fof(t6_grfunc_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( r1_tarski(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d1_relat_1,d1_funct_1,t2_funct_1]),
    [file(grfunc_1,t6_grfunc_1),interesting(1.00)]).

fof(t27_grfunc_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k3_xboole_0(B,A))
        & v1_funct_1(k3_xboole_0(B,A)) ) ) ),
    inference(mizar_proof,[status(thm)],[t17_xboole_1,t6_grfunc_1]),
    [file(grfunc_1,t27_grfunc_1),interesting(1.00)]).

fof(t26_grfunc_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( r1_tarski(A,B)
              & v2_funct_1(B) )
           => v2_funct_1(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t25_grfunc_1,t25_grfunc_1]),
    [file(grfunc_1,t26_grfunc_1),interesting(0.93)]).

fof(t38_grfunc_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k4_xboole_0(B,A))
        & v1_funct_1(k4_xboole_0(B,A)) ) ) ),
    inference(mizar_proof,[status(thm)],[t36_xboole_1,t6_grfunc_1]),
    [file(grfunc_1,t38_grfunc_1),interesting(0.89)]).

fof(t46_grfunc_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( A = k1_xboole_0
       => v2_funct_1(A) ) ) ),
    inference(mizar_proof,[status(thm)],[t25_grfunc_1]),
    [file(grfunc_1,t46_grfunc_1),interesting(0.89)]).

fof(t15_grfunc_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(k1_tarski(k4_tarski(A,B)))
      & v1_funct_1(k1_tarski(k4_tarski(A,B))) ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,d1_tarski,t33_zfmisc_1,t2_funct_1]),
    [file(grfunc_1,t15_grfunc_1),interesting(0.88)]).

fof(t30_grfunc_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( C = k3_xboole_0(A,B)
               => ( ( ~ v2_funct_1(A)
                    & ~ v2_funct_1(B) )
                  | v2_funct_1(C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t27_grfunc_1,t17_xboole_1,t26_grfunc_1]),
    [file(grfunc_1,t30_grfunc_1),interesting(0.86)]).

fof(l17_grfunc_1,theorem,(
    ! [A,B,C,D] : 
      ( r2_hidden(k4_tarski(A,B),k1_tarski(k4_tarski(C,D)))
     => ( A = C
        & B = D ) ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,t33_zfmisc_1]),
    [file(grfunc_1,l17_grfunc_1),interesting(0.85)]).

fof(t49_grfunc_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( A = k1_xboole_0
       => k2_funct_1(A) = k1_xboole_0 ) ) ),
    inference(mizar_proof,[status(thm)],[t46_grfunc_1,t60_relat_1,t55_funct_1,t64_relat_1]),
    [file(grfunc_1,t49_grfunc_1),interesting(0.83)]).

fof(t18_grfunc_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( k1_relat_1(B) = k1_tarski(A)
       => B = k1_tarski(k4_tarski(A,k1_funct_1(B,A))) ) ) ),
    inference(mizar_proof,[status(thm)],[t15_grfunc_1,t14_funct_1,d4_relat_1,d5_relat_1,d1_tarski,d1_tarski,l17_grfunc_1,d1_tarski,d4_funct_1,d2_relat_1]),
    [file(grfunc_1,t18_grfunc_1),interesting(0.81)]).

fof(t64_grfunc_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_tarski(A,B)
           => k7_relat_1(B,k1_relat_1(A)) = A ) ) ) ),
    inference(mizar_proof,[status(thm)],[t105_relat_1,t97_relat_1,d11_relat_1,d4_funct_1,d11_relat_1,d1_funct_1,d3_relat_1,d10_xboole_0]),
    [file(grfunc_1,t64_grfunc_1),interesting(0.75)]).

fof(t25_grfunc_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
      <=> ! [B,C,D] : 
            ( ( r2_hidden(k4_tarski(B,D),A)
              & r2_hidden(k4_tarski(C,D),A) )
           => B = C ) ) ) ),
    inference(mizar_proof,[status(thm)],[t8_funct_1,d8_funct_1,d8_funct_1,t8_funct_1]),
    [file(grfunc_1,t25_grfunc_1),interesting(0.64)]).

fof(t32_grfunc_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( ( r1_tarski(A,B)
                  & r1_tarski(C,B) )
               => ( v1_relat_1(k2_xboole_0(A,C))
                  & v1_funct_1(k2_xboole_0(A,C)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t8_xboole_1,t6_grfunc_1]),
    [file(grfunc_1,t32_grfunc_1),interesting(0.59)]).

