fof(t18_funcop_1,theorem,(
    ! [A,B,C] : k7_relat_1(k2_funcop_1(A,B),C) = k2_funcop_1(k3_xboole_0(A,C),B) ),
    inference(mizar_proof,[status(thm)],[t90_relat_1,t1_funcop_1,t16_funcop_1,t1_funcop_1,t16_funcop_1,t1_funcop_1,t16_funcop_1,d3_xboole_0,t70_funct_1,t13_funcop_1,t13_funcop_1,t9_funct_1]),
    [file(funcop_1,t18_funcop_1),interesting(1.00)]).

fof(t20_funcop_1,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(B,C)
     => k10_relat_1(k2_funcop_1(A,B),C) = A ) ),
    inference(mizar_proof,[status(thm)],[d7_xboole_0,t173_relat_1,t1_funcop_1,t37_zfmisc_1,t28_xboole_1,t168_relat_1,t169_relat_1,t19_funcop_1]),
    [file(funcop_1,t20_funcop_1),interesting(0.98)]).

fof(t9_funcop_1,theorem,(
    ! [A] : k1_funcop_1(k12_funct_3(A)) = k12_funct_3(A) ),
    inference(mizar_proof,[status(thm)],[t2_funcop_1,t6_funcop_1,t2_funcop_1]),
    [file(funcop_1,t9_funcop_1),interesting(0.95)]).

fof(t21_funcop_1,theorem,(
    ! [A,B] : k10_relat_1(k2_funcop_1(A,B),k1_tarski(B)) = A ),
    inference(mizar_proof,[status(thm)],[d1_tarski,t20_funcop_1]),
    [file(funcop_1,t21_funcop_1),interesting(0.93)]).

fof(t36_funcop_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C,D] : 
              ( ( v1_relat_1(D)
                & v1_funct_1(D) )
             => ! [E] : 
                  ( k7_relat_1(A,C) = k7_relat_1(B,C)
                 => k7_relat_1(k4_funcop_1(D,A,E),C) = k7_relat_1(k4_funcop_1(D,B,E),C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t90_relat_1,t90_relat_1,t18_funcop_1,t18_funcop_1,t29_funcop_1,t30_funcop_1]),
    [file(funcop_1,t36_funcop_1),interesting(0.93)]).

fof(t43_funcop_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C,D] : 
              ( ( v1_relat_1(D)
                & v1_funct_1(D) )
             => ! [E] : 
                  ( k7_relat_1(A,C) = k7_relat_1(B,C)
                 => k7_relat_1(k5_funcop_1(D,E,A),C) = k7_relat_1(k5_funcop_1(D,E,B),C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t90_relat_1,t90_relat_1,t18_funcop_1,t18_funcop_1,t30_funcop_1,t29_funcop_1]),
    [file(funcop_1,t43_funcop_1),interesting(0.93)]).

fof(t7_funcop_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : k1_funcop_1(k7_relat_1(A,B)) = k7_relat_1(k1_funcop_1(A),B) ) ),
    inference(mizar_proof,[status(thm)],[d1_funcop_1,t90_relat_1,d1_funcop_1,t90_relat_1,t76_funct_1,t70_funct_1,d1_funcop_1,d1_funcop_1,t70_funct_1,d1_funcop_1,t70_funct_1,d1_funcop_1,t70_funct_1,t9_funct_1]),
    [file(funcop_1,t7_funcop_1),interesting(0.92)]).

fof(t26_funcop_1,theorem,(
    ! [A,B,C] : k1_funcop_1(k2_funcop_1(A,k4_tarski(B,C))) = k2_funcop_1(A,k4_tarski(C,B)) ),
    inference(mizar_proof,[status(thm)],[d1_funcop_1,t19_funcop_1,t19_funcop_1,t13_funcop_1,d1_funcop_1,t13_funcop_1,t9_funct_1]),
    [file(funcop_1,t26_funcop_1),interesting(0.91)]).

fof(t37_funcop_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) )
             => ! [D] : k5_relat_1(B,k4_funcop_1(C,A,D)) = k4_funcop_1(C,k5_relat_1(B,A),D) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t19_funcop_1,t3_funcop_1,t21_funct_1,t22_funct_1,t13_funcop_1,t31_funcop_1,t17_funcop_1]),
    [file(funcop_1,t37_funcop_1),interesting(0.91)]).

fof(t44_funcop_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) )
             => ! [D] : k5_relat_1(B,k5_funcop_1(C,D,A)) = k5_funcop_1(C,D,k5_relat_1(B,A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t19_funcop_1,t3_funcop_1,t21_funct_1,t22_funct_1,t13_funcop_1,t31_funcop_1,t17_funcop_1]),
    [file(funcop_1,t44_funcop_1),interesting(0.91)]).

fof(t25_funcop_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : k5_relat_1(A,k2_funcop_1(B,C)) = k2_funcop_1(k10_relat_1(A,B),C) ) ),
    inference(mizar_proof,[status(thm)],[t182_relat_1,t19_funcop_1,t19_funcop_1,t21_funct_1,t19_funcop_1,t22_funct_1,t13_funcop_1,t13_funcop_1,t9_funct_1]),
    [file(funcop_1,t25_funcop_1),interesting(0.90)]).

fof(t6_funcop_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => k13_funct_3(A,B) = k1_funcop_1(k13_funct_3(B,A)) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_funct_3,d8_funct_3,d1_funcop_1,d8_funct_3,d8_funct_3,d1_funcop_1,t9_funct_1]),
    [file(funcop_1,t6_funcop_1),interesting(0.90)]).

