fof(t71_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k5_finsub_1(A))
         => k10_setwiseo(A,A,B,k11_setwiseo(A)) = B ) ) ),
    inference(mizar_proof,[status(thm)],[t70_setwiseo,t68_setwiseo,t14_setwiseo,t68_setwiseo,t70_setwiseo,t2_tarski]),
    [file(setwiseo,t71_setwiseo),interesting(1.00)]).

fof(t62_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B,C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,k5_finsub_1(B))
            & m2_relset_1(C,A,k5_finsub_1(B)) )
         => ! [D] : 
              ( m1_subset_1(D,k5_finsub_1(A))
             => ! [E] : 
                  ( m1_subset_1(E,k5_finsub_1(A))
                 => k10_setwiseo(A,B,k5_setwiseo(A,D,E),C) = k5_setwiseo(B,k10_setwiseo(A,B,D,C),k10_setwiseo(A,B,E,C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t61_setwiseo,t153_relat_1,t96_zfmisc_1,t61_setwiseo,t61_setwiseo]),
    [file(setwiseo,t62_setwiseo),interesting(0.84)]).

fof(t52_setwiseo,theorem,(
    ! [A] : r3_binop_1(k5_finsub_1(A),k1_setwiseo(A),k9_setwiseo(A)) ),
    inference(mizar_proof,[status(thm)],[d4_setwiseo,d7_binop_1,d16_binop_1,d17_binop_1,d4_setwiseo]),
    [file(setwiseo,t52_setwiseo),interesting(0.79)]).

fof(t61_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B,C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,k5_finsub_1(B))
            & m2_relset_1(C,A,k5_finsub_1(B)) )
         => ! [D] : 
              ( m1_subset_1(D,k5_finsub_1(A))
             => k10_setwiseo(A,B,D,C) = k3_tarski(k8_setwiseo(A,k5_finsub_1(B),C,D)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t59_setwiseo,t2_zfmisc_1,t149_relat_1,t60_setwiseo,t31_zfmisc_1,t96_zfmisc_1,t13_setwiseo,t153_relat_1,s4_setwiseo]),
    [file(setwiseo,t61_setwiseo),interesting(0.79)]).

fof(t53_setwiseo,theorem,(
    ! [A] : v1_setwiseo(k9_setwiseo(A),k5_finsub_1(A)) ),
    inference(mizar_proof,[status(thm)],[t52_setwiseo,d2_setwiseo]),
    [file(setwiseo,t53_setwiseo),interesting(0.77)]).

fof(t70_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B,C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,k5_finsub_1(B))
            & m2_relset_1(C,A,k5_finsub_1(B)) )
         => ! [D] : 
              ( m1_subset_1(D,k5_finsub_1(A))
             => ! [E] : 
                  ( r2_hidden(E,k10_setwiseo(A,B,D,C))
                <=> ? [F] : 
                      ( m1_subset_1(F,A)
                      & r2_hidden(F,D)
                      & r2_hidden(E,k8_funct_2(A,k5_finsub_1(B),C,F)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_tarski,l77_setwiseo,t116_funct_2,t43_funct_2,d4_tarski,t61_setwiseo]),
    [file(setwiseo,t70_setwiseo),interesting(0.77)]).

fof(t59_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B,C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,k5_finsub_1(B))
            & m2_relset_1(C,A,k5_finsub_1(B)) )
         => k10_setwiseo(A,B,k1_setwiseo(A),C) = k1_xboole_0 ) ) ),
    inference(mizar_proof,[status(thm)],[t49_setwiseo,t50_setwiseo,t51_setwiseo,t53_setwiseo,t40_setwiseo,t55_setwiseo]),
    [file(setwiseo,t59_setwiseo),interesting(0.75)]).

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) ) ) ),
    inference(mizar_proof,[status(thm)],[t11_xboole_1,t8_xboole_1,t37_zfmisc_1]),
    [file(setwiseo,t8_setwiseo),interesting(0.74)]).

fof(t51_setwiseo,theorem,(
    ! [A] : v2_binop_1(k9_setwiseo(A),k5_finsub_1(A)) ),
    inference(mizar_proof,[status(thm)],[d14_binop_1,d4_setwiseo,d4_setwiseo,t4_xboole_1,d4_setwiseo,d4_setwiseo]),
    [file(setwiseo,t51_setwiseo),interesting(0.74)]).

fof(t50_setwiseo,theorem,(
    ! [A] : v1_binop_1(k9_setwiseo(A),k5_finsub_1(A)) ),
    inference(mizar_proof,[status(thm)],[d13_binop_1,d4_setwiseo,d4_setwiseo]),
    [file(setwiseo,t50_setwiseo),interesting(0.73)]).

fof(t63_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C,D] : 
              ( m1_subset_1(D,k5_finsub_1(A))
             => ! [E] : 
                  ( ( v1_funct_1(E)
                    & v1_funct_2(E,A,B)
                    & m2_relset_1(E,A,B) )
                 => ! [F] : 
                      ( ( v1_funct_1(F)
                        & v1_funct_2(F,B,k5_finsub_1(C))
                        & m2_relset_1(F,B,k5_finsub_1(C)) )
                     => k10_setwiseo(B,C,k8_setwiseo(A,B,E,D),F) = k10_setwiseo(A,C,D,k7_funct_2(A,B,k5_finsub_1(C),E,F)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t61_setwiseo,t159_relat_1,t61_setwiseo]),
    [file(setwiseo,t63_setwiseo),interesting(0.73)]).

fof(t49_setwiseo,theorem,(
    ! [A] : v3_binop_1(k9_setwiseo(A),k5_finsub_1(A)) ),
    inference(mizar_proof,[status(thm)],[d15_binop_1,d4_setwiseo]),
    [file(setwiseo,t49_setwiseo),interesting(0.72)]).

fof(t54_setwiseo,theorem,(
    ! [A] : r3_binop_1(k5_finsub_1(A),k3_binop_1(k5_finsub_1(A),k9_setwiseo(A)),k9_setwiseo(A)) ),
    inference(mizar_proof,[status(thm)],[t53_setwiseo,t22_setwiseo]),
    [file(setwiseo,t54_setwiseo),interesting(0.70)]).

fof(t60_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B,C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,k5_finsub_1(B))
            & m2_relset_1(C,A,k5_finsub_1(B)) )
         => ! [D] : 
              ( m1_subset_1(D,A)
             => ! [E] : 
                  ( m1_subset_1(E,k5_finsub_1(A))
                 => k10_setwiseo(A,B,k5_setwiseo(A,E,k2_setwiseo(A,D)),C) = k5_setwiseo(B,k10_setwiseo(A,B,E,C),k8_funct_2(A,k5_finsub_1(B),C,D)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t49_setwiseo,t50_setwiseo,t51_setwiseo,t53_setwiseo,t41_setwiseo,d4_setwiseo]),
    [file(setwiseo,t60_setwiseo),interesting(0.70)]).

fof(t18_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k5_finsub_1(A))
         => ~ ( B != k1_xboole_0
              & ! [C] : 
                  ( m1_subset_1(C,A)
                 => ~ r2_hidden(C,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t14_setwiseo]),
    [file(setwiseo,t18_setwiseo),interesting(0.68)]).

fof(t55_setwiseo,theorem,(
    ! [A] : k3_binop_1(k5_finsub_1(A),k9_setwiseo(A)) = k1_xboole_0 ),
    inference(mizar_proof,[status(thm)],[t52_setwiseo,d8_binop_1]),
    [file(setwiseo,t55_setwiseo),interesting(0.68)]).

fof(t68_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B,C] : 
          ( m1_subset_1(C,A)
         => ( r2_hidden(B,k8_funct_2(A,k5_finsub_1(A),k11_setwiseo(A),C))
          <=> B = C ) ) ) ),
    inference(mizar_proof,[status(thm)],[t67_setwiseo,d1_tarski]),
    [file(setwiseo,t68_setwiseo),interesting(0.68)]).

fof(t5_setwiseo,theorem,(
    ! [A,B,C] : ~ ( r1_tarski(A,k2_xboole_0(B,k1_tarski(C)))
      & ~ r2_hidden(C,A)
      & ~ r1_tarski(A,B) ) ),
    inference(mizar_proof,[status(thm)],[t56_zfmisc_1,t28_xboole_1,t23_xboole_1,d7_xboole_0,t17_xboole_1]),
    [file(setwiseo,t5_setwiseo),interesting(0.66)]).

fof(t14_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k5_finsub_1(A))
         => ! [C] : 
              ( r2_hidden(C,B)
             => m1_subset_1(C,A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_finsub_1]),
    [file(setwiseo,t14_setwiseo),interesting(0.63)]).

