fof(t76_finseq_2,theorem,(
    ! [A] : k2_finseq_2(3,A) = k11_finseq_1(A,A,A) ),
    inference(mizar_proof,[status(thm)],[t74_finseq_2,t75_finseq_2]),
    [file(finseq_2,t76_finseq_2),interesting(1.00)]).

fof(t75_finseq_2,theorem,(
    ! [A] : k2_finseq_2(2,A) = k10_finseq_1(A,A) ),
    inference(mizar_proof,[status(thm)],[t74_finseq_2,t73_finseq_2]),
    [file(finseq_2,t75_finseq_2),interesting(0.92)]).

fof(t62_finseq_2,theorem,(
    k1_finseq_2(3) = k11_finseq_1(1,2,3) ),
    inference(mizar_proof,[status(thm)],[t60_finseq_2,t61_finseq_2]),
    [file(finseq_2,t62_finseq_2),interesting(0.84)]).

fof(t61_finseq_2,theorem,(
    k1_finseq_2(2) = k10_finseq_1(1,2) ),
    inference(mizar_proof,[status(thm)],[t59_finseq_2,t60_finseq_2]),
    [file(finseq_2,t61_finseq_2),interesting(0.82)]).

fof(t122_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => k4_finseq_2(3,A) = a_1_2_finseq_2(A) ) ),
    inference(mizar_proof,[status(thm)],[d3_finseq_1,t13_finseq_2,t62_finseq_1,t16_finseq_2,t62_finseq_1,d11_finseq_1,t2_tarski]),
    [file(finseq_2,t122_finseq_2),interesting(0.73)]).

fof(t143_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : k2_finseq_2(k1_nat_1(A,B),C) = k7_finseq_1(k2_finseq_2(A,C),k2_finseq_2(B,C)) ) ) ),
    inference(mizar_proof,[status(thm)],[t47_finseq_1,t72_finseq_2,t74_finseq_2,t45_finseq_1,t74_finseq_2,s1_nat_1]),
    [file(finseq_2,t143_finseq_2),interesting(0.71)]).

fof(t119_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => k4_finseq_2(2,A) = a_1_1_finseq_2(A) ) ),
    inference(mizar_proof,[status(thm)],[d3_finseq_1,t13_finseq_2,t61_finseq_1,t15_finseq_2,t61_finseq_1,d11_finseq_1,t2_tarski]),
    [file(finseq_2,t119_finseq_2),interesting(0.70)]).

fof(l16_finseq_2,theorem,(
    ! [A,B] : k2_relat_1(k10_finseq_1(A,B)) = k2_tarski(A,B) ),
    inference(mizar_proof,[status(thm)],[t44_finseq_1,t55_finseq_1,t56_finseq_1,t41_enumset1]),
    [file(finseq_2,l16_finseq_2),interesting(0.69)]).

fof(l18_finseq_2,theorem,(
    ! [A,B,C] : k2_relat_1(k11_finseq_1(A,B,C)) = k1_enumset1(A,B,C) ),
    inference(mizar_proof,[status(thm)],[t60_finseq_1,t44_finseq_1,t55_finseq_1,l16_finseq_2,t42_enumset1]),
    [file(finseq_2,l18_finseq_2),interesting(0.68)]).

fof(t15_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ! [C] : 
              ( m1_subset_1(C,A)
             => m2_finseq_1(k10_finseq_1(B,C),A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l16_finseq_2,d4_finseq_1]),
    [file(finseq_2,t15_finseq_2),interesting(0.67)]).

fof(t73_finseq_2,theorem,(
    ! [A] : k2_finseq_2(1,A) = k9_finseq_1(A) ),
    inference(mizar_proof,[status(thm)],[t69_finseq_2,t70_finseq_2,t57_finseq_1]),
    [file(finseq_2,t73_finseq_2),interesting(0.67)]).

fof(t16_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ! [C] : 
              ( m1_subset_1(C,A)
             => ! [D] : 
                  ( m1_subset_1(D,A)
                 => m2_finseq_1(k11_finseq_1(B,C,D),A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l18_finseq_2,d4_finseq_1]),
    [file(finseq_2,t16_finseq_2),interesting(0.66)]).

fof(t148_finseq_2,theorem,(
    ! [A,B,C] : k2_relat_1(k11_finseq_1(A,B,C)) = k1_enumset1(A,B,C) ),
    inference(mizar_proof,[status(thm)],[l18_finseq_2]),
    [file(finseq_2,t148_finseq_2),interesting(0.66)]).

fof(t72_finseq_2,theorem,(
    ! [A] : k2_finseq_2(0,A) = k1_xboole_0 ),
    inference(mizar_proof,[status(thm)],[t69_finseq_2,t25_finseq_1]),
    [file(finseq_2,t72_finseq_2),interesting(0.65)]).

fof(t116_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => k4_finseq_2(1,A) = a_1_0_finseq_2(A) ) ),
    inference(mizar_proof,[status(thm)],[d3_finseq_1,t13_finseq_2,t57_finseq_1,t57_finseq_1,d11_finseq_1,t2_tarski]),
    [file(finseq_2,t116_finseq_2),interesting(0.64)]).

fof(t74_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : k2_finseq_2(k1_nat_1(A,1),B) = k7_finseq_1(k2_finseq_2(A,B),k9_finseq_1(B)) ) ),
    inference(mizar_proof,[status(thm)],[t69_finseq_2,t21_finseq_2,t19_finseq_2,t6_finseq_1,t70_finseq_2,t69_finseq_2,t25_finseq_1,t25_finseq_1,d3_finseq_1,t5_finseq_1,t6_finseq_1,d5_funct_1,t42_finseq_1,t14_funcop_1,t39_zfmisc_1,t15_funcop_1,t59_finseq_1]),
    [file(finseq_2,t74_finseq_2),interesting(0.64)]).

fof(t69_finseq_2,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : k3_finseq_1(k2_finseq_2(A,B)) = A ) ),
    inference(mizar_proof,[status(thm)],[d21_ordinal2,t68_finseq_2,d3_finseq_1]),
    [file(finseq_2,t69_finseq_2),interesting(0.63)]).

fof(t55_finseq_2,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => k3_finseq_1(k1_finseq_2(A)) = A ) ),
    inference(mizar_proof,[status(thm)],[d21_ordinal2,t54_finseq_2,d3_finseq_1]),
    [file(finseq_2,t55_finseq_2),interesting(0.63)]).

fof(t147_finseq_2,theorem,(
    ! [A,B] : k2_relat_1(k10_finseq_1(A,B)) = k2_tarski(A,B) ),
    inference(mizar_proof,[status(thm)],[l16_finseq_2]),
    [file(finseq_2,t147_finseq_2),interesting(0.63)]).

fof(t36_finseq_2,theorem,(
    ! [A,B,C] : 
      ( m2_finseq_1(C,A)
     => ! [D] : 
          ( ( v1_funct_1(D)
            & v1_funct_2(D,A,B)
            & m2_relset_1(D,A,B) )
         => m2_finseq_1(k1_partfun1(k5_numbers,A,A,B,C,D),B) ) ) ),
    inference(mizar_proof,[status(thm)],[t27_relset_1,d1_funct_2,t45_relat_1,t12_relset_1,t20_finseq_1,t1_xboole_1,d4_finseq_1]),
    [file(finseq_2,t36_finseq_2),interesting(0.62)]).