fof(t13_funcop_1,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(B,A)
     => k1_funct_1(k2_funcop_1(A,C),B) = C ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,t106_zfmisc_1,t8_funct_1]),
    [file(funcop_1,t13_funcop_1),interesting(0.89)]).

fof(t2_funcop_1,theorem,(
    ! [A] : k12_funct_3(A) = k13_funct_3(k6_partfun1(A),k6_partfun1(A)) ),
    inference(mizar_proof,[status(thm)],[t23_funct_2,t90_funct_3,t99_funct_3]),
    [file(funcop_1,t2_funcop_1),interesting(0.85)]).

fof(t23_funcop_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( r2_hidden(C,k1_relat_1(A))
         => k5_relat_1(k2_funcop_1(B,C),A) = k2_funcop_1(B,k1_funct_1(A,C)) ) ) ),
    inference(mizar_proof,[status(thm)],[t182_relat_1,t20_funcop_1,t19_funcop_1,t21_funct_1,t19_funcop_1,t22_funct_1,t13_funcop_1,t13_funcop_1,t9_funct_1]),
    [file(funcop_1,t23_funcop_1),interesting(0.84)]).

fof(t39_funcop_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ! [D] : k5_relat_1(k6_partfun1(B),k4_funcop_1(C,A,D)) = k4_funcop_1(C,k7_relat_1(A,B),D) ) ) ),
    inference(mizar_proof,[status(thm)],[t37_funcop_1,t94_relat_1]),
    [file(funcop_1,t39_funcop_1),interesting(0.84)]).

fof(t46_funcop_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ! [D] : k5_relat_1(k6_partfun1(B),k5_funcop_1(C,D,A)) = k5_funcop_1(C,D,k7_relat_1(A,B)) ) ) ),
    inference(mizar_proof,[status(thm)],[t44_funcop_1,t94_relat_1]),
    [file(funcop_1,t46_funcop_1),interesting(0.84)]).

fof(t11_funcop_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : k7_relat_1(k13_funct_3(A,B),C) = k13_funct_3(A,k7_relat_1(B,C)) ) ) ),
    inference(mizar_proof,[status(thm)],[t6_funcop_1,t7_funcop_1,t10_funcop_1,t6_funcop_1]),
    [file(funcop_1,t11_funcop_1),interesting(0.82)]).

fof(t17_funcop_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ! [C] : 
              ( r2_hidden(C,k1_relat_1(A))
             => k1_funct_1(A,C) = B )
         => A = k2_funcop_1(k1_relat_1(A),B) ) ) ),
    inference(mizar_proof,[status(thm)],[t9_funct_1,d1_tarski,d1_tarski,d5_funct_1,t15_funcop_1]),
    [file(funcop_1,t17_funcop_1),interesting(0.81)]).

fof(t19_funcop_1,theorem,(
    ! [A,B] : 
      ( k1_relat_1(k2_funcop_1(A,B)) = A
      & r1_tarski(k2_relat_1(k2_funcop_1(A,B)),k1_tarski(B)) ) ),
    inference(mizar_proof,[status(thm)],[t2_xboole_1,t1_funcop_1]),
    [file(funcop_1,t19_funcop_1),interesting(0.78)]).

fof(t22_funcop_1,theorem,(
    ! [A,B,C] : 
      ( ~ r2_hidden(B,C)
     => k10_relat_1(k2_funcop_1(A,B),C) = k1_xboole_0 ) ),
    inference(mizar_proof,[status(thm)],[t19_funcop_1,t56_zfmisc_1,t63_xboole_1,t173_relat_1]),
    [file(funcop_1,t22_funcop_1),interesting(0.78)]).

fof(t57_funcop_1,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(C,B)
     => ( v1_funct_1(k2_funcop_1(A,C))
        & v1_funct_2(k2_funcop_1(A,C),A,B)
        & m2_relset_1(k2_funcop_1(A,C),A,B) ) ) ),
    inference(mizar_proof,[status(thm)],[t37_zfmisc_1,t19_funcop_1,t1_xboole_1,d1_funct_2,t11_relset_1]),
    [file(funcop_1,t57_funcop_1),interesting(0.77)]).

fof(t10_funcop_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : k7_relat_1(k13_funct_3(A,B),C) = k13_funct_3(k7_relat_1(A,C),B) ) ) ),
    inference(mizar_proof,[status(thm)],[t90_relat_1,d8_funct_3,t16_xboole_1,t90_relat_1,t76_funct_1,d3_xboole_0,t70_funct_1,d8_funct_3,t70_funct_1,d8_funct_3]),
    [file(funcop_1,t10_funcop_1),interesting(0.76)]).

fof(t15_funcop_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( k2_relat_1(A) = k1_tarski(B)
         => A = k2_funcop_1(k1_relat_1(A),B) ) ) ),
    inference(mizar_proof,[status(thm)],[t65_relat_1,t1_funcop_1,t17_funct_1]),
    [file(funcop_1,t15_funcop_1),interesting(0.76)]).

fof(t35_funcop_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C,D] : 
              ( r2_hidden(C,k1_relat_1(k4_funcop_1(B,A,D)))
             => k1_funct_1(k4_funcop_1(B,A,D),C) = k1_binop_1(B,k1_funct_1(A,C),D) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t21_funct_1,d8_funct_3,d3_xboole_0,l30_funcop_1,t13_funcop_1]),
    [file(funcop_1,t35_funcop_1),interesting(0.75)]).