fof(t6_setwiseo,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(A,k2_xboole_0(B,k1_tarski(C)))
    <=> ( r2_hidden(A,B)
        | A = C ) ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,d2_xboole_0]),
    [file(setwiseo,t6_setwiseo),interesting(0.63)]).

fof(t44_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(A,A),A)
                    & m2_relset_1(D,k2_zfmisc_1(A,A),A) )
                 => ( ( v3_binop_1(D,A)
                      & v1_binop_1(D,A)
                      & v2_binop_1(D,A)
                      & v1_setwiseo(D,A) )
                   => ! [E] : 
                        ( m1_subset_1(E,k5_finsub_1(B))
                       => ! [F] : 
                            ( ( v1_funct_1(F)
                              & v1_funct_2(F,B,C)
                              & m2_relset_1(F,B,C) )
                           => ! [G] : 
                                ( ( v1_funct_1(G)
                                  & v1_funct_2(G,C,A)
                                  & m2_relset_1(G,C,A) )
                               => k7_setwiseo(C,A,D,k8_setwiseo(B,C,F,E),G) = k7_setwiseo(B,A,D,E,k7_funct_2(B,C,A,F,G)) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t149_relat_1,t40_setwiseo,t38_setwiseo]),
    [file(setwiseo,t44_setwiseo),interesting(0.63)]).

fof(t23_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(A,A),A)
            & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
         => ( v1_setwiseo(B,A)
           => ! [C] : 
                ( m1_subset_1(C,A)
               => ( k2_binop_1(A,A,A,B,k3_binop_1(A,B),C) = C
                  & k2_binop_1(A,A,A,B,C,k3_binop_1(A,B)) = C ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t22_setwiseo,t11_binop_1]),
    [file(setwiseo,t23_setwiseo),interesting(0.62)]).

fof(t38_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(A,A),A)
                    & m2_relset_1(D,k2_zfmisc_1(A,A),A) )
                 => ( ( v3_binop_1(D,A)
                      & v1_binop_1(D,A)
                      & v2_binop_1(D,A) )
                   => ! [E] : 
                        ( m1_subset_1(E,k5_finsub_1(B))
                       => ( E != k1_xboole_0
                         => ! [F] : 
                              ( ( v1_funct_1(F)
                                & v1_funct_2(F,B,C)
                                & m2_relset_1(F,B,C) )
                             => ! [G] : 
                                  ( ( v1_funct_1(G)
                                    & v1_funct_2(G,C,A)
                                    & m2_relset_1(G,C,A) )
                                 => k7_setwiseo(C,A,D,k8_setwiseo(B,C,F,E),G) = k7_setwiseo(B,A,D,E,k7_funct_2(B,C,A,F,G)) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,t117_funct_1,t26_setwiseo,t21_funct_2,t26_setwiseo,d5_finsub_1,t28_xboole_1,d7_xboole_0,t151_relat_1,t153_relat_1,t30_setwiseo,t30_setwiseo,s3_setwiseo]),
    [file(setwiseo,t38_setwiseo),interesting(0.61)]).

fof(t22_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(A,A),A)
            & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
         => ( v1_setwiseo(B,A)
          <=> r3_binop_1(A,k3_binop_1(A,B),B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_setwiseo,d8_binop_1,d2_setwiseo]),
    [file(setwiseo,t22_setwiseo),interesting(0.59)]).

fof(t56_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B,C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,k5_finsub_1(B))
            & m2_relset_1(C,A,k5_finsub_1(B)) )
         => ! [D] : 
              ( m1_subset_1(D,A)
             => k10_setwiseo(A,B,k2_setwiseo(A,D),C) = k8_funct_2(A,k5_finsub_1(B),C,D) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t49_setwiseo,t50_setwiseo,t51_setwiseo,t26_setwiseo]),
    [file(setwiseo,t56_setwiseo),interesting(0.59)]).

fof(t67_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,k5_finsub_1(A))
            & m2_relset_1(B,A,k5_finsub_1(A)) )
         => ( B = k11_setwiseo(A)
          <=> ! [C] : 
                ( m1_subset_1(C,A)
               => k8_funct_2(A,k5_finsub_1(A),B,C) = k2_setwiseo(A,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_setwiseo,d6_setwiseo]),
    [file(setwiseo,t67_setwiseo),interesting(0.59)]).

fof(t57_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B,C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,k5_finsub_1(B))
            & m2_relset_1(C,A,k5_finsub_1(B)) )
         => ! [D] : 
              ( m1_subset_1(D,A)
             => ! [E] : 
                  ( m1_subset_1(E,A)
                 => k10_setwiseo(A,B,k3_setwiseo(A,D,E),C) = k5_setwiseo(B,k8_funct_2(A,k5_finsub_1(B),C,D),k8_funct_2(A,k5_finsub_1(B),C,E)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t49_setwiseo,t50_setwiseo,t51_setwiseo,t27_setwiseo,d4_setwiseo]),
    [file(setwiseo,t57_setwiseo),interesting(0.56)]).

fof(l17_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ! [D] : 
                  ( m1_subset_1(D,k5_finsub_1(A))
                 => m1_subset_1(k2_funct_2(A,B,C,D),k5_finsub_1(B)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_finsub_1]),
    [file(setwiseo,l17_setwiseo),interesting(0.55)]).

fof(t3_setwiseo,theorem,(
    ! [A,B,C] : r1_tarski(k1_tarski(A),k1_enumset1(A,B,C)) ),
    inference(mizar_proof,[status(thm)],[t42_enumset1,t7_xboole_1]),
    [file(setwiseo,t3_setwiseo),interesting(0.54)]).

fof(t4_setwiseo,theorem,(
    ! [A,B,C] : r1_tarski(k2_tarski(A,B),k1_enumset1(A,B,C)) ),
    inference(mizar_proof,[status(thm)],[t43_enumset1,t7_xboole_1]),
    [file(setwiseo,t4_setwiseo),interesting(0.54)]).

fof(t69_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ! [C] : 
              ( m1_subset_1(C,A)
             => ! [D] : 
                  ( m1_subset_1(D,A)
                 => ( ( r2_hidden(B,k8_funct_2(A,k5_finsub_1(A),k11_setwiseo(A),D))
                      & r2_hidden(C,k8_funct_2(A,k5_finsub_1(A),k11_setwiseo(A),D)) )
                   => B = C ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t68_setwiseo]),
    [file(setwiseo,t69_setwiseo),interesting(0.54)]).

fof(t16_setwiseo,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k5_finsub_1(A))
     => ! [C] : 
          ( r1_tarski(C,B)
         => m1_subset_1(C,k5_finsub_1(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_finsub_1,t1_xboole_1,t13_finset_1,d5_finsub_1]),
    [file(setwiseo,t16_setwiseo),interesting(0.53)]).

fof(t13_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,B,A)
                & m2_relset_1(C,B,A) )
             => ! [D] : 
                  ( m1_subset_1(D,B)
                 => k2_funct_2(B,A,C,k1_tarski(D)) = k1_tarski(k8_funct_2(B,A,C,D)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d12_funct_1,d1_tarski,d1_tarski,t43_funct_2,d1_tarski]),
    [file(setwiseo,t13_setwiseo),interesting(0.53)]).

fof(t30_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ( ( v3_binop_1(C,A)
                      & v1_binop_1(C,A)
                      & v2_binop_1(C,A) )
                   => ! [E] : 
                        ( m1_subset_1(E,k5_finsub_1(B))
                       => ! [F] : 
                            ( m1_subset_1(F,k5_finsub_1(B))
                           => ~ ( E != k1_xboole_0
                                & F != k1_xboole_0
                                & k7_setwiseo(B,A,C,k5_setwiseo(B,E,F),D) != k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,E,D),k7_setwiseo(B,A,C,F,D)) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t29_setwiseo,t26_setwiseo,t15_xboole_1,t4_xboole_1,t29_setwiseo,d3_binop_1,t29_setwiseo,s4_setwiseo]),
    [file(setwiseo,t30_setwiseo),interesting(0.51)]).

fof(t11_setwiseo,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => k9_relat_1(C,k4_xboole_0(B,k10_relat_1(C,A))) = k4_xboole_0(k9_relat_1(C,B),A) ) ),
    inference(mizar_proof,[status(thm)],[d12_funct_1,d4_xboole_0,d13_funct_1,d4_xboole_0,d12_funct_1,d4_xboole_0,d4_xboole_0,d12_funct_1,d4_xboole_0,d13_funct_1,d4_xboole_0,d12_funct_1,t2_tarski]),
    [file(setwiseo,t11_setwiseo),interesting(0.50)]).

