fof(t87_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( ( v2_rlvect_1(B)
            & m1_rlsub_1(B,A) )
         => ! [C] : 
              ( ( v2_rlvect_1(C)
                & m1_rlsub_1(C,A) )
             => ! [D] : 
                  ( m2_rlsub_1(D,A,B)
                 => ! [E] : 
                      ( m2_rlsub_1(E,A,C)
                     => ( D = E
                       => B = C ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_rlsub_1,d6_rlsub_1,t85_rlsub_1]),
    [file(rlsub_1,t87_rlsub_1),interesting(1.00)]).

fof(t85_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( ( v2_rlvect_1(D)
                    & m1_rlsub_1(D,A) )
                 => ! [E] : 
                      ( ( v2_rlvect_1(E)
                        & m1_rlsub_1(E,A) )
                     => ( k3_rlsub_1(A,B,D) = k3_rlsub_1(A,C,E)
                       => D = E ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t38_rlsub_1,d10_xboole_0,d4_xboole_0,d1_rlvect_1,t17_rlsub_1,d1_rlvect_1,t10_rlvect_1,t28_rlvect_1,d6_rlvect_1,t68_rlsub_1,d6_rlvect_1,t28_rlvect_1,t10_rlvect_1,t68_rlsub_1,t84_rlsub_1,d4_xboole_0,d1_rlvect_1,t17_rlsub_1,d1_rlvect_1,t10_rlvect_1,t28_rlvect_1,d6_rlvect_1,t68_rlsub_1,d6_rlvect_1,t28_rlvect_1,t10_rlvect_1,t68_rlsub_1,t84_rlsub_1,t37_xboole_1]),
    [file(rlsub_1,t85_rlsub_1),interesting(0.94)]).

fof(t71_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_rlsub_1(C,A)
             => ( k3_rlsub_1(A,B,C) = k3_rlsub_1(A,k5_rlvect_1(A,B),C)
              <=> r1_rlvect_1(C,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t59_rlsub_1,t28_rlvect_1,t41_rlvect_1,t30_rlvect_1,d9_rlvect_1,d9_rlvect_1,d9_rlvect_1,t35_rlvect_1,d9_rlvect_1,d9_rlvect_1,t29_rlsub_1,l70_rlsub_1,t67_rlsub_1]),
    [file(rlsub_1,t71_rlsub_1),interesting(0.92)]).

fof(t73_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_rlsub_1(D,A)
                 => ( ( r2_hidden(B,k3_rlsub_1(A,C,D))
                      & r2_hidden(B,k3_rlsub_1(A,k5_rlvect_1(A,C),D)) )
                   => r1_rlvect_1(D,C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t72_rlsub_1,t71_rlsub_1]),
    [file(rlsub_1,t73_rlsub_1),interesting(0.85)]).

fof(t86_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_rlsub_1(B,A)
         => ! [C] : 
              ( m2_rlsub_1(C,A,B)
             => ( v1_rlsub_1(C,A)
              <=> C = u1_struct_0(B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_rlsub_1,t59_rlsub_1,t4_rlsub_1,t63_rlsub_1,l27_rlsub_1]),
    [file(rlsub_1,t86_rlsub_1),interesting(0.84)]).

fof(t91_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => m2_rlsub_1(u1_struct_0(A),A,k2_rlsub_1(A)) ) ),
    inference(mizar_proof,[status(thm)],[t62_rlsub_1,d6_rlsub_1]),
    [file(rlsub_1,t91_rlsub_1),interesting(0.81)]).

fof(t67_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_rlsub_1(C,A)
             => ( r1_rlvect_1(C,B)
              <=> k3_rlsub_1(A,k5_rlvect_1(A,B),C) = u1_struct_0(C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t65_rlsub_1,t66_rlsub_1,t29_rlvect_1]),
    [file(rlsub_1,t67_rlsub_1),interesting(0.79)]).

fof(t48_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_rlsub_1(B,A)
         => k1_rlsub_1(B) = k1_rlsub_1(A) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_rlsub_1,t19_rlsub_1,t35_rlsub_1,t38_rlsub_1]),
    [file(rlsub_1,t48_rlsub_1),interesting(0.78)]).

fof(t62_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k3_rlsub_1(A,B,k2_rlsub_1(A)) = u1_struct_0(A) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_rlvect_1,l70_rlsub_1]),
    [file(rlsub_1,t62_rlsub_1),interesting(0.77)]).

fof(t49_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_rlsub_1(B,A)
         => ! [C] : 
              ( m1_rlsub_1(C,A)
             => k1_rlsub_1(B) = k1_rlsub_1(C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t48_rlsub_1]),
    [file(rlsub_1,t49_rlsub_1),interesting(0.75)]).

fof(t93_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_rlsub_1(B,A)
         => ! [C] : 
              ( m2_rlsub_1(C,A,B)
             => ( r2_hidden(k1_rlvect_1(A),C)
              <=> C = u1_struct_0(B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_rlsub_1,t63_rlsub_1]),
    [file(rlsub_1,t93_rlsub_1),interesting(0.74)]).

fof(t94_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_rlsub_1(C,A)
             => ! [D] : 
                  ( m2_rlsub_1(D,A,C)
                 => ( r2_hidden(B,D)
                  <=> D = k3_rlsub_1(A,B,C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_rlsub_1,t70_rlsub_1,t59_rlsub_1]),
    [file(rlsub_1,t94_rlsub_1),interesting(0.74)]).

fof(t17_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B,C] : 
          ( m1_rlsub_1(C,A)
         => ( r1_rlvect_1(C,B)
           => r1_rlvect_1(A,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_rlsub_1,d1_rlvect_1,d1_rlvect_1]),
    [file(rlsub_1,t17_rlsub_1),interesting(0.71)]).

fof(t68_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_rlsub_1(D,A)
                 => ( r1_rlvect_1(D,B)
                  <=> k3_rlsub_1(A,C,D) = k3_rlsub_1(A,k4_rlvect_1(A,C,B),D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t31_rlsub_1,d6_rlvect_1,d6_rlvect_1,d6_rlvect_1,t28_rlvect_1,t10_rlvect_1,d10_xboole_0,d3_tarski,t28_rlsub_1,d6_rlvect_1,t25_rlsub_1,t10_rlvect_1,t10_rlvect_1,d6_rlvect_1,t21_rlvect_1,d10_rlvect_1,t30_rlsub_1]),
    [file(rlsub_1,t68_rlsub_1),interesting(0.71)]).

