fof(t4_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r6_pboole(A,B,k1_pzfmisc1(A,C))
          <=> ! [D] : 
                ( m1_pboole(D,A)
               => ( r1_pboole(A,D,B)
                <=> r6_pboole(A,D,C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_pboole,d1_pzfmisc1,d1_tarski,t3_pboole,d4_pboole,d1_pzfmisc1,d1_tarski,t5_cqc_lang,t1_pzfmisc1,d3_pboole,d1_tarski,t14_funct_4,t6_cqc_lang,d4_pboole,d1_tarski,t12_funct_4,d4_pboole,d4_pboole,d1_tarski,d1_pzfmisc1,t3_pboole]),
    [file(pzfmisc1,t4_pzfmisc1),interesting(1.00)]).

fof(t5_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( ! [E] : 
                    ( m1_pboole(E,A)
                   => ( r1_pboole(A,E,B)
                    <=> ( r6_pboole(A,E,C)
                        | r6_pboole(A,E,D) ) ) )
               => r6_pboole(A,B,k2_pzfmisc1(A,C,D)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t5_cqc_lang,t1_pzfmisc1,d3_pboole,d1_tarski,t14_funct_4,t6_cqc_lang,d4_pboole,d1_tarski,t12_funct_4,d4_pboole,d4_pboole,d4_pboole,d2_tarski,d2_pzfmisc1,t3_pboole]),
    [file(pzfmisc1,t5_pzfmisc1),interesting(0.88)]).

fof(t9_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => r1_pboole(A,B,k1_pzfmisc1(A,B)) ) ),
    inference(mizar_proof,[status(thm)],[d4_pboole,d1_tarski,d1_pzfmisc1]),
    [file(pzfmisc1,t9_pzfmisc1),interesting(0.79)]).

fof(t12_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => r6_pboole(A,k2_pzfmisc1(A,B,B),k1_pzfmisc1(A,B)) ) ),
    inference(mizar_proof,[status(thm)],[d2_pzfmisc1,t69_enumset1,d1_pzfmisc1,t3_pboole]),
    [file(pzfmisc1,t12_pzfmisc1),interesting(0.77)]).

fof(t33_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => r6_pboole(A,k2_mboolean(A,k1_pzfmisc1(A,B)),B) ) ),
    inference(mizar_proof,[status(thm)],[d2_mboolean,d1_pzfmisc1,t31_zfmisc_1,t3_pboole]),
    [file(pzfmisc1,t33_pzfmisc1),interesting(0.75)]).

fof(t8_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r1_pboole(A,B,k1_pzfmisc1(A,C))
           => r6_pboole(A,B,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_pboole,d1_pzfmisc1,d1_tarski,t3_pboole]),
    [file(pzfmisc1,t8_pzfmisc1),interesting(0.66)]).

fof(t63_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r6_pboole(A,k11_pboole(A,B,B),k11_pboole(A,C,C))
           => r6_pboole(A,B,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d21_pboole,d21_pboole,t115_zfmisc_1,t3_pboole]),
    [file(pzfmisc1,t63_pzfmisc1),interesting(0.65)]).

fof(t32_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => r2_pboole(A,k1_pzfmisc1(A,B),k1_mboolean(A,B)) ) ),
    inference(mizar_proof,[status(thm)],[d5_pboole,t80_zfmisc_1,d1_pzfmisc1,d1_mboolean]),
    [file(pzfmisc1,t32_pzfmisc1),interesting(0.64)]).

fof(t15_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r6_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C))
           => r6_pboole(A,B,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_pzfmisc1,d1_pzfmisc1,t6_zfmisc_1,t3_pboole]),
    [file(pzfmisc1,t15_pzfmisc1),interesting(0.61)]).

fof(t81_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r2_pboole(A,B,C)
           => r2_pboole(A,k11_pboole(A,B,B),k11_pboole(A,C,C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_pboole,d5_pboole,t119_zfmisc_1,d21_pboole,d21_pboole]),
    [file(pzfmisc1,t81_pzfmisc1),interesting(0.59)]).

fof(t14_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r2_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C))
           => r6_pboole(A,B,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_pboole,d1_pzfmisc1,d1_pzfmisc1,t24_zfmisc_1,t3_pboole]),
    [file(pzfmisc1,t14_pzfmisc1),interesting(0.58)]).

fof(t35_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => r6_pboole(A,k2_mboolean(A,k2_pzfmisc1(A,B,C)),k2_pboole(A,B,C)) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_mboolean,d2_pzfmisc1,t93_zfmisc_1,d7_pboole,t3_pboole]),
    [file(pzfmisc1,t35_pzfmisc1),interesting(0.58)]).

fof(t36_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r2_pboole(A,k1_pzfmisc1(A,B),C)
          <=> r1_pboole(A,B,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_pboole,d5_pboole,d1_pzfmisc1,t37_zfmisc_1,d5_pboole,d4_pboole,t37_zfmisc_1,d1_pzfmisc1]),
    [file(pzfmisc1,t36_pzfmisc1),interesting(0.57)]).

fof(t17_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( r6_pboole(A,k1_pzfmisc1(A,B),k2_pzfmisc1(A,C,D))
               => r6_pboole(A,C,D) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_pzfmisc1,d2_pzfmisc1,t9_zfmisc_1,t3_pboole]),
    [file(pzfmisc1,t17_pzfmisc1),interesting(0.56)]).

fof(t42_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r1_pboole(A,B,C)
           => r6_pboole(A,k2_pboole(A,k1_pzfmisc1(A,B),C),C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_pboole,d7_pboole,d1_pzfmisc1,t46_zfmisc_1,t3_pboole]),
    [file(pzfmisc1,t42_pzfmisc1),interesting(0.56)]).

fof(t3_pzfmisc1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => ~ ( v3_relat_1(B)
              & v2_relat_1(B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_xboole_0,d15_pboole,d16_pboole]),
    [file(pzfmisc1,t3_pzfmisc1),interesting(0.53)]).

fof(t1_pzfmisc1,theorem,(
    ! [A,B,C,D] : 
      ( m1_pboole(D,A)
     => ( r2_hidden(B,A)
       => k1_relat_1(k1_funct_4(D,k3_cqc_lang(B,C))) = A ) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_4,d3_pboole,t5_cqc_lang,t46_zfmisc_1]),
    [file(pzfmisc1,t1_pzfmisc1),interesting(0.53)]).

fof(t11_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => r6_pboole(A,k2_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C)),k2_pzfmisc1(A,B,C)) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_pboole,d1_pzfmisc1,d1_pzfmisc1,t41_enumset1,d2_pzfmisc1,t3_pboole]),
    [file(pzfmisc1,t11_pzfmisc1),interesting(0.51)]).

fof(t16_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( r6_pboole(A,k1_pzfmisc1(A,B),k2_pzfmisc1(A,C,D))
               => ( r6_pboole(A,B,C)
                  & r6_pboole(A,B,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_pzfmisc1,d2_pzfmisc1,t8_zfmisc_1,t3_pboole,d1_pzfmisc1,d2_pzfmisc1,t8_zfmisc_1,t3_pboole]),
    [file(pzfmisc1,t16_pzfmisc1),interesting(0.51)]).

fof(t20_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => r6_pboole(A,k2_pboole(A,k1_pzfmisc1(A,B),k2_pzfmisc1(A,B,C)),k2_pzfmisc1(A,B,C)) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_pboole,d1_pzfmisc1,d2_pzfmisc1,t14_zfmisc_1,d2_pzfmisc1,t3_pboole]),
    [file(pzfmisc1,t20_pzfmisc1),interesting(0.51)]).

fof(t10_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( ( r6_pboole(A,B,C)
                  | r6_pboole(A,B,D) )
               => r1_pboole(A,B,k2_pzfmisc1(A,C,D)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_pboole,d2_tarski,d2_pzfmisc1,d4_pboole,d2_tarski,d2_pzfmisc1]),
    [file(pzfmisc1,t10_pzfmisc1),interesting(0.50)]).

