% Mizar ND problem: t7_boole,boole,116,54 
fof(dh_c1_6__boole,definition,
    ( ! [A] : 
        ~ ( r2_hidden(c1_6__boole,A)
          & v1_xboole_0(A) )
   => ! [B,C] : 
        ~ ( r2_hidden(B,C)
          & v1_xboole_0(C) ) ),
    introduced(definition,[new_symbol(c1_6__boole),file(boole,c1_6__boole)]),
    [interesting(0.8),axiom,file(boole,c1_6__boole)]).

fof(dh_c2_6__boole,definition,
    ( ~ ( r2_hidden(c1_6__boole,c2_6__boole)
        & v1_xboole_0(c2_6__boole) )
   => ! [A] : 
        ~ ( r2_hidden(c1_6__boole,A)
          & v1_xboole_0(A) ) ),
    introduced(definition,[new_symbol(c2_6__boole),file(boole,c2_6__boole)]),
    [interesting(0.8),axiom,file(boole,c2_6__boole)]).

fof(e1_6__boole,assumption,(
    r2_hidden(c1_6__boole,c2_6__boole) ),
    introduced(assumption,[file(boole,e1_6__boole)]),
    [interesting(0.8),axiom,file(boole,e1_6__boole)]).

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

fof(dt_c2_6__boole,assumption,(
    $true ),
    introduced(assumption,[file(boole,c2_6__boole)]),
    [interesting(0.8),axiom,file(boole,c2_6__boole)]).

fof(fc1_xboole_0,theorem,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,fc1_xboole_0)]).

fof(rc1_xboole_0,theorem,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc1_xboole_0)]).

fof(rc2_xboole_0,theorem,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc2_xboole_0)]).

fof(antisymmetry_r2_hidden,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    [interesting(0.9),axiom,file(hidden,r2_hidden)]).

fof(dt_c1_6__boole,assumption,(
    $true ),
    introduced(assumption,[file(boole,c1_6__boole)]),
    [interesting(0.8),axiom,file(boole,c1_6__boole)]).

fof(d1_xboole_0,definition,(
    ! [A] : 
      ( A = k1_xboole_0
    <=> ! [B] : ~ r2_hidden(B,A) ) ),
    file(xboole_0,d1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,d1_xboole_0)]).

fof(e2_6__boole,plain,(
    c2_6__boole != k1_xboole_0 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__boole,dt_c2_6__boole,e1_6__boole])],[rc1_xboole_0,rc2_xboole_0,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_c1_6__boole,dt_c2_6__boole,fc1_xboole_0,e1_6__boole,d1_xboole_0]),
    [interesting(0.8),file(boole,e2_6__boole),[file(boole,e2_6__boole)]]).

fof(d5_xboole_0,definition,(
    ! [A] : 
      ( v1_xboole_0(A)
    <=> A = k1_xboole_0 ) ),
    file(xboole_0,d5_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,d5_xboole_0)]).

fof(e3_6__boole,plain,(
    ~ v1_xboole_0(c2_6__boole) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__boole,dt_c2_6__boole,e1_6__boole])],[dt_k1_xboole_0,dt_c2_6__boole,fc1_xboole_0,rc1_xboole_0,rc2_xboole_0,e2_6__boole,d5_xboole_0]),
    [interesting(0.8),file(boole,e3_6__boole),[file(boole,e3_6__boole)]]).

fof(i3_6__boole,theorem,(
    $true ),
    introduced(tautology,[file(boole,i3_6__boole)]),
    [interesting(0.8),trivial,file(boole,i3_6__boole)]).

fof(i2_6__boole,plain,(
    ~ v1_xboole_0(c2_6__boole) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_6__boole,dt_c2_6__boole,e1_6__boole])],[e3_6__boole,i3_6__boole]),
    [interesting(0.8),file(boole,i2_6__boole),[file(boole,i2_6__boole)]]).

fof(i1_6__boole,plain,(
    ~ ( r2_hidden(c1_6__boole,c2_6__boole)
      & v1_xboole_0(c2_6__boole) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6__boole,dt_c2_6__boole]),discharge_asm(discharge,[e1_6__boole])],[e1_6__boole,i2_6__boole]),
    [interesting(0.8),file(boole,i1_6__boole),[file(boole,i1_6__boole)]]).

fof(i1_6_tmp__boole,plain,(
    ~ ( r2_hidden(c1_6__boole,c2_6__boole)
      & v1_xboole_0(c2_6__boole) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_6__boole,dt_c2_6__boole])],[dt_c1_6__boole,dt_c2_6__boole,i1_6__boole]),
    [interesting(1),t7_boole]).

fof(t7_boole,theorem,(
    ! [A,B] : 
      ~ ( r2_hidden(A,B)
        & v1_xboole_0(B) ) ),
    inference(let,[status(thm),assumptions([])],[i1_6_tmp__boole,dh_c1_6__boole,dh_c2_6__boole]),
    [interesting(1),file(boole,t7_boole),[file(boole,t7_boole)]]).