fof(t25_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_rlsub_1(B,A)
         => r1_rlvect_1(B,k1_rlvect_1(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[t19_rlsub_1,t3_rlvect_1]),
    [file(rlsub_1,t25_rlsub_1),interesting(0.70)]).

fof(t33_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => m1_rlsub_1(A,A) ) ),
    inference(mizar_proof,[status(thm)],[d2_rlsub_1,t40_funct_2]),
    [file(rlsub_1,t33_rlsub_1),interesting(0.70)]).

fof(l70_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_rlsub_1(C,A)
             => ( r1_rlvect_1(C,B)
              <=> k3_rlsub_1(A,B,C) = u1_struct_0(C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t28_rlsub_1,d1_rlvect_1,d10_xboole_0,d3_tarski,d1_rlvect_1,t18_rlsub_1,d1_rlvect_1,d6_rlvect_1,d6_rlvect_1,t28_rlvect_1,t10_rlvect_1,t24_rlsub_1,t24_rlsub_1,t21_rlsub_1,t25_rlsub_1,t10_rlvect_1,d1_rlvect_1]),
    [file(rlsub_1,l70_rlsub_1),interesting(0.70)]).

fof(t19_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_rlsub_1(B,A)
         => k1_rlvect_1(B) = k1_rlvect_1(A) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_rlsub_1]),
    [file(rlsub_1,t19_rlsub_1),interesting(0.68)]).

fof(t52_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_rlsub_1(B,A)
         => ! [C] : 
              ( m1_rlsub_1(C,A)
             => m1_rlsub_1(k1_rlsub_1(B),C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t49_rlsub_1]),
    [file(rlsub_1,t52_rlsub_1),interesting(0.68)]).

fof(t50_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_rlsub_1(B,A)
         => m1_rlsub_1(k1_rlsub_1(B),A) ) ) ),
    inference(mizar_proof,[status(thm)],[t35_rlsub_1]),
    [file(rlsub_1,t50_rlsub_1),interesting(0.67)]).

fof(t51_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_rlsub_1(B,A)
         => m1_rlsub_1(k1_rlsub_1(A),B) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_rlsub_1,t19_rlsub_1,t36_rlsub_1]),
    [file(rlsub_1,t51_rlsub_1),interesting(0.67)]).

fof(t97_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_rlsub_1(D,A)
                 => ( ? [E] : 
                        ( m2_rlsub_1(E,A,D)
                        & r2_hidden(B,E)
                        & r2_hidden(C,E) )
                  <=> r1_rlvect_1(D,k6_rlvect_1(A,B,C)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_rlsub_1,t81_rlsub_1,t81_rlsub_1,d6_rlsub_1]),
    [file(rlsub_1,t97_rlsub_1),interesting(0.67)]).

fof(l61_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_rlsub_1(B,A)
         => k3_rlsub_1(A,k1_rlvect_1(A),B) = u1_struct_0(B) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t10_rlvect_1,d1_rlvect_1,d3_tarski,d1_rlvect_1,t17_rlsub_1,d1_rlvect_1,t10_rlvect_1,d10_xboole_0]),
    [file(rlsub_1,l61_rlsub_1),interesting(0.66)]).

fof(t76_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_rlsub_1(C,A)
             => ( r2_hidden(k5_rlvect_1(A,B),k3_rlsub_1(A,B,C))
              <=> r1_rlvect_1(C,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t74_rlsub_1,t75_rlsub_1,t29_rlvect_1]),
    [file(rlsub_1,t76_rlsub_1),interesting(0.66)]).

fof(t69_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_rlsub_1(D,A)
                 => ( r1_rlvect_1(D,B)
                  <=> k3_rlsub_1(A,C,D) = k3_rlsub_1(A,k6_rlvect_1(A,C,B),D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t68_rlsub_1,t30_rlsub_1,t30_rlvect_1,t30_rlsub_1]),
    [file(rlsub_1,t69_rlsub_1),interesting(0.65)]).

fof(t65_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,k1_numbers)
             => ! [D] : 
                  ( m1_rlsub_1(D,A)
                 => ( r1_rlvect_1(D,B)
                   => k3_rlsub_1(A,k3_rlvect_1(A,B,C),D) = u1_struct_0(D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t29_rlsub_1,t28_rlsub_1,d1_rlvect_1,d10_xboole_0,d3_tarski,d2_rlsub_1,t3_rlvect_1,t29_rlsub_1,d1_rlvect_1,t31_rlsub_1,d6_rlvect_1,d6_rlvect_1,t28_rlvect_1,t10_rlvect_1]),
    [file(rlsub_1,t65_rlsub_1),interesting(0.65)]).

fof(t7_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => v1_rlsub_1(k1_struct_0(A,k1_rlvect_1(A)),A) ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,t10_rlvect_1,d1_tarski,d1_rlsub_1,d1_tarski,t23_rlvect_1]),
    [file(rlsub_1,t7_rlsub_1),interesting(0.65)]).

fof(t61_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k3_rlsub_1(A,B,k1_rlsub_1(A)) = k1_struct_0(A,B) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d3_rlsub_1,d1_rlvect_1,d1_tarski,t10_rlvect_1,d1_tarski,d10_xboole_0,d3_tarski,d1_tarski,t25_rlsub_1,t10_rlvect_1]),
    [file(rlsub_1,t61_rlsub_1),interesting(0.65)]).

fof(t36_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_rlsub_1(B,A)
         => ! [C] : 
              ( m1_rlsub_1(C,A)
             => ( r1_tarski(u1_struct_0(B),u1_struct_0(C))
               => m1_rlsub_1(B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_rlsub_1,d2_rlsub_1,d2_rlsub_1,t119_zfmisc_1,t82_funct_1,d2_rlsub_1,t118_zfmisc_1,t82_funct_1]),
    [file(rlsub_1,t36_rlsub_1),interesting(0.64)]).

fof(t90_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_rlsub_1(B,A)
         => m2_rlsub_1(u1_struct_0(B),A,B) ) ) ),
    inference(mizar_proof,[status(thm)],[l61_rlsub_1,d6_rlsub_1]),
    [file(rlsub_1,t90_rlsub_1),interesting(0.64)]).