fof(t88_grfunc_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( ( r1_tarski(A,k1_relat_1(B))
              & r1_tarski(B,C) )
           => k7_relat_1(B,A) = k7_relat_1(C,A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t64_grfunc_1,t100_relat_1,t28_xboole_1]),
    [file(grfunc_1,t88_grfunc_1),interesting(0.58)]).

fof(t47_grfunc_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
       => ! [B,C] : 
            ( r2_hidden(k4_tarski(C,B),k2_funct_1(A))
          <=> r2_hidden(k4_tarski(B,C),A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t55_funct_1,t54_funct_1,t8_funct_1]),
    [file(grfunc_1,t47_grfunc_1),interesting(0.57)]).

fof(t9_grfunc_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & r1_tarski(A,B) )
           => A = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_relat_1,t8_funct_1,d1_funct_1,d2_relat_1]),
    [file(grfunc_1,t9_grfunc_1),interesting(0.57)]).

fof(t19_grfunc_1,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_relat_1(k2_tarski(k4_tarski(A,B),k4_tarski(C,D)))
        & v1_funct_1(k2_tarski(k4_tarski(A,B),k4_tarski(C,D))) )
    <=> ( A = C
       => B = D ) ) ),
    inference(mizar_proof,[status(thm)],[d2_tarski,d1_funct_1,d2_tarski,t33_zfmisc_1,t33_zfmisc_1,d2_tarski,t2_funct_1]),
    [file(grfunc_1,t19_grfunc_1),interesting(0.54)]).

fof(t79_grfunc_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( r1_tarski(A,B)
              & v2_funct_1(B) )
           => k8_relat_1(k2_relat_1(A),B) = A ) ) ) ),
    inference(mizar_proof,[status(thm)],[t132_relat_1,t125_relat_1,d12_relat_1,d5_relat_1,d12_relat_1,t25_grfunc_1,d3_relat_1,d10_xboole_0]),
    [file(grfunc_1,t79_grfunc_1),interesting(0.51)]).

fof(t89_grfunc_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( r2_hidden(B,k1_relat_1(A))
         => k7_relat_1(A,k1_tarski(B)) = k1_tarski(k4_tarski(B,k1_funct_1(A,B))) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,t90_relat_1,t52_zfmisc_1,t18_grfunc_1,t72_funct_1]),
    [file(grfunc_1,t89_grfunc_1),interesting(0.51)]).

fof(t13_grfunc_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r1_tarski(A,B)
               => ( r1_tarski(k5_relat_1(A,C),k5_relat_1(B,C))
                  & r1_tarski(k5_relat_1(C,A),k5_relat_1(C,B)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t48_relat_1,t49_relat_1]),
    [file(grfunc_1,t13_grfunc_1),interesting(0.50)]).

fof(t31_grfunc_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_xboole_0(k1_relat_1(A),k1_relat_1(B))
           => ( v1_relat_1(k2_xboole_0(A,B))
              & v1_funct_1(k2_xboole_0(A,B)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_xboole_0,d2_xboole_0,d1_relat_1,d3_xboole_0,d2_xboole_0,d2_xboole_0,d1_funct_1,d4_relat_1,t2_funct_1]),
    [file(grfunc_1,t31_grfunc_1),interesting(0.47)]).

fof(l35_grfunc_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ! [D] : 
              ( ( v1_relat_1(D)
                & v1_funct_1(D) )
             => ( B = k2_xboole_0(C,D)
               => ( r2_hidden(A,k1_relat_1(B))
                <=> ( r2_hidden(A,k1_relat_1(C))
                    | r2_hidden(A,k1_relat_1(D)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_funct_1,d2_xboole_0,d4_relat_1,d4_funct_1,d2_xboole_0,d4_relat_1]),
    [file(grfunc_1,l35_grfunc_1),interesting(0.46)]).

fof(t37_grfunc_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( ( v2_funct_1(A)
                  & v2_funct_1(B)
                  & C = k2_xboole_0(A,B)
                  & r1_xboole_0(k2_relat_1(A),k2_relat_1(B)) )
               => v2_funct_1(C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_xboole_0,t34_grfunc_1,d8_funct_1,l10_grfunc_1,t34_grfunc_1,l35_grfunc_1,d8_funct_1]),
    [file(grfunc_1,t37_grfunc_1),interesting(0.46)]).