fof(t41_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] : 
                  ( m1_subset_1(D,k5_finsub_1(B))
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,B,A)
                        & m2_relset_1(E,B,A) )
                     => ( ( v3_binop_1(C,A)
                          & v1_binop_1(C,A)
                          & v2_binop_1(C,A)
                          & v1_setwiseo(C,A) )
                       => ! [F] : 
                            ( m1_subset_1(F,B)
                           => k7_setwiseo(B,A,C,k5_setwiseo(B,D,k2_setwiseo(B,F)),E) = k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,D,E),k8_funct_2(B,A,E,F)) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t26_setwiseo,t23_setwiseo,t40_setwiseo,t29_setwiseo]),
    [file(setwiseo,t41_setwiseo),interesting(0.50)]).

fof(t15_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m1_subset_1(C,k5_finsub_1(A))
             => ! [D,E] : 
                  ( ( v1_funct_1(E)
                    & v1_funct_2(E,A,B)
                    & m2_relset_1(E,A,B) )
                 => ( ! [F] : 
                        ( m1_subset_1(F,A)
                       => ( r2_hidden(F,C)
                         => r2_hidden(k8_funct_2(A,B,E,F),D) ) )
                   => r1_tarski(k2_funct_2(A,B,E,C),D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d12_funct_1,t14_setwiseo]),
    [file(setwiseo,t15_setwiseo),interesting(0.49)]).

fof(t36_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(A,A),A)
                    & m2_relset_1(D,k2_zfmisc_1(A,A),A) )
                 => ( ( v3_binop_1(C,A)
                      & v1_binop_1(C,A)
                      & v2_binop_1(C,A)
                      & r6_binop_1(A,D,C) )
                   => ! [E] : 
                        ( m1_subset_1(E,k5_finsub_1(B))
                       => ( E != k1_xboole_0
                         => ! [F] : 
                              ( ( v1_funct_1(F)
                                & v1_funct_2(F,B,A)
                                & m2_relset_1(F,B,A) )
                             => ! [G] : 
                                  ( m1_subset_1(G,A)
                                 => k2_binop_1(A,A,A,D,G,k7_setwiseo(B,A,C,E,F)) = k7_setwiseo(B,A,C,E,k8_funcop_1(A,B,D,G,F)) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t26_setwiseo,t66_funcop_1,t26_setwiseo,t30_setwiseo,t23_binop_1,t30_setwiseo,s3_setwiseo]),
    [file(setwiseo,t36_setwiseo),interesting(0.47)]).

fof(t37_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(A,A),A)
                    & m2_relset_1(D,k2_zfmisc_1(A,A),A) )
                 => ( ( v3_binop_1(C,A)
                      & v1_binop_1(C,A)
                      & v2_binop_1(C,A)
                      & r6_binop_1(A,D,C) )
                   => ! [E] : 
                        ( m1_subset_1(E,k5_finsub_1(B))
                       => ( E != k1_xboole_0
                         => ! [F] : 
                              ( ( v1_funct_1(F)
                                & v1_funct_2(F,B,A)
                                & m2_relset_1(F,B,A) )
                             => ! [G] : 
                                  ( m1_subset_1(G,A)
                                 => k2_binop_1(A,A,A,D,k7_setwiseo(B,A,C,E,F),G) = k7_setwiseo(B,A,C,E,k7_funcop_1(A,B,D,F,G)) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t26_setwiseo,t60_funcop_1,t26_setwiseo,t30_setwiseo,t23_binop_1,t30_setwiseo,s3_setwiseo]),
    [file(setwiseo,t37_setwiseo),interesting(0.47)]).

fof(t42_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ( ( v3_binop_1(C,A)
                      & v1_binop_1(C,A)
                      & v2_binop_1(C,A)
                      & v1_setwiseo(C,A) )
                   => ! [E] : 
                        ( m1_subset_1(E,k5_finsub_1(B))
                       => ! [F] : 
                            ( m1_subset_1(F,k5_finsub_1(B))
                           => k7_setwiseo(B,A,C,k5_setwiseo(B,E,F),D) = k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,E,D),k7_setwiseo(B,A,C,F,D)) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t23_setwiseo,t40_setwiseo,t23_setwiseo,t40_setwiseo,t30_setwiseo]),
    [file(setwiseo,t42_setwiseo),interesting(0.47)]).

fof(t31_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] : 
                  ( m1_subset_1(D,k5_finsub_1(B))
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,B,A)
                        & m2_relset_1(E,B,A) )
                     => ( ( v1_binop_1(C,A)
                          & v2_binop_1(C,A)
                          & v3_binop_1(C,A) )
                       => ! [F] : 
                            ( m1_subset_1(F,B)
                           => ( r2_hidden(F,D)
                             => k2_binop_1(A,A,A,C,k8_funct_2(B,A,E,F),k7_setwiseo(B,A,C,D,E)) = k7_setwiseo(B,A,C,D,E) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t26_setwiseo,t30_setwiseo,t46_zfmisc_1]),
    [file(setwiseo,t31_setwiseo),interesting(0.46)]).

fof(t32_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ( ( v1_binop_1(C,A)
                      & v2_binop_1(C,A)
                      & v3_binop_1(C,A) )
                   => ! [E] : 
                        ( m1_subset_1(E,k5_finsub_1(B))
                       => ! [F] : 
                            ( m1_subset_1(F,k5_finsub_1(B))
                           => ( r1_tarski(E,F)
                             => ( E = k1_xboole_0
                                | k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,E,D),k7_setwiseo(B,A,C,F,D)) = k7_setwiseo(B,A,C,F,D) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t3_xboole_1,t30_setwiseo,t12_xboole_1]),
    [file(setwiseo,t32_setwiseo),interesting(0.43)]).

fof(t12_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,B,A)
                & m2_relset_1(C,B,A) )
             => ! [D] : 
                  ( m1_subset_1(D,B)
                 => r2_hidden(D,k3_funct_2(B,A,C,k1_tarski(k8_funct_2(B,A,C,D)))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,t46_funct_2]),
    [file(setwiseo,t12_setwiseo),interesting(0.42)]).

fof(t29_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] : 
                  ( m1_subset_1(D,k5_finsub_1(B))
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,B,A)
                        & m2_relset_1(E,B,A) )
                     => ( ( v3_binop_1(C,A)
                          & v1_binop_1(C,A)
                          & v2_binop_1(C,A) )
                       => ( D = k1_xboole_0
                          | ! [F] : 
                              ( m1_subset_1(F,B)
                             => k7_setwiseo(B,A,C,k5_setwiseo(B,D,k2_setwiseo(B,F)),E) = k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,D,E),k8_funct_2(B,A,E,F)) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t25_setwiseo,t25_setwiseo,t8_setwiseo,t7_xboole_1,t1_xboole_1,s4_setwiseo,t7_xboole_1,t6_setwiseo]),
    [file(setwiseo,t29_setwiseo),interesting(0.41)]).

fof(t19_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,B,A)
                & m2_relset_1(C,B,A) )
             => ! [D] : 
                  ( m1_subset_1(D,k5_finsub_1(B))
                 => ( k2_funct_2(B,A,C,D) = k1_xboole_0
                   => D = k1_xboole_0 ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t18_setwiseo,t43_funct_2]),
    [file(setwiseo,t19_setwiseo),interesting(0.41)]).

fof(t39_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ( ( v1_binop_1(C,B)
                  & v2_binop_1(C,B)
                  & v3_binop_1(C,B) )
               => ! [D] : 
                    ( ~ v1_xboole_0(D)
                   => ! [E] : 
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,k2_zfmisc_1(D,D),D)
                          & m2_relset_1(E,k2_zfmisc_1(D,D),D) )
                       => ( ( v1_binop_1(E,D)
                            & v2_binop_1(E,D)
                            & v3_binop_1(E,D) )
                         => ! [F] : 
                              ( ( v1_funct_1(F)
                                & v1_funct_2(F,A,B)
                                & m2_relset_1(F,A,B) )
                             => ! [G] : 
                                  ( ( v1_funct_1(G)
                                    & v1_funct_2(G,B,D)
                                    & m2_relset_1(G,B,D) )
                                 => ( ! [H] : 
                                        ( m1_subset_1(H,B)
                                       => ! [I] : 
                                            ( m1_subset_1(I,B)
                                           => k8_funct_2(B,D,G,k2_binop_1(B,B,B,C,H,I)) = k2_binop_1(D,D,D,E,k8_funct_2(B,D,G,H),k8_funct_2(B,D,G,I)) ) )
                                   => ! [H] : 
                                        ( m1_subset_1(H,k5_finsub_1(A))
                                       => ( H != k1_xboole_0
                                         => k8_funct_2(B,D,G,k7_setwiseo(A,B,C,H,F)) = k7_setwiseo(A,D,E,H,k7_funct_2(A,B,D,F,G)) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t26_setwiseo,t21_funct_2,t26_setwiseo,t29_setwiseo,t21_funct_2,t29_setwiseo,s4_setwiseo]),
    [file(setwiseo,t39_setwiseo),interesting(0.41)]).