fof(t47_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r1_pboole(A,B,C)
           => r6_pboole(A,k3_pboole(A,C,k1_pzfmisc1(A,B)),k1_pzfmisc1(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_pboole,d8_pboole,d1_pzfmisc1,t52_zfmisc_1,d1_pzfmisc1,t3_pboole]),
    [file(pzfmisc1,t47_pzfmisc1),interesting(0.50)]).

fof(t51_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( r1_pboole(A,B,k4_pboole(A,C,k1_pzfmisc1(A,D)))
               => r1_pboole(A,B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_pboole,d4_pboole,d9_pboole,d1_pzfmisc1,t64_zfmisc_1]),
    [file(pzfmisc1,t51_pzfmisc1),interesting(0.50)]).

fof(t28_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r2_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C))
           => r6_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_pboole,d1_pzfmisc1,d1_pzfmisc1,d1_pzfmisc1,t24_zfmisc_1,d1_pzfmisc1,t3_pboole]),
    [file(pzfmisc1,t28_pzfmisc1),interesting(0.49)]).

fof(t62_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( ( v2_relat_1(B)
              & v2_relat_1(C)
              & r6_pboole(A,k11_pboole(A,B,C),k11_pboole(A,C,B)) )
           => r6_pboole(A,B,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d16_pboole,d21_pboole,d21_pboole,t114_zfmisc_1,t3_pboole]),
    [file(pzfmisc1,t62_pzfmisc1),interesting(0.49)]).

fof(t66_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ! [E] : 
                  ( m1_pboole(E,A)
                 => ( ( r2_pboole(A,B,C)
                      & r2_pboole(A,D,E) )
                   => r2_pboole(A,k11_pboole(A,B,D),k11_pboole(A,C,E)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_pboole,d5_pboole,t119_zfmisc_1,d21_pboole,d21_pboole]),
    [file(pzfmisc1,t66_pzfmisc1),interesting(0.49)]).

fof(t37_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( r2_pboole(A,k2_pzfmisc1(A,B,C),D)
              <=> ( r1_pboole(A,B,D)
                  & r1_pboole(A,C,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_pboole,d5_pboole,d2_pzfmisc1,t38_zfmisc_1,d4_pboole,d5_pboole,d2_pzfmisc1,t38_zfmisc_1,d5_pboole,d4_pboole,t38_zfmisc_1,d2_pzfmisc1]),
    [file(pzfmisc1,t37_pzfmisc1),interesting(0.48)]).

fof(t65_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( r2_pboole(A,B,C)
               => ( r2_pboole(A,k11_pboole(A,B,D),k11_pboole(A,C,D))
                  & r2_pboole(A,k11_pboole(A,D,B),k11_pboole(A,D,C)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_pboole,d5_pboole,t118_zfmisc_1,d21_pboole,d21_pboole,d5_pboole,d5_pboole,t118_zfmisc_1,d21_pboole,d21_pboole]),
    [file(pzfmisc1,t65_pzfmisc1),interesting(0.47)]).

fof(t41_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r6_pboole(A,k2_pboole(A,k1_pzfmisc1(A,B),C),C)
           => r1_pboole(A,B,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_pboole,d1_pzfmisc1,d7_pboole,t45_zfmisc_1]),
    [file(pzfmisc1,t41_pzfmisc1),interesting(0.46)]).

fof(t61_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( ( r6_pboole(A,B,k1_pboole(A))
              | r6_pboole(A,C,k1_pboole(A)) )
           => r6_pboole(A,k11_pboole(A,B,C),k1_pboole(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t5_pboole,d21_pboole,t113_zfmisc_1,t5_pboole,t3_pboole,t5_pboole,d21_pboole,t113_zfmisc_1,t5_pboole,t3_pboole]),
    [file(pzfmisc1,t61_pzfmisc1),interesting(0.46)]).

fof(t34_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => r6_pboole(A,k2_mboolean(A,k2_pzfmisc1(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C))),k2_pzfmisc1(A,B,C)) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_mboolean,d2_pzfmisc1,d1_pzfmisc1,d1_pzfmisc1,t32_zfmisc_1,d2_pzfmisc1,t3_pboole]),
    [file(pzfmisc1,t34_pzfmisc1),interesting(0.45)]).

fof(t43_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( r6_pboole(A,k2_pboole(A,k2_pzfmisc1(A,B,C),D),D)
              <=> ( r1_pboole(A,B,D)
                  & r1_pboole(A,C,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_pboole,d2_pzfmisc1,d7_pboole,t47_zfmisc_1,d4_pboole,d2_pzfmisc1,d7_pboole,t47_zfmisc_1,d4_pboole,d7_pboole,d2_pzfmisc1,t48_zfmisc_1,t3_pboole]),
    [file(pzfmisc1,t43_pzfmisc1),interesting(0.45)]).

fof(t46_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r6_pboole(A,k3_pboole(A,B,k1_pzfmisc1(A,C)),k1_pzfmisc1(A,C))
           => r1_pboole(A,C,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_pboole,d1_pzfmisc1,d8_pboole,d1_pzfmisc1,t51_zfmisc_1]),
    [file(pzfmisc1,t46_pzfmisc1),interesting(0.44)]).

fof(t48_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( ( r1_pboole(A,B,C)
                  & r1_pboole(A,D,C) )
              <=> r6_pboole(A,k3_pboole(A,k2_pzfmisc1(A,B,D),C),k2_pzfmisc1(A,B,D)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_pboole,d8_pboole,d2_pzfmisc1,t53_zfmisc_1,d2_pzfmisc1,t3_pboole,d4_pboole,d2_pzfmisc1,d8_pboole,d2_pzfmisc1,t63_zfmisc_1,d4_pboole,d2_pzfmisc1,d8_pboole,d2_pzfmisc1,t63_zfmisc_1]),
    [file(pzfmisc1,t48_pzfmisc1),interesting(0.44)]).

fof(t18_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r2_pboole(A,k1_pzfmisc1(A,B),k2_pzfmisc1(A,B,C))
            & r2_pboole(A,k1_pzfmisc1(A,C),k2_pzfmisc1(A,B,C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_pboole,t12_zfmisc_1,d1_pzfmisc1,d2_pzfmisc1,d5_pboole,t12_zfmisc_1,d1_pzfmisc1,d2_pzfmisc1]),
    [file(pzfmisc1,t18_pzfmisc1),interesting(0.43)]).

fof(t70_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ! [E] : 
                  ( m1_pboole(E,A)
                 => r6_pboole(A,k11_pboole(A,k3_pboole(A,B,C),k3_pboole(A,D,E)),k3_pboole(A,k11_pboole(A,B,D),k11_pboole(A,C,E))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d21_pboole,d8_pboole,d8_pboole,t123_zfmisc_1,d21_pboole,d21_pboole,d8_pboole,t3_pboole]),
    [file(pzfmisc1,t70_pzfmisc1),interesting(0.43)]).

fof(t26_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r6_pboole(A,k4_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C)),k1_pboole(A))
           => r6_pboole(A,B,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_pzfmisc1,d1_pzfmisc1,d9_pboole,t5_pboole,t21_zfmisc_1,t3_pboole]),
    [file(pzfmisc1,t26_pzfmisc1),interesting(0.42)]).

fof(t29_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( r2_pboole(A,k2_pzfmisc1(A,B,C),k1_pzfmisc1(A,D))
               => ( r6_pboole(A,B,D)
                  & r6_pboole(A,C,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_pboole,d1_pzfmisc1,d2_pzfmisc1,t26_zfmisc_1,t3_pboole,d5_pboole,d1_pzfmisc1,d2_pzfmisc1,t26_zfmisc_1,t3_pboole]),
    [file(pzfmisc1,t29_pzfmisc1),interesting(0.42)]).

fof(t6_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( r6_pboole(A,B,k2_pzfmisc1(A,C,D))
               => ! [E] : 
                    ( m1_pboole(E,A)
                   => ( ( r6_pboole(A,E,C)
                        | r6_pboole(A,E,D) )
                     => r1_pboole(A,E,B) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_pboole,d2_pzfmisc1,d2_tarski,d2_tarski]),
    [file(pzfmisc1,t6_pzfmisc1),interesting(0.42)]).