fof(t92_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( m2_rlsub_1(B,A,k2_rlsub_1(A))
           => B = u1_struct_0(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_rlsub_1,t62_rlsub_1]),
    [file(rlsub_1,t92_rlsub_1),interesting(0.64)]).

fof(t81_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_rlsub_1(D,A)
                 => ( ? [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                        & r2_hidden(B,k3_rlsub_1(A,E,D))
                        & r2_hidden(C,k3_rlsub_1(A,E,D)) )
                  <=> r1_rlvect_1(D,k6_rlvect_1(A,B,C)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t79_rlsub_1,t79_rlsub_1,t44_rlvect_1,d6_rlvect_1,d6_rlvect_1,t16_rlvect_1,t10_rlvect_1,t31_rlsub_1,t30_rlsub_1,t59_rlsub_1,t47_rlvect_1,d6_rlvect_1,t16_rlvect_1,t10_rlvect_1]),
    [file(rlsub_1,t81_rlsub_1),interesting(0.64)]).

fof(t30_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_rlsub_1(C,A)
             => ( r1_rlvect_1(C,B)
               => r1_rlvect_1(C,k5_rlvect_1(A,B)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t29_rlsub_1,t29_rlvect_1]),
    [file(rlsub_1,t30_rlsub_1),interesting(0.63)]).

fof(t43_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ~ ( B != k1_xboole_0
              & v1_rlsub_1(B,A)
              & ! [C] : 
                  ( ( v2_rlvect_1(C)
                    & m1_rlsub_1(C,A) )
                 => B != u1_struct_0(C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t4_rlsub_1,d1_funct_2,t90_relat_1,t28_xboole_1,d1_funct_2,t90_relat_1,t118_zfmisc_1,t28_xboole_1,t106_zfmisc_1,t72_funct_1,t10_rlvect_1,d2_zfmisc_1,t106_zfmisc_1,t72_funct_1,d1_rlsub_1,d5_funct_1,t106_zfmisc_1,t72_funct_1,d9_rlvect_1,d2_zfmisc_1,t106_zfmisc_1,t72_funct_1,d1_rlsub_1,d5_funct_1,d1_funct_2,t11_relset_1,d1_funct_2,t11_relset_1,t32_rlsub_1]),
    [file(rlsub_1,t43_rlsub_1),interesting(0.62)]).

fof(t64_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_rlsub_1(C,A)
             => ( r1_rlvect_1(C,B)
              <=> k3_rlsub_1(A,B,C) = u1_struct_0(C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l70_rlsub_1]),
    [file(rlsub_1,t64_rlsub_1),interesting(0.62)]).

fof(t75_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,k1_numbers)
             => ! [D] : 
                  ( m1_rlsub_1(D,A)
                 => ( r1_rlvect_1(D,B)
                   => r2_hidden(k3_rlvect_1(A,B,C),k3_rlsub_1(A,B,D)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d9_rlvect_1,d9_rlvect_1,t29_rlsub_1]),
    [file(rlsub_1,t75_rlsub_1),interesting(0.60)]).

fof(t27_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_rlsub_1(B,A)
         => r1_rlvect_1(A,k1_rlvect_1(B)) ) ) ),
    inference(mizar_proof,[status(thm)],[t3_rlvect_1,t17_rlsub_1]),
    [file(rlsub_1,t27_rlsub_1),interesting(0.59)]).

fof(t59_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_rlsub_1(C,A)
             => r2_hidden(B,k3_rlsub_1(A,B,C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t25_rlsub_1,t10_rlvect_1]),
    [file(rlsub_1,t59_rlsub_1),interesting(0.59)]).

fof(t88_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => m2_rlsub_1(k1_struct_0(A,B),A,k1_rlsub_1(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[t61_rlsub_1,d6_rlsub_1]),
    [file(rlsub_1,t88_rlsub_1),interesting(0.59)]).

fof(t18_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_rlsub_1(B,A)
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(B))
             => m1_subset_1(C,u1_struct_0(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t3_rlvect_1,t17_rlsub_1,d1_rlvect_1]),
    [file(rlsub_1,t18_rlsub_1),interesting(0.58)]).

fof(t74_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,k1_numbers)
             => ! [D] : 
                  ( m1_rlsub_1(D,A)
                 => ( r2_hidden(k3_rlvect_1(A,B,C),k3_rlsub_1(A,B,D))
                   => ( C = 1
                      | r1_rlvect_1(D,B) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t10_rlvect_1,t28_rlvect_1,d6_rlvect_1,d9_rlvect_1,t49_rlvect_1,d9_rlvect_1,d7_xcmplx_0,d9_rlvect_1,t29_rlsub_1]),
    [file(rlsub_1,t74_rlsub_1),interesting(0.58)]).

fof(t26_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_rlsub_1(B,A)
         => ! [C] : 
              ( m1_rlsub_1(C,A)
             => r1_rlvect_1(C,k1_rlvect_1(B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t19_rlsub_1,t25_rlsub_1]),
    [file(rlsub_1,t26_rlsub_1),interesting(0.56)]).

fof(t40_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_rlvect_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( ( v2_rlvect_1(B)
            & m1_rlsub_1(B,A) )
         => ( u1_struct_0(B) = u1_struct_0(A)
           => B = A ) ) ) ),
    inference(mizar_proof,[status(thm)],[t33_rlsub_1,t38_rlsub_1]),
    [file(rlsub_1,t40_rlsub_1),interesting(0.55)]).

fof(l27_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_rlsub_1(C,A)
             => ( u1_struct_0(C) = B
               => v1_rlsub_1(B,A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t21_rlsub_1,d1_rlsub_1,t22_rlsub_1]),
    [file(rlsub_1,l27_rlsub_1),interesting(0.55)]).

fof(t16_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B,C] : 
          ( m1_rlsub_1(C,A)
         => ! [D] : 
              ( m1_rlsub_1(D,A)
             => ( ( r1_rlvect_1(C,B)
                  & m1_rlsub_1(C,D) )
               => r1_rlvect_1(D,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_rlsub_1,d1_rlvect_1,d1_rlvect_1]),
    [file(rlsub_1,t16_rlsub_1),interesting(0.54)]).