fof(t16_grfunc_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( C = k1_tarski(k4_tarski(A,B))
       => k1_funct_1(C,A) = B ) ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,t8_funct_1]),
    [file(grfunc_1,t16_grfunc_1),interesting(0.45)]).

fof(t34_grfunc_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ! [D] : 
              ( ( v1_relat_1(D)
                & v1_funct_1(D) )
             => ( ( r2_hidden(A,k1_relat_1(B))
                  & C = k2_xboole_0(B,D) )
               => k1_funct_1(C,A) = k1_funct_1(B,A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_funct_1,d2_xboole_0,t8_funct_1]),
    [file(grfunc_1,t34_grfunc_1),interesting(0.41)]).

fof(t87_grfunc_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(A,k10_relat_1(C,B))
      <=> ( r2_hidden(k4_tarski(A,k1_funct_1(C,A)),C)
          & r2_hidden(k1_funct_1(C,A),B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d14_relat_1,t8_funct_1,d14_relat_1]),
    [file(grfunc_1,t87_grfunc_1),interesting(0.39)]).

fof(t52_grfunc_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( ( r2_hidden(A,k1_relat_1(C))
          & r2_hidden(A,B) )
      <=> r2_hidden(k4_tarski(A,k1_funct_1(C,A)),k7_relat_1(C,B)) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_funct_1,d4_relat_1,d11_relat_1]),
    [file(grfunc_1,t52_grfunc_1),interesting(0.36)]).

fof(t54_grfunc_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ! [D] : 
              ( ( v1_relat_1(D)
                & v1_funct_1(D) )
             => ( r1_tarski(k5_relat_1(C,k7_relat_1(B,A)),k5_relat_1(C,B))
                & r1_tarski(k5_relat_1(k7_relat_1(B,A),D),k5_relat_1(B,D)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t92_relat_1,t93_relat_1]),
    [file(grfunc_1,t54_grfunc_1),interesting(0.34)]).

fof(t69_grfunc_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ! [D] : 
              ( ( v1_relat_1(D)
                & v1_funct_1(D) )
             => ( r1_tarski(k5_relat_1(C,k8_relat_1(A,B)),k5_relat_1(C,B))
                & r1_tarski(k5_relat_1(k8_relat_1(A,B),D),k5_relat_1(B,D)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t121_relat_1,t122_relat_1]),
    [file(grfunc_1,t69_grfunc_1),interesting(0.34)]).

fof(t67_grfunc_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( ( r2_hidden(A,k1_relat_1(C))
          & r2_hidden(k1_funct_1(C,A),B) )
      <=> r2_hidden(k4_tarski(A,k1_funct_1(C,A)),k8_relat_1(B,C)) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_funct_1,d4_relat_1,d12_relat_1]),
    [file(grfunc_1,t67_grfunc_1),interesting(0.31)]).

fof(t12_grfunc_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ! [D] : 
          ( ( v1_relat_1(D)
            & v1_funct_1(D) )
         => ( r2_hidden(k4_tarski(A,B),k5_relat_1(D,C))
           => ( r2_hidden(k4_tarski(A,k1_funct_1(D,A)),D)
              & r2_hidden(k4_tarski(k1_funct_1(D,A),B),C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_relat_1,t8_funct_1]),
    [file(grfunc_1,t12_grfunc_1),interesting(0.26)]).

fof(t8_grfunc_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_tarski(A,B)
          <=> ( r1_tarski(k1_relat_1(A),k1_relat_1(B))
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t25_relat_1,d4_funct_1,t8_funct_1,d3_relat_1,t8_funct_1,d4_funct_1]),
    [file(grfunc_1,t8_grfunc_1),interesting(0.22)]).

fof(t35_grfunc_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ! [D] : 
              ( ( v1_relat_1(D)
                & v1_funct_1(D) )
             => ( ( r2_hidden(A,k1_relat_1(B))
                  & C = k2_xboole_0(D,B) )
               => k1_funct_1(C,A) = k1_funct_1(B,A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_funct_1,d2_xboole_0,t8_funct_1]),
    [file(grfunc_1,t35_grfunc_1),interesting(0.18)]).