fof(t59_finseq_2,theorem,(
    k1_finseq_2(1) = k12_finseq_1(k5_numbers,1) ),
    inference(mizar_proof,[status(thm)],[t55_finseq_2,t56_finseq_2,t57_finseq_1]),
    [file(finseq_2,t59_finseq_2),interesting(0.62)]).

fof(t113_finseq_2,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k4_finseq_2(0,A))
     => B = k6_finseq_1(A) ) ),
    inference(mizar_proof,[status(thm)],[t112_finseq_2,d1_tarski]),
    [file(finseq_2,t113_finseq_2),interesting(0.61)]).

fof(t77_finseq_2,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m1_subset_1(C,B)
             => m2_finseq_1(k2_finseq_2(A,C),B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t19_funcop_1,t1_xboole_1,d4_finseq_1]),
    [file(finseq_2,t77_finseq_2),interesting(0.60)]).

fof(t54_finseq_2,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => k4_finseq_1(k1_finseq_2(A)) = k2_finseq_1(A) ) ),
    inference(mizar_proof,[status(thm)],[t71_relat_1]),
    [file(finseq_2,t54_finseq_2),interesting(0.60)]).

fof(t121_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ! [C] : 
              ( m1_subset_1(C,A)
             => m2_finseq_2(k10_finseq_1(B,C),A,k4_finseq_2(2,A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t119_finseq_2]),
    [file(finseq_2,t121_finseq_2),interesting(0.59)]).

fof(t27_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(A)) )
         => ! [C] : 
              ( m2_finseq_1(C,B)
             => m2_finseq_1(C,A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_finseq_1,t1_xboole_1,d4_finseq_1]),
    [file(finseq_2,t27_finseq_2),interesting(0.59)]).

fof(t52_finseq_2,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => m2_finseq_1(k6_partfun1(k2_finseq_1(A)),k5_numbers) ) ),
    inference(mizar_proof,[status(thm)],[d21_ordinal2,t71_relat_1,d2_finseq_1,d4_finseq_1]),
    [file(finseq_2,t52_finseq_2),interesting(0.59)]).

fof(t117_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_finseq_2(B,A,k4_finseq_2(1,A))
         => ? [C] : 
              ( m1_subset_1(C,A)
              & B = k12_finseq_1(A,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t116_finseq_2]),
    [file(finseq_2,t117_finseq_2),interesting(0.59)]).

fof(t124_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ! [C] : 
              ( m1_subset_1(C,A)
             => ! [D] : 
                  ( m1_subset_1(D,A)
                 => m2_finseq_2(k11_finseq_1(B,C,D),A,k4_finseq_2(3,A)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t122_finseq_2]),
    [file(finseq_2,t124_finseq_2),interesting(0.58)]).

fof(t110_finseq_2,theorem,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
     => m1_subset_1(B,k4_finseq_2(k3_finseq_1(B),A)) ) ),
    inference(mizar_proof,[status(thm)],[d11_finseq_1]),
    [file(finseq_2,t110_finseq_2),interesting(0.58)]).

fof(t68_finseq_2,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : k4_finseq_1(k2_finseq_2(A,B)) = k2_finseq_1(A) ) ),
    inference(mizar_proof,[status(thm)],[t19_funcop_1]),
    [file(finseq_2,t68_finseq_2),interesting(0.58)]).

fof(t58_finseq_2,theorem,(
    k1_finseq_2(0) = k1_xboole_0 ),
    inference(mizar_proof,[status(thm)],[t55_finseq_2,t25_finseq_1]),
    [file(finseq_2,t58_finseq_2),interesting(0.58)]).

fof(t114_finseq_2,theorem,(
    ! [A] : m1_subset_1(k6_finseq_1(A),k4_finseq_2(0,A)) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,t112_finseq_2]),
    [file(finseq_2,t114_finseq_2),interesting(0.57)]).

fof(t128_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => k3_finseq_2(A) = k3_tarski(a_1_3_finseq_2(A)) ) ),
    inference(mizar_proof,[status(thm)],[d11_finseq_1,t110_finseq_2,d4_tarski,d4_tarski,d11_finseq_1,t2_tarski]),
    [file(finseq_2,t128_finseq_2),interesting(0.57)]).

fof(t105_finseq_2,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & m1_finseq_2(B,A) )
     => r1_tarski(B,k3_finseq_2(A)) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d3_finseq_2,d11_finseq_1]),
    [file(finseq_2,t105_finseq_2),interesting(0.56)]).

fof(t60_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k1_finseq_2(k1_nat_1(A,1)) = k7_finseq_1(k1_finseq_2(A),k12_finseq_1(k5_numbers,k1_nat_1(A,1))) ) ),
    inference(mizar_proof,[status(thm)],[t55_finseq_2,t21_finseq_2,t19_finseq_2,t6_finseq_1,t56_finseq_2,t59_finseq_1,d3_finseq_1,t29_nat_1,t7_finseq_1,d7_finseq_1,t56_finseq_2,t34_funct_1]),
    [file(finseq_2,t60_finseq_2),interesting(0.56)]).

fof(t22_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_finseq_1(B,A)
         => ~ ( k3_finseq_1(B) != 0
              & ! [C] : 
                  ( m2_finseq_1(C,A)
                 => ! [D] : 
                      ( m1_subset_1(D,A)
                     => B != k8_finseq_1(A,C,k12_finseq_1(A,D)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t25_finseq_1,t63_finseq_1,t18_finseq_2,d7_finseq_1,t13_finseq_2,t5_finseq_1,t19_finseq_2,t59_finseq_1,d3_finseq_1,t13_finseq_2,t14_finseq_2]),
    [file(finseq_2,t22_finseq_2),interesting(0.55)]).

fof(t104_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(k13_finseq_1(A))
      & m1_finseq_2(k13_finseq_1(A),A) ) ),
    inference(mizar_proof,[status(thm)],[d3_finseq_2,d11_finseq_1]),
    [file(finseq_2,t104_finseq_2),interesting(0.55)]).

fof(t118_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => m2_finseq_2(k12_finseq_1(A,B),A,k4_finseq_2(1,A)) ) ) ),
    inference(mizar_proof,[status(thm)],[t116_finseq_2]),
    [file(finseq_2,t118_finseq_2),interesting(0.55)]).

fof(t120_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_finseq_2(B,A,k4_finseq_2(2,A))
         => ? [C] : 
              ( m1_subset_1(C,A)
              & ? [D] : 
                  ( m1_subset_1(D,A)
                  & B = k10_finseq_1(C,D) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t119_finseq_2]),
    [file(finseq_2,t120_finseq_2),interesting(0.55)]).

fof(t123_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_finseq_2(B,A,k4_finseq_2(3,A))
         => ? [C] : 
              ( m1_subset_1(C,A)
              & ? [D] : 
                  ( m1_subset_1(D,A)
                  & ? [E] : 
                      ( m1_subset_1(E,A)
                      & B = k11_finseq_1(C,D,E) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t122_finseq_2]),
    [file(finseq_2,t123_finseq_2),interesting(0.54)]).

fof(t70_finseq_2,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B,C] : 
          ( r2_hidden(B,k2_finseq_1(A))
         => k1_funct_1(k2_finseq_2(A,C),B) = C ) ) ),
    inference(mizar_proof,[status(thm)],[t13_funcop_1]),
    [file(finseq_2,t70_finseq_2),interesting(0.54)]).