fof(t42_funcop_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C,D] : 
              ( r2_hidden(C,k1_relat_1(k5_funcop_1(B,D,A)))
             => k1_funct_1(k5_funcop_1(B,D,A),C) = k1_binop_1(B,D,k1_funct_1(A,C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t21_funct_1,d8_funct_3,d3_xboole_0,l30_funcop_1,t13_funcop_1]),
    [file(funcop_1,t42_funcop_1),interesting(0.75)]).

fof(t14_funcop_1,theorem,(
    ! [A,B] : 
      ( A != k1_xboole_0
     => k2_relat_1(k2_funcop_1(A,B)) = k1_tarski(B) ) ),
    inference(mizar_proof,[status(thm)],[t1_funcop_1]),
    [file(funcop_1,t14_funcop_1),interesting(0.72)]).

fof(t58_funcop_1,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( m1_subset_1(C,B)
         => ( v1_funct_1(k2_funcop_1(A,C))
            & v1_funct_2(k2_funcop_1(A,C),A,B)
            & m2_relset_1(k2_funcop_1(A,C),A,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t57_funcop_1]),
    [file(funcop_1,t58_funcop_1),interesting(0.71)]).

fof(t31_funcop_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) )
             => ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => k5_relat_1(C,k3_funcop_1(D,A,B)) = k3_funcop_1(D,k5_relat_1(C,A),k5_relat_1(C,B)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t55_relat_1,t75_funct_3]),
    [file(funcop_1,t31_funcop_1),interesting(0.69)]).

fof(t1_funcop_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( A = k2_zfmisc_1(B,C)
         => ( B = k1_xboole_0
            | C = k1_xboole_0
            | ( k1_relat_1(A) = B
              & k2_relat_1(A) = C ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_relset_1,t106_zfmisc_1,t22_relset_1,t106_zfmisc_1,t23_relset_1]),
    [file(funcop_1,t1_funcop_1),interesting(0.68)]).

fof(t3_funcop_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) )
             => ( k1_relat_1(A) = k1_relat_1(B)
               => k1_relat_1(k5_relat_1(C,A)) = k1_relat_1(k5_relat_1(C,B)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t182_relat_1,t182_relat_1]),
    [file(funcop_1,t3_funcop_1),interesting(0.64)]).

fof(t38_funcop_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) )
             => ! [D] : k5_relat_1(k4_funcop_1(C,B,D),A) = k4_funcop_1(k5_relat_1(C,A),B,D) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t55_relat_1]),
    [file(funcop_1,t38_funcop_1),interesting(0.59)]).

fof(t45_funcop_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) )
             => ! [D] : k5_relat_1(k5_funcop_1(C,D,B),A) = k5_funcop_1(k5_relat_1(C,A),D,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t55_relat_1]),
    [file(funcop_1,t45_funcop_1),interesting(0.59)]).

fof(t4_funcop_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_xboole_0
              & k1_relat_1(B) = k1_xboole_0 )
           => A = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[t9_funct_1]),
    [file(funcop_1,t4_funcop_1),interesting(0.58)]).

fof(t32_funcop_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) )
             => ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => k5_relat_1(k3_funcop_1(D,B,C),A) = k3_funcop_1(k5_relat_1(D,A),B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t55_relat_1]),
    [file(funcop_1,t32_funcop_1),interesting(0.55)]).

fof(t60_funcop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ! [E] : 
                      ( m1_subset_1(E,A)
                     => ! [F] : 
                          ( m1_subset_1(F,B)
                         => k8_funct_2(B,A,k7_funcop_1(A,B,C,D,E),F) = k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,F),E) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,t35_funcop_1]),
    [file(funcop_1,t60_funcop_1),interesting(0.54)]).

fof(t66_funcop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ! [E] : 
                      ( m1_subset_1(E,A)
                     => ! [F] : 
                          ( m1_subset_1(F,B)
                         => k8_funct_2(B,A,k8_funcop_1(A,B,C,E,D),F) = k2_binop_1(A,A,A,C,E,k8_funct_2(B,A,D,F)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,t42_funcop_1]),
    [file(funcop_1,t66_funcop_1),interesting(0.54)]).

fof(t81_funcop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ( v3_binop_1(C,B)
                   => k6_funcop_1(B,A,C,D,D) = D ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_binop_1,t49_funcop_1]),
    [file(funcop_1,t81_funcop_1),interesting(0.54)]).

fof(t24_funcop_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : ~ ( B != k1_xboole_0
          & r2_hidden(C,k1_relat_1(A))
          & k1_relat_1(k5_relat_1(k2_funcop_1(B,C),A)) = k1_xboole_0 ) ) ),
    inference(mizar_proof,[status(thm)],[t19_funcop_1,t13_funcop_1,t21_funct_1]),
    [file(funcop_1,t24_funcop_1),interesting(0.53)]).

fof(l30_funcop_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) )
             => ! [D] : 
                  ( r2_hidden(D,k1_relat_1(k5_relat_1(k13_funct_3(A,B),C)))
                 => k1_funct_1(k5_relat_1(k13_funct_3(A,B),C),D) = k1_binop_1(C,k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t21_funct_1,t22_funct_1,d8_funct_3]),
    [file(funcop_1,l30_funcop_1),interesting(0.53)]).