fof(t75_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( v2_relat_1(B)
           => ( v2_relat_1(k11_pboole(A,k1_pzfmisc1(A,C),B))
              & v2_relat_1(k11_pboole(A,B,k1_pzfmisc1(A,C))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d16_pboole,d16_pboole,t130_zfmisc_1,d1_pzfmisc1,d21_pboole,d16_pboole,d16_pboole,t130_zfmisc_1,d1_pzfmisc1,d21_pboole]),
    [file(pzfmisc1,t75_pzfmisc1),interesting(0.40)]).

fof(t78_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( ( r2_pboole(A,B,k11_pboole(A,B,C))
              | r2_pboole(A,B,k11_pboole(A,C,B)) )
           => r6_pboole(A,B,k1_pboole(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_pboole,d21_pboole,t135_zfmisc_1,t5_pboole,t3_pboole,d5_pboole,d21_pboole,t135_zfmisc_1,t5_pboole,t3_pboole]),
    [file(pzfmisc1,t78_pzfmisc1),interesting(0.40)]).

fof(t30_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( r2_pboole(A,k2_pzfmisc1(A,B,C),k1_pzfmisc1(A,D))
               => r6_pboole(A,k2_pzfmisc1(A,B,C),k1_pzfmisc1(A,D)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_pboole,d2_pzfmisc1,d1_pzfmisc1,d2_pzfmisc1,t27_zfmisc_1,d1_pzfmisc1,t3_pboole]),
    [file(pzfmisc1,t30_pzfmisc1),interesting(0.39)]).

fof(t39_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( ( r1_pboole(A,B,C)
                  | r6_pboole(A,B,D) )
               => r1_pboole(A,B,k2_pboole(A,C,k1_pzfmisc1(A,D))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_pboole,d4_pboole,t6_setwiseo,d1_pzfmisc1,d7_pboole,t6_setwiseo,d1_pzfmisc1,d7_pboole]),
    [file(pzfmisc1,t39_pzfmisc1),interesting(0.39)]).

fof(t77_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ! [E] : 
                  ( m1_pboole(E,A)
                 => ( ( v2_relat_1(B)
                      & v2_relat_1(C)
                      & r6_pboole(A,k11_pboole(A,B,C),k11_pboole(A,D,E)) )
                   => ( r6_pboole(A,B,D)
                      & r6_pboole(A,C,E) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d16_pboole,d21_pboole,d21_pboole,t134_zfmisc_1,t3_pboole,d16_pboole,d21_pboole,d21_pboole,t134_zfmisc_1,t3_pboole]),
    [file(pzfmisc1,t77_pzfmisc1),interesting(0.39)]).

fof(t31_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => r6_pboole(A,k1_mboolean(A,k1_pzfmisc1(A,B)),k2_pzfmisc1(A,k1_pboole(A),k1_pzfmisc1(A,B))) ) ),
    inference(mizar_proof,[status(thm)],[d1_mboolean,d1_pzfmisc1,t30_zfmisc_1,t5_pboole,d1_pzfmisc1,d2_pzfmisc1,t3_pboole]),
    [file(pzfmisc1,t31_pzfmisc1),interesting(0.38)]).

fof(t55_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r6_pboole(A,k4_pboole(A,k1_pzfmisc1(A,B),C),k1_pboole(A))
          <=> r1_pboole(A,B,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_pboole,d1_pzfmisc1,d9_pboole,t5_pboole,t68_zfmisc_1,d4_pboole,d9_pboole,d1_pzfmisc1,t68_zfmisc_1,t5_pboole,t3_pboole]),
    [file(pzfmisc1,t55_pzfmisc1),interesting(0.37)]).

fof(t19_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( ( r6_pboole(A,k2_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C)),k1_pzfmisc1(A,B))
              | r6_pboole(A,k2_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C)),k1_pzfmisc1(A,C)) )
           => r6_pboole(A,B,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_pzfmisc1,d1_pzfmisc1,d7_pboole,d1_pzfmisc1,t13_zfmisc_1,d1_pzfmisc1,d1_pzfmisc1,d7_pboole,d1_pzfmisc1,t13_zfmisc_1,t3_pboole]),
    [file(pzfmisc1,t19_pzfmisc1),interesting(0.35)]).

fof(t23_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( ( r6_pboole(A,k3_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C)),k1_pzfmisc1(A,B))
              | r6_pboole(A,k3_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C)),k1_pzfmisc1(A,C)) )
           => r6_pboole(A,B,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_pzfmisc1,d1_pzfmisc1,d8_pboole,d1_pzfmisc1,t18_zfmisc_1,t3_pboole,d1_pzfmisc1,d1_pzfmisc1,d8_pboole,d1_pzfmisc1,t18_zfmisc_1,t3_pboole]),
    [file(pzfmisc1,t23_pzfmisc1),interesting(0.35)]).

fof(t40_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( r2_pboole(A,k2_pboole(A,B,k1_pzfmisc1(A,C)),D)
              <=> ( r1_pboole(A,C,D)
                  & r2_pboole(A,B,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_pboole,d7_pboole,d1_pzfmisc1,d4_pboole,t8_setwiseo,d5_pboole,t8_setwiseo,d5_pboole,d4_pboole,d5_pboole,t8_setwiseo,d1_pzfmisc1,d7_pboole]),
    [file(pzfmisc1,t40_pzfmisc1),interesting(0.35)]).

fof(t2_pzfmisc1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( A = k1_xboole_0
       => m1_pboole(A,k1_xboole_0) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_pboole,t60_relat_1]),
    [file(pzfmisc1,t2_pzfmisc1),interesting(0.34)]).

fof(t82_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r6_pboole(A,k3_pboole(A,B,C),k1_pboole(A))
           => r6_pboole(A,k3_pboole(A,k11_pboole(A,B,C),k11_pboole(A,C,B)),k1_pboole(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_pboole,t5_pboole,d7_xboole_0,t127_zfmisc_1,d8_pboole,d21_pboole,d21_pboole,d7_xboole_0,t5_pboole,t3_pboole]),
    [file(pzfmisc1,t82_pzfmisc1),interesting(0.34)]).

fof(t53_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ~ ( ~ v1_xboole_0(A)
              & r6_pboole(A,k4_pboole(A,B,k1_pzfmisc1(A,C)),B)
              & r1_pboole(A,C,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_pzfmisc1,d9_pboole,d1_xboole_0,t65_zfmisc_1,d4_pboole]),
    [file(pzfmisc1,t53_pzfmisc1),interesting(0.33)]).

fof(t64_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( v2_relat_1(B)
               => ( ( ~ r2_pboole(A,k11_pboole(A,C,B),k11_pboole(A,D,B))
                    & ~ r2_pboole(A,k11_pboole(A,B,C),k11_pboole(A,B,D)) )
                  | r2_pboole(A,C,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_pboole,d16_pboole,d5_pboole,d21_pboole,d21_pboole,t117_zfmisc_1,d5_pboole,d16_pboole,d5_pboole,d21_pboole,d21_pboole,t117_zfmisc_1]),
    [file(pzfmisc1,t64_pzfmisc1),interesting(0.33)]).

fof(t71_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ! [E] : 
                  ( m1_pboole(E,A)
                 => ( ( r2_pboole(A,B,C)
                      & r2_pboole(A,D,E) )
                   => r6_pboole(A,k3_pboole(A,k11_pboole(A,B,E),k11_pboole(A,C,D)),k11_pboole(A,B,D)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_pboole,d8_pboole,d21_pboole,d21_pboole,t124_zfmisc_1,d21_pboole,t3_pboole]),
    [file(pzfmisc1,t71_pzfmisc1),interesting(0.32)]).

fof(t80_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ! [E] : 
                  ( m1_pboole(E,A)
                 => ( ( r2_pboole(A,k11_pboole(A,B,C),k11_pboole(A,D,E))
                      & v2_relat_1(k11_pboole(A,B,C)) )
                   => ( r2_pboole(A,B,D)
                      & r2_pboole(A,C,E) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_pboole,d5_pboole,d21_pboole,d21_pboole,d16_pboole,d21_pboole,t138_zfmisc_1,d5_pboole,d5_pboole,d21_pboole,d21_pboole,d16_pboole,d21_pboole,t138_zfmisc_1]),
    [file(pzfmisc1,t80_pzfmisc1),interesting(0.32)]).