fof(t64_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C,D] : 
              ( ( v1_funct_1(D)
                & v1_funct_2(D,k2_zfmisc_1(A,A),A)
                & m2_relset_1(D,k2_zfmisc_1(A,A),A) )
             => ( ( v1_binop_1(D,A)
                  & v2_binop_1(D,A)
                  & v3_binop_1(D,A) )
               => ! [E] : 
                    ( m1_subset_1(E,k5_finsub_1(B))
                   => ( E != k1_xboole_0
                     => ! [F] : 
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,B,k5_finsub_1(C))
                            & m2_relset_1(F,B,k5_finsub_1(C)) )
                         => ! [G] : 
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,k5_finsub_1(C),A)
                                & m2_relset_1(G,k5_finsub_1(C),A) )
                             => ( ! [H] : 
                                    ( m1_subset_1(H,k5_finsub_1(C))
                                   => ! [I] : 
                                        ( m1_subset_1(I,k5_finsub_1(C))
                                       => k8_funct_2(k5_finsub_1(C),A,G,k5_setwiseo(C,H,I)) = k2_binop_1(A,A,A,D,k8_funct_2(k5_finsub_1(C),A,G,H),k8_funct_2(k5_finsub_1(C),A,G,I)) ) )
                               => k8_funct_2(k5_finsub_1(C),A,G,k10_setwiseo(B,C,E,F)) = k7_setwiseo(B,A,D,E,k7_funct_2(B,k5_finsub_1(C),A,F,G)) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t49_setwiseo,t50_setwiseo,t51_setwiseo,d4_setwiseo,t39_setwiseo]),
    [file(setwiseo,t64_setwiseo),interesting(0.38)]).

fof(t33_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] : 
                  ( m1_subset_1(D,k5_finsub_1(B))
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,B,A)
                        & m2_relset_1(E,B,A) )
                     => ( ( v1_binop_1(C,A)
                          & v2_binop_1(C,A)
                          & v3_binop_1(C,A) )
                       => ( D = k1_xboole_0
                          | ! [F] : 
                              ( m1_subset_1(F,A)
                             => ( ! [G] : 
                                    ( m1_subset_1(G,B)
                                   => ( r2_hidden(G,D)
                                     => k8_funct_2(B,A,E,G) = F ) )
                               => k7_setwiseo(B,A,C,D,E) = F ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,t26_setwiseo,d2_xboole_0,d2_xboole_0,t30_setwiseo,d4_binop_1,s3_setwiseo]),
    [file(setwiseo,t33_setwiseo),interesting(0.35)]).

fof(t65_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C,D] : 
              ( ( v1_funct_1(D)
                & v1_funct_2(D,k2_zfmisc_1(B,B),B)
                & m2_relset_1(D,k2_zfmisc_1(B,B),B) )
             => ( ( v1_binop_1(D,B)
                  & v2_binop_1(D,B)
                  & v3_binop_1(D,B)
                  & v1_setwiseo(D,B) )
               => ! [E] : 
                    ( ( v1_funct_1(E)
                      & v1_funct_2(E,A,k5_finsub_1(C))
                      & m2_relset_1(E,A,k5_finsub_1(C)) )
                   => ! [F] : 
                        ( ( v1_funct_1(F)
                          & v1_funct_2(F,k5_finsub_1(C),B)
                          & m2_relset_1(F,k5_finsub_1(C),B) )
                       => ( ( k8_funct_2(k5_finsub_1(C),B,F,k1_setwiseo(C)) = k3_binop_1(B,D)
                            & ! [G] : 
                                ( m1_subset_1(G,k5_finsub_1(C))
                               => ! [H] : 
                                    ( m1_subset_1(H,k5_finsub_1(C))
                                   => k8_funct_2(k5_finsub_1(C),B,F,k5_setwiseo(C,G,H)) = k2_binop_1(B,B,B,D,k8_funct_2(k5_finsub_1(C),B,F,G),k8_funct_2(k5_finsub_1(C),B,F,H)) ) ) )
                         => ! [G] : 
                              ( m1_subset_1(G,k5_finsub_1(A))
                             => k8_funct_2(k5_finsub_1(C),B,F,k10_setwiseo(A,C,G,E)) = k7_setwiseo(A,B,D,G,k7_funct_2(A,k5_finsub_1(C),B,E,F)) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t149_relat_1,t59_setwiseo,t40_setwiseo,t44_setwiseo,t64_setwiseo]),
    [file(setwiseo,t65_setwiseo),interesting(0.28)]).

fof(t45_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ( ( v1_binop_1(C,B)
                  & v2_binop_1(C,B)
                  & v3_binop_1(C,B)
                  & v1_setwiseo(C,B) )
               => ! [D] : 
                    ( ~ v1_xboole_0(D)
                   => ! [E] : 
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,k2_zfmisc_1(D,D),D)
                          & m2_relset_1(E,k2_zfmisc_1(D,D),D) )
                       => ( ( v1_binop_1(E,D)
                            & v2_binop_1(E,D)
                            & v3_binop_1(E,D)
                            & v1_setwiseo(E,D) )
                         => ! [F] : 
                              ( ( v1_funct_1(F)
                                & v1_funct_2(F,A,B)
                                & m2_relset_1(F,A,B) )
                             => ! [G] : 
                                  ( ( v1_funct_1(G)
                                    & v1_funct_2(G,B,D)
                                    & m2_relset_1(G,B,D) )
                                 => ( ( k8_funct_2(B,D,G,k3_binop_1(B,C)) = k3_binop_1(D,E)
                                      & ! [H] : 
                                          ( m1_subset_1(H,B)
                                         => ! [I] : 
                                              ( m1_subset_1(I,B)
                                             => k8_funct_2(B,D,G,k2_binop_1(B,B,B,C,H,I)) = k2_binop_1(D,D,D,E,k8_funct_2(B,D,G,H),k8_funct_2(B,D,G,I)) ) ) )
                                   => ! [H] : 
                                        ( m1_subset_1(H,k5_finsub_1(A))
                                       => k8_funct_2(B,D,G,k7_setwiseo(A,B,C,H,F)) = k7_setwiseo(A,D,E,H,k7_funct_2(A,B,D,F,G)) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t40_setwiseo,t40_setwiseo,t39_setwiseo]),
    [file(setwiseo,t45_setwiseo),interesting(0.23)]).

fof(d5_finsub_1,definition,(
    ! [A,B] : 
      ( v4_finsub_1(B)
     => ( B = k5_finsub_1(A)
      <=> ! [C] : 
            ( r2_hidden(C,B)
          <=> ( r1_tarski(C,A)
              & v1_finset_1(C) ) ) ) ) ),
    file(finsub_1,d5_finsub_1),
    [interesting(0.00)]).

fof(s3_subset_1,theorem,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(f1_s3_subset_1))
      & ! [B] : 
          ( m1_subset_1(B,f1_s3_subset_1)
         => ( r2_hidden(B,A)
          <=> p1_s3_subset_1(B) ) ) ) ),
    file(subset_1,s3_subset_1),
    [interesting(0.00)]).

fof(t7_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( ! [D] : 
                ( m1_subset_1(D,A)
               => ( r2_hidden(D,B)
                 => r2_hidden(D,C) ) )
           => r1_tarski(B,C) ) ) ) ),
    file(subset_1,t7_subset_1),
    [interesting(0.00)]).

fof(t13_finset_1,theorem,(
    ! [A,B] : 
      ( ( r1_tarski(A,B)
        & v1_finset_1(B) )
     => v1_finset_1(A) ) ),
    file(finset_1,t13_finset_1),
    [interesting(0.00)]).

fof(s3_funct_2,theorem,
    ( ! [A] : 
        ( m1_subset_1(A,f1_s3_funct_2)
       => ? [B] : 
            ( m1_subset_1(B,f2_s3_funct_2)
            & p1_s3_funct_2(A,B) ) )
   => ? [A] : 
        ( v1_funct_1(A)
        & v1_funct_2(A,f1_s3_funct_2,f2_s3_funct_2)
        & m2_relset_1(A,f1_s3_funct_2,f2_s3_funct_2)
        & ! [B] : 
            ( m1_subset_1(B,f1_s3_funct_2)
           => p1_s3_funct_2(B,k8_funct_2(f1_s3_funct_2,f2_s3_funct_2,A,B)) ) ) ),
    file(funct_2,s3_funct_2),
    [interesting(0.00)]).

fof(s1_setwiseo,theorem,(
    ? [A] : 
      ( v1_funct_1(A)
      & v1_funct_2(A,f1_s1_setwiseo,k5_finsub_1(f1_s1_setwiseo))
      & m2_relset_1(A,f1_s1_setwiseo,k5_finsub_1(f1_s1_setwiseo))
      & ! [B] : 
          ( m1_subset_1(B,f1_s1_setwiseo)
         => ! [C] : 
              ( m1_subset_1(C,f1_s1_setwiseo)
             => ( r2_hidden(C,k8_funct_2(f1_s1_setwiseo,k5_finsub_1(f1_s1_setwiseo),A,B))
              <=> ( r2_hidden(C,f2_s1_setwiseo)
                  & p1_s1_setwiseo(C,B) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s3_subset_1,d5_finsub_1,t7_subset_1,t13_finset_1,d5_finsub_1,s3_funct_2]),
    [file(setwiseo,s1_setwiseo),interesting(0.00)]).

fof(t10_setwiseo,theorem,(
    $true ),
    file(setwiseo,t10_setwiseo),
    [interesting(0.00)]).