fof(t29_grfunc_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ! [D] : 
              ( ( v1_relat_1(D)
                & v1_funct_1(D) )
             => ( ( B = k3_xboole_0(C,D)
                  & r2_hidden(A,k1_relat_1(B)) )
               => ( k1_funct_1(B,A) = k1_funct_1(C,A)
                  & k1_funct_1(B,A) = k1_funct_1(D,A) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_funct_1,d3_xboole_0,t8_funct_1]),
    [file(grfunc_1,t29_grfunc_1),interesting(0.08)]).

fof(t36_grfunc_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ! [D] : 
              ( ( v1_relat_1(D)
                & v1_funct_1(D) )
             => ~ ( r2_hidden(A,k1_relat_1(B))
                  & B = k2_xboole_0(C,D)
                  & k1_funct_1(B,A) != k1_funct_1(C,A)
                  & k1_funct_1(B,A) != k1_funct_1(D,A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_funct_1,d2_xboole_0,t8_funct_1]),
    [file(grfunc_1,t36_grfunc_1),interesting(0.08)]).

fof(l10_grfunc_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ! [D] : 
          ( ( v1_relat_1(D)
            & v1_funct_1(D) )
         => ~ ( k3_xboole_0(k2_relat_1(C),k2_relat_1(D)) = k1_xboole_0
              & r2_hidden(A,k1_relat_1(C))
              & r2_hidden(B,k1_relat_1(D))
              & k1_funct_1(C,A) = k1_funct_1(D,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_funct_1,d3_xboole_0]),
    [file(grfunc_1,l10_grfunc_1),interesting(0.05)]).

fof(t10_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t10_grfunc_1),
    [interesting(0.00)]).

fof(t11_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t11_grfunc_1),
    [interesting(0.00)]).

fof(d8_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ! [C] : 
              ( v1_relat_1(C)
             => ( C = k5_relat_1(A,B)
              <=> ! [D,E] : 
                    ( r2_hidden(k4_tarski(D,E),C)
                  <=> ? [F] : 
                        ( r2_hidden(k4_tarski(D,F),A)
                        & r2_hidden(k4_tarski(F,E),B) ) ) ) ) ) ) ),
    file(relat_1,d8_relat_1),
    [interesting(0.00)]).

fof(t8_funct_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(k4_tarski(A,B),C)
      <=> ( r2_hidden(A,k1_relat_1(C))
          & B = k1_funct_1(C,A) ) ) ) ),
    file(funct_1,t8_funct_1),
    [interesting(0.00)]).

fof(t48_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ! [C] : 
              ( v1_relat_1(C)
             => ( r1_tarski(A,B)
               => r1_tarski(k5_relat_1(C,A),k5_relat_1(C,B)) ) ) ) ) ),
    file(relat_1,t48_relat_1),
    [interesting(0.00)]).

fof(t49_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ! [C] : 
              ( v1_relat_1(C)
             => ( r1_tarski(A,B)
               => r1_tarski(k5_relat_1(A,C),k5_relat_1(B,C)) ) ) ) ) ),
    file(relat_1,t49_relat_1),
    [interesting(0.00)]).

fof(t14_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t14_grfunc_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(t17_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t17_grfunc_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(d1_funct_1,definition,(
    ! [A] : 
      ( v1_funct_1(A)
    <=> ! [B,C,D] : 
          ( ( r2_hidden(k4_tarski(B,C),A)
            & r2_hidden(k4_tarski(B,D),A) )
         => C = D ) ) ),
    file(funct_1,d1_funct_1),
    [interesting(0.00)]).

fof(t33_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( k4_tarski(A,B) = k4_tarski(C,D)
     => ( A = C
        & B = D ) ) ),
    file(zfmisc_1,t33_zfmisc_1),
    [interesting(0.00)]).

fof(t2_funct_1,theorem,(
    ! [A] : 
      ( ( ! [B] : ~ ( r2_hidden(B,A)
            & ! [C,D] : k4_tarski(C,D) != B )
        & ! [B,C,D] : 
            ( ( r2_hidden(k4_tarski(B,C),A)
              & r2_hidden(k4_tarski(B,D),A) )
           => C = D ) )
     => ( v1_relat_1(A)
        & v1_funct_1(A) ) ) ),
    file(funct_1,t2_funct_1),
    [interesting(0.00)]).

fof(t1_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t1_grfunc_1),
    [interesting(0.00)]).

fof(t20_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t20_grfunc_1),
    [interesting(0.00)]).

fof(t21_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t21_grfunc_1),
    [interesting(0.00)]).

fof(t22_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t22_grfunc_1),
    [interesting(0.00)]).