fof(l14_finseq_2,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( A != 0
       => ! [B] : 
            ( m1_subset_1(B,k2_finseq_1(A))
           => r2_hidden(B,k2_finseq_1(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d21_ordinal2,t5_finseq_1]),
    [file(finseq_2,l14_finseq_2),interesting(0.54)]).

fof(t13_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B,C] : 
          ( m2_finseq_1(C,B)
         => ( r2_hidden(A,k4_finseq_1(C))
           => r2_hidden(k1_funct_1(C,A),B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_finseq_1,d5_funct_1]),
    [file(finseq_2,t13_finseq_2),interesting(0.51)]).

fof(t38_finseq_2,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,B)
            & m2_relset_1(C,A,B) )
         => k1_partfun1(k5_numbers,A,A,B,k6_finseq_1(A),C) = k6_finseq_1(B) ) ) ),
    inference(mizar_proof,[status(thm)],[t36_finseq_2,t32_finseq_1,t37_finseq_2,t32_finseq_1]),
    [file(finseq_2,t38_finseq_2),interesting(0.51)]).

fof(t131_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => m2_finseq_2(k1_finseq_2(A),k5_numbers,k4_finseq_2(A,k5_numbers)) ) ),
    inference(mizar_proof,[status(thm)],[t52_finseq_2,t55_finseq_2,t110_finseq_2]),
    [file(finseq_2,t131_finseq_2),interesting(0.50)]).

fof(t145_finseq_2,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( ( r2_hidden(B,k1_relat_1(A))
            & r2_hidden(C,k1_relat_1(A)) )
         => k5_relat_1(k10_finseq_1(B,C),A) = k10_finseq_1(k1_funct_1(A,B),k1_funct_1(A,C)) ) ) ),
    inference(mizar_proof,[status(thm)],[t12_funct_1,d1_funct_2,t11_relset_1,l16_finseq_2,t38_zfmisc_1,d4_finseq_1,t40_finseq_2]),
    [file(finseq_2,t145_finseq_2),interesting(0.50)]).

fof(t97_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( m1_subset_1(D,B)
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(A,B),C)
                        & m2_relset_1(E,k2_zfmisc_1(A,B),C) )
                     => ! [F] : 
                          ( m2_finseq_1(F,A)
                         => m2_finseq_1(k4_funcop_1(E,F,D),C) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_finseq_1,d4_funcop_1,t119_zfmisc_1,d1_funct_2,t45_relat_1,t12_relset_1,t82_finseq_2,t1_xboole_1,d4_finseq_1]),
    [file(finseq_2,t97_finseq_2),interesting(0.49)]).

fof(t91_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( m1_subset_1(D,A)
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(A,B),C)
                        & m2_relset_1(E,k2_zfmisc_1(A,B),C) )
                     => ! [F] : 
                          ( m2_finseq_1(F,B)
                         => m2_finseq_1(k5_funcop_1(E,D,F),C) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_finseq_1,d5_funcop_1,t119_zfmisc_1,d1_funct_2,t45_relat_1,t12_relset_1,t80_finseq_2,t1_xboole_1,d4_finseq_1]),
    [file(finseq_2,t91_finseq_2),interesting(0.49)]).

fof(t112_finseq_2,theorem,(
    ! [A] : k4_finseq_2(0,A) = k6_domain_1(k1_zfmisc_1(k2_zfmisc_1(k5_numbers,A)),k6_finseq_1(A)) ),
    inference(mizar_proof,[status(thm)],[t32_finseq_1,t32_finseq_1,d11_finseq_1,d1_tarski]),
    [file(finseq_2,t112_finseq_2),interesting(0.48)]).

fof(t51_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_finseq_1(B,A)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k4_finseq_1(B),k4_finseq_1(B))
                & m2_relset_1(C,k4_finseq_1(B),k4_finseq_1(B)) )
             => m2_finseq_1(k1_partfun1(k4_finseq_1(B),k4_finseq_1(B),k5_numbers,A,C,B),A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_finseq_1,t50_finseq_2]),
    [file(finseq_2,t51_finseq_2),interesting(0.48)]).

fof(t3_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_xreal_0(A,B)
           => k2_square_1(0,k6_xcmplx_0(A,B)) = 0 ) ) ) ),
    inference(mizar_proof,[status(thm)],[t11_xreal_1,t26_xreal_1,d2_square_1]),
    [file(finseq_2,t3_finseq_2),interesting(0.48)]).

fof(t107_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(A)) )
         => ! [C] : 
              ( ( ~ v1_xboole_0(C)
                & m1_finseq_2(C,B) )
             => ( ~ v1_xboole_0(C)
                & m1_finseq_2(C,A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_finseq_2,d3_finseq_2,d4_finseq_1,t1_xboole_1,d4_finseq_1]),
    [file(finseq_2,t107_finseq_2),interesting(0.47)]).

fof(t4_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_xreal_0(A,B)
           => k2_square_1(0,k6_xcmplx_0(B,A)) = k6_xcmplx_0(B,A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t11_xreal_1,d2_square_1]),
    [file(finseq_2,t4_finseq_2),interesting(0.47)]).

fof(t125_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => k4_finseq_2(k1_nat_1(A,B),C) = a_3_0_finseq_2(A,B,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t26_finseq_2,t110_finseq_2,t109_finseq_2,d11_finseq_1,t35_finseq_1,t2_tarski]),
    [file(finseq_2,t125_finseq_2),interesting(0.46)]).

fof(t132_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m1_subset_1(C,B)
             => m2_finseq_2(k2_finseq_2(A,C),B,k4_finseq_2(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t69_finseq_2,t77_finseq_2,t110_finseq_2]),
    [file(finseq_2,t132_finseq_2),interesting(0.46)]).

fof(t130_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ( k4_finseq_2(A,C) = k4_finseq_2(B,C)
               => A = B ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t69_finseq_2,t77_finseq_2,t110_finseq_2,t109_finseq_2]),
    [file(finseq_2,t130_finseq_2),interesting(0.45)]).

fof(t84_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(A,B),C)
                    & m2_relset_1(D,k2_zfmisc_1(A,B),C) )
                 => ! [E] : 
                      ( m2_finseq_1(E,A)
                     => ! [F] : 
                          ( m2_finseq_1(F,B)
                         => m2_finseq_1(k3_funcop_1(D,E,F),C) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_finseq_1,d3_funcop_1,t119_zfmisc_1,d1_funct_2,t45_relat_1,t12_relset_1,t78_finseq_2,t1_xboole_1,d4_finseq_1]),
    [file(finseq_2,t84_finseq_2),interesting(0.45)]).

fof(t40_finseq_2,theorem,(
    ! [A,B,C] : 
      ( ~ v1_xboole_0(C)
     => ! [D] : 
          ( ~ v1_xboole_0(D)
         => ! [E] : 
              ( m2_finseq_1(E,C)
             => ! [F] : 
                  ( ( v1_funct_1(F)
                    & v1_funct_2(F,C,D)
                    & m2_relset_1(F,C,D) )
                 => ( E = k10_finseq_1(A,B)
                   => k1_partfun1(k5_numbers,C,C,D,E,F) = k10_finseq_1(k1_funct_1(F,A),k1_funct_1(F,B)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t36_finseq_2,t61_finseq_1,t37_finseq_2,t61_finseq_1,d3_finseq_1,t22_funct_1,t61_finseq_1]),
    [file(finseq_2,t40_finseq_2),interesting(0.45)]).