fof(t20_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_rlsub_1(B,A)
         => ! [C] : 
              ( m1_rlsub_1(C,A)
             => k1_rlvect_1(B) = k1_rlvect_1(C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t19_rlsub_1,t19_rlsub_1]),
    [file(rlsub_1,t20_rlsub_1),interesting(0.54)]).

fof(t37_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_rlsub_1(B,A)
         => ! [C] : 
              ( m1_rlsub_1(C,A)
             => ( ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r1_rlvect_1(B,D)
                     => r1_rlvect_1(C,D) ) )
               => m1_rlsub_1(B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d2_rlsub_1,d1_rlvect_1,d1_rlvect_1,t36_rlsub_1]),
    [file(rlsub_1,t37_rlsub_1),interesting(0.53)]).

fof(t4_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_rlsub_1(B,A)
           => ( B = k1_xboole_0
              | r2_hidden(k1_rlvect_1(A),B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d1_rlsub_1,t23_rlvect_1]),
    [file(rlsub_1,t4_rlsub_1),interesting(0.53)]).

fof(t60_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_rlsub_1(B,A)
         => k3_rlsub_1(A,k1_rlvect_1(A),B) = u1_struct_0(B) ) ) ),
    inference(mizar_proof,[status(thm)],[l61_rlsub_1]),
    [file(rlsub_1,t60_rlsub_1),interesting(0.53)]).

fof(t66_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,k1_numbers)
             => ! [D] : 
                  ( m1_rlsub_1(D,A)
                 => ( k3_rlsub_1(A,k3_rlvect_1(A,B,C),D) = u1_struct_0(D)
                   => ( C = 0
                      | r1_rlvect_1(D,B) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d9_rlvect_1,d7_xcmplx_0,d9_rlvect_1,t29_rlsub_1,t25_rlsub_1,t10_rlvect_1,d1_rlvect_1]),
    [file(rlsub_1,t66_rlsub_1),interesting(0.53)]).

fof(t58_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_rlsub_1(C,A)
             => ( r2_hidden(k1_rlvect_1(A),k3_rlsub_1(A,B,C))
              <=> r1_rlvect_1(C,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d10_rlvect_1,t30_rlsub_1,t30_rlsub_1,t28_rlvect_1]),
    [file(rlsub_1,t58_rlsub_1),interesting(0.51)]).

fof(t96_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_rlsub_1(D,A)
                 => ! [E] : 
                      ( m2_rlsub_1(E,A,D)
                     => ~ ( r2_hidden(B,E)
                          & r2_hidden(C,E)
                          & ! [F] : 
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ~ ( r1_rlvect_1(D,F)
                                  & k6_rlvect_1(A,B,F) = C ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t94_rlsub_1,t83_rlsub_1]),
    [file(rlsub_1,t96_rlsub_1),interesting(0.51)]).

fof(t78_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_rlsub_1(D,A)
                 => ( r2_hidden(k6_rlvect_1(A,B,C),k3_rlsub_1(A,B,D))
                  <=> r1_rlvect_1(D,C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t30_rlsub_1,t30_rlsub_1,t77_rlsub_1,t30_rlvect_1]),
    [file(rlsub_1,t78_rlsub_1),interesting(0.50)]).

fof(t42_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_rlsub_1(C,A)
             => ( u1_struct_0(C) = B
               => v1_rlsub_1(B,A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l27_rlsub_1]),
    [file(rlsub_1,t42_rlsub_1),interesting(0.49)]).

fof(t95_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_rlsub_1(D,A)
                 => ! [E] : 
                      ( m2_rlsub_1(E,A,D)
                     => ~ ( r2_hidden(B,E)
                          & r2_hidden(C,E)
                          & ! [F] : 
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ~ ( r1_rlvect_1(D,F)
                                  & k4_rlvect_1(A,B,F) = C ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t94_rlsub_1,t82_rlsub_1]),
    [file(rlsub_1,t95_rlsub_1),interesting(0.48)]).

fof(t8_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( u1_struct_0(A) = B
           => v1_rlsub_1(B,A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_rlsub_1]),
    [file(rlsub_1,t8_rlsub_1),interesting(0.45)]).

fof(t89_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ~ ( m2_rlsub_1(B,A,k1_rlsub_1(A))
              & ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(A))
                 => B != k1_struct_0(A,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_rlsub_1,t61_rlsub_1]),
    [file(rlsub_1,t89_rlsub_1),interesting(0.44)]).

fof(t80_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_rlsub_1(D,A)
                 => ( r2_hidden(B,k3_rlsub_1(A,C,D))
                  <=> ? [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                        & r1_rlvect_1(D,E)
                        & B = k6_rlvect_1(A,C,E) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t30_rlsub_1,t30_rlvect_1,t30_rlsub_1]),
    [file(rlsub_1,t80_rlsub_1),interesting(0.37)]).

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(d1_rlsub_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_rlsub_1(B,A)
          <=> ( ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( ( r2_hidden(C,B)
                          & r2_hidden(D,B) )
                       => r2_hidden(k4_rlvect_1(A,C,D),B) ) ) )
              & ! [C] : 
                  ( m1_subset_1(C,k1_numbers)
                 => ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( r2_hidden(D,B)
                       => r2_hidden(k3_rlvect_1(A,D,C),B) ) ) ) ) ) ) ) ),
    file(rlsub_1,d1_rlsub_1),
    [interesting(0.00)]).

fof(t10_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v1_rlsub_1(B,A)
                  & v1_rlsub_1(C,A) )
               => v1_rlsub_1(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_xboole_0,d1_rlsub_1,d3_xboole_0,d1_rlsub_1,d3_xboole_0,d1_rlsub_1,d3_xboole_0]),
    [file(rlsub_1,t10_rlsub_1),interesting(0.00)]).

fof(t11_rlsub_1,theorem,(
    $true ),
    file(rlsub_1,t11_rlsub_1),
    [interesting(0.00)]).

fof(t12_rlsub_1,theorem,(
    $true ),
    file(rlsub_1,t12_rlsub_1),
    [interesting(0.00)]).

fof(t13_rlsub_1,theorem,(
    $true ),
    file(rlsub_1,t13_rlsub_1),
    [interesting(0.00)]).