fof(t79_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ! [E] : 
                  ( m1_pboole(E,A)
                 => ! [F] : 
                      ( m1_pboole(F,A)
                     => ( ( r1_pboole(A,B,k11_pboole(A,C,D))
                          & r1_pboole(A,B,k11_pboole(A,E,F)) )
                       => r1_pboole(A,B,k11_pboole(A,k3_pboole(A,C,E),k3_pboole(A,D,F))) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_pboole,d4_pboole,d21_pboole,t137_zfmisc_1,d8_pboole,d8_pboole,d21_pboole]),
    [file(pzfmisc1,t79_pzfmisc1),interesting(0.31)]).

fof(t83_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ! [E] : 
                  ( m1_pboole(E,A)
                 => ( v2_relat_1(B)
                   => ( ( ~ r2_pboole(A,k11_pboole(A,B,C),k11_pboole(A,D,E))
                        & ~ r2_pboole(A,k11_pboole(A,C,B),k11_pboole(A,E,D)) )
                      | r2_pboole(A,C,E) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_pboole,d5_pboole,d21_pboole,d21_pboole,d16_pboole,t139_zfmisc_1,d5_pboole,d5_pboole,d21_pboole,d21_pboole,d16_pboole,t139_zfmisc_1]),
    [file(pzfmisc1,t83_pzfmisc1),interesting(0.31)]).

fof(t24_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r6_pboole(A,k3_pboole(A,k1_pzfmisc1(A,B),k2_pzfmisc1(A,B,C)),k1_pzfmisc1(A,B))
            & r6_pboole(A,k3_pboole(A,k1_pzfmisc1(A,C),k2_pzfmisc1(A,B,C)),k1_pzfmisc1(A,C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_pboole,d1_pzfmisc1,d2_pzfmisc1,t19_zfmisc_1,d1_pzfmisc1,t3_pboole,d8_pboole,d1_pzfmisc1,d2_pzfmisc1,t19_zfmisc_1,d1_pzfmisc1,t3_pboole]),
    [file(pzfmisc1,t24_pzfmisc1),interesting(0.29)]).

fof(t54_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ~ ( ~ v1_xboole_0(A)
              & r6_pboole(A,k4_pboole(A,k1_pzfmisc1(A,B),C),k1_pzfmisc1(A,B))
              & r1_pboole(A,B,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_xboole_0,d1_pzfmisc1,d9_pboole,d1_pzfmisc1,t67_zfmisc_1,d4_pboole]),
    [file(pzfmisc1,t54_pzfmisc1),interesting(0.28)]).

fof(t73_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ! [E] : 
                  ( m1_pboole(E,A)
                 => r6_pboole(A,k4_pboole(A,k11_pboole(A,B,C),k11_pboole(A,D,E)),k2_pboole(A,k11_pboole(A,k4_pboole(A,B,D),C),k11_pboole(A,B,k4_pboole(A,C,E)))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d9_pboole,d21_pboole,d21_pboole,t126_zfmisc_1,d9_pboole,d9_pboole,d21_pboole,d21_pboole,d7_pboole,t3_pboole]),
    [file(pzfmisc1,t73_pzfmisc1),interesting(0.28)]).

fof(t59_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( r6_pboole(A,k4_pboole(A,k2_pzfmisc1(A,B,C),D),k1_pboole(A))
              <=> ( r1_pboole(A,B,D)
                  & r1_pboole(A,C,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_pboole,d2_pzfmisc1,d9_pboole,t5_pboole,t73_zfmisc_1,d4_pboole,d2_pzfmisc1,d9_pboole,t5_pboole,t73_zfmisc_1,d4_pboole,d9_pboole,d2_pzfmisc1,t73_zfmisc_1,t5_pboole,t3_pboole]),
    [file(pzfmisc1,t59_pzfmisc1),interesting(0.27)]).

fof(t52_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ~ ( ~ v1_xboole_0(A)
                  & r1_pboole(A,B,k4_pboole(A,C,k1_pzfmisc1(A,D)))
                  & B = D ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_xboole_0,d4_pboole,d9_pboole,d1_pzfmisc1,t64_zfmisc_1]),
    [file(pzfmisc1,t52_pzfmisc1),interesting(0.22)]).

fof(t25_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ~ ( ~ v1_xboole_0(A)
              & r6_pboole(A,k4_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C)),k1_pzfmisc1(A,B))
              & B = C ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_xboole_0,d1_pzfmisc1,d1_pzfmisc1,d9_pboole,d1_pzfmisc1,t20_zfmisc_1]),
    [file(pzfmisc1,t25_pzfmisc1),interesting(0.21)]).

fof(t44_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ~ ( ~ v1_xboole_0(A)
              & k2_pboole(A,k1_pzfmisc1(A,B),C) = k1_pboole(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_xboole_0,d1_pzfmisc1,d7_pboole,t5_pboole]),
    [file(pzfmisc1,t44_pzfmisc1),interesting(0.21)]).

fof(t58_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( r6_pboole(A,k4_pboole(A,k2_pzfmisc1(A,B,C),D),k2_pzfmisc1(A,B,C))
               => ( v1_xboole_0(A)
                  | ( ~ r1_pboole(A,B,D)
                    & ~ r1_pboole(A,C,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_xboole_0,d2_pzfmisc1,d9_pboole,d2_pzfmisc1,t72_zfmisc_1,d4_pboole,d2_pzfmisc1,d9_pboole,d2_pzfmisc1,t72_zfmisc_1,d4_pboole]),
    [file(pzfmisc1,t58_pzfmisc1),interesting(0.21)]).

fof(t74_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ! [E] : 
                  ( m1_pboole(E,A)
                 => ( ( r6_pboole(A,k3_pboole(A,B,C),k1_pboole(A))
                      | r6_pboole(A,k3_pboole(A,D,E),k1_pboole(A)) )
                   => r6_pboole(A,k3_pboole(A,k11_pboole(A,B,D),k11_pboole(A,C,E)),k1_pboole(A)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_pboole,t5_pboole,d7_xboole_0,t127_zfmisc_1,d8_pboole,d21_pboole,d21_pboole,d7_xboole_0,t5_pboole,t3_pboole,d8_pboole,t5_pboole,d7_xboole_0,t127_zfmisc_1,d8_pboole,d21_pboole,d21_pboole,d7_xboole_0,t5_pboole,t3_pboole]),
    [file(pzfmisc1,t74_pzfmisc1),interesting(0.18)]).

fof(t45_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ~ ( ~ v1_xboole_0(A)
                  & k2_pboole(A,k2_pzfmisc1(A,B,C),D) = k1_pboole(A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_xboole_0,d2_pzfmisc1,d7_pboole,t5_pboole]),
    [file(pzfmisc1,t45_pzfmisc1),interesting(0.17)]).

fof(t27_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r6_pboole(A,k4_pboole(A,k1_pzfmisc1(A,B),k2_pzfmisc1(A,B,C)),k1_pboole(A))
            & r6_pboole(A,k4_pboole(A,k1_pzfmisc1(A,C),k2_pzfmisc1(A,B,C)),k1_pboole(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d9_pboole,d1_pzfmisc1,d2_pzfmisc1,t22_zfmisc_1,t5_pboole,t3_pboole,d9_pboole,d1_pzfmisc1,d2_pzfmisc1,t22_zfmisc_1,t5_pboole,t3_pboole]),
    [file(pzfmisc1,t27_pzfmisc1),interesting(0.15)]).

fof(t49_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ~ ( ~ v1_xboole_0(A)
              & r6_pboole(A,k3_pboole(A,k1_pzfmisc1(A,B),C),k1_pboole(A))
              & r1_pboole(A,B,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_xboole_0,d1_pzfmisc1,d8_pboole,t5_pboole,d7_xboole_0,t54_zfmisc_1,d4_pboole]),
    [file(pzfmisc1,t49_pzfmisc1),interesting(0.14)]).