fof(t30_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_finseq_1(B,A)
         => ( v1_funct_1(B)
            & v1_funct_2(B,k4_finseq_1(B),A)
            & m2_relset_1(B,k4_finseq_1(B),A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_finseq_1,t4_funct_2]),
    [file(finseq_2,t30_finseq_2),interesting(0.45)]).

fof(t28_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_finseq_1(A),B)
                & m2_relset_1(C,k2_finseq_1(A),B) )
             => m2_finseq_1(C,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,d2_finseq_1,t12_relset_1,d4_finseq_1]),
    [file(finseq_2,t28_finseq_2),interesting(0.45)]).

fof(t93_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( m1_subset_1(D,A)
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(A,B),C)
                        & m2_relset_1(E,k2_zfmisc_1(A,B),C) )
                     => k5_funcop_1(E,D,k6_finseq_1(B)) = k6_finseq_1(C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t91_finseq_2,t32_finseq_1,t92_finseq_2,t32_finseq_1]),
    [file(finseq_2,t93_finseq_2),interesting(0.45)]).

fof(t99_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( m1_subset_1(D,B)
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(A,B),C)
                        & m2_relset_1(E,k2_zfmisc_1(A,B),C) )
                     => k4_funcop_1(E,k6_finseq_1(A),D) = k6_finseq_1(C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t97_finseq_2,t32_finseq_1,t98_finseq_2,t32_finseq_1]),
    [file(finseq_2,t99_finseq_2),interesting(0.45)]).

fof(t19_finseq_2,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => k3_finseq_1(k7_finseq_1(B,k9_finseq_1(A))) = k1_nat_1(k3_finseq_1(B),1) ) ),
    inference(mizar_proof,[status(thm)],[t35_finseq_1,t56_finseq_1]),
    [file(finseq_2,t19_finseq_2),interesting(0.44)]).

fof(t64_finseq_2,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( r1_xreal_0(k3_finseq_1(B),A)
           => k5_relat_1(k1_finseq_2(A),B) = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[d21_ordinal2,d3_finseq_1,t7_finseq_1,t77_relat_1]),
    [file(finseq_2,t64_finseq_2),interesting(0.44)]).

fof(t5_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => m2_subset_1(k2_square_1(0,k6_xcmplx_0(A,B)),k1_numbers,k5_numbers) ) ) ),
    inference(mizar_proof,[status(thm)],[t3_finseq_2,d5_real_1,t61_nat_1,t4_finseq_2]),
    [file(finseq_2,t5_finseq_2),interesting(0.44)]).

fof(t111_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => k4_finseq_2(A,B) = k1_funct_2(k2_finseq_1(A),B) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_finseq_1,d4_finseq_1,d2_funct_2,d2_funct_2,d2_finseq_1,d4_finseq_1,d11_finseq_1,d3_finseq_1,t2_tarski]),
    [file(finseq_2,t111_finseq_2),interesting(0.43)]).

fof(t20_finseq_2,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C)
        & v1_finseq_1(C) )
     => ! [D] : 
          ( ( v1_relat_1(D)
            & v1_funct_1(D)
            & v1_finseq_1(D) )
         => ( k7_finseq_1(C,k9_finseq_1(A)) = k7_finseq_1(D,k9_finseq_1(B))
           => ( C = D
              & A = B ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t19_finseq_2,t59_finseq_1,t46_finseq_1]),
    [file(finseq_2,t20_finseq_2),interesting(0.43)]).

fof(t56_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r2_hidden(A,k2_finseq_1(B))
           => k1_funct_1(k1_finseq_2(B),A) = A ) ) ) ),
    inference(mizar_proof,[status(thm)],[t35_funct_1]),
    [file(finseq_2,t56_finseq_2),interesting(0.43)]).

fof(t14_finseq_2,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r2_hidden(C,k4_finseq_1(A))
               => r2_hidden(k1_funct_1(A,C),B) ) )
         => m2_finseq_1(A,B) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d4_finseq_1,t11_finseq_2]),
    [file(finseq_2,t14_finseq_2),interesting(0.41)]).

fof(t1_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( m2_subset_1(k3_square_1(A,B),k1_numbers,k5_numbers)
            & m2_subset_1(k4_square_1(A,B),k1_numbers,k5_numbers) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t38_square_1,t49_square_1]),
    [file(finseq_2,t1_finseq_2),interesting(0.40)]).

fof(t18_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( r2_hidden(A,k4_finseq_1(B))
               => r2_hidden(A,k4_finseq_1(k7_finseq_1(B,C))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t39_finseq_1]),
    [file(finseq_2,t18_finseq_2),interesting(0.39)]).

fof(t66_finseq_2,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v1_relat_1(k2_funcop_1(k2_finseq_1(A),B))
          & v1_funct_1(k2_funcop_1(k2_finseq_1(A),B))
          & v1_finseq_1(k2_funcop_1(k2_finseq_1(A),B)) ) ) ),
    inference(mizar_proof,[status(thm)],[d21_ordinal2,t19_funcop_1,d2_finseq_1]),
    [file(finseq_2,t66_finseq_2),interesting(0.39)]).

fof(t137_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m2_finseq_2(C,B,k4_finseq_2(k1_nat_1(A,1),B))
             => ? [D] : 
                  ( m2_finseq_2(D,B,k4_finseq_2(A,B))
                  & ? [E] : 
                      ( m1_subset_1(E,B)
                      & C = k8_finseq_1(B,D,k12_finseq_1(B,E)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t126_finseq_2,t117_finseq_2]),
    [file(finseq_2,t137_finseq_2),interesting(0.38)]).

fof(t39_finseq_2,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( ~ v1_xboole_0(C)
         => ! [D] : 
              ( m2_finseq_1(D,B)
             => ! [E] : 
                  ( ( v1_funct_1(E)
                    & v1_funct_2(E,B,C)
                    & m2_relset_1(E,B,C) )
                 => ( D = k9_finseq_1(A)
                   => k1_partfun1(k5_numbers,B,B,C,D,E) = k9_finseq_1(k1_funct_1(E,A)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t36_finseq_2,t56_finseq_1,t37_finseq_2,t57_finseq_1,d3_finseq_1,t22_funct_1,t57_finseq_1]),
    [file(finseq_2,t39_finseq_2),interesting(0.38)]).

fof(t129_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(B)) )
             => ! [D] : 
                  ( m2_finseq_2(D,C,k4_finseq_2(A,C))
                 => m2_finseq_2(D,B,k4_finseq_2(A,B)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t27_finseq_2,t109_finseq_2,t110_finseq_2]),
    [file(finseq_2,t129_finseq_2),interesting(0.37)]).

fof(t71_finseq_2,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m1_subset_1(C,B)
             => ( A != 0
               => ! [D] : 
                    ( m1_subset_1(D,k2_finseq_1(A))
                   => k1_funct_1(k2_finseq_2(A,C),D) = C ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l14_finseq_2,t70_finseq_2]),
    [file(finseq_2,t71_finseq_2),interesting(0.37)]).

fof(t9_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r2_hidden(A,k2_finseq_1(B))
               => r2_hidden(A,k2_finseq_1(k1_nat_1(B,C))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t29_nat_1,t7_finseq_1]),
    [file(finseq_2,t9_finseq_2),interesting(0.36)]).