fof(t14_rlsub_1,theorem,(
    $true ),
    file(rlsub_1,t14_rlsub_1),
    [interesting(0.00)]).

fof(t15_rlsub_1,theorem,(
    $true ),
    file(rlsub_1,t15_rlsub_1),
    [interesting(0.00)]).

fof(d2_rlsub_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & l2_rlvect_1(B) )
         => ( m1_rlsub_1(B,A)
          <=> ( r1_tarski(u1_struct_0(B),u1_struct_0(A))
              & u2_struct_0(B) = u2_struct_0(A)
              & u1_rlvect_1(B) = k1_realset1(u1_rlvect_1(A),u1_struct_0(B))
              & u2_rlvect_1(B) = k8_relset_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A),u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,u1_struct_0(B))) ) ) ) ) ),
    file(rlsub_1,d2_rlsub_1),
    [interesting(0.00)]).

fof(d1_rlvect_1,definition,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( r1_rlvect_1(A,B)
        <=> r2_hidden(B,u1_struct_0(A)) ) ) ),
    file(rlvect_1,d1_rlvect_1),
    [interesting(0.00)]).

fof(t1_rlsub_1,theorem,(
    $true ),
    file(rlsub_1,t1_rlsub_1),
    [interesting(0.00)]).

fof(t3_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => r1_rlvect_1(A,B) ) ) ),
    file(rlvect_1,t3_rlvect_1),
    [interesting(0.00)]).

fof(t2_rlsub_1,theorem,(
    $true ),
    file(rlsub_1,t2_rlsub_1),
    [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(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(t82_funct_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r1_tarski(A,B)
       => ( k7_relat_1(k7_relat_1(C,A),B) = k7_relat_1(C,A)
          & k7_relat_1(k7_relat_1(C,B),A) = k7_relat_1(C,A) ) ) ) ),
    file(funct_1,t82_funct_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(t3_rlsub_1,theorem,(
    $true ),
    file(rlsub_1,t3_rlsub_1),
    [interesting(0.00)]).

fof(t40_funct_2,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( r1_tarski(A,C)
       => k2_partfun1(A,B,D,C) = D ) ) ),
    file(funct_2,t40_funct_2),
    [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(t101_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => k7_relat_1(k7_relat_1(B,A),A) = k7_relat_1(B,A) ) ),
    file(relat_1,t101_relat_1),
    [interesting(0.00)]).

fof(t34_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_rlvect_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v2_rlvect_1(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & l2_rlvect_1(B) )
         => ( ( m1_rlsub_1(A,B)
              & m1_rlsub_1(B,A) )
           => A = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_rlsub_1,d10_xboole_0,d2_rlsub_1,d2_rlsub_1,t101_relat_1,d2_rlsub_1,t101_relat_1]),
    [file(rlsub_1,t34_rlsub_1),interesting(0.00)]).

fof(t38_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( ( v2_rlvect_1(B)
            & m1_rlsub_1(B,A) )
         => ! [C] : 
              ( ( v2_rlvect_1(C)
                & m1_rlsub_1(C,A) )
             => ( u1_struct_0(B) = u1_struct_0(C)
               => B = C ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t36_rlsub_1,t34_rlsub_1]),
    [file(rlsub_1,t38_rlsub_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(t39_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( ( v2_rlvect_1(B)
            & m1_rlsub_1(B,A) )
         => ! [C] : 
              ( ( v2_rlvect_1(C)
                & m1_rlsub_1(C,A) )
             => ( ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r1_rlvect_1(B,D)
                    <=> r1_rlvect_1(C,D) ) )
               => B = C ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_rlsub_1,d1_rlvect_1,d1_rlvect_1,d2_rlsub_1,d1_rlvect_1,d1_rlvect_1,t2_tarski,t38_rlsub_1]),
    [file(rlsub_1,t39_rlsub_1),interesting(0.00)]).

fof(t41_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_rlvect_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( ( v2_rlvect_1(B)
            & m1_rlsub_1(B,A) )
         => ( ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ( r1_rlvect_1(B,C)
                <=> r1_rlvect_1(A,C) ) )
           => B = A ) ) ) ),
    inference(mizar_proof,[status(thm)],[t33_rlsub_1,t39_rlsub_1]),
    [file(rlsub_1,t41_rlsub_1),interesting(0.00)]).

fof(t72_funct_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(B,A)
       => k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B) ) ) ),
    file(funct_1,t72_funct_1),
    [interesting(0.00)]).

fof(t21_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_rlsub_1(D,A)
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(D))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(D))
                         => ( ( E = B
                              & F = C )
                           => k4_rlvect_1(D,E,F) = k4_rlvect_1(A,B,C) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t18_rlsub_1,d2_rlsub_1,t72_funct_1]),
    [file(rlsub_1,t21_rlsub_1),interesting(0.00)]).

fof(t22_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,k1_numbers)
             => ! [D] : 
                  ( m1_rlsub_1(D,A)
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(D))
                     => ( E = B
                       => k3_rlvect_1(D,E,C) = k3_rlvect_1(A,B,C) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t18_rlsub_1,d2_rlsub_1,t72_funct_1]),
    [file(rlsub_1,t22_rlsub_1),interesting(0.00)]).

fof(t23_rlvect_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & l2_rlvect_1(B) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(B))
             => ( ( A = 0
                  | C = k1_rlvect_1(B) )
               => k3_rlvect_1(B,C,A) = k1_rlvect_1(B) ) ) ) ) ),
    file(rlvect_1,t23_rlvect_1),
    [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(t90_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => k1_relat_1(k7_relat_1(B,A)) = k3_xboole_0(k1_relat_1(B),A) ) ),
    file(relat_1,t90_relat_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(t106_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D))
    <=> ( r2_hidden(A,C)
        & r2_hidden(B,D) ) ) ),
    file(zfmisc_1,t106_zfmisc_1),
    [interesting(0.00)]).

fof(t10_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( k2_rlvect_1(A,B,k1_rlvect_1(A)) = B
            & k2_rlvect_1(A,k1_rlvect_1(A),B) = B ) ) ) ),
    file(rlvect_1,t10_rlvect_1),
    [interesting(0.00)]).