fof(t23_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t23_grfunc_1),
    [interesting(0.00)]).

fof(t24_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t24_grfunc_1),
    [interesting(0.00)]).

fof(t14_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => r1_tarski(k1_relat_1(k3_xboole_0(A,B)),k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) ) ) ),
    file(relat_1,t14_relat_1),
    [interesting(0.00)]).

fof(t27_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => r1_tarski(k2_relat_1(k3_xboole_0(A,B)),k3_xboole_0(k2_relat_1(A),k2_relat_1(B))) ) ) ),
    file(relat_1,t27_relat_1),
    [interesting(0.00)]).

fof(t28_grfunc_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( A = k3_xboole_0(B,C)
               => ( r1_tarski(k1_relat_1(A),k3_xboole_0(k1_relat_1(B),k1_relat_1(C)))
                  & r1_tarski(k2_relat_1(A),k3_xboole_0(k2_relat_1(B),k2_relat_1(C))) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t14_relat_1,t27_relat_1]),
    [file(grfunc_1,t28_grfunc_1),interesting(0.00)]).

fof(d4_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( ( r2_hidden(B,k1_relat_1(A))
           => ( C = k1_funct_1(A,B)
            <=> r2_hidden(k4_tarski(B,C),A) ) )
          & ( ~ r2_hidden(B,k1_relat_1(A))
           => ( C = k1_funct_1(A,B)
            <=> C = k1_xboole_0 ) ) ) ) ),
    file(funct_1,d4_funct_1),
    [interesting(0.00)]).

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

fof(t2_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t2_grfunc_1),
    [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(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(d1_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
    <=> ! [B] : ~ ( r2_hidden(B,A)
          & ! [C,D] : B != k4_tarski(C,D) ) ) ),
    file(relat_1,d1_relat_1),
    [interesting(0.00)]).

fof(d8_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
      <=> ! [B,C] : 
            ( ( r2_hidden(B,k1_relat_1(A))
              & r2_hidden(C,k1_relat_1(A))
              & k1_funct_1(A,B) = k1_funct_1(A,C) )
           => B = C ) ) ) ),
    file(funct_1,d8_funct_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(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(d4_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( B = k1_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : r2_hidden(k4_tarski(C,D),A) ) ) ) ),
    file(relat_1,d4_relat_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(t13_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => k1_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k1_relat_1(A),k1_relat_1(B)) ) ) ),
    file(relat_1,t13_relat_1),
    [interesting(0.00)]).

fof(t26_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => k2_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k2_relat_1(A),k2_relat_1(B)) ) ) ),
    file(relat_1,t26_relat_1),
    [interesting(0.00)]).

fof(t33_grfunc_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( A = k2_xboole_0(B,C)
               => ( k1_relat_1(A) = k2_xboole_0(k1_relat_1(B),k1_relat_1(C))
                  & k2_relat_1(A) = k2_xboole_0(k2_relat_1(B),k2_relat_1(C)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t13_relat_1,t26_relat_1]),
    [file(grfunc_1,t33_grfunc_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(t36_xboole_1,theorem,(
    ! [A,B] : r1_tarski(k4_xboole_0(A,B),A) ),
    file(xboole_1,t36_xboole_1),
    [interesting(0.00)]).

fof(t39_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t39_grfunc_1),
    [interesting(0.00)]).

fof(t3_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t3_grfunc_1),
    [interesting(0.00)]).

fof(t40_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t40_grfunc_1),
    [interesting(0.00)]).

fof(t41_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t41_grfunc_1),
    [interesting(0.00)]).

fof(t42_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t42_grfunc_1),
    [interesting(0.00)]).

fof(t43_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t43_grfunc_1),
    [interesting(0.00)]).

fof(t44_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t44_grfunc_1),
    [interesting(0.00)]).

fof(t45_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t45_grfunc_1),
    [interesting(0.00)]).

fof(t55_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
       => ( k2_relat_1(A) = k1_relat_1(k2_funct_1(A))
          & k1_relat_1(A) = k2_relat_1(k2_funct_1(A)) ) ) ) ),
    file(funct_1,t55_funct_1),
    [interesting(0.00)]).