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(d12_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( C = k9_relat_1(A,B)
        <=> ! [D] : 
              ( r2_hidden(D,C)
            <=> ? [E] : 
                  ( r2_hidden(E,k1_relat_1(A))
                  & r2_hidden(E,B)
                  & D = k1_funct_1(A,E) ) ) ) ) ),
    file(funct_1,d12_funct_1),
    [interesting(0.00)]).

fof(t17_setwiseo,theorem,(
    $true ),
    file(setwiseo,t17_setwiseo),
    [interesting(0.00)]).

fof(t1_setwiseo,theorem,(
    $true ),
    file(setwiseo,t1_setwiseo),
    [interesting(0.00)]).

fof(t20_setwiseo,theorem,(
    $true ),
    file(setwiseo,t20_setwiseo),
    [interesting(0.00)]).

fof(t21_setwiseo,theorem,(
    $true ),
    file(setwiseo,t21_setwiseo),
    [interesting(0.00)]).

fof(t24_setwiseo,theorem,(
    $true ),
    file(setwiseo,t24_setwiseo),
    [interesting(0.00)]).

fof(t2_setwiseo,theorem,(
    $true ),
    file(setwiseo,t2_setwiseo),
    [interesting(0.00)]).

fof(d3_setwiseo,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] : 
                  ( m1_subset_1(D,k5_finsub_1(A))
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,B)
                        & m2_relset_1(E,A,B) )
                     => ( ( v1_binop_1(C,B)
                          & v2_binop_1(C,B) )
                       => ( ( D = k1_xboole_0
                            & ~ v1_setwiseo(C,B) )
                          | ! [F] : 
                              ( m1_subset_1(F,B)
                             => ( F = k7_setwiseo(A,B,C,D,E)
                              <=> ? [G] : 
                                    ( v1_funct_1(G)
                                    & v1_funct_2(G,k5_finsub_1(A),B)
                                    & m2_relset_1(G,k5_finsub_1(A),B)
                                    & F = k8_funct_2(k5_finsub_1(A),B,G,D)
                                    & ! [H] : 
                                        ( m1_subset_1(H,B)
                                       => ( r3_binop_1(B,H,C)
                                         => k1_funct_1(G,k1_xboole_0) = H ) )
                                    & ! [H] : 
                                        ( m1_subset_1(H,A)
                                       => k8_funct_2(k5_finsub_1(A),B,G,k2_setwiseo(A,H)) = k8_funct_2(A,B,E,H) )
                                    & ! [H] : 
                                        ( m1_subset_1(H,k5_finsub_1(A))
                                       => ( r1_tarski(H,D)
                                         => ( H = k1_xboole_0
                                            | ! [I] : 
                                                ( m1_subset_1(I,A)
                                               => ( r2_hidden(I,k6_setwiseo(A,D,H))
                                                 => k8_funct_2(k5_finsub_1(A),B,G,k5_setwiseo(A,H,k2_setwiseo(A,I))) = k2_binop_1(B,B,B,C,k8_funct_2(k5_finsub_1(A),B,G,H),k8_funct_2(A,B,E,I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(setwiseo,d3_setwiseo),
    [interesting(0.00)]).

fof(t26_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ( ( v1_binop_1(C,A)
                      & v2_binop_1(C,A) )
                   => ! [E] : 
                        ( m1_subset_1(E,B)
                       => k7_setwiseo(B,A,C,k2_setwiseo(B,E),D) = k8_funct_2(B,A,D,E) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_setwiseo]),
    [file(setwiseo,t26_setwiseo),interesting(0.00)]).

fof(t36_xboole_1,theorem,(
    ! [A,B] : r1_tarski(k4_xboole_0(A,B),A) ),
    file(xboole_1,t36_xboole_1),
    [interesting(0.00)]).

fof(t1_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_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(t7_xboole_1,theorem,(
    ! [A,B] : r1_tarski(A,k2_xboole_0(A,B)) ),
    file(xboole_1,t7_xboole_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(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(d4_binop_1,definition,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
     => ( v3_binop_1(B,A)
      <=> ! [C] : 
            ( m1_subset_1(C,A)
           => k1_binop_1(B,C,C) = C ) ) ) ),
    file(binop_1,d4_binop_1),
    [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(t37_xboole_1,theorem,(
    ! [A,B] : 
      ( k4_xboole_0(A,B) = k1_xboole_0
    <=> r1_tarski(A,B) ) ),
    file(xboole_1,t37_xboole_1),
    [interesting(0.00)]).

fof(t39_xboole_1,theorem,(
    ! [A,B] : k2_xboole_0(A,k4_xboole_0(B,A)) = k2_xboole_0(A,B) ),
    file(xboole_1,t39_xboole_1),
    [interesting(0.00)]).

fof(d3_binop_1,definition,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
     => ( v2_binop_1(B,A)
      <=> ! [C] : 
            ( m1_subset_1(C,A)
           => ! [D] : 
                ( m1_subset_1(D,A)
               => ! [E] : 
                    ( m1_subset_1(E,A)
                   => k1_binop_1(B,C,k1_binop_1(B,D,E)) = k1_binop_1(B,k1_binop_1(B,C,D),E) ) ) ) ) ) ),
    file(binop_1,d3_binop_1),
    [interesting(0.00)]).

fof(t25_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] : 
                  ( m1_subset_1(D,k5_finsub_1(A))
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,B)
                        & m2_relset_1(E,A,B) )
                     => ( ( v3_binop_1(C,B)
                          & v1_binop_1(C,B)
                          & v2_binop_1(C,B) )
                       => ( ( D = k1_xboole_0
                            & ~ v1_setwiseo(C,B) )
                          | ! [F] : 
                              ( m1_subset_1(F,B)
                             => ( F = k7_setwiseo(A,B,C,D,E)
                              <=> ? [G] : 
                                    ( v1_funct_1(G)
                                    & v1_funct_2(G,k5_finsub_1(A),B)
                                    & m2_relset_1(G,k5_finsub_1(A),B)
                                    & F = k8_funct_2(k5_finsub_1(A),B,G,D)
                                    & ! [H] : 
                                        ( m1_subset_1(H,B)
                                       => ( r3_binop_1(B,H,C)
                                         => k1_funct_1(G,k1_xboole_0) = H ) )
                                    & ! [H] : 
                                        ( m1_subset_1(H,A)
                                       => k8_funct_2(k5_finsub_1(A),B,G,k2_setwiseo(A,H)) = k8_funct_2(A,B,E,H) )
                                    & ! [H] : 
                                        ( m1_subset_1(H,k5_finsub_1(A))
                                       => ( r1_tarski(H,D)
                                         => ( H = k1_xboole_0
                                            | ! [I] : 
                                                ( m1_subset_1(I,A)
                                               => ( r2_hidden(I,D)
                                                 => k8_funct_2(k5_finsub_1(A),B,G,k5_setwiseo(A,H,k2_setwiseo(A,I))) = k2_binop_1(B,B,B,C,k8_funct_2(k5_finsub_1(A),B,G,H),k8_funct_2(A,B,E,I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_setwiseo,t36_xboole_1,t1_xboole_1,t46_zfmisc_1,t7_xboole_1,t64_zfmisc_1,d4_xboole_0,d4_binop_1,d10_xboole_0,t37_xboole_1,t39_xboole_1,d4_binop_1,d3_binop_1,t39_xboole_1,d4_xboole_0,d4_xboole_0,d3_setwiseo]),
    [file(setwiseo,t25_setwiseo),interesting(0.00)]).

fof(t11_xboole_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(k2_xboole_0(A,B),C)
     => r1_tarski(A,C) ) ),
    file(xboole_1,t11_xboole_1),
    [interesting(0.00)]).