fof(d2_zfmisc_1,definition,(
    ! [A,B,C] : 
      ( C = k2_zfmisc_1(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ? [E,F] : 
              ( r2_hidden(E,A)
              & r2_hidden(F,B)
              & D = k4_tarski(E,F) ) ) ) ),
    file(zfmisc_1,d2_zfmisc_1),
    [interesting(0.00)]).

fof(d5_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( r2_hidden(D,k1_relat_1(A))
                  & C = k1_funct_1(A,D) ) ) ) ) ),
    file(funct_1,d5_funct_1),
    [interesting(0.00)]).

fof(d9_rlvect_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_rlvect_1(A) )
     => ( v7_rlvect_1(A)
      <=> ( ! [B] : 
              ( m1_subset_1(B,k1_numbers)
             => ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => k3_rlvect_1(A,k2_rlvect_1(A,C,D),B) = k2_rlvect_1(A,k3_rlvect_1(A,C,B),k3_rlvect_1(A,D,B)) ) ) )
          & ! [B] : 
              ( m1_subset_1(B,k1_numbers)
             => ! [C] : 
                  ( m1_subset_1(C,k1_numbers)
                 => ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => k3_rlvect_1(A,D,k3_real_1(B,C)) = k2_rlvect_1(A,k3_rlvect_1(A,D,B),k3_rlvect_1(A,D,C)) ) ) )
          & ! [B] : 
              ( m1_subset_1(B,k1_numbers)
             => ! [C] : 
                  ( m1_subset_1(C,k1_numbers)
                 => ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => k3_rlvect_1(A,D,k4_real_1(B,C)) = k3_rlvect_1(A,k3_rlvect_1(A,D,C),B) ) ) )
          & ! [B] : 
              ( m1_subset_1(B,u1_struct_0(A))
             => k3_rlvect_1(A,B,1) = B ) ) ) ) ),
    file(rlvect_1,d9_rlvect_1),
    [interesting(0.00)]).

fof(t11_relset_1,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( ( r1_tarski(k1_relat_1(C),A)
          & r1_tarski(k2_relat_1(C),B) )
       => m2_relset_1(C,A,B) ) ) ),
    file(relset_1,t11_relset_1),
    [interesting(0.00)]).

fof(d3_rlvect_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k2_rlvect_1(A,B,C) = k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A),u1_rlvect_1(A),k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C)) ) ) ) ),
    file(rlvect_1,d3_rlvect_1),
    [interesting(0.00)]).

fof(d5_rlvect_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( v3_rlvect_1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => k2_rlvect_1(A,B,C) = k2_rlvect_1(A,C,B) ) ) ) ) ),
    file(rlvect_1,d5_rlvect_1),
    [interesting(0.00)]).

fof(d6_rlvect_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( v4_rlvect_1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k2_rlvect_1(A,k2_rlvect_1(A,B,C),D) = k2_rlvect_1(A,B,k2_rlvect_1(A,C,D)) ) ) ) ) ) ),
    file(rlvect_1,d6_rlvect_1),
    [interesting(0.00)]).

fof(d7_rlvect_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( v5_rlvect_1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => k2_rlvect_1(A,B,k1_rlvect_1(A)) = B ) ) ) ),
    file(rlvect_1,d7_rlvect_1),
    [interesting(0.00)]).

fof(d8_rlvect_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( v6_rlvect_1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ? [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
                & k2_rlvect_1(A,B,C) = k1_rlvect_1(A) ) ) ) ) ),
    file(rlvect_1,d8_rlvect_1),
    [interesting(0.00)]).

fof(d10_rlvect_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( ( v4_rlvect_1(A)
              & v5_rlvect_1(A)
              & v6_rlvect_1(A) )
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ( C = k5_rlvect_1(A,B)
                <=> k2_rlvect_1(A,B,C) = k1_rlvect_1(A) ) ) ) ) ) ),
    file(rlvect_1,d10_rlvect_1),
    [interesting(0.00)]).

fof(t29_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k5_rlvect_1(A,B) = k3_rlvect_1(A,B,k1_real_1(1)) ) ) ),
    file(rlvect_1,t29_rlvect_1),
    [interesting(0.00)]).

fof(t32_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( m1_subset_1(D,C)
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(C,C),C)
                        & m2_relset_1(E,k2_zfmisc_1(C,C),C) )
                     => ! [F] : 
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(k1_numbers,C),C)
                            & m2_relset_1(F,k2_zfmisc_1(k1_numbers,C),C) )
                         => ( ( B = C
                              & D = k1_rlvect_1(A)
                              & E = k1_realset1(u1_rlvect_1(A),B)
                              & F = k8_relset_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A),u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,B)) )
                           => m1_rlsub_1(g2_rlvect_1(C,D,E,F),A) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t72_funct_1,t72_funct_1,d3_tarski,d3_rlvect_1,d5_rlvect_1,d3_tarski,d6_rlvect_1,d6_rlvect_1,d3_tarski,t10_rlvect_1,d7_rlvect_1,d3_tarski,d8_rlvect_1,d10_rlvect_1,t29_rlvect_1,d8_rlvect_1,d3_tarski,d9_rlvect_1,d9_rlvect_1,d3_tarski,d9_rlvect_1,d3_tarski,d9_rlvect_1,d3_tarski,d9_rlvect_1,d2_rlsub_1]),
    [file(rlsub_1,t32_rlsub_1),interesting(0.00)]).

fof(t44_rlsub_1,theorem,(
    $true ),
    file(rlsub_1,t44_rlsub_1),
    [interesting(0.00)]).

fof(t45_rlsub_1,theorem,(
    $true ),
    file(rlsub_1,t45_rlsub_1),
    [interesting(0.00)]).

fof(t46_rlsub_1,theorem,(
    $true ),
    file(rlsub_1,t46_rlsub_1),
    [interesting(0.00)]).

fof(t47_rlsub_1,theorem,(
    $true ),
    file(rlsub_1,t47_rlsub_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(t35_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & l2_rlvect_1(B) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_rlvect_1(C)
                & l2_rlvect_1(C) )
             => ( ( m1_rlsub_1(A,B)
                  & m1_rlsub_1(B,C) )
               => m1_rlsub_1(A,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_rlsub_1,t1_xboole_1,d2_rlsub_1,d2_rlsub_1,d2_rlsub_1,t119_zfmisc_1,t82_funct_1,d2_rlsub_1,t118_zfmisc_1,t82_funct_1]),
    [file(rlsub_1,t35_rlsub_1),interesting(0.00)]).