fof(t56_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ~ ( ~ v1_xboole_0(A)
                  & r6_pboole(A,k4_pboole(A,k2_pzfmisc1(A,B,C),D),k1_pzfmisc1(A,B))
                  & r1_pboole(A,B,D) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_xboole_0,d2_pzfmisc1,d9_pboole,d1_pzfmisc1,t70_zfmisc_1,d4_pboole]),
    [file(pzfmisc1,t56_pzfmisc1),interesting(0.14)]).

fof(t38_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( ~ ( ~ r6_pboole(A,B,k1_pboole(A))
                    & ~ r6_pboole(A,B,k1_pzfmisc1(A,C))
                    & ~ r6_pboole(A,B,k1_pzfmisc1(A,D))
                    & ~ r6_pboole(A,B,k2_pzfmisc1(A,C,D)) )
               => r2_pboole(A,B,k2_pzfmisc1(A,C,D)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_pboole,t5_pboole,t42_zfmisc_1,d2_pzfmisc1,d1_pzfmisc1,t42_zfmisc_1,d2_pzfmisc1,d1_pzfmisc1,t42_zfmisc_1,d2_pzfmisc1]),
    [file(pzfmisc1,t38_pzfmisc1),interesting(0.10)]).

fof(t60_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( ~ ( ~ r6_pboole(A,B,k1_pboole(A))
                    & ~ r6_pboole(A,B,k1_pzfmisc1(A,C))
                    & ~ r6_pboole(A,B,k1_pzfmisc1(A,D))
                    & ~ r6_pboole(A,B,k2_pzfmisc1(A,C,D)) )
               => r6_pboole(A,k4_pboole(A,B,k2_pzfmisc1(A,C,D)),k1_pboole(A)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t5_pboole,d9_pboole,t5_pboole,d1_pzfmisc1,d9_pboole,d2_pzfmisc1,t75_zfmisc_1,t5_pboole,d1_pzfmisc1,d9_pboole,d2_pzfmisc1,t75_zfmisc_1,t5_pboole,d2_pzfmisc1,d9_pboole,d2_pzfmisc1,t75_zfmisc_1,t5_pboole,t3_pboole]),
    [file(pzfmisc1,t60_pzfmisc1),interesting(0.08)]).

fof(t50_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( r6_pboole(A,k3_pboole(A,k2_pzfmisc1(A,B,C),D),k1_pboole(A))
               => ( v1_xboole_0(A)
                  | ( ~ r1_pboole(A,B,D)
                    & ~ r1_pboole(A,C,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_pzfmisc1,d8_pboole,t5_pboole,d1_xboole_0,d7_xboole_0,t55_zfmisc_1,d4_pboole,d1_xboole_0,d7_xboole_0,t55_zfmisc_1,d4_pboole]),
    [file(pzfmisc1,t50_pzfmisc1),interesting(0.05)]).

fof(t22_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ~ ( ~ v1_xboole_0(A)
              & r6_pboole(A,k3_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C)),k1_pboole(A))
              & B = C ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_xboole_0,d1_pzfmisc1,d1_pzfmisc1,d8_pboole,t5_pboole]),
    [file(pzfmisc1,t22_pzfmisc1),interesting(0.03)]).

fof(d4_pboole,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r1_pboole(A,B,C)
          <=> ! [D] : 
                ( r2_hidden(D,A)
               => r2_hidden(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) ) ),
    file(pboole,d4_pboole),
    [interesting(0.00)]).

fof(d2_tarski,definition,(
    ! [A,B,C] : 
      ( C = k2_tarski(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( D = A
            | D = B ) ) ) ),
    file(tarski,d2_tarski),
    [interesting(0.00)]).

fof(d2_pzfmisc1,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( D = k2_pzfmisc1(A,B,C)
              <=> ! [E] : 
                    ( r2_hidden(E,A)
                   => k1_funct_1(D,E) = k2_tarski(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ),
    file(pzfmisc1,d2_pzfmisc1),
    [interesting(0.00)]).

fof(d7_pboole,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( D = k2_pboole(A,B,C)
              <=> ! [E] : 
                    ( r2_hidden(E,A)
                   => k1_funct_1(D,E) = k2_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ),
    file(pboole,d7_pboole),
    [interesting(0.00)]).

fof(d1_pzfmisc1,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( C = k1_pzfmisc1(A,B)
          <=> ! [D] : 
                ( r2_hidden(D,A)
               => k1_funct_1(C,D) = k1_tarski(k1_funct_1(B,D)) ) ) ) ) ),
    file(pzfmisc1,d1_pzfmisc1),
    [interesting(0.00)]).

fof(t41_enumset1,theorem,(
    ! [A,B] : k2_tarski(A,B) = k2_xboole_0(k1_tarski(A),k1_tarski(B)) ),
    file(enumset1,t41_enumset1),
    [interesting(0.00)]).

fof(t3_pboole,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( ! [D] : 
                ( r2_hidden(D,A)
               => k1_funct_1(B,D) = k1_funct_1(C,D) )
           => B = C ) ) ) ),
    file(pboole,t3_pboole),
    [interesting(0.00)]).

fof(t69_enumset1,theorem,(
    ! [A] : k2_tarski(A,A) = k1_tarski(A) ),
    file(enumset1,t69_enumset1),
    [interesting(0.00)]).

fof(t13_pzfmisc1,theorem,(
    $true ),
    file(pzfmisc1,t13_pzfmisc1),
    [interesting(0.00)]).

fof(d5_pboole,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r2_pboole(A,B,C)
          <=> ! [D] : 
                ( r2_hidden(D,A)
               => r1_tarski(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) ) ),
    file(pboole,d5_pboole),
    [interesting(0.00)]).

fof(t24_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(k1_tarski(A),k1_tarski(B))
     => A = B ) ),
    file(zfmisc_1,t24_zfmisc_1),
    [interesting(0.00)]).

fof(t6_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(k1_tarski(A),k1_tarski(B))
     => A = B ) ),
    file(zfmisc_1,t6_zfmisc_1),
    [interesting(0.00)]).

fof(t8_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( k1_tarski(A) = k2_tarski(B,C)
     => A = B ) ),
    file(zfmisc_1,t8_zfmisc_1),
    [interesting(0.00)]).

fof(t9_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( k1_tarski(A) = k2_tarski(B,C)
     => B = C ) ),
    file(zfmisc_1,t9_zfmisc_1),
    [interesting(0.00)]).

fof(t12_zfmisc_1,theorem,(
    ! [A,B] : r1_tarski(k1_tarski(A),k2_tarski(A,B)) ),
    file(zfmisc_1,t12_zfmisc_1),
    [interesting(0.00)]).

fof(t13_zfmisc_1,theorem,(
    ! [A,B] : 
      ( k2_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A)
     => A = B ) ),
    file(zfmisc_1,t13_zfmisc_1),
    [interesting(0.00)]).

fof(t14_zfmisc_1,theorem,(
    ! [A,B] : k2_xboole_0(k1_tarski(A),k2_tarski(A,B)) = k2_tarski(A,B) ),
    file(zfmisc_1,t14_zfmisc_1),
    [interesting(0.00)]).

fof(t21_pzfmisc1,theorem,(
    $true ),
    file(pzfmisc1,t21_pzfmisc1),
    [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(d8_pboole,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( D = k3_pboole(A,B,C)
              <=> ! [E] : 
                    ( r2_hidden(E,A)
                   => k1_funct_1(D,E) = k3_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ),
    file(pboole,d8_pboole),
    [interesting(0.00)]).

fof(t5_pboole,theorem,(
    ! [A,B] : k1_funct_1(k1_pboole(B),A) = k1_xboole_0 ),
    file(pboole,t5_pboole),
    [interesting(0.00)]).

fof(t18_zfmisc_1,theorem,(
    ! [A,B] : 
      ( k3_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A)
     => A = B ) ),
    file(zfmisc_1,t18_zfmisc_1),
    [interesting(0.00)]).

fof(t19_zfmisc_1,theorem,(
    ! [A,B] : k3_xboole_0(k1_tarski(A),k2_tarski(A,B)) = k1_tarski(A) ),
    file(zfmisc_1,t19_zfmisc_1),
    [interesting(0.00)]).