fof(t54_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
       => ! [B] : 
            ( ( v1_relat_1(B)
              & v1_funct_1(B) )
           => ( B = k2_funct_1(A)
            <=> ( k1_relat_1(B) = k2_relat_1(A)
                & ! [C,D] : 
                    ( ( ( r2_hidden(C,k2_relat_1(A))
                        & D = k1_funct_1(B,C) )
                     => ( r2_hidden(D,k1_relat_1(A))
                        & C = k1_funct_1(A,D) ) )
                    & ( ( r2_hidden(D,k1_relat_1(A))
                        & C = k1_funct_1(A,D) )
                     => ( r2_hidden(C,k2_relat_1(A))
                        & D = k1_funct_1(B,C) ) ) ) ) ) ) ) ) ),
    file(funct_1,t54_funct_1),
    [interesting(0.00)]).

fof(t48_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t48_grfunc_1),
    [interesting(0.00)]).

fof(t60_relat_1,theorem,
    ( k1_relat_1(k1_xboole_0) = k1_xboole_0
    & k2_relat_1(k1_xboole_0) = k1_xboole_0 ),
    file(relat_1,t60_relat_1),
    [interesting(0.00)]).

fof(t64_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( ( k1_relat_1(A) = k1_xboole_0
          | k2_relat_1(A) = k1_xboole_0 )
       => A = k1_xboole_0 ) ) ),
    file(relat_1,t64_relat_1),
    [interesting(0.00)]).

fof(t4_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t4_grfunc_1),
    [interesting(0.00)]).

fof(t50_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t50_grfunc_1),
    [interesting(0.00)]).

fof(t51_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t51_grfunc_1),
    [interesting(0.00)]).

fof(d11_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( v1_relat_1(C)
         => ( C = k7_relat_1(A,B)
          <=> ! [D,E] : 
                ( r2_hidden(k4_tarski(D,E),C)
              <=> ( r2_hidden(D,B)
                  & r2_hidden(k4_tarski(D,E),A) ) ) ) ) ) ),
    file(relat_1,d11_relat_1),
    [interesting(0.00)]).

fof(t53_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t53_grfunc_1),
    [interesting(0.00)]).

fof(t92_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ! [C] : 
          ( v1_relat_1(C)
         => r1_tarski(k5_relat_1(k7_relat_1(B,A),C),k5_relat_1(B,C)) ) ) ),
    file(relat_1,t92_relat_1),
    [interesting(0.00)]).

fof(t93_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ! [C] : 
          ( v1_relat_1(C)
         => r1_tarski(k5_relat_1(B,k7_relat_1(C,A)),k5_relat_1(B,C)) ) ) ),
    file(relat_1,t93_relat_1),
    [interesting(0.00)]).

fof(t55_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t55_grfunc_1),
    [interesting(0.00)]).

fof(t56_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t56_grfunc_1),
    [interesting(0.00)]).

fof(t57_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t57_grfunc_1),
    [interesting(0.00)]).

fof(t58_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t58_grfunc_1),
    [interesting(0.00)]).

fof(t59_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t59_grfunc_1),
    [interesting(0.00)]).

fof(t5_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t5_grfunc_1),
    [interesting(0.00)]).

fof(t60_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t60_grfunc_1),
    [interesting(0.00)]).

fof(t61_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t61_grfunc_1),
    [interesting(0.00)]).

fof(t62_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t62_grfunc_1),
    [interesting(0.00)]).

fof(t63_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t63_grfunc_1),
    [interesting(0.00)]).

fof(t65_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t65_grfunc_1),
    [interesting(0.00)]).

fof(t66_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t66_grfunc_1),
    [interesting(0.00)]).

fof(d12_relat_1,definition,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ! [C] : 
          ( v1_relat_1(C)
         => ( C = k8_relat_1(A,B)
          <=> ! [D,E] : 
                ( r2_hidden(k4_tarski(D,E),C)
              <=> ( r2_hidden(E,A)
                  & r2_hidden(k4_tarski(D,E),B) ) ) ) ) ) ),
    file(relat_1,d12_relat_1),
    [interesting(0.00)]).

fof(t68_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t68_grfunc_1),
    [interesting(0.00)]).

fof(t121_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ! [C] : 
          ( v1_relat_1(C)
         => r1_tarski(k5_relat_1(k8_relat_1(A,B),C),k5_relat_1(B,C)) ) ) ),
    file(relat_1,t121_relat_1),
    [interesting(0.00)]).

fof(t122_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ! [C] : 
          ( v1_relat_1(C)
         => r1_tarski(k5_relat_1(B,k8_relat_1(A,C)),k5_relat_1(B,C)) ) ) ),
    file(relat_1,t122_relat_1),
    [interesting(0.00)]).