fof(d3_rlsub_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( ( v2_rlvect_1(B)
            & m1_rlsub_1(B,A) )
         => ( B = k1_rlsub_1(A)
          <=> u1_struct_0(B) = k1_struct_0(A,k1_rlvect_1(A)) ) ) ) ),
    file(rlsub_1,d3_rlsub_1),
    [interesting(0.00)]).

fof(t53_rlsub_1,theorem,(
    $true ),
    file(rlsub_1,t53_rlsub_1),
    [interesting(0.00)]).

fof(t54_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_rlvect_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => m1_rlsub_1(A,k2_rlsub_1(A)) ) ),
    file(rlsub_1,t54_rlsub_1),
    [interesting(0.00)]).

fof(t55_rlsub_1,theorem,(
    $true ),
    file(rlsub_1,t55_rlsub_1),
    [interesting(0.00)]).

fof(t56_rlsub_1,theorem,(
    $true ),
    file(rlsub_1,t56_rlsub_1),
    [interesting(0.00)]).

fof(t57_rlsub_1,theorem,(
    $true ),
    file(rlsub_1,t57_rlsub_1),
    [interesting(0.00)]).

fof(t28_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_rlsub_1(D,A)
                 => ( ( r1_rlvect_1(D,B)
                      & r1_rlvect_1(D,C) )
                   => r1_rlvect_1(D,k4_rlvect_1(A,B,C)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_rlvect_1,d2_rlsub_1,l27_rlsub_1,d1_rlsub_1,d1_rlvect_1]),
    [file(rlsub_1,t28_rlsub_1),interesting(0.00)]).

fof(t28_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k6_rlvect_1(A,B,B) = k1_rlvect_1(A) ) ) ),
    file(rlvect_1,t28_rlvect_1),
    [interesting(0.00)]).

fof(t23_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_rlsub_1(C,A)
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ( D = B
                   => k5_rlvect_1(A,B) = k5_rlvect_1(C,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t29_rlvect_1,t22_rlsub_1]),
    [file(rlsub_1,t23_rlsub_1),interesting(0.00)]).

fof(t24_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_rlsub_1(D,A)
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(D))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(D))
                         => ( ( E = B
                              & F = C )
                           => k6_rlvect_1(D,E,F) = k6_rlvect_1(A,B,C) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t23_rlsub_1,t21_rlsub_1]),
    [file(rlsub_1,t24_rlsub_1),interesting(0.00)]).

fof(t29_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,k1_numbers)
             => ! [D] : 
                  ( m1_rlsub_1(D,A)
                 => ( r1_rlvect_1(D,B)
                   => r1_rlvect_1(D,k3_rlvect_1(A,B,C)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_rlvect_1,d2_rlsub_1,l27_rlsub_1,d1_rlsub_1,d1_rlvect_1]),
    [file(rlsub_1,t29_rlsub_1),interesting(0.00)]).

fof(t31_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_rlsub_1(D,A)
                 => ( ( r1_rlvect_1(D,B)
                      & r1_rlvect_1(D,C) )
                   => r1_rlvect_1(D,k6_rlvect_1(A,B,C)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t30_rlsub_1,t28_rlsub_1]),
    [file(rlsub_1,t31_rlsub_1),interesting(0.00)]).

fof(t21_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( k2_rlvect_1(A,B,D) = k2_rlvect_1(A,B,E)
                          | k2_rlvect_1(A,D,B) = k2_rlvect_1(A,E,B) )
                       => D = E ) ) ) ) ) ) ),
    file(rlvect_1,t21_rlvect_1),
    [interesting(0.00)]).

fof(t30_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k5_rlvect_1(A,k5_rlvect_1(A,B)) = B ) ) ),
    file(rlvect_1,t30_rlvect_1),
    [interesting(0.00)]).

fof(t5_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_rlsub_1(B,A)
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ( r2_hidden(C,B)
                 => r2_hidden(k5_rlvect_1(A,C),B) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_rlsub_1,t29_rlvect_1]),
    [file(rlsub_1,t5_rlsub_1),interesting(0.00)]).

fof(t6_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_rlsub_1(B,A)
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( ( r2_hidden(C,B)
                        & r2_hidden(D,B) )
                     => r2_hidden(k6_rlvect_1(A,C,D),B) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t5_rlsub_1,d1_rlsub_1]),
    [file(rlsub_1,t6_rlsub_1),interesting(0.00)]).

fof(t72_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_rlsub_1(E,A)
                     => ( ( r2_hidden(B,k3_rlsub_1(A,C,E))
                          & r2_hidden(B,k3_rlsub_1(A,D,E)) )
                       => k3_rlsub_1(A,C,E) = k3_rlsub_1(A,D,E) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d6_rlvect_1,t28_rlvect_1,t10_rlvect_1,d6_rlvect_1,d6_rlvect_1,t31_rlsub_1,t28_rlsub_1,d10_xboole_0,d3_tarski,d6_rlvect_1,t28_rlvect_1,t10_rlvect_1,d6_rlvect_1,d6_rlvect_1,t31_rlsub_1,t28_rlsub_1]),
    [file(rlsub_1,t72_rlsub_1),interesting(0.00)]).

fof(t41_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k6_rlvect_1(A,B,k2_rlvect_1(A,C,D)) = k6_rlvect_1(A,k6_rlvect_1(A,B,D),C) ) ) ) ) ),
    file(rlvect_1,t41_rlvect_1),
    [interesting(0.00)]).

fof(t35_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k6_rlvect_1(A,B,C) = k1_rlvect_1(A)
               => B = C ) ) ) ) ),
    file(rlvect_1,t35_rlvect_1),
    [interesting(0.00)]).

fof(d7_xcmplx_0,definition,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => ( ( A != 0
             => ( B = k5_xcmplx_0(A)
              <=> k3_xcmplx_0(A,B) = 1 ) )
            & ( A = 0
             => ( B = k5_xcmplx_0(A)
              <=> B = 0 ) ) ) ) ) ),
    file(xcmplx_0,d7_xcmplx_0),
    [interesting(0.00)]).