fof(d9_pboole,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( D = k4_pboole(A,B,C)
              <=> ! [E] : 
                    ( r2_hidden(E,A)
                   => k1_funct_1(D,E) = k4_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ),
    file(pboole,d9_pboole),
    [interesting(0.00)]).

fof(t20_zfmisc_1,theorem,(
    ! [A,B] : 
      ( k4_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A)
    <=> A != B ) ),
    file(zfmisc_1,t20_zfmisc_1),
    [interesting(0.00)]).

fof(t21_zfmisc_1,theorem,(
    ! [A,B] : 
      ( k4_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_xboole_0
     => A = B ) ),
    file(zfmisc_1,t21_zfmisc_1),
    [interesting(0.00)]).

fof(t22_zfmisc_1,theorem,(
    ! [A,B] : k4_xboole_0(k1_tarski(A),k2_tarski(A,B)) = k1_xboole_0 ),
    file(zfmisc_1,t22_zfmisc_1),
    [interesting(0.00)]).

fof(t26_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(k2_tarski(A,B),k1_tarski(C))
     => A = C ) ),
    file(zfmisc_1,t26_zfmisc_1),
    [interesting(0.00)]).

fof(d3_pboole,definition,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( m1_pboole(B,A)
      <=> k1_relat_1(B) = A ) ) ),
    file(pboole,d3_pboole),
    [interesting(0.00)]).

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(0.00)]).

fof(t27_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(k2_tarski(A,B),k1_tarski(C))
     => k2_tarski(A,B) = k1_tarski(C) ) ),
    file(zfmisc_1,t27_zfmisc_1),
    [interesting(0.00)]).

fof(d1_mboolean,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( C = k1_mboolean(A,B)
          <=> ! [D] : 
                ( r2_hidden(D,A)
               => k1_funct_1(C,D) = k1_zfmisc_1(k1_funct_1(B,D)) ) ) ) ) ),
    file(mboolean,d1_mboolean),
    [interesting(0.00)]).

fof(t30_zfmisc_1,theorem,(
    ! [A] : k1_zfmisc_1(k1_tarski(A)) = k2_tarski(k1_xboole_0,k1_tarski(A)) ),
    file(zfmisc_1,t30_zfmisc_1),
    [interesting(0.00)]).

fof(t80_zfmisc_1,theorem,(
    ! [A] : r1_tarski(k1_tarski(A),k1_zfmisc_1(A)) ),
    file(zfmisc_1,t80_zfmisc_1),
    [interesting(0.00)]).

fof(d2_mboolean,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( C = k2_mboolean(A,B)
          <=> ! [D] : 
                ( r2_hidden(D,A)
               => k1_funct_1(C,D) = k3_tarski(k1_funct_1(B,D)) ) ) ) ) ),
    file(mboolean,d2_mboolean),
    [interesting(0.00)]).

fof(t31_zfmisc_1,theorem,(
    ! [A] : k3_tarski(k1_tarski(A)) = A ),
    file(zfmisc_1,t31_zfmisc_1),
    [interesting(0.00)]).

fof(t32_zfmisc_1,theorem,(
    ! [A,B] : k3_tarski(k2_tarski(k1_tarski(A),k1_tarski(B))) = k2_tarski(A,B) ),
    file(zfmisc_1,t32_zfmisc_1),
    [interesting(0.00)]).

fof(t93_zfmisc_1,theorem,(
    ! [A,B] : k3_tarski(k2_tarski(A,B)) = k2_xboole_0(A,B) ),
    file(zfmisc_1,t93_zfmisc_1),
    [interesting(0.00)]).

fof(t37_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(k1_tarski(A),B)
    <=> r2_hidden(A,B) ) ),
    file(zfmisc_1,t37_zfmisc_1),
    [interesting(0.00)]).

fof(t38_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(k2_tarski(A,B),C)
    <=> ( r2_hidden(A,C)
        & r2_hidden(B,C) ) ) ),
    file(zfmisc_1,t38_zfmisc_1),
    [interesting(0.00)]).

fof(t42_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(A,k2_tarski(B,C))
    <=> ~ ( A != k1_xboole_0
          & A != k1_tarski(B)
          & A != k1_tarski(C)
          & A != k2_tarski(B,C) ) ) ),
    file(zfmisc_1,t42_zfmisc_1),
    [interesting(0.00)]).

fof(t6_setwiseo,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(A,k2_xboole_0(B,k1_tarski(C)))
    <=> ( r2_hidden(A,B)
        | A = C ) ) ),
    file(setwiseo,t6_setwiseo),
    [interesting(0.00)]).

fof(d15_pboole,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v3_relat_1(B)
      <=> ! [C] : 
            ( r2_hidden(C,A)
           => v1_xboole_0(k1_funct_1(B,C)) ) ) ) ),
    file(pboole,d15_pboole),
    [interesting(0.00)]).

fof(d16_pboole,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v2_relat_1(B)
      <=> ! [C] : ~ ( r2_hidden(C,A)
            & v1_xboole_0(k1_funct_1(B,C)) ) ) ) ),
    file(pboole,d16_pboole),
    [interesting(0.00)]).

fof(t8_setwiseo,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(k2_xboole_0(A,k1_tarski(B)),C)
    <=> ( r2_hidden(B,C)
        & r1_tarski(A,C) ) ) ),
    file(setwiseo,t8_setwiseo),
    [interesting(0.00)]).

fof(t45_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(k2_xboole_0(k1_tarski(A),B),B)
     => r2_hidden(A,B) ) ),
    file(zfmisc_1,t45_zfmisc_1),
    [interesting(0.00)]).

fof(t46_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => k2_xboole_0(k1_tarski(A),B) = B ) ),
    file(zfmisc_1,t46_zfmisc_1),
    [interesting(0.00)]).

fof(t47_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(k2_xboole_0(k2_tarski(A,B),C),C)
     => r2_hidden(A,C) ) ),
    file(zfmisc_1,t47_zfmisc_1),
    [interesting(0.00)]).

fof(t48_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & r2_hidden(C,B) )
     => k2_xboole_0(k2_tarski(A,C),B) = B ) ),
    file(zfmisc_1,t48_zfmisc_1),
    [interesting(0.00)]).

fof(t51_zfmisc_1,theorem,(
    ! [A,B] : 
      ( k3_xboole_0(A,k1_tarski(B)) = k1_tarski(B)
     => r2_hidden(B,A) ) ),
    file(zfmisc_1,t51_zfmisc_1),
    [interesting(0.00)]).

fof(t52_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => k3_xboole_0(B,k1_tarski(A)) = k1_tarski(A) ) ),
    file(zfmisc_1,t52_zfmisc_1),
    [interesting(0.00)]).

fof(t53_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & r2_hidden(C,B) )
     => k3_xboole_0(k2_tarski(A,C),B) = k2_tarski(A,C) ) ),
    file(zfmisc_1,t53_zfmisc_1),
    [interesting(0.00)]).

fof(t63_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( k3_xboole_0(k2_tarski(A,B),C) = k2_tarski(A,B)
     => r2_hidden(A,C) ) ),
    file(zfmisc_1,t63_zfmisc_1),
    [interesting(0.00)]).

fof(d7_xboole_0,definition,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
    <=> k3_xboole_0(A,B) = k1_xboole_0 ) ),
    file(xboole_0,d7_xboole_0),
    [interesting(0.00)]).

fof(t54_zfmisc_1,theorem,(
    ! [A,B] : ~ ( r1_xboole_0(k1_tarski(A),B)
      & r2_hidden(A,B) ) ),
    file(zfmisc_1,t54_zfmisc_1),
    [interesting(0.00)]).

fof(d1_tarski,definition,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    [interesting(0.00)]).

fof(t5_cqc_lang,theorem,(
    ! [A,B] : 
      ( k1_relat_1(k3_cqc_lang(A,B)) = k1_tarski(A)
      & k2_relat_1(k3_cqc_lang(A,B)) = k1_tarski(B) ) ),
    file(cqc_lang,t5_cqc_lang),
    [interesting(0.00)]).