fof(t63_funcop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] : 
                      ( m1_subset_1(E,B)
                     => k7_funct_2(A,B,B,D,k7_funcop_1(B,B,C,k6_partfun1(B),E)) = k7_funcop_1(B,A,C,D,E) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t37_funcop_1,t23_funct_2]),
    [file(funcop_1,t63_funcop_1),interesting(0.53)]).

fof(t69_funcop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] : 
                      ( m1_subset_1(E,B)
                     => k7_funct_2(A,B,B,D,k8_funcop_1(B,B,C,E,k6_partfun1(B))) = k8_funcop_1(B,A,C,E,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t44_funcop_1,t23_funct_2]),
    [file(funcop_1,t69_funcop_1),interesting(0.53)]).

fof(t72_funcop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,k2_zfmisc_1(B,C))
                    & m2_relset_1(D,A,k2_zfmisc_1(B,C)) )
                 => m2_relset_1(k2_relat_1(D),B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t12_relset_1,d1_relset_1]),
    [file(funcop_1,t72_funcop_1),interesting(0.53)]).

fof(t74_funcop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] : 
                      ( m1_subset_1(E,B)
                     => ! [F] : 
                          ( m1_subset_1(F,B)
                         => ( v2_binop_1(C,B)
                           => k7_funcop_1(B,A,C,k8_funcop_1(B,A,C,E,D),F) = k8_funcop_1(B,A,C,E,k7_funcop_1(B,A,C,D,F)) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t60_funcop_1,t66_funcop_1,d3_binop_1,t60_funcop_1,t67_funcop_1]),
    [file(funcop_1,t74_funcop_1),interesting(0.53)]).

fof(t79_funcop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] : 
                      ( m1_subset_1(E,B)
                     => ( v1_binop_1(C,B)
                       => k8_funcop_1(B,A,C,E,D) = k7_funcop_1(B,A,C,D,E) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t66_funcop_1,d2_binop_1,t61_funcop_1]),
    [file(funcop_1,t79_funcop_1),interesting(0.52)]).

fof(t64_funcop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(A,A),A)
            & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
         => ! [C] : 
              ( m1_subset_1(C,A)
             => k8_funct_2(A,A,k7_funcop_1(A,A,B,k6_partfun1(A),C),C) = k2_binop_1(A,A,A,B,C,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t60_funcop_1,t35_funct_1]),
    [file(funcop_1,t64_funcop_1),interesting(0.51)]).

fof(t70_funcop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(A,A),A)
            & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
         => ! [C] : 
              ( m1_subset_1(C,A)
             => k8_funct_2(A,A,k8_funcop_1(A,A,B,C,k6_partfun1(A)),C) = k2_binop_1(A,A,A,B,C,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t66_funcop_1,t35_funct_1]),
    [file(funcop_1,t70_funcop_1),interesting(0.51)]).

fof(t73_funcop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,k2_zfmisc_1(B,C))
                    & m2_relset_1(D,A,k2_zfmisc_1(B,C)) )
                 => k9_funcop_1(A,C,B,k10_funcop_1(A,B,C,D)) = k4_relat_1(k9_funcop_1(A,B,C,D)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_relat_1,d5_funct_1,d1_funcop_1,d1_funcop_1,d5_funct_1,d7_relat_1,d7_relat_1,d5_funct_1,d1_funcop_1,d1_funcop_1,d5_funct_1]),
    [file(funcop_1,t73_funcop_1),interesting(0.48)]).

fof(t77_funcop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] : 
                      ( m1_subset_1(E,B)
                     => ! [F] : 
                          ( m1_subset_1(F,B)
                         => ( v2_binop_1(C,B)
                           => k8_funcop_1(B,A,C,k2_binop_1(B,B,B,C,E,F),D) = k8_funcop_1(B,A,C,E,k8_funcop_1(B,A,C,F,D)) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t66_funcop_1,d3_binop_1,t66_funcop_1,t67_funcop_1]),
    [file(funcop_1,t77_funcop_1),interesting(0.48)]).

fof(t78_funcop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] : 
                      ( m1_subset_1(E,B)
                     => ! [F] : 
                          ( m1_subset_1(F,B)
                         => ( v2_binop_1(C,B)
                           => k7_funcop_1(B,A,C,D,k2_binop_1(B,B,B,C,E,F)) = k7_funcop_1(B,A,C,k7_funcop_1(B,A,C,D,E),F) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t60_funcop_1,d3_binop_1,t60_funcop_1,t61_funcop_1]),
    [file(funcop_1,t78_funcop_1),interesting(0.48)]).

fof(t28_funcop_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) )
             => ! [D] : 
                  ( r2_hidden(D,k1_relat_1(k3_funcop_1(C,A,B)))
                 => k1_funct_1(k3_funcop_1(C,A,B),D) = k1_binop_1(C,k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l30_funcop_1]),
    [file(funcop_1,t28_funcop_1),interesting(0.47)]).

fof(t67_funcop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,B,A)
                        & m2_relset_1(E,B,A) )
                     => ! [F] : 
                          ( m1_subset_1(F,A)
                         => ( ! [G] : 
                                ( m1_subset_1(G,B)
                               => k8_funct_2(B,A,D,G) = k2_binop_1(A,A,A,C,F,k8_funct_2(B,A,E,G)) )
                           => D = k8_funcop_1(A,B,C,F,E) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t66_funcop_1,t113_funct_2]),
    [file(funcop_1,t67_funcop_1),interesting(0.47)]).

