fof(t7_boole,theorem,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & v1_xboole_0(B) ) ),
    inference(mizar_proof,[status(thm)],[d1_xboole_0,d5_xboole_0]),
    [file(boole,t7_boole),interesting(1.00)]).

fof(t8_boole,theorem,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    inference(mizar_proof,[status(thm)],[d5_xboole_0,d5_xboole_0]),
    [file(boole,t8_boole),interesting(0.71)]).

fof(t5_boole,theorem,(
    ! [A] : k5_xboole_0(A,k1_xboole_0) = A ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d2_xboole_0,d1_xboole_0,d4_xboole_0,d10_xboole_0,d3_tarski,d1_xboole_0,d4_xboole_0,d2_xboole_0]),
    [file(boole,t5_boole),interesting(0.32)]).

fof(t1_boole,theorem,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d2_xboole_0,d1_xboole_0,d10_xboole_0,d3_tarski,d2_xboole_0]),
    [file(boole,t1_boole),interesting(0.30)]).

fof(t3_boole,theorem,(
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d4_xboole_0,d10_xboole_0,d3_tarski,d1_xboole_0,d4_xboole_0]),
    [file(boole,t3_boole),interesting(0.30)]).

fof(t6_boole,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    inference(mizar_proof,[status(thm)],[d5_xboole_0]),
    [file(boole,t6_boole),interesting(0.13)]).

fof(d3_tarski,definition,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    [interesting(0.00)]).

fof(d2_xboole_0,definition,(
    ! [A,B,C] : 
      ( C = k2_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            | r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d2_xboole_0),
    [interesting(0.00)]).

fof(d1_xboole_0,definition,(
    ! [A] : 
      ( A = k1_xboole_0
    <=> ! [B] : ~ r2_hidden(B,A) ) ),
    file(xboole_0,d1_xboole_0),
    [interesting(0.00)]).

fof(d10_xboole_0,definition,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    [interesting(0.00)]).

fof(d3_xboole_0,definition,(
    ! [A,B,C] : 
      ( C = k3_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d3_xboole_0),
    [interesting(0.00)]).

fof(t2_boole,theorem,(
    ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d3_xboole_0,d10_xboole_0,d3_tarski,d1_xboole_0]),
    [file(boole,t2_boole),interesting(0.00)]).

fof(d4_xboole_0,definition,(
    ! [A,B,C] : 
      ( C = k4_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & ~ r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d4_xboole_0),
    [interesting(0.00)]).

fof(t4_boole,theorem,(
    ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d4_xboole_0,d10_xboole_0,d3_tarski,d1_xboole_0]),
    [file(boole,t4_boole),interesting(0.00)]).

fof(d5_xboole_0,definition,(
    ! [A] : 
      ( v1_xboole_0(A)
    <=> A = k1_xboole_0 ) ),
    file(xboole_0,d5_xboole_0),
    [interesting(0.00)]).