fof(t138_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m2_finseq_2(C,B,k4_finseq_2(A,B))
             => k5_relat_1(k1_finseq_2(A),C) = C ) ) ) ),
    inference(mizar_proof,[status(thm)],[t109_finseq_2,t64_finseq_2]),
    [file(finseq_2,t138_finseq_2),interesting(0.35)]).

fof(t57_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( A != 0
       => ! [B] : 
            ( m1_subset_1(B,k2_finseq_1(A))
           => k1_funct_1(k1_finseq_2(A),B) = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[l14_finseq_2,t56_finseq_2]),
    [file(finseq_2,t57_finseq_2),interesting(0.35)]).

fof(t11_finseq_2,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ~ ( r2_hidden(A,k2_relat_1(B))
          & ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ~ ( r2_hidden(C,k4_finseq_1(B))
                  & k1_funct_1(B,C) = A ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_funct_1]),
    [file(finseq_2,t11_finseq_2),interesting(0.34)]).

fof(t100_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( m1_subset_1(D,A)
                 => ! [E] : 
                      ( m1_subset_1(E,B)
                     => ! [F] : 
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(A,B),C)
                            & m2_relset_1(F,k2_zfmisc_1(A,B),C) )
                         => ! [G] : 
                              ( m2_finseq_1(G,A)
                             => ( G = k12_finseq_1(A,D)
                               => k4_funcop_1(F,G,E) = k12_finseq_1(C,k2_binop_1(A,B,C,F,D,E)) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t97_finseq_2,t56_finseq_1,t98_finseq_2,t57_finseq_1,d3_finseq_1,t35_funcop_1,t57_finseq_1]),
    [file(finseq_2,t100_finseq_2),interesting(0.34)]).

fof(t133_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( m2_finseq_2(D,B,k4_finseq_2(A,B))
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,B,C)
                        & m2_relset_1(E,B,C) )
                     => m2_finseq_2(k1_partfun1(k5_numbers,B,B,C,D,E),C,k4_finseq_2(A,C)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t36_finseq_2,t109_finseq_2,t37_finseq_2,t110_finseq_2]),
    [file(finseq_2,t133_finseq_2),interesting(0.34)]).

fof(t94_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( m1_subset_1(D,A)
                 => ! [E] : 
                      ( m1_subset_1(E,B)
                     => ! [F] : 
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(A,B),C)
                            & m2_relset_1(F,k2_zfmisc_1(A,B),C) )
                         => ! [G] : 
                              ( m2_finseq_1(G,B)
                             => ( G = k12_finseq_1(B,E)
                               => k5_funcop_1(F,D,G) = k12_finseq_1(C,k2_binop_1(A,B,C,F,D,E)) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t91_finseq_2,t56_finseq_1,t92_finseq_2,t57_finseq_1,d3_finseq_1,t42_funcop_1,t57_finseq_1]),
    [file(finseq_2,t94_finseq_2),interesting(0.34)]).

fof(t37_finseq_2,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C)
            & v1_finseq_1(C) )
         => ! [D] : 
              ( m2_finseq_1(D,A)
             => ! [E] : 
                  ( ( v1_funct_1(E)
                    & v1_funct_2(E,A,B)
                    & m2_relset_1(E,A,B) )
                 => ( C = k1_partfun1(k5_numbers,A,A,B,D,E)
                   => k3_finseq_1(C) = k3_finseq_1(D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_finseq_1,d1_funct_2,t33_finseq_2]),
    [file(finseq_2,t37_finseq_2),interesting(0.33)]).

fof(t144_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m2_finseq_2(C,B,k4_finseq_2(A,B))
             => k4_finseq_1(C) = k2_finseq_1(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t109_finseq_2,d3_finseq_1]),
    [file(finseq_2,t144_finseq_2),interesting(0.33)]).

fof(l89_finseq_2,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r1_tarski(k2_zfmisc_1(k2_relat_1(B),k1_tarski(A)),k1_relat_1(C))
           => k1_relat_1(k4_funcop_1(C,B,A)) = k4_finseq_1(B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t19_funcop_1,t71_funct_3,t118_zfmisc_1,t19_funcop_1,t1_xboole_1,d4_funcop_1,t70_funct_3,t1_xboole_1,t46_relat_1]),
    [file(finseq_2,l89_finseq_2),interesting(0.32)]).

fof(l86_finseq_2,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r1_tarski(k2_zfmisc_1(k1_tarski(A),k2_relat_1(B)),k1_relat_1(C))
           => k1_relat_1(k5_funcop_1(C,A,B)) = k4_finseq_1(B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t19_funcop_1,t71_funct_3,t118_zfmisc_1,t19_funcop_1,t1_xboole_1,d5_funcop_1,t70_funct_3,t1_xboole_1,t46_relat_1]),
    [file(finseq_2,l86_finseq_2),interesting(0.32)]).

fof(t115_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m2_finseq_2(C,B,k4_finseq_2(0,B))
             => ! [D] : 
                  ( m2_finseq_2(D,B,k4_finseq_2(A,B))
                 => ( k8_finseq_1(B,C,D) = D
                    & k8_finseq_1(B,D,C) = D ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t113_finseq_2,t47_finseq_1]),
    [file(finseq_2,t115_finseq_2),interesting(0.30)]).

fof(t63_finseq_2,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => k5_relat_1(k1_finseq_2(A),B) = k7_relat_1(B,k2_finseq_1(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[t94_relat_1]),
    [file(finseq_2,t63_finseq_2),interesting(0.30)]).

fof(t50_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m2_finseq_1(C,B)
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A))
                    & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) )
                 => ( r1_xreal_0(A,k3_finseq_1(C))
                   => m2_finseq_1(k1_partfun1(k2_finseq_1(A),k2_finseq_1(A),k5_numbers,B,D,C),B) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t49_finseq_2]),
    [file(finseq_2,t50_finseq_2),interesting(0.29)]).

fof(t21_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ~ ( k3_finseq_1(B) = k1_nat_1(A,1)
              & ! [C] : 
                  ( ( v1_relat_1(C)
                    & v1_funct_1(C)
                    & v1_finseq_1(C) )
                 => ! [D] : B != k7_finseq_1(C,k9_finseq_1(D)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t25_finseq_1,t63_finseq_1]),
    [file(finseq_2,t21_finseq_2),interesting(0.29)]).

fof(t31_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,B)
                & m2_relset_1(C,k5_numbers,B) )
             => m2_finseq_1(k2_partfun1(k5_numbers,B,C,k2_finseq_1(A)),B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t38_funct_2,t28_finseq_2]),
    [file(finseq_2,t31_finseq_2),interesting(0.28)]).

fof(t98_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( m1_subset_1(D,B)
                 => ! [E] : 
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E)
                        & v1_finseq_1(E) )
                     => ! [F] : 
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(A,B),C)
                            & m2_relset_1(F,k2_zfmisc_1(A,B),C) )
                         => ! [G] : 
                              ( m2_finseq_1(G,A)
                             => ( E = k4_funcop_1(F,G,D)
                               => k3_finseq_1(E) = k3_finseq_1(G) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_finseq_1,t119_zfmisc_1,d1_funct_2,t83_finseq_2]),
    [file(finseq_2,t98_finseq_2),interesting(0.27)]).

