),[file(orders_1,t119_orders_1)]]).