fof(d1_funct_4,definition,(
    ! [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) )
             => ( C = k1_funct_4(A,B)
              <=> ( k1_relat_1(C) = k2_xboole_0(k1_relat_1(A),k1_relat_1(B))
                  & ! [D] : 
                      ( r2_hidden(D,k2_xboole_0(k1_relat_1(A),k1_relat_1(B)))
                     => ( ( r2_hidden(D,k1_relat_1(B))
                         => k1_funct_1(C,D) = k1_funct_1(B,D) )
                        & ( ~ r2_hidden(D,k1_relat_1(B))
                         => k1_funct_1(C,D) = k1_funct_1(A,D) ) ) ) ) ) ) ) ) ),
    file(funct_4,d1_funct_4),
    [interesting(0.00)]).

fof(t14_funct_4,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(B))
           => k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(B,A) ) ) ) ),
    file(funct_4,t14_funct_4),
    [interesting(0.00)]).

fof(t6_cqc_lang,theorem,(
    ! [A,B] : k1_funct_1(k3_cqc_lang(A,B),A) = B ),
    file(cqc_lang,t6_cqc_lang),
    [interesting(0.00)]).

fof(t12_funct_4,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( ~ r2_hidden(A,k1_relat_1(B))
           => k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(C,A) ) ) ) ),
    file(funct_4,t12_funct_4),
    [interesting(0.00)]).

fof(t55_zfmisc_1,theorem,(
    ! [A,B,C] : ~ ( r1_xboole_0(k2_tarski(A,B),C)
      & r2_hidden(A,C) ) ),
    file(zfmisc_1,t55_zfmisc_1),
    [interesting(0.00)]).

fof(t64_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(A,k4_xboole_0(B,k1_tarski(C)))
    <=> ( r2_hidden(A,B)
        & A != C ) ) ),
    file(zfmisc_1,t64_zfmisc_1),
    [interesting(0.00)]).

fof(t65_zfmisc_1,theorem,(
    ! [A,B] : 
      ( k4_xboole_0(A,k1_tarski(B)) = A
    <=> ~ r2_hidden(B,A) ) ),
    file(zfmisc_1,t65_zfmisc_1),
    [interesting(0.00)]).

fof(t67_zfmisc_1,theorem,(
    ! [A,B] : 
      ( k4_xboole_0(k1_tarski(A),B) = k1_tarski(A)
    <=> ~ r2_hidden(A,B) ) ),
    file(zfmisc_1,t67_zfmisc_1),
    [interesting(0.00)]).

fof(t68_zfmisc_1,theorem,(
    ! [A,B] : 
      ( k4_xboole_0(k1_tarski(A),B) = k1_xboole_0
    <=> r2_hidden(A,B) ) ),
    file(zfmisc_1,t68_zfmisc_1),
    [interesting(0.00)]).

fof(t70_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( k4_xboole_0(k2_tarski(A,B),C) = k1_tarski(A)
    <=> ( ~ r2_hidden(A,C)
        & ( r2_hidden(B,C)
          | A = B ) ) ) ),
    file(zfmisc_1,t70_zfmisc_1),
    [interesting(0.00)]).

fof(t57_pzfmisc1,theorem,(
    $true ),
    file(pzfmisc1,t57_pzfmisc1),
    [interesting(0.00)]).

fof(t72_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( k4_xboole_0(k2_tarski(A,B),C) = k2_tarski(A,B)
    <=> ( ~ r2_hidden(A,C)
        & ~ r2_hidden(B,C) ) ) ),
    file(zfmisc_1,t72_zfmisc_1),
    [interesting(0.00)]).

fof(t73_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( k4_xboole_0(k2_tarski(A,B),C) = k1_xboole_0
    <=> ( r2_hidden(A,C)
        & r2_hidden(B,C) ) ) ),
    file(zfmisc_1,t73_zfmisc_1),
    [interesting(0.00)]).

fof(t75_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( k4_xboole_0(A,k2_tarski(B,C)) = k1_xboole_0
    <=> ~ ( A != k1_xboole_0
          & A != k1_tarski(B)
          & A != k1_tarski(C)
          & A != k2_tarski(B,C) ) ) ),
    file(zfmisc_1,t75_zfmisc_1),
    [interesting(0.00)]).

fof(d21_pboole,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( D = k11_pboole(A,B,C)
              <=> ! [E] : 
                    ( r2_hidden(E,A)
                   => k1_funct_1(D,E) = k2_zfmisc_1(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ),
    file(pboole,d21_pboole),
    [interesting(0.00)]).

fof(t113_zfmisc_1,theorem,(
    ! [A,B] : 
      ( k2_zfmisc_1(A,B) = k1_xboole_0
    <=> ( A = k1_xboole_0
        | B = k1_xboole_0 ) ) ),
    file(zfmisc_1,t113_zfmisc_1),
    [interesting(0.00)]).

fof(t114_zfmisc_1,theorem,(
    ! [A,B] : 
      ( k2_zfmisc_1(A,B) = k2_zfmisc_1(B,A)
     => ( A = k1_xboole_0
        | B = k1_xboole_0
        | A = B ) ) ),
    file(zfmisc_1,t114_zfmisc_1),
    [interesting(0.00)]).

fof(t115_zfmisc_1,theorem,(
    ! [A,B] : 
      ( k2_zfmisc_1(A,A) = k2_zfmisc_1(B,B)
     => A = B ) ),
    file(zfmisc_1,t115_zfmisc_1),
    [interesting(0.00)]).

fof(t117_zfmisc_1,theorem,(
    ! [A,B,C] : ~ ( A != k1_xboole_0
      & ( r1_tarski(k2_zfmisc_1(B,A),k2_zfmisc_1(C,A))
        | r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(A,C)) )
      & ~ r1_tarski(B,C) ) ),
    file(zfmisc_1,t117_zfmisc_1),
    [interesting(0.00)]).

fof(t118_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(A,B)
     => ( r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C))
        & r1_tarski(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) ) ) ),
    file(zfmisc_1,t118_zfmisc_1),
    [interesting(0.00)]).

fof(t119_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D) )
     => r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) ) ),
    file(zfmisc_1,t119_zfmisc_1),
    [interesting(0.00)]).

fof(t120_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( k2_zfmisc_1(k2_xboole_0(A,B),C) = k2_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C))
      & k2_zfmisc_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) ) ),
    file(zfmisc_1,t120_zfmisc_1),
    [interesting(0.00)]).

fof(t67_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( r6_pboole(A,k11_pboole(A,k2_pboole(A,B,C),D),k2_pboole(A,k11_pboole(A,B,D),k11_pboole(A,C,D)))
                & r6_pboole(A,k11_pboole(A,D,k2_pboole(A,B,C)),k2_pboole(A,k11_pboole(A,D,B),k11_pboole(A,D,C))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d21_pboole,d7_pboole,t120_zfmisc_1,d21_pboole,d21_pboole,d7_pboole,t3_pboole,d21_pboole,d7_pboole,t120_zfmisc_1,d21_pboole,d21_pboole,d7_pboole,t3_pboole]),
    [file(pzfmisc1,t67_pzfmisc1),interesting(0.00)]).

fof(t121_zfmisc_1,theorem,(
    ! [A,B,C,D] : k2_zfmisc_1(k2_xboole_0(A,B),k2_xboole_0(C,D)) = k2_xboole_0(k2_xboole_0(k2_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(A,D)),k2_zfmisc_1(B,C)),k2_zfmisc_1(B,D)) ),
    file(zfmisc_1,t121_zfmisc_1),
    [interesting(0.00)]).

fof(t68_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ! [E] : 
                  ( m1_pboole(E,A)
                 => r6_pboole(A,k11_pboole(A,k2_pboole(A,B,C),k2_pboole(A,D,E)),k2_pboole(A,k2_pboole(A,k2_pboole(A,k11_pboole(A,B,D),k11_pboole(A,B,E)),k11_pboole(A,C,D)),k11_pboole(A,C,E))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d21_pboole,d7_pboole,d7_pboole,t121_zfmisc_1,d21_pboole,d21_pboole,d21_pboole,d21_pboole,d7_pboole,d7_pboole,d7_pboole,t3_pboole]),
    [file(pzfmisc1,t68_pzfmisc1),interesting(0.00)]).