fof(t134_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m2_finseq_2(C,B,k4_finseq_2(A,B))
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A))
                    & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) )
                 => ( k2_relat_1(D) = k2_finseq_1(A)
                   => m2_finseq_2(k1_partfun1(k2_finseq_1(A),k2_finseq_1(A),k5_numbers,B,D,C),B,k4_finseq_2(A,B)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t109_finseq_2,d3_finseq_1,t51_finseq_2,t46_finseq_2,t110_finseq_2]),
    [file(finseq_2,t134_finseq_2),interesting(0.27)]).

fof(t92_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( m1_subset_1(D,A)
                 => ! [E] : 
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E)
                        & v1_finseq_1(E) )
                     => ! [F] : 
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(A,B),C)
                            & m2_relset_1(F,k2_zfmisc_1(A,B),C) )
                         => ! [G] : 
                              ( m2_finseq_1(G,B)
                             => ( E = k5_funcop_1(F,D,G)
                               => k3_finseq_1(E) = k3_finseq_1(G) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_finseq_1,t119_zfmisc_1,d1_funct_2,t81_finseq_2]),
    [file(finseq_2,t92_finseq_2),interesting(0.27)]).

fof(s1_finseq_2,theorem,(
    ? [A] : 
      ( m2_finseq_1(A,f2_s1_finseq_2)
      & k3_finseq_1(A) = f1_s1_finseq_2
      & ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r2_hidden(B,k2_finseq_1(f1_s1_finseq_2))
           => k1_funct_1(A,B) = f3_s1_finseq_2(B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s2_finseq_1,d3_finseq_1,t14_finseq_2]),
    [file(finseq_2,s1_finseq_2),interesting(0.22)]).

fof(t135_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m2_finseq_2(C,B,k4_finseq_2(A,B))
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A))
                    & v3_funct_2(D,k2_finseq_1(A),k2_finseq_1(A))
                    & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) )
                 => m2_finseq_2(k1_partfun1(k2_finseq_1(A),k2_finseq_1(A),k5_numbers,B,D,C),B,k4_finseq_2(A,B)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_funct_2,t134_finseq_2]),
    [file(finseq_2,t135_finseq_2),interesting(0.18)]).

fof(t85_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D) )
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(A,B),C)
                        & m2_relset_1(E,k2_zfmisc_1(A,B),C) )
                     => ! [F] : 
                          ( m2_finseq_1(F,A)
                         => ! [G] : 
                              ( m2_finseq_1(G,B)
                             => ( D = k3_funcop_1(E,F,G)
                               => k3_finseq_1(D) = k3_square_1(k3_finseq_1(F),k3_finseq_1(G)) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_finseq_1,t119_zfmisc_1,d1_funct_2,t79_finseq_2]),
    [file(finseq_2,t85_finseq_2),interesting(0.18)]).

fof(t43_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_finseq_1(A),k2_finseq_1(A))
                & m2_relset_1(C,k2_finseq_1(A),k2_finseq_1(A)) )
             => ( r1_xreal_0(A,k3_finseq_1(B))
               => ( v1_relat_1(k5_relat_1(C,B))
                  & v1_funct_1(k5_relat_1(C,B))
                  & v1_finseq_1(k5_relat_1(C,B)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t42_finseq_2]),
    [file(finseq_2,t43_finseq_2),interesting(0.15)]).

fof(t34_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ( B = k2_finseq_1(A)
           => ! [C] : 
                ( ( v1_relat_1(C)
                  & v1_funct_1(C)
                  & v1_finseq_1(C) )
               => ! [D] : 
                    ( m2_finseq_1(D,B)
                   => ( r1_xreal_0(A,k3_finseq_1(C))
                     => ( v1_relat_1(k5_relat_1(D,C))
                        & v1_funct_1(k5_relat_1(D,C))
                        & v1_finseq_1(k5_relat_1(D,C)) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t7_finseq_1,d3_finseq_1,d4_finseq_1,t1_xboole_1,t46_relat_1,d3_finseq_1,d2_finseq_1]),
    [file(finseq_2,t34_finseq_2),interesting(0.13)]).

fof(t49_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( m2_finseq_1(D,C)
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_finseq_1(A),k2_finseq_1(B))
                        & m2_relset_1(E,k2_finseq_1(A),k2_finseq_1(B)) )
                     => ( r1_xreal_0(B,k3_finseq_1(D))
                       => ( ( B = 0
                            & A != 0 )
                          | m2_finseq_1(k1_partfun1(k2_finseq_1(A),k2_finseq_1(B),k5_numbers,C,E,D),C) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_finseq_1,t45_relat_1,t42_finseq_2,t1_xboole_1,d4_finseq_1]),
    [file(finseq_2,t49_finseq_2),interesting(0.12)]).

fof(t136_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m2_finseq_2(C,B,k4_finseq_2(A,B))
             => ! [D] : 
                  ( m1_subset_1(D,B)
                 => k1_funct_1(k8_finseq_1(B,C,k12_finseq_1(B,D)),k1_nat_1(A,1)) = D ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t109_finseq_2,t59_finseq_1]),
    [file(finseq_2,t136_finseq_2),interesting(0.11)]).

fof(t42_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(B))
                    & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(B)) )
                 => ( r1_xreal_0(B,k3_finseq_1(C))
                   => ( ( B = 0
                        & A != 0 )
                      | ( v1_relat_1(k5_relat_1(D,C))
                        & v1_funct_1(k5_relat_1(D,C))
                        & v1_finseq_1(k5_relat_1(D,C)) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t5_finseq_1,t7_finseq_1,t12_relset_1,t1_xboole_1,d3_finseq_1,d1_funct_2,t46_relat_1,d2_finseq_1]),
    [file(finseq_2,t42_finseq_2),interesting(0.08)]).

fof(t32_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k5_numbers,B)
                    & m2_relset_1(D,k5_numbers,B) )
                 => ( C = k2_partfun1(k5_numbers,B,D,k2_finseq_1(A))
                   => k3_finseq_1(C) = A ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t38_funct_2,d1_funct_2,d3_finseq_1]),
    [file(finseq_2,t32_finseq_2),interesting(0.07)]).

fof(t45_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A))
                    & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) )
                 => ( ( k2_relat_1(D) = k2_finseq_1(A)
                      & r1_xreal_0(A,k3_finseq_1(B))
                      & C = k5_relat_1(D,B) )
                   => k3_finseq_1(C) = A ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t7_finseq_1,d3_finseq_1,t67_funct_2,t46_relat_1,d3_finseq_1]),
    [file(finseq_2,t45_finseq_2),interesting(0.04)]).

fof(s2_finseq_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A)
      & k3_finseq_1(A) = f1_s2_finseq_1
      & ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r2_hidden(B,k2_finseq_1(f1_s2_finseq_1))
           => k1_funct_1(A,B) = f2_s2_finseq_1(B) ) ) ) ),
    file(finseq_1,s2_finseq_1),
    [interesting(0.00)]).

fof(d3_finseq_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( B = k3_finseq_1(A)
          <=> k2_finseq_1(B) = k1_relat_1(A) ) ) ) ),
    file(finseq_1,d3_finseq_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(d4_finseq_1,definition,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( m1_finseq_1(B,A)
      <=> r1_tarski(k2_relat_1(B),A) ) ) ),
    file(finseq_1,d4_finseq_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(t32_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( A = k6_finseq_1(B)
        <=> k3_finseq_1(A) = 0 ) ) ),
    file(finseq_1,t32_finseq_1),
    [interesting(0.00)]).