fof(t61_funcop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,B,A)
                        & m2_relset_1(E,B,A) )
                     => ! [F] : 
                          ( m1_subset_1(F,A)
                         => ( ! [G] : 
                                ( m1_subset_1(G,B)
                               => k8_funct_2(B,A,D,G) = k2_binop_1(A,A,A,C,k8_funct_2(B,A,E,G),F) )
                           => D = k7_funcop_1(A,B,C,E,F) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t60_funcop_1,t113_funct_2]),
    [file(funcop_1,t61_funcop_1),interesting(0.47)]).

fof(t80_funcop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,B)
                        & m2_relset_1(E,A,B) )
                     => ( v1_binop_1(C,B)
                       => k6_funcop_1(B,A,C,D,E) = k6_funcop_1(B,A,C,E,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t48_funcop_1,d2_binop_1,t49_funcop_1]),
    [file(funcop_1,t80_funcop_1),interesting(0.46)]).

fof(t48_funcop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,B,A)
                        & m2_relset_1(E,B,A) )
                     => ! [F] : 
                          ( m1_subset_1(F,B)
                         => k8_funct_2(B,A,k6_funcop_1(A,B,C,D,E),F) = k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,F),k8_funct_2(B,A,E,F)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,l30_funcop_1]),
    [file(funcop_1,t48_funcop_1),interesting(0.43)]).

fof(t56_funcop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(A,A),A)
            & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
         => ! [C] : 
              ( m1_subset_1(C,A)
             => k8_funct_2(A,A,k6_funcop_1(A,A,B,k6_partfun1(A),k6_partfun1(A)),C) = k2_binop_1(A,A,A,B,C,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t48_funcop_1,t35_funct_1,t35_funct_1]),
    [file(funcop_1,t56_funcop_1),interesting(0.40)]).

fof(t76_funcop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,B)
                        & m2_relset_1(E,A,B) )
                     => ! [F] : 
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,A,B)
                            & m2_relset_1(F,A,B) )
                         => ( v2_binop_1(C,B)
                           => k6_funcop_1(B,A,C,k6_funcop_1(B,A,C,D,E),F) = k6_funcop_1(B,A,C,D,k6_funcop_1(B,A,C,E,F)) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t48_funcop_1,t48_funcop_1,d3_binop_1,t48_funcop_1,t49_funcop_1]),
    [file(funcop_1,t76_funcop_1),interesting(0.40)]).

fof(t75_funcop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,B)
                        & m2_relset_1(E,A,B) )
                     => ! [F] : 
                          ( m1_subset_1(F,B)
                         => ( v2_binop_1(C,B)
                           => k6_funcop_1(B,A,C,k7_funcop_1(B,A,C,D,F),E) = k6_funcop_1(B,A,C,D,k8_funcop_1(B,A,C,F,E)) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t48_funcop_1,t60_funcop_1,d3_binop_1,t66_funcop_1,t49_funcop_1]),
    [file(funcop_1,t75_funcop_1),interesting(0.38)]).

fof(t49_funcop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,B)
                        & m2_relset_1(E,A,B) )
                     => ! [F] : 
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,A,B)
                            & m2_relset_1(F,A,B) )
                         => ( ! [G] : 
                                ( m1_subset_1(G,A)
                               => k8_funct_2(A,B,F,G) = k2_binop_1(B,B,B,C,k8_funct_2(A,B,D,G),k8_funct_2(A,B,E,G)) )
                           => F = k6_funcop_1(B,A,C,D,E) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t48_funcop_1,t113_funct_2]),
    [file(funcop_1,t49_funcop_1),interesting(0.37)]).

fof(t82_funcop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ! [E] : 
                      ( m1_subset_1(E,B)
                     => ( v3_binop_1(C,A)
                       => k8_funct_2(B,A,k8_funcop_1(A,B,C,k8_funct_2(B,A,D,E),D),E) = k8_funct_2(B,A,D,E) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t66_funcop_1,d4_binop_1]),
    [file(funcop_1,t82_funcop_1),interesting(0.37)]).

fof(t83_funcop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ! [E] : 
                      ( m1_subset_1(E,B)
                     => ( v3_binop_1(C,A)
                       => k8_funct_2(B,A,k7_funcop_1(A,B,C,D,k8_funct_2(B,A,D,E)),E) = k8_funct_2(B,A,D,E) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t60_funcop_1,d4_binop_1]),
    [file(funcop_1,t83_funcop_1),interesting(0.37)]).

fof(t27_funcop_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) )
             => ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( ( k1_relat_1(D) = k1_relat_1(k3_funcop_1(C,A,B))
                      & ! [E] : 
                          ( r2_hidden(E,k1_relat_1(k3_funcop_1(C,A,B)))
                         => k1_funct_1(D,E) = k1_binop_1(C,k1_funct_1(A,E),k1_funct_1(B,E)) ) )
                   => D = k3_funcop_1(C,A,B) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l30_funcop_1,t9_funct_1]),
    [file(funcop_1,t27_funcop_1),interesting(0.34)]).

fof(t53_funcop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,k6_partfun1(B),k6_partfun1(B))) = k6_funcop_1(B,A,C,D,D) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t31_funcop_1,t23_funct_2,t23_funct_2]),
    [file(funcop_1,t53_funcop_1),interesting(0.34)]).

fof(t84_funcop_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(k2_zfmisc_1(k2_relat_1(B),k2_relat_1(C)),k1_relat_1(A))
               => k1_relat_1(k3_funcop_1(A,B,C)) = k3_xboole_0(k1_relat_1(B),k1_relat_1(C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t71_funct_3,t1_xboole_1,t46_relat_1,d8_funct_3]),
    [file(funcop_1,t84_funcop_1),interesting(0.31)]).