fof(t49_rlvect_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( m1_subset_1(B,k1_numbers)
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_rlvect_1(C)
                & l2_rlvect_1(C) )
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(C))
                 => k3_rlvect_1(C,D,k5_real_1(A,B)) = k6_rlvect_1(C,k3_rlvect_1(C,D,A),k3_rlvect_1(C,D,B)) ) ) ) ) ),
    file(rlvect_1,t49_rlvect_1),
    [interesting(0.00)]).

fof(t77_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_rlsub_1(D,A)
                 => ( r2_hidden(k4_rlvect_1(A,B,C),k3_rlsub_1(A,C,D))
                  <=> r1_rlvect_1(D,B) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t21_rlvect_1]),
    [file(rlsub_1,t77_rlsub_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(d6_rlsub_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_rlsub_1(B,A)
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( m2_rlsub_1(C,A,B)
              <=> ? [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                    & C = k3_rlsub_1(A,D,B) ) ) ) ) ) ),
    file(rlsub_1,d6_rlsub_1),
    [interesting(0.00)]).

fof(t63_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_rlsub_1(C,A)
             => ( r2_hidden(k1_rlvect_1(A),k3_rlsub_1(A,B,C))
              <=> k3_rlsub_1(A,B,C) = u1_struct_0(C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l70_rlsub_1,t58_rlsub_1]),
    [file(rlsub_1,t63_rlsub_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(t84_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( ( v2_rlvect_1(C)
                & m1_rlsub_1(C,A) )
             => ! [D] : 
                  ( ( v2_rlvect_1(D)
                    & m1_rlsub_1(D,A) )
                 => ( k3_rlsub_1(A,B,C) = k3_rlsub_1(A,B,D)
                  <=> C = D ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_rlsub_1,d2_rlsub_1,d3_tarski,d1_rlvect_1,t21_rlvect_1,d1_rlvect_1,d10_xboole_0,d3_tarski,d1_rlvect_1,t21_rlvect_1,d1_rlvect_1,t38_rlsub_1]),
    [file(rlsub_1,t84_rlsub_1),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(t70_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_rlsub_1(D,A)
                 => ( r2_hidden(B,k3_rlsub_1(A,C,D))
                  <=> k3_rlsub_1(A,C,D) = k3_rlsub_1(A,B,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t31_rlsub_1,d6_rlvect_1,t28_rlvect_1,t10_rlvect_1,d6_rlvect_1,d10_xboole_0,d3_tarski,t28_rlsub_1,d6_rlvect_1,t59_rlsub_1]),
    [file(rlsub_1,t70_rlsub_1),interesting(0.00)]).

fof(t82_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_rlsub_1(D,A)
                 => ~ ( k3_rlsub_1(A,B,D) = k3_rlsub_1(A,C,D)
                      & ! [E] : 
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ~ ( r1_rlvect_1(D,E)
                              & k4_rlvect_1(A,B,E) = C ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t59_rlsub_1,t28_rlvect_1,d6_rlvect_1,d6_rlvect_1,d10_rlvect_1,t30_rlsub_1,d6_rlvect_1,d6_rlvect_1,t28_rlvect_1,t10_rlvect_1]),
    [file(rlsub_1,t82_rlsub_1),interesting(0.00)]).

fof(t43_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k6_rlvect_1(A,B,k6_rlvect_1(A,C,D)) = k4_rlvect_1(A,k6_rlvect_1(A,B,C),D) ) ) ) ) ),
    file(rlvect_1,t43_rlvect_1),
    [interesting(0.00)]).

fof(t83_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_rlsub_1(D,A)
                 => ~ ( k3_rlsub_1(A,B,D) = k3_rlsub_1(A,C,D)
                      & ! [E] : 
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ~ ( r1_rlvect_1(D,E)
                              & k6_rlvect_1(A,B,E) = C ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t59_rlsub_1,t28_rlvect_1,d6_rlvect_1,d6_rlvect_1,d10_rlvect_1,t30_rlsub_1,t43_rlvect_1,t28_rlvect_1,t10_rlvect_1]),
    [file(rlsub_1,t83_rlsub_1),interesting(0.00)]).

fof(t79_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_rlsub_1(D,A)
                 => ( r2_hidden(B,k3_rlsub_1(A,C,D))
                  <=> ? [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                        & r1_rlvect_1(D,E)
                        & B = k4_rlvect_1(A,C,E) ) ) ) ) ) ) ),
    file(rlsub_1,t79_rlsub_1),
    [interesting(0.00)]).

fof(t44_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k5_rlvect_1(A,k2_rlvect_1(A,B,C)) = k6_rlvect_1(A,k5_rlvect_1(A,C),B) ) ) ) ),
    file(rlvect_1,t44_rlvect_1),
    [interesting(0.00)]).

fof(t16_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( k2_rlvect_1(A,B,k5_rlvect_1(A,B)) = k1_rlvect_1(A)
            & k2_rlvect_1(A,k5_rlvect_1(A,B),B) = k1_rlvect_1(A) ) ) ) ),
    file(rlvect_1,t16_rlvect_1),
    [interesting(0.00)]).

fof(t47_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k5_rlvect_1(A,k6_rlvect_1(A,B,C)) = k2_rlvect_1(A,C,k5_rlvect_1(A,B)) ) ) ) ),
    file(rlvect_1,t47_rlvect_1),
    [interesting(0.00)]).

fof(t98_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_rlsub_1(C,A)
             => ! [D] : 
                  ( m2_rlsub_1(D,A,C)
                 => ! [E] : 
                      ( m2_rlsub_1(E,A,C)
                     => ( ( r2_hidden(B,D)
                          & r2_hidden(B,E) )
                       => D = E ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_rlsub_1,d6_rlsub_1,t72_rlsub_1]),
    [file(rlsub_1,t98_rlsub_1),interesting(0.00)]).

fof(t9_rlsub_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( v1_rlsub_1(B,A)
                      & v1_rlsub_1(C,A)
                      & D = a_3_0_rlsub_1(A,B,C) )
                   => v1_rlsub_1(D,A) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_rlsub_1,d6_rlvect_1,d6_rlvect_1,d6_rlvect_1,d1_rlsub_1,d1_rlsub_1,d9_rlvect_1]),
    [file(rlsub_1,t9_rlsub_1),interesting(0.00)]).