fof(t25_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( k3_finseq_1(A) = 0
      <=> A = k1_xboole_0 ) ) ),
    file(finseq_1,t25_finseq_1),
    [interesting(0.00)]).

fof(t63_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ~ ( A != k1_xboole_0
          & ! [B] : 
              ( ( v1_relat_1(B)
                & v1_funct_1(B)
                & v1_finseq_1(B) )
             => ! [C] : A != k7_finseq_1(B,k9_finseq_1(C)) ) ) ) ),
    file(finseq_1,t63_finseq_1),
    [interesting(0.00)]).

fof(t39_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => r1_tarski(k4_finseq_1(A),k4_finseq_1(k7_finseq_1(A,B))) ) ) ),
    file(finseq_1,t39_finseq_1),
    [interesting(0.00)]).

fof(d7_finseq_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( C = k7_finseq_1(A,B)
              <=> ( k4_finseq_1(C) = k2_finseq_1(k1_nat_1(k3_finseq_1(A),k3_finseq_1(B)))
                  & ! [D] : 
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r2_hidden(D,k4_finseq_1(A))
                       => k1_funct_1(C,D) = k1_funct_1(A,D) ) )
                  & ! [D] : 
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r2_hidden(D,k4_finseq_1(B))
                       => k1_funct_1(C,k1_nat_1(k3_finseq_1(A),D)) = k1_funct_1(B,D) ) ) ) ) ) ) ) ),
    file(finseq_1,d7_finseq_1),
    [interesting(0.00)]).

fof(t5_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( A = 0
        | r2_hidden(A,k2_finseq_1(A)) ) ) ),
    file(finseq_1,t5_finseq_1),
    [interesting(0.00)]).

fof(t35_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => k3_finseq_1(k7_finseq_1(A,B)) = k1_nat_1(k3_finseq_1(A),k3_finseq_1(B)) ) ) ),
    file(finseq_1,t35_finseq_1),
    [interesting(0.00)]).

fof(t56_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( B = k9_finseq_1(A)
      <=> ( k3_finseq_1(B) = 1
          & k2_relat_1(B) = k1_tarski(A) ) ) ) ),
    file(finseq_1,t56_finseq_1),
    [interesting(0.00)]).

fof(t59_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => k1_funct_1(k7_finseq_1(B,k9_finseq_1(A)),k1_nat_1(k3_finseq_1(B),1)) = A ) ),
    file(finseq_1,t59_finseq_1),
    [interesting(0.00)]).

fof(s1_nat_1,theorem,
    ( ( p1_s1_nat_1(0)
      & ! [A] : 
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ( p1_s1_nat_1(A)
           => p1_s1_nat_1(k1_nat_1(A,1)) ) ) )
   => ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => p1_s1_nat_1(A) ) ),
    file(nat_1,s1_nat_1),
    [interesting(0.00)]).

fof(s2_finseq_2,theorem,
    ( ( p1_s2_finseq_2(k6_finseq_1(f1_s2_finseq_2))
      & ! [A] : 
          ( m2_finseq_1(A,f1_s2_finseq_2)
         => ! [B] : 
              ( m1_subset_1(B,f1_s2_finseq_2)
             => ( p1_s2_finseq_2(A)
               => p1_s2_finseq_2(k8_finseq_1(f1_s2_finseq_2,A,k12_finseq_1(f1_s2_finseq_2,B))) ) ) ) )
   => ! [A] : 
        ( m2_finseq_1(A,f1_s2_finseq_2)
       => p1_s2_finseq_2(A) ) ),
    inference(mizar_proof,[status(thm)],[t32_finseq_1,t22_finseq_2,t19_finseq_2,s1_nat_1]),
    [file(finseq_2,s2_finseq_2),interesting(0.00)]).

fof(d4_funcop_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : k4_funcop_1(A,B,C) = k5_relat_1(k13_funct_3(B,k2_funcop_1(k1_relat_1(B),C)),A) ) ) ),
    file(funcop_1,d4_funcop_1),
    [interesting(0.00)]).

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

fof(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(t45_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => r1_tarski(k2_relat_1(k5_relat_1(A,B)),k2_relat_1(B)) ) ) ),
    file(relat_1,t45_relat_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(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)) ) ),
    file(funcop_1,t19_funcop_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(t118_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(A,B)
     => ( r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C))
        & r1_tarski(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) ) ) ),
    file(zfmisc_1,t118_zfmisc_1),
    [interesting(0.00)]).

fof(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(t70_funct_3,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( ( k1_relat_1(B) = A
              & k1_relat_1(C) = A )
           => k1_relat_1(k13_funct_3(B,C)) = A ) ) ) ),
    file(funct_3,t70_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(d2_finseq_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v1_finseq_1(A)
      <=> ? [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
            & k1_relat_1(A) = k2_finseq_1(B) ) ) ) ),
    file(finseq_1,d2_finseq_1),
    [interesting(0.00)]).

fof(t82_finseq_2,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r1_tarski(k2_zfmisc_1(k2_relat_1(B),k1_tarski(A)),k1_relat_1(C))
           => ( v1_relat_1(k4_funcop_1(C,B,A))
              & v1_funct_1(k4_funcop_1(C,B,A))
              & v1_finseq_1(k4_funcop_1(C,B,A)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l89_finseq_2,d3_finseq_1,d2_finseq_1]),
    [file(finseq_2,t82_finseq_2),interesting(0.00)]).

fof(t83_finseq_2,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C)
            & v1_finseq_1(C) )
         => ! [D] : 
              ( ( v1_relat_1(D)
                & v1_funct_1(D) )
             => ( ( r1_tarski(k2_zfmisc_1(k2_relat_1(B),k1_tarski(A)),k1_relat_1(D))
                  & C = k4_funcop_1(D,B,A) )
               => k3_finseq_1(C) = k3_finseq_1(B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l89_finseq_2,d3_finseq_1,d3_finseq_1]),
    [file(finseq_2,t83_finseq_2),interesting(0.00)]).

fof(t57_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( B = k9_finseq_1(A)
      <=> ( k3_finseq_1(B) = 1
          & k1_funct_1(B,1) = A ) ) ) ),
    file(finseq_1,t57_finseq_1),
    [interesting(0.00)]).

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) ) ) ) ),
    file(funcop_1,t35_funcop_1),
    [interesting(0.00)]).

fof(t61_finseq_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C)
        & v1_finseq_1(C) )
     => ( C = k10_finseq_1(A,B)
      <=> ( k3_finseq_1(C) = 2
          & k1_funct_1(C,1) = A
          & k1_funct_1(C,2) = B ) ) ) ),
    file(finseq_1,t61_finseq_1),
    [interesting(0.00)]).

fof(t101_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( m1_subset_1(D,A)
                 => ! [E] : 
                      ( m1_subset_1(E,A)
                     => ! [F] : 
                          ( m1_subset_1(F,B)
                         => ! [G] : 
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,k2_zfmisc_1(A,B),C)
                                & m2_relset_1(G,k2_zfmisc_1(A,B),C) )
                             => ! [H] : 
                                  ( m2_finseq_1(H,A)
                                 => ( H = k10_finseq_1(D,E)
                                   => k4_funcop_1(G,H,F) = k10_finseq_1(k2_binop_1(A,B,C,G,D,F),k2_binop_1(A,B,C,G,E,F)) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t97_finseq_2,t61_finseq_1,t98_finseq_2,t61_finseq_1,d3_finseq_1,t35_funcop_1,t61_finseq_1]),
    [file(finseq_2,t101_finseq_2),interesting(0.00)]).