fof(t8_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,B) )
     => r1_tarski(k2_xboole_0(A,C),B) ) ),
    file(xboole_1,t8_xboole_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(s2_finset_1,theorem,
    ( ( v1_finset_1(f1_s2_finset_1)
      & p1_s2_finset_1(k1_xboole_0)
      & ! [A,B] : 
          ( ( r2_hidden(A,f1_s2_finset_1)
            & r1_tarski(B,f1_s2_finset_1)
            & p1_s2_finset_1(B) )
         => p1_s2_finset_1(k2_xboole_0(B,k1_tarski(A))) ) )
   => p1_s2_finset_1(f1_s2_finset_1) ),
    file(finset_1,s2_finset_1),
    [interesting(0.00)]).

fof(s2_setwiseo,theorem,
    ( ( p1_s2_setwiseo(k1_setwiseo(f1_s2_setwiseo))
      & ! [A] : 
          ( m1_subset_1(A,k5_finsub_1(f1_s2_setwiseo))
         => ! [B] : 
              ( m1_subset_1(B,f1_s2_setwiseo)
             => ( p1_s2_setwiseo(A)
               => ( r2_hidden(B,A)
                  | p1_s2_setwiseo(k5_setwiseo(f1_s2_setwiseo,A,k2_setwiseo(f1_s2_setwiseo,B))) ) ) ) ) )
   => ! [A] : 
        ( m1_subset_1(A,k5_finsub_1(f1_s2_setwiseo))
       => p1_s2_setwiseo(A) ) ),
    inference(mizar_proof,[status(thm)],[t16_setwiseo,t14_setwiseo,t46_zfmisc_1,s2_finset_1]),
    [file(setwiseo,s2_setwiseo),interesting(0.00)]).

fof(s4_setwiseo,theorem,
    ( ( p1_s4_setwiseo(k1_setwiseo(f1_s4_setwiseo))
      & ! [A] : 
          ( m1_subset_1(A,k5_finsub_1(f1_s4_setwiseo))
         => ! [B] : 
              ( m1_subset_1(B,f1_s4_setwiseo)
             => ( p1_s4_setwiseo(A)
               => p1_s4_setwiseo(k5_setwiseo(f1_s4_setwiseo,A,k2_setwiseo(f1_s4_setwiseo,B))) ) ) ) )
   => ! [A] : 
        ( m1_subset_1(A,k5_finsub_1(f1_s4_setwiseo))
       => p1_s4_setwiseo(A) ) ),
    inference(mizar_proof,[status(thm)],[s2_setwiseo]),
    [file(setwiseo,s4_setwiseo),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(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(t15_xboole_1,theorem,(
    ! [A,B] : 
      ( k2_xboole_0(A,B) = k1_xboole_0
     => A = k1_xboole_0 ) ),
    file(xboole_1,t15_xboole_1),
    [interesting(0.00)]).

fof(t4_xboole_1,theorem,(
    ! [A,B,C] : k2_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(A,k2_xboole_0(B,C)) ),
    file(xboole_1,t4_xboole_1),
    [interesting(0.00)]).

fof(t3_xboole_1,theorem,(
    ! [A] : 
      ( r1_tarski(A,k1_xboole_0)
     => A = k1_xboole_0 ) ),
    file(xboole_1,t3_xboole_1),
    [interesting(0.00)]).

fof(t12_xboole_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => k2_xboole_0(A,B) = B ) ),
    file(xboole_1,t12_xboole_1),
    [interesting(0.00)]).

fof(t66_funcop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ! [E] : 
                      ( m1_subset_1(E,A)
                     => ! [F] : 
                          ( m1_subset_1(F,B)
                         => k8_funct_2(B,A,k8_funcop_1(A,B,C,E,D),F) = k2_binop_1(A,A,A,C,E,k8_funct_2(B,A,D,F)) ) ) ) ) ) ) ),
    file(funcop_1,t66_funcop_1),
    [interesting(0.00)]).

fof(t23_binop_1,theorem,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
     => ! [C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,k2_zfmisc_1(A,A),A)
            & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
         => ( r6_binop_1(A,B,C)
          <=> ! [D] : 
                ( m1_subset_1(D,A)
               => ! [E] : 
                    ( m1_subset_1(E,A)
                   => ! [F] : 
                        ( m1_subset_1(F,A)
                       => ( k1_binop_1(B,D,k1_binop_1(C,E,F)) = k1_binop_1(C,k1_binop_1(B,D,E),k1_binop_1(B,D,F))
                          & k1_binop_1(B,k1_binop_1(C,D,E),F) = k1_binop_1(C,k1_binop_1(B,D,F),k1_binop_1(B,E,F)) ) ) ) ) ) ) ) ),
    file(binop_1,t23_binop_1),
    [interesting(0.00)]).

fof(s3_setwiseo,theorem,
    ( ( ! [A] : 
          ( m1_subset_1(A,f1_s3_setwiseo)
         => p1_s3_setwiseo(k2_setwiseo(f1_s3_setwiseo,A)) )
      & ! [A] : 
          ( m1_subset_1(A,k5_finsub_1(f1_s3_setwiseo))
         => ! [B] : 
              ( m1_subset_1(B,k5_finsub_1(f1_s3_setwiseo))
             => ( ( p1_s3_setwiseo(A)
                  & p1_s3_setwiseo(B) )
               => ( A = k1_xboole_0
                  | B = k1_xboole_0
                  | p1_s3_setwiseo(k5_setwiseo(f1_s3_setwiseo,A,B)) ) ) ) ) )
   => ! [A] : 
        ( m1_subset_1(A,k5_finsub_1(f1_s3_setwiseo))
       => ( A != k1_xboole_0
         => p1_s3_setwiseo(A) ) ) ),
    inference(mizar_proof,[status(thm)],[t16_setwiseo,t14_setwiseo,s2_finset_1]),
    [file(setwiseo,s3_setwiseo),interesting(0.00)]).

fof(t60_funcop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ! [E] : 
                      ( m1_subset_1(E,A)
                     => ! [F] : 
                          ( m1_subset_1(F,B)
                         => k8_funct_2(B,A,k7_funcop_1(A,B,C,D,E),F) = k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,F),E) ) ) ) ) ) ) ),
    file(funcop_1,t60_funcop_1),
    [interesting(0.00)]).

fof(d2_setwiseo,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(A,A),A)
            & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
         => ( v1_setwiseo(B,A)
          <=> ? [C] : 
                ( m1_subset_1(C,A)
                & r3_binop_1(A,C,B) ) ) ) ) ),
    file(setwiseo,d2_setwiseo),
    [interesting(0.00)]).

fof(d8_binop_1,definition,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
     => ( ? [C] : 
            ( m1_subset_1(C,A)
            & r3_binop_1(A,C,B) )
       => ! [C] : 
            ( m1_subset_1(C,A)
           => ( C = k3_binop_1(A,B)
            <=> r3_binop_1(A,C,B) ) ) ) ) ),
    file(binop_1,d8_binop_1),
    [interesting(0.00)]).

fof(t11_binop_1,theorem,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
     => ! [C] : 
          ( m1_subset_1(C,A)
         => ( r3_binop_1(A,C,B)
          <=> ! [D] : 
                ( m1_subset_1(D,A)
               => ( k1_binop_1(B,C,D) = D
                  & k1_binop_1(B,D,C) = D ) ) ) ) ) ),
    file(binop_1,t11_binop_1),
    [interesting(0.00)]).

fof(t40_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ( ( v1_binop_1(C,A)
                  & v2_binop_1(C,A)
                  & v1_setwiseo(C,A) )
               => ! [D] : 
                    ( ( v1_funct_1(D)
                      & v1_funct_2(D,B,A)
                      & m2_relset_1(D,B,A) )
                   => k7_setwiseo(B,A,C,k1_setwiseo(B),D) = k3_binop_1(A,C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t22_setwiseo,d3_setwiseo]),
    [file(setwiseo,t40_setwiseo),interesting(0.00)]).

fof(t149_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => k9_relat_1(A,k1_xboole_0) = k1_xboole_0 ) ),
    file(relat_1,t149_relat_1),
    [interesting(0.00)]).

fof(t43_funct_2,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( B != k1_xboole_0
       => ! [E] : 
            ( ? [F] : 
                ( r2_hidden(F,A)
                & r2_hidden(F,C)
                & E = k1_funct_1(D,F) )
           => r2_hidden(E,k9_relat_1(D,C)) ) ) ) ),
    file(funct_2,t43_funct_2),
    [interesting(0.00)]).

fof(t116_funct_2,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ! [E] : ~ ( r2_hidden(E,k2_funct_2(A,B,D,C))
          & ! [F] : 
              ( m1_subset_1(F,A)
             => ~ ( r2_hidden(F,C)
                  & E = k1_funct_1(D,F) ) ) ) ) ),
    file(funct_2,t116_funct_2),
    [interesting(0.00)]).