fof(t70_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t70_grfunc_1),
    [interesting(0.00)]).

fof(t71_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t71_grfunc_1),
    [interesting(0.00)]).

fof(t72_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t72_grfunc_1),
    [interesting(0.00)]).

fof(t73_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t73_grfunc_1),
    [interesting(0.00)]).

fof(t74_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t74_grfunc_1),
    [interesting(0.00)]).

fof(t75_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t75_grfunc_1),
    [interesting(0.00)]).

fof(t76_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t76_grfunc_1),
    [interesting(0.00)]).

fof(t77_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t77_grfunc_1),
    [interesting(0.00)]).

fof(t78_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t78_grfunc_1),
    [interesting(0.00)]).

fof(t132_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ! [C] : 
          ( v1_relat_1(C)
         => ( r1_tarski(B,C)
           => r1_tarski(k8_relat_1(A,B),k8_relat_1(A,C)) ) ) ) ),
    file(relat_1,t132_relat_1),
    [interesting(0.00)]).

fof(t125_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(k2_relat_1(B),A)
       => k8_relat_1(A,B) = B ) ) ),
    file(relat_1,t125_relat_1),
    [interesting(0.00)]).

fof(d5_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : r2_hidden(k4_tarski(D,C),A) ) ) ) ),
    file(relat_1,d5_relat_1),
    [interesting(0.00)]).

fof(d3_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(A,B)
          <=> ! [C,D] : 
                ( r2_hidden(k4_tarski(C,D),A)
               => r2_hidden(k4_tarski(C,D),B) ) ) ) ) ),
    file(relat_1,d3_relat_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(t7_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t7_grfunc_1),
    [interesting(0.00)]).

fof(t80_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t80_grfunc_1),
    [interesting(0.00)]).

fof(t81_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t81_grfunc_1),
    [interesting(0.00)]).

fof(t82_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t82_grfunc_1),
    [interesting(0.00)]).

fof(t83_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t83_grfunc_1),
    [interesting(0.00)]).

fof(t84_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t84_grfunc_1),
    [interesting(0.00)]).

fof(t85_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t85_grfunc_1),
    [interesting(0.00)]).

fof(t86_grfunc_1,theorem,(
    $true ),
    file(grfunc_1,t86_grfunc_1),
    [interesting(0.00)]).

fof(d14_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( C = k10_relat_1(A,B)
        <=> ! [D] : 
              ( r2_hidden(D,C)
            <=> ? [E] : 
                  ( r2_hidden(k4_tarski(D,E),A)
                  & r2_hidden(E,B) ) ) ) ) ),
    file(relat_1,d14_relat_1),
    [interesting(0.00)]).

fof(t105_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ! [C] : 
          ( v1_relat_1(C)
         => ( r1_tarski(B,C)
           => r1_tarski(k7_relat_1(B,A),k7_relat_1(C,A)) ) ) ) ),
    file(relat_1,t105_relat_1),
    [interesting(0.00)]).

fof(t97_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(k1_relat_1(B),A)
       => k7_relat_1(B,A) = B ) ) ),
    file(relat_1,t97_relat_1),
    [interesting(0.00)]).

fof(t100_relat_1,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => k7_relat_1(k7_relat_1(C,A),B) = k7_relat_1(C,k3_xboole_0(A,B)) ) ),
    file(relat_1,t100_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(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(t52_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => k3_xboole_0(B,k1_tarski(A)) = k1_tarski(A) ) ),
    file(zfmisc_1,t52_zfmisc_1),
    [interesting(0.00)]).

fof(t14_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( k1_relat_1(B) = k1_tarski(A)
       => k2_relat_1(B) = k1_tarski(k1_funct_1(B,A)) ) ) ),
    file(funct_1,t14_funct_1),
    [interesting(0.00)]).

fof(d2_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( A = B
          <=> ! [C,D] : 
                ( r2_hidden(k4_tarski(C,D),A)
              <=> r2_hidden(k4_tarski(C,D),B) ) ) ) ) ),
    file(relat_1,d2_relat_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(t25_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(A,B)
           => ( r1_tarski(k1_relat_1(A),k1_relat_1(B))
              & r1_tarski(k2_relat_1(A),k2_relat_1(B)) ) ) ) ) ),
    file(relat_1,t25_relat_1),
    [interesting(0.00)]).