fof(t122_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( k2_zfmisc_1(k3_xboole_0(A,B),C) = k3_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C))
      & k2_zfmisc_1(C,k3_xboole_0(A,B)) = k3_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) ) ),
    file(zfmisc_1,t122_zfmisc_1),
    [interesting(0.00)]).

fof(t69_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( r6_pboole(A,k11_pboole(A,k3_pboole(A,B,C),D),k3_pboole(A,k11_pboole(A,B,D),k11_pboole(A,C,D)))
                & r6_pboole(A,k11_pboole(A,D,k3_pboole(A,B,C)),k3_pboole(A,k11_pboole(A,D,B),k11_pboole(A,D,C))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d21_pboole,d8_pboole,t122_zfmisc_1,d21_pboole,d21_pboole,d8_pboole,t3_pboole,d21_pboole,d8_pboole,t122_zfmisc_1,d21_pboole,d21_pboole,d8_pboole,t3_pboole]),
    [file(pzfmisc1,t69_pzfmisc1),interesting(0.00)]).

fof(t123_zfmisc_1,theorem,(
    ! [A,B,C,D] : k2_zfmisc_1(k3_xboole_0(A,B),k3_xboole_0(C,D)) = k3_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) ),
    file(zfmisc_1,t123_zfmisc_1),
    [interesting(0.00)]).

fof(t124_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D) )
     => k3_xboole_0(k2_zfmisc_1(A,D),k2_zfmisc_1(B,C)) = k2_zfmisc_1(A,C) ) ),
    file(zfmisc_1,t124_zfmisc_1),
    [interesting(0.00)]).

fof(t125_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( k2_zfmisc_1(k4_xboole_0(A,B),C) = k4_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C))
      & k2_zfmisc_1(C,k4_xboole_0(A,B)) = k4_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) ) ),
    file(zfmisc_1,t125_zfmisc_1),
    [interesting(0.00)]).

fof(t72_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( r6_pboole(A,k11_pboole(A,k4_pboole(A,B,C),D),k4_pboole(A,k11_pboole(A,B,D),k11_pboole(A,C,D)))
                & r6_pboole(A,k11_pboole(A,D,k4_pboole(A,B,C)),k4_pboole(A,k11_pboole(A,D,B),k11_pboole(A,D,C))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d21_pboole,d9_pboole,t125_zfmisc_1,d21_pboole,d21_pboole,d9_pboole,t3_pboole,d21_pboole,d9_pboole,t125_zfmisc_1,d21_pboole,d21_pboole,d9_pboole,t3_pboole]),
    [file(pzfmisc1,t72_pzfmisc1),interesting(0.00)]).

fof(t126_zfmisc_1,theorem,(
    ! [A,B,C,D] : k4_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) = k2_xboole_0(k2_zfmisc_1(k4_xboole_0(A,C),B),k2_zfmisc_1(A,k4_xboole_0(B,D))) ),
    file(zfmisc_1,t126_zfmisc_1),
    [interesting(0.00)]).

fof(t127_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( ( r1_xboole_0(A,B)
        | r1_xboole_0(C,D) )
     => r1_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) ) ),
    file(zfmisc_1,t127_zfmisc_1),
    [interesting(0.00)]).

fof(t130_zfmisc_1,theorem,(
    ! [A,B] : 
      ( A != k1_xboole_0
     => ( k2_zfmisc_1(k1_tarski(B),A) != k1_xboole_0
        & k2_zfmisc_1(A,k1_tarski(B)) != k1_xboole_0 ) ) ),
    file(zfmisc_1,t130_zfmisc_1),
    [interesting(0.00)]).

fof(t132_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( k2_zfmisc_1(k2_tarski(A,B),C) = k2_xboole_0(k2_zfmisc_1(k1_tarski(A),C),k2_zfmisc_1(k1_tarski(B),C))
      & k2_zfmisc_1(C,k2_tarski(A,B)) = k2_xboole_0(k2_zfmisc_1(C,k1_tarski(A)),k2_zfmisc_1(C,k1_tarski(B))) ) ),
    file(zfmisc_1,t132_zfmisc_1),
    [interesting(0.00)]).

fof(t76_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( r6_pboole(A,k11_pboole(A,k2_pzfmisc1(A,B,C),D),k2_pboole(A,k11_pboole(A,k1_pzfmisc1(A,B),D),k11_pboole(A,k1_pzfmisc1(A,C),D)))
                & r6_pboole(A,k11_pboole(A,D,k2_pzfmisc1(A,B,C)),k2_pboole(A,k11_pboole(A,D,k1_pzfmisc1(A,B)),k11_pboole(A,D,k1_pzfmisc1(A,C)))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d21_pboole,d2_pzfmisc1,t132_zfmisc_1,d1_pzfmisc1,d1_pzfmisc1,d21_pboole,d21_pboole,d7_pboole,t3_pboole,d21_pboole,d2_pzfmisc1,t132_zfmisc_1,d1_pzfmisc1,d1_pzfmisc1,d21_pboole,d21_pboole,d7_pboole,t3_pboole]),
    [file(pzfmisc1,t76_pzfmisc1),interesting(0.00)]).

fof(t134_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( k2_zfmisc_1(A,B) = k2_zfmisc_1(C,D)
     => ( A = k1_xboole_0
        | B = k1_xboole_0
        | ( A = C
          & B = D ) ) ) ),
    file(zfmisc_1,t134_zfmisc_1),
    [interesting(0.00)]).

fof(t135_zfmisc_1,theorem,(
    ! [A,B] : 
      ( ( r1_tarski(A,k2_zfmisc_1(A,B))
        | r1_tarski(A,k2_zfmisc_1(B,A)) )
     => A = k1_xboole_0 ) ),
    file(zfmisc_1,t135_zfmisc_1),
    [interesting(0.00)]).

fof(t137_zfmisc_1,theorem,(
    ! [A,B,C,D,E] : 
      ( ( r2_hidden(A,k2_zfmisc_1(B,C))
        & r2_hidden(A,k2_zfmisc_1(D,E)) )
     => r2_hidden(A,k2_zfmisc_1(k3_xboole_0(B,D),k3_xboole_0(C,E))) ) ),
    file(zfmisc_1,t137_zfmisc_1),
    [interesting(0.00)]).

fof(t7_pzfmisc1,theorem,(
    $true ),
    file(pzfmisc1,t7_pzfmisc1),
    [interesting(0.00)]).

fof(t138_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D))
     => ( k2_zfmisc_1(A,B) = k1_xboole_0
        | ( r1_tarski(A,C)
          & r1_tarski(B,D) ) ) ) ),
    file(zfmisc_1,t138_zfmisc_1),
    [interesting(0.00)]).

fof(t139_zfmisc_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B,C,D] : 
          ( ( r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D))
            | r1_tarski(k2_zfmisc_1(B,A),k2_zfmisc_1(D,C)) )
         => r1_tarski(B,D) ) ) ),
    file(zfmisc_1,t139_zfmisc_1),
    [interesting(0.00)]).

fof(t1_partfun1,theorem,(
    ! [A,B,C,D,E,F] : 
      ( ( r1_tarski(A,k2_zfmisc_1(B,C))
        & r1_tarski(D,k2_zfmisc_1(E,F)) )
     => r1_tarski(k2_xboole_0(A,D),k2_zfmisc_1(k2_xboole_0(B,E),k2_xboole_0(C,F))) ) ),
    file(partfun1,t1_partfun1),
    [interesting(0.00)]).

fof(t84_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ! [E] : 
                  ( m1_pboole(E,A)
                 => ! [F] : 
                      ( m1_pboole(F,A)
                     => ! [G] : 
                          ( m1_pboole(G,A)
                         => ( ( r2_pboole(A,B,k11_pboole(A,C,D))
                              & r2_pboole(A,E,k11_pboole(A,F,G)) )
                           => r2_pboole(A,k2_pboole(A,B,E),k11_pboole(A,k2_pboole(A,C,F),k2_pboole(A,D,G))) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_pboole,d5_pboole,d21_pboole,t1_partfun1,d7_pboole,d7_pboole,d7_pboole,d21_pboole]),
    [file(pzfmisc1,t84_pzfmisc1),interesting(0.00)]).