fof(t153_relat_1,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => k9_relat_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)) ) ),
    file(relat_1,t153_relat_1),
    [interesting(0.00)]).

fof(t34_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] : 
                  ( m1_subset_1(D,k5_finsub_1(A))
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,B)
                        & m2_relset_1(E,A,B) )
                     => ( ( v1_binop_1(C,B)
                          & v2_binop_1(C,B)
                          & v3_binop_1(C,B) )
                       => ! [F] : 
                            ( m1_subset_1(F,B)
                           => ( k2_funct_2(A,B,E,D) = k2_setwiseo(B,F)
                             => k7_setwiseo(A,B,C,D,E) = F ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t149_relat_1,t43_funct_2,d1_tarski,t33_setwiseo]),
    [file(setwiseo,t34_setwiseo),interesting(0.00)]).

fof(t17_xboole_1,theorem,(
    ! [A,B] : r1_tarski(k3_xboole_0(A,B),A) ),
    file(xboole_1,t17_xboole_1),
    [interesting(0.00)]).

fof(t51_xboole_1,theorem,(
    ! [A,B] : k2_xboole_0(k3_xboole_0(A,B),k4_xboole_0(A,B)) = A ),
    file(xboole_1,t51_xboole_1),
    [interesting(0.00)]).

fof(t156_relat_1,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( r1_tarski(A,B)
       => r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B)) ) ) ),
    file(relat_1,t156_relat_1),
    [interesting(0.00)]).

fof(t56_zfmisc_1,theorem,(
    ! [A,B] : 
      ( ~ r2_hidden(A,B)
     => r1_xboole_0(k1_tarski(A),B) ) ),
    file(zfmisc_1,t56_zfmisc_1),
    [interesting(0.00)]).

fof(t145_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => r1_tarski(k9_relat_1(B,k10_relat_1(B,A)),A) ) ),
    file(funct_1,t145_funct_1),
    [interesting(0.00)]).

fof(t28_xboole_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => k3_xboole_0(A,B) = A ) ),
    file(xboole_1,t28_xboole_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(t46_funct_2,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( B != k1_xboole_0
       => ! [E] : 
            ( r2_hidden(E,k10_relat_1(D,C))
          <=> ( r2_hidden(E,A)
              & r2_hidden(k1_funct_1(D,E),C) ) ) ) ) ),
    file(funct_2,t46_funct_2),
    [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(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(t40_xboole_1,theorem,(
    ! [A,B] : k4_xboole_0(k2_xboole_0(A,B),B) = k4_xboole_0(A,B) ),
    file(xboole_1,t40_xboole_1),
    [interesting(0.00)]).

fof(d13_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( C = k10_relat_1(A,B)
        <=> ! [D] : 
              ( r2_hidden(D,C)
            <=> ( r2_hidden(D,k1_relat_1(A))
                & r2_hidden(k1_funct_1(A,D),B) ) ) ) ) ),
    file(funct_1,d13_funct_1),
    [interesting(0.00)]).

fof(t2_tarski,theorem,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    [interesting(0.00)]).

fof(t35_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ( ( v1_binop_1(C,B)
                  & v2_binop_1(C,B)
                  & v3_binop_1(C,B) )
               => ! [D] : 
                    ( ( v1_funct_1(D)
                      & v1_funct_2(D,A,B)
                      & m2_relset_1(D,A,B) )
                   => ! [E] : 
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,A,B)
                          & m2_relset_1(E,A,B) )
                       => ! [F] : 
                            ( m1_subset_1(F,k5_finsub_1(A))
                           => ! [G] : 
                                ( m1_subset_1(G,k5_finsub_1(A))
                               => ( k2_funct_2(A,B,D,F) = k2_funct_2(A,B,E,G)
                                 => ( F = k1_xboole_0
                                    | k7_setwiseo(A,B,C,F,D) = k7_setwiseo(A,B,C,G,E) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t116_funct_2,t43_funct_2,t153_relat_1,t13_setwiseo,t46_zfmisc_1,t29_setwiseo,t46_zfmisc_1,t29_setwiseo,d3_binop_1,d4_binop_1,t29_setwiseo,t46_zfmisc_1,t13_setwiseo,t26_setwiseo,t34_setwiseo,t17_xboole_1,t16_setwiseo,t36_xboole_1,t16_setwiseo,t51_xboole_1,t37_xboole_1,t156_relat_1,t56_zfmisc_1,t145_funct_1,t1_xboole_1,t153_relat_1,t11_xboole_1,t28_xboole_1,d7_xboole_0,t19_setwiseo,t6_setwiseo,t43_funct_2,t116_funct_2,t12_setwiseo,d3_xboole_0,t65_zfmisc_1,t13_setwiseo,t40_xboole_1,t153_relat_1,t13_setwiseo,t11_setwiseo,d3_xboole_0,d13_funct_1,d1_tarski,t29_setwiseo,t33_setwiseo,t30_setwiseo,s4_setwiseo]),
    [file(setwiseo,t35_setwiseo),interesting(0.00)]).

fof(t43_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ( ( v1_binop_1(C,B)
                  & v2_binop_1(C,B)
                  & v3_binop_1(C,B)
                  & v1_setwiseo(C,B) )
               => ! [D] : 
                    ( ( v1_funct_1(D)
                      & v1_funct_2(D,A,B)
                      & m2_relset_1(D,A,B) )
                   => ! [E] : 
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,A,B)
                          & m2_relset_1(E,A,B) )
                       => ! [F] : 
                            ( m1_subset_1(F,k5_finsub_1(A))
                           => ! [G] : 
                                ( m1_subset_1(G,k5_finsub_1(A))
                               => ( k8_setwiseo(A,B,D,F) = k8_setwiseo(A,B,E,G)
                                 => k7_setwiseo(A,B,C,F,D) = k7_setwiseo(A,B,C,G,E) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t149_relat_1,t19_setwiseo,t40_setwiseo,t35_setwiseo]),
    [file(setwiseo,t43_setwiseo),interesting(0.00)]).

fof(t21_funct_2,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ! [E] : 
          ( ( v1_relat_1(E)
            & v1_funct_1(E) )
         => ( r2_hidden(C,A)
           => ( B = k1_xboole_0
              | k1_funct_1(k5_relat_1(D,E),C) = k1_funct_1(E,k1_funct_1(D,C)) ) ) ) ) ),
    file(funct_2,t21_funct_2),
    [interesting(0.00)]).

fof(t46_setwiseo,theorem,(
    $true ),
    file(setwiseo,t46_setwiseo),
    [interesting(0.00)]).

fof(t47_setwiseo,theorem,(
    $true ),
    file(setwiseo,t47_setwiseo),
    [interesting(0.00)]).

fof(t48_setwiseo,theorem,(
    $true ),
    file(setwiseo,t48_setwiseo),
    [interesting(0.00)]).

fof(d4_setwiseo,definition,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k5_finsub_1(A))
        & m2_relset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k5_finsub_1(A)) )
     => ( B = k9_setwiseo(A)
      <=> ! [C] : 
            ( m1_subset_1(C,k5_finsub_1(A))
           => ! [D] : 
                ( m1_subset_1(D,k5_finsub_1(A))
               => k2_binop_1(k5_finsub_1(A),k5_finsub_1(A),k5_finsub_1(A),B,C,D) = k5_setwiseo(A,C,D) ) ) ) ) ),
    file(setwiseo,d4_setwiseo),
    [interesting(0.00)]).

fof(d7_binop_1,definition,(
    ! [A,B] : 
      ( m1_subset_1(B,A)
     => ! [C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,k2_zfmisc_1(A,A),A)
            & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
         => ( r3_binop_1(A,B,C)
          <=> ( r1_binop_1(A,B,C)
              & r2_binop_1(A,B,C) ) ) ) ) ),
    file(binop_1,d7_binop_1),
    [interesting(0.00)]).

fof(d16_binop_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ( r1_binop_1(A,B,C)
              <=> ! [D] : 
                    ( m1_subset_1(D,A)
                   => k2_binop_1(A,A,A,C,B,D) = D ) ) ) ) ) ),
    file(binop_1,d16_binop_1),
    [interesting(0.00)]).

fof(d17_binop_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ( r2_binop_1(A,B,C)
              <=> ! [D] : 
                    ( m1_subset_1(D,A)
                   => k2_binop_1(A,A,A,C,D,B) = D ) ) ) ) ) ),
    file(binop_1,d17_binop_1),
    [interesting(0.00)]).

fof(d15_binop_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(A,A),A)
            & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
         => ( v3_binop_1(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,A)
               => k2_binop_1(A,A,A,B,C,C) = C ) ) ) ) ),
    file(binop_1,d15_binop_1),
    [interesting(0.00)]).