fof(t54_funcop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(A,A),A)
            & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
         => ! [C] : 
              ( m1_subset_1(C,A)
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,A)
                    & m2_relset_1(D,A,A) )
                 => k8_funct_2(A,A,k6_funcop_1(A,A,B,k6_partfun1(A),D),C) = k2_binop_1(A,A,A,B,C,k8_funct_2(A,A,D,C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t48_funcop_1,t35_funct_1]),
    [file(funcop_1,t54_funcop_1),interesting(0.30)]).

fof(t55_funcop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(A,A),A)
            & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
         => ! [C] : 
              ( m1_subset_1(C,A)
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,A)
                    & m2_relset_1(D,A,A) )
                 => k8_funct_2(A,A,k6_funcop_1(A,A,B,D,k6_partfun1(A)),C) = k2_binop_1(A,A,A,B,k8_funct_2(A,A,D,C),C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t48_funcop_1,t35_funct_1]),
    [file(funcop_1,t55_funcop_1),interesting(0.30)]).

fof(t51_funcop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,B,B)
                        & m2_relset_1(E,B,B) )
                     => k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,k6_partfun1(B),E)) = k6_funcop_1(B,A,C,D,k7_funct_2(A,B,B,D,E)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t31_funcop_1,t23_funct_2]),
    [file(funcop_1,t51_funcop_1),interesting(0.28)]).

fof(t52_funcop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,B,B)
                        & m2_relset_1(E,B,B) )
                     => k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,E,k6_partfun1(B))) = k6_funcop_1(B,A,C,k7_funct_2(A,B,B,D,E),D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t31_funcop_1,t23_funct_2]),
    [file(funcop_1,t52_funcop_1),interesting(0.28)]).

fof(t12_funcop_1,theorem,(
    $true ),
    file(funcop_1,t12_funcop_1),
    [interesting(0.00)]).

fof(d1_relset_1,definition,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
    <=> r1_tarski(C,k2_zfmisc_1(A,B)) ) ),
    file(relset_1,d1_relset_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(t22_relset_1,theorem,(
    ! [A,B,C] : 
      ( m2_relset_1(C,B,A)
     => ( ! [D] : ~ ( r2_hidden(D,B)
            & ! [E] : ~ r2_hidden(k4_tarski(D,E),C) )
      <=> k4_relset_1(B,A,C) = B ) ) ),
    file(relset_1,t22_relset_1),
    [interesting(0.00)]).

fof(t23_relset_1,theorem,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( ! [D] : ~ ( r2_hidden(D,B)
            & ! [E] : ~ r2_hidden(k4_tarski(E,D),C) )
      <=> k5_relset_1(A,B,C) = B ) ) ),
    file(relset_1,t23_relset_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(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(t173_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( k10_relat_1(B,A) = k1_xboole_0
      <=> r1_xboole_0(k2_relat_1(B),A) ) ) ),
    file(relat_1,t173_relat_1),
    [interesting(0.00)]).

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

fof(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(t168_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => k10_relat_1(B,A) = k10_relat_1(B,k3_xboole_0(k2_relat_1(B),A)) ) ),
    file(relat_1,t168_relat_1),
    [interesting(0.00)]).

fof(t169_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => k10_relat_1(A,k2_relat_1(A)) = k1_relat_1(A) ) ),
    file(relat_1,t169_relat_1),
    [interesting(0.00)]).

fof(t2_xboole_1,theorem,(
    ! [A] : r1_tarski(k1_xboole_0,A) ),
    file(xboole_1,t2_xboole_1),
    [interesting(0.00)]).

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

fof(t63_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_xboole_0(B,C) )
     => r1_xboole_0(A,C) ) ),
    file(xboole_1,t63_xboole_1),
    [interesting(0.00)]).

fof(t182_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => k1_relat_1(k5_relat_1(A,B)) = k10_relat_1(A,k1_relat_1(B)) ) ) ),
    file(relat_1,t182_relat_1),
    [interesting(0.00)]).

fof(t21_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(k5_relat_1(C,B)))
          <=> ( r2_hidden(A,k1_relat_1(C))
              & r2_hidden(k1_funct_1(C,A),k1_relat_1(B)) ) ) ) ) ),
    file(funct_1,t21_funct_1),
    [interesting(0.00)]).

fof(t22_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(k5_relat_1(C,B)))
           => k1_funct_1(k5_relat_1(C,B),A) = k1_funct_1(B,k1_funct_1(C,A)) ) ) ) ),
    file(funct_1,t22_funct_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(t9_funct_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)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) ) )
           => A = B ) ) ) ),
    file(funct_1,t9_funct_1),
    [interesting(0.00)]).

fof(d1_funcop_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( B = k1_funcop_1(A)
          <=> ( k1_relat_1(B) = k1_relat_1(A)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => ( ! [D,E] : 
                        ( k1_funct_1(A,C) = k4_tarski(D,E)
                       => k1_funct_1(B,C) = k4_tarski(E,D) )
                    & ~ ( k1_funct_1(A,C) != k1_funct_1(B,C)
                        & ! [D,E] : k1_funct_1(A,C) != k4_tarski(D,E) ) ) ) ) ) ) ) ),
    file(funcop_1,d1_funcop_1),
    [interesting(0.00)]).

fof(d8_funct_3,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( C = k13_funct_3(A,B)
              <=> ( k1_relat_1(C) = k3_xboole_0(k1_relat_1(A),k1_relat_1(B))
                  & ! [D] : 
                      ( r2_hidden(D,k1_relat_1(C))
                     => k1_funct_1(C,D) = k4_tarski(k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) ) ) ),
    file(funct_3,d8_funct_3),
    [interesting(0.00)]).

fof(t55_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ! [C] : 
              ( v1_relat_1(C)
             => k5_relat_1(k5_relat_1(A,B),C) = k5_relat_1(A,k5_relat_1(B,C)) ) ) ) ),
    file(relat_1,t55_relat_1),
    [interesting(0.00)]).

fof(t33_funcop_1,theorem,(
    $true ),
    file(funcop_1,t33_funcop_1),
    [interesting(0.00)]).

fof(t34_funcop_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : k4_funcop_1(B,A,C) = k3_funcop_1(B,A,k2_funcop_1(k1_relat_1(A),C)) ) ) ),
    file(funcop_1,t34_funcop_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(t16_funcop_1,theorem,(
    ! [A] : 
      ( k1_relat_1(k2_funcop_1(k1_xboole_0,A)) = k1_xboole_0
      & k2_relat_1(k2_funcop_1(k1_xboole_0,A)) = k1_xboole_0 ) ),
    file(funcop_1,t16_funcop_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(t70_funct_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(B,k1_relat_1(k7_relat_1(C,A)))
       => k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B) ) ) ),
    file(funct_1,t70_funct_1),
    [interesting(0.00)]).

fof(t112_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ! [C] : 
          ( v1_relat_1(C)
         => k7_relat_1(k5_relat_1(B,C),A) = k5_relat_1(k7_relat_1(B,A),C) ) ) ),
    file(relat_1,t112_relat_1),
    [interesting(0.00)]).

fof(t16_xboole_1,theorem,(
    ! [A,B,C] : k3_xboole_0(k3_xboole_0(A,B),C) = k3_xboole_0(A,k3_xboole_0(B,C)) ),
    file(xboole_1,t16_xboole_1),
    [interesting(0.00)]).

fof(t76_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r1_tarski(k1_relat_1(k7_relat_1(B,A)),k1_relat_1(B))
        & r1_tarski(k2_relat_1(k7_relat_1(B,A)),k2_relat_1(B)) ) ) ),
    file(funct_1,t76_funct_1),
    [interesting(0.00)]).

fof(t29_funcop_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) )
             => ! [D,E] : 
                  ( ( v1_relat_1(E)
                    & v1_funct_1(E) )
                 => ( k7_relat_1(A,D) = k7_relat_1(B,D)
                   => k7_relat_1(k3_funcop_1(E,A,C),D) = k7_relat_1(k3_funcop_1(E,B,C),D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t112_relat_1,t10_funcop_1,t10_funcop_1,t112_relat_1]),
    [file(funcop_1,t29_funcop_1),interesting(0.00)]).

fof(t30_funcop_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) )
             => ! [D,E] : 
                  ( ( v1_relat_1(E)
                    & v1_funct_1(E) )
                 => ( k7_relat_1(A,D) = k7_relat_1(B,D)
                   => k7_relat_1(k3_funcop_1(E,C,A),D) = k7_relat_1(k3_funcop_1(E,C,B),D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t112_relat_1,t11_funcop_1,t11_funcop_1,t112_relat_1]),
    [file(funcop_1,t30_funcop_1),interesting(0.00)]).

fof(t75_funct_3,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) )
             => k13_funct_3(k5_relat_1(C,A),k5_relat_1(C,B)) = k5_relat_1(C,k13_funct_3(A,B)) ) ) ) ),
    file(funct_3,t75_funct_3),
    [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(t65_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( k1_relat_1(A) = k1_xboole_0
      <=> k2_relat_1(A) = k1_xboole_0 ) ) ),
    file(relat_1,t65_relat_1),
    [interesting(0.00)]).

fof(t17_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( ( k1_relat_1(B) = k1_relat_1(C)
              & k2_relat_1(B) = k1_tarski(A)
              & k2_relat_1(C) = k1_tarski(A) )
           => B = C ) ) ) ),
    file(funct_1,t17_funct_1),
    [interesting(0.00)]).

fof(t94_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => k7_relat_1(B,A) = k5_relat_1(k6_relat_1(A),B) ) ),
    file(relat_1,t94_relat_1),
    [interesting(0.00)]).

fof(t40_funcop_1,theorem,(
    $true ),
    file(funcop_1,t40_funcop_1),
    [interesting(0.00)]).

fof(t41_funcop_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : k5_funcop_1(B,C,A) = k3_funcop_1(B,k2_funcop_1(k1_relat_1(A),C),A) ) ) ),
    file(funcop_1,t41_funcop_1),
    [interesting(0.00)]).

fof(t47_funcop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,B)
                        & m2_relset_1(E,A,B) )
                     => ( v1_funct_1(k3_funcop_1(C,D,E))
                        & v1_funct_2(k3_funcop_1(C,D,E),A,B)
                        & m2_relset_1(k3_funcop_1(C,D,E),A,B) ) ) ) ) ) ) ),
    file(funcop_1,t47_funcop_1),
    [interesting(0.00)]).

fof(t50_funcop_1,theorem,(
    $true ),
    file(funcop_1,t50_funcop_1),
    [interesting(0.00)]).