fof(d13_binop_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(A,A),A)
            & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
         => ( v1_binop_1(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,A)
               => ! [D] : 
                    ( m1_subset_1(D,A)
                   => k2_binop_1(A,A,A,B,C,D) = k2_binop_1(A,A,A,B,D,C) ) ) ) ) ) ),
    file(binop_1,d13_binop_1),
    [interesting(0.00)]).

fof(d14_binop_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(A,A),A)
            & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
         => ( v2_binop_1(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,A)
               => ! [D] : 
                    ( m1_subset_1(D,A)
                   => ! [E] : 
                        ( m1_subset_1(E,A)
                       => k2_binop_1(A,A,A,B,C,k2_binop_1(A,A,A,B,D,E)) = k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,B,C,D),E) ) ) ) ) ) ) ),
    file(binop_1,d14_binop_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(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(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(t27_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ( ( v3_binop_1(C,A)
                      & v1_binop_1(C,A)
                      & v2_binop_1(C,A) )
                   => ! [E] : 
                        ( m1_subset_1(E,B)
                       => ! [F] : 
                            ( m1_subset_1(F,B)
                           => k7_setwiseo(B,A,C,k3_setwiseo(B,E,F),D) = k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,E),k8_funct_2(B,A,D,F)) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t25_setwiseo,t12_zfmisc_1,d2_tarski,t41_enumset1]),
    [file(setwiseo,t27_setwiseo),interesting(0.00)]).

fof(d1_enumset1,definition,(
    ! [A,B,C,D] : 
      ( D = k1_enumset1(A,B,C)
    <=> ! [E] : 
          ( r2_hidden(E,D)
        <=> ~ ( E != A
              & E != B
              & E != C ) ) ) ),
    file(enumset1,d1_enumset1),
    [interesting(0.00)]).

fof(t42_enumset1,theorem,(
    ! [A,B,C] : k1_enumset1(A,B,C) = k2_xboole_0(k1_tarski(A),k2_tarski(B,C)) ),
    file(enumset1,t42_enumset1),
    [interesting(0.00)]).

fof(t43_enumset1,theorem,(
    ! [A,B,C] : k1_enumset1(A,B,C) = k2_xboole_0(k2_tarski(A,B),k1_tarski(C)) ),
    file(enumset1,t43_enumset1),
    [interesting(0.00)]).

fof(t28_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ( ( v3_binop_1(C,A)
                      & v1_binop_1(C,A)
                      & v2_binop_1(C,A) )
                   => ! [E] : 
                        ( m1_subset_1(E,B)
                       => ! [F] : 
                            ( m1_subset_1(F,B)
                           => ! [G] : 
                                ( m1_subset_1(G,B)
                               => k7_setwiseo(B,A,C,k4_setwiseo(B,E,F,G),D) = k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,E),k8_funct_2(B,A,D,F)),k8_funct_2(B,A,D,G)) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_enumset1,t25_setwiseo,t3_setwiseo,d1_enumset1,t41_enumset1,t4_setwiseo,d1_enumset1,t43_enumset1]),
    [file(setwiseo,t28_setwiseo),interesting(0.00)]).

fof(t58_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B,C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,k5_finsub_1(B))
            & m2_relset_1(C,A,k5_finsub_1(B)) )
         => ! [D] : 
              ( m1_subset_1(D,A)
             => ! [E] : 
                  ( m1_subset_1(E,A)
                 => ! [F] : 
                      ( m1_subset_1(F,A)
                     => k10_setwiseo(A,B,k4_setwiseo(A,D,E,F),C) = k5_setwiseo(B,k5_setwiseo(B,k8_funct_2(A,k5_finsub_1(B),C,D),k8_funct_2(A,k5_finsub_1(B),C,E)),k8_funct_2(A,k5_finsub_1(B),C,F)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t49_setwiseo,t50_setwiseo,t51_setwiseo,t28_setwiseo,d4_setwiseo,d4_setwiseo]),
    [file(setwiseo,t58_setwiseo),interesting(0.00)]).

fof(t23_xboole_1,theorem,(
    ! [A,B,C] : k3_xboole_0(A,k2_xboole_0(B,C)) = k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C)) ),
    file(xboole_1,t23_xboole_1),
    [interesting(0.00)]).

fof(t2_zfmisc_1,theorem,(
    k3_tarski(k1_xboole_0) = k1_xboole_0 ),
    file(zfmisc_1,t2_zfmisc_1),
    [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(t96_zfmisc_1,theorem,(
    ! [A,B] : k3_tarski(k2_xboole_0(A,B)) = k2_xboole_0(k3_tarski(A),k3_tarski(B)) ),
    file(zfmisc_1,t96_zfmisc_1),
    [interesting(0.00)]).

fof(t159_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ! [C] : 
          ( v1_relat_1(C)
         => k9_relat_1(k5_relat_1(B,C),A) = k9_relat_1(C,k9_relat_1(B,A)) ) ) ),
    file(relat_1,t159_relat_1),
    [interesting(0.00)]).

fof(t66_setwiseo,theorem,(
    $true ),
    file(setwiseo,t66_setwiseo),
    [interesting(0.00)]).

fof(d6_setwiseo,definition,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,k5_finsub_1(A))
        & m2_relset_1(B,A,k5_finsub_1(A)) )
     => ( B = k11_setwiseo(A)
      <=> ! [C] : 
            ( r2_hidden(C,A)
           => k1_funct_1(B,C) = k1_tarski(C) ) ) ) ),
    file(setwiseo,d6_setwiseo),
    [interesting(0.00)]).

fof(d4_tarski,definition,(
    ! [A,B] : 
      ( B = k3_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> ? [D] : 
              ( r2_hidden(C,D)
              & r2_hidden(D,A) ) ) ) ),
    file(tarski,d4_tarski),
    [interesting(0.00)]).

fof(l77_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B,C,D] : 
          ( ( v1_funct_1(D)
            & v1_funct_2(D,B,A)
            & m2_relset_1(D,B,A) )
         => r1_tarski(k2_funct_2(B,A,D,C),A) ) ) ),
    file(setwiseo,l77_setwiseo),
    [interesting(0.00)]).

fof(d1_funct_2,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( ( ( B = k1_xboole_0
           => A = k1_xboole_0 )
         => ( v1_funct_2(C,A,B)
          <=> A = k4_relset_1(A,B,C) ) )
        & ( B = k1_xboole_0
         => ( A = k1_xboole_0
            | ( v1_funct_2(C,A,B)
            <=> C = k1_xboole_0 ) ) ) ) ) ),
    file(funct_2,d1_funct_2),
    [interesting(0.00)]).

fof(t117_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r2_hidden(A,k1_relat_1(B))
       => k9_relat_1(B,k1_tarski(A)) = k1_tarski(k1_funct_1(B,A)) ) ) ),
    file(funct_1,t117_funct_1),
    [interesting(0.00)]).

fof(t151_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( k9_relat_1(B,A) = k1_xboole_0
      <=> r1_xboole_0(k1_relat_1(B),A) ) ) ),
    file(relat_1,t151_relat_1),
    [interesting(0.00)]).

fof(t72_setwiseo,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B,C,D] : 
          ( ( v1_funct_1(D)
            & v1_funct_2(D,A,k5_finsub_1(B))
            & m2_relset_1(D,A,k5_finsub_1(B)) )
         => ! [E] : 
              ( ( v1_funct_1(E)
                & v1_funct_2(E,k5_finsub_1(B),k5_finsub_1(C))
                & m2_relset_1(E,k5_finsub_1(B),k5_finsub_1(C)) )
             => ( ( k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,k1_setwiseo(B)) = k1_setwiseo(C)
                  & ! [F] : 
                      ( m1_subset_1(F,k5_finsub_1(B))
                     => ! [G] : 
                          ( m1_subset_1(G,k5_finsub_1(B))
                         => k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,k5_setwiseo(B,F,G)) = k5_setwiseo(C,k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,F),k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,G)) ) ) )
               => ! [F] : 
                    ( m1_subset_1(F,k5_finsub_1(A))
                   => k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,k10_setwiseo(A,B,F,D)) = k10_setwiseo(A,C,F,k7_funct_2(A,k5_finsub_1(B),k5_finsub_1(C),D,E)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t49_setwiseo,t50_setwiseo,t51_setwiseo,t53_setwiseo,t55_setwiseo,d4_setwiseo,t65_setwiseo]),
    [file(setwiseo,t72_setwiseo),interesting(0.00)]).

fof(t7_setwiseo,theorem,(
    $true ),
    file(setwiseo,t7_setwiseo),
    [interesting(0.00)]).

fof(t9_setwiseo,theorem,(
    $true ),
    file(setwiseo,t9_setwiseo),
    [interesting(0.00)]).