fof(t23_funct_2,theorem,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( k7_relset_1(A,A,A,B,k6_partfun1(A),C) = C
        & k7_relset_1(A,B,B,B,C,k6_partfun1(B)) = C ) ) ),
    file(funct_2,t23_funct_2),
    [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(t35_funct_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(B,A)
     => k1_funct_1(k6_relat_1(A),B) = B ) ),
    file(funct_1,t35_funct_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(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(t59_funcop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] : 
                      ( m1_subset_1(E,B)
                     => ( v1_funct_1(k4_funcop_1(C,D,E))
                        & v1_funct_2(k4_funcop_1(C,D,E),A,B)
                        & m2_relset_1(k4_funcop_1(C,D,E),A,B) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,t57_funcop_1]),
    [file(funcop_1,t59_funcop_1),interesting(0.00)]).

fof(t5_funcop_1,theorem,(
    $true ),
    file(funcop_1,t5_funcop_1),
    [interesting(0.00)]).

fof(t62_funcop_1,theorem,(
    $true ),
    file(funcop_1,t62_funcop_1),
    [interesting(0.00)]).

fof(t65_funcop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] : 
                      ( m1_subset_1(E,B)
                     => ( v1_funct_1(k5_funcop_1(C,E,D))
                        & v1_funct_2(k5_funcop_1(C,E,D),A,B)
                        & m2_relset_1(k5_funcop_1(C,E,D),A,B) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,t57_funcop_1]),
    [file(funcop_1,t65_funcop_1),interesting(0.00)]).

fof(t68_funcop_1,theorem,(
    $true ),
    file(funcop_1,t68_funcop_1),
    [interesting(0.00)]).

fof(t24_mcart_1,theorem,(
    ! [A,B] : ~ ( A != k1_xboole_0
      & B != k1_xboole_0
      & ~ ! [C] : 
            ( m1_subset_1(C,k2_zfmisc_1(A,B))
           => C = k4_tarski(k1_mcart_1(C),k2_mcart_1(C)) ) ) ),
    file(mcart_1,t24_mcart_1),
    [interesting(0.00)]).

fof(t71_funcop_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,k2_zfmisc_1(B,C))
                    & m2_relset_1(D,A,k2_zfmisc_1(B,C)) )
                 => ! [E] : 
                      ( m1_subset_1(E,A)
                     => k1_funct_1(k1_funcop_1(D),E) = k4_tarski(k2_mcart_1(k8_funct_2(A,k2_zfmisc_1(B,C),D,E)),k1_mcart_1(k8_funct_2(A,k2_zfmisc_1(B,C),D,E))) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,t24_mcart_1,d1_funcop_1]),
    [file(funcop_1,t71_funcop_1),interesting(0.00)]).

fof(t12_relset_1,theorem,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( r1_tarski(k1_relat_1(C),A)
        & r1_tarski(k2_relat_1(C),B) ) ) ),
    file(relset_1,t12_relset_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(d7_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( B = k4_relat_1(A)
          <=> ! [C,D] : 
                ( r2_hidden(k4_tarski(C,D),B)
              <=> r2_hidden(k4_tarski(D,C),A) ) ) ) ) ),
    file(relat_1,d7_relat_1),
    [interesting(0.00)]).

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

fof(t113_funct_2,theorem,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ! [D] : 
          ( ( v1_funct_1(D)
            & v1_funct_2(D,A,B)
            & m2_relset_1(D,A,B) )
         => ( ! [E] : 
                ( m1_subset_1(E,A)
               => k1_funct_1(C,E) = k1_funct_1(D,E) )
           => C = D ) ) ) ),
    file(funct_2,t113_funct_2),
    [interesting(0.00)]).

fof(d2_binop_1,definition,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
     => ( v1_binop_1(B,A)
      <=> ! [C] : 
            ( m1_subset_1(C,A)
           => ! [D] : 
                ( m1_subset_1(D,A)
               => k1_binop_1(B,C,D) = k1_binop_1(B,D,C) ) ) ) ) ),
    file(binop_1,d2_binop_1),
    [interesting(0.00)]).

fof(d4_binop_1,definition,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
     => ( v3_binop_1(B,A)
      <=> ! [C] : 
            ( m1_subset_1(C,A)
           => k1_binop_1(B,C,C) = C ) ) ) ),
    file(binop_1,d4_binop_1),
    [interesting(0.00)]).

fof(t71_funct_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => r1_tarski(k2_relat_1(k13_funct_3(A,B)),k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B))) ) ) ),
    file(funct_3,t71_funct_3),
    [interesting(0.00)]).

fof(t46_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(k2_relat_1(A),k1_relat_1(B))
           => k1_relat_1(k5_relat_1(A,B)) = k1_relat_1(A) ) ) ) ),
    file(relat_1,t46_relat_1),
    [interesting(0.00)]).

fof(t8_funcop_1,theorem,(
    $true ),
    file(funcop_1,t8_funcop_1),
    [interesting(0.00)]).

fof(t90_funct_3,theorem,(
    ! [A,B] : k15_funct_3(k6_relat_1(A),k6_relat_1(B)) = k6_relat_1(k2_zfmisc_1(A,B)) ),
    file(funct_3,t90_funct_3),
    [interesting(0.00)]).

fof(t99_funct_3,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ! [E] : 
          ( ( v1_funct_1(E)
            & v1_funct_2(E,A,C)
            & m2_relset_1(E,A,C) )
         => k13_funct_3(D,E) = k5_relat_1(k12_funct_3(A),k16_funct_3(A,A,B,C,D,E)) ) ) ),
    file(funct_3,t99_funct_3),
    [interesting(0.00)]).