fof(t62_finseq_1,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_relat_1(D)
        & v1_funct_1(D)
        & v1_finseq_1(D) )
     => ( D = k11_finseq_1(A,B,C)
      <=> ( k3_finseq_1(D) = 3
          & k1_funct_1(D,1) = A
          & k1_funct_1(D,2) = B
          & k1_funct_1(D,3) = C ) ) ) ),
    file(finseq_1,t62_finseq_1),
    [interesting(0.00)]).

fof(t102_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( m1_subset_1(D,A)
                 => ! [E] : 
                      ( m1_subset_1(E,A)
                     => ! [F] : 
                          ( m1_subset_1(F,A)
                         => ! [G] : 
                              ( m1_subset_1(G,B)
                             => ! [H] : 
                                  ( ( v1_funct_1(H)
                                    & v1_funct_2(H,k2_zfmisc_1(A,B),C)
                                    & m2_relset_1(H,k2_zfmisc_1(A,B),C) )
                                 => ! [I] : 
                                      ( m2_finseq_1(I,A)
                                     => ( I = k11_finseq_1(D,E,F)
                                       => k4_funcop_1(H,I,G) = k11_finseq_1(k2_binop_1(A,B,C,H,D,G),k2_binop_1(A,B,C,H,E,G),k2_binop_1(A,B,C,H,F,G)) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t97_finseq_2,t62_finseq_1,t98_finseq_2,t62_finseq_1,d3_finseq_1,t35_funcop_1,t62_finseq_1]),
    [file(finseq_2,t102_finseq_2),interesting(0.00)]).

fof(t103_finseq_2,theorem,(
    $true ),
    file(finseq_2,t103_finseq_2),
    [interesting(0.00)]).

fof(d3_finseq_2,definition,(
    ! [A,B] : 
      ( m1_finseq_2(B,A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
         => m2_finseq_1(C,A) ) ) ),
    file(finseq_2,d3_finseq_2),
    [interesting(0.00)]).

fof(d11_finseq_1,definition,(
    ! [A,B] : 
      ( B = k13_finseq_1(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> m2_finseq_1(C,A) ) ) ),
    file(finseq_1,d11_finseq_1),
    [interesting(0.00)]).

fof(t106_finseq_2,theorem,(
    $true ),
    file(finseq_2,t106_finseq_2),
    [interesting(0.00)]).

fof(t108_finseq_2,theorem,(
    $true ),
    file(finseq_2,t108_finseq_2),
    [interesting(0.00)]).

fof(d2_funct_2,definition,(
    ! [A,B,C] : 
      ( C = k1_funct_2(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ? [E] : 
              ( v1_relat_1(E)
              & v1_funct_1(E)
              & D = E
              & k1_relat_1(E) = A
              & r1_tarski(k2_relat_1(E),B) ) ) ) ),
    file(funct_2,d2_funct_2),
    [interesting(0.00)]).

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

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

fof(t47_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( k7_finseq_1(A,k1_xboole_0) = A
        & k7_finseq_1(k1_xboole_0,A) = A ) ) ),
    file(finseq_1,t47_finseq_1),
    [interesting(0.00)]).

fof(t44_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => k2_relat_1(k7_finseq_1(A,B)) = k2_xboole_0(k2_relat_1(A),k2_relat_1(B)) ) ) ),
    file(finseq_1,t44_finseq_1),
    [interesting(0.00)]).

fof(t55_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( B = k9_finseq_1(A)
      <=> ( k4_finseq_1(B) = k2_finseq_1(1)
          & k2_relat_1(B) = k1_tarski(A) ) ) ) ),
    file(finseq_1,t55_finseq_1),
    [interesting(0.00)]).

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

fof(t60_finseq_1,theorem,(
    ! [A,B,C] : 
      ( k11_finseq_1(A,B,C) = k7_finseq_1(k9_finseq_1(A),k10_finseq_1(B,C))
      & k11_finseq_1(A,B,C) = k7_finseq_1(k10_finseq_1(A,B),k9_finseq_1(C)) ) ),
    file(finseq_1,t60_finseq_1),
    [interesting(0.00)]).

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

fof(t19_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( v1_relat_1(k7_relat_1(B,k2_finseq_1(A)))
            & v1_funct_1(k7_relat_1(B,k2_finseq_1(A)))
            & v1_finseq_1(k7_relat_1(B,k2_finseq_1(A))) ) ) ) ),
    file(finseq_1,t19_finseq_1),
    [interesting(0.00)]).

fof(t3_trees_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ~ ( C = k7_relat_1(B,k2_finseq_1(A))
                  & ! [D] : 
                      ( ( v1_relat_1(D)
                        & v1_funct_1(D)
                        & v1_finseq_1(D) )
                     => B != k7_finseq_1(C,D) ) ) ) ) ) ),
    file(trees_1,t3_trees_1),
    [interesting(0.00)]).

fof(t29_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => r1_xreal_0(A,k2_xcmplx_0(A,B)) ) ) ),
    file(nat_1,t29_nat_1),
    [interesting(0.00)]).

fof(t21_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( ( r1_xreal_0(A,k3_finseq_1(B))
                  & C = k7_relat_1(B,k2_finseq_1(A)) )
               => ( k3_finseq_1(C) = A
                  & k4_finseq_1(C) = k2_finseq_1(A) ) ) ) ) ) ),
    file(finseq_1,t21_finseq_1),
    [interesting(0.00)]).

fof(t25_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ~ ( k3_finseq_1(C) = k1_nat_1(A,B)
                  & ! [D] : 
                      ( ( v1_relat_1(D)
                        & v1_funct_1(D)
                        & v1_finseq_1(D) )
                     => ! [E] : 
                          ( ( v1_relat_1(E)
                            & v1_funct_1(E)
                            & v1_finseq_1(E) )
                         => ~ ( k3_finseq_1(D) = A
                              & k3_finseq_1(E) = B
                              & C = k7_finseq_1(D,E) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t19_finseq_1,t3_trees_1,t29_nat_1,t21_finseq_1,t35_finseq_1]),
    [file(finseq_2,t25_finseq_2),interesting(0.00)]).

fof(t50_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( m2_finseq_1(k7_finseq_1(A,B),C)
             => ( m2_finseq_1(A,C)
                & m2_finseq_1(B,C) ) ) ) ) ),
    file(finseq_1,t50_finseq_1),
    [interesting(0.00)]).

fof(t26_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( m2_finseq_1(D,C)
                 => ~ ( k3_finseq_1(D) = k1_nat_1(A,B)
                      & ! [E] : 
                          ( m2_finseq_1(E,C)
                         => ! [F] : 
                              ( m2_finseq_1(F,C)
                             => ~ ( k3_finseq_1(E) = A
                                  & k3_finseq_1(F) = B
                                  & D = k8_finseq_1(C,E,F) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t25_finseq_2,t50_finseq_1]),
    [file(finseq_2,t26_finseq_2),interesting(0.00)]).

fof(t109_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m2_finseq_2(C,B,k4_finseq_2(A,B))
             => k3_finseq_1(C) = A ) ) ) ),
    file(finseq_2,t109_finseq_2),
    [interesting(0.00)]).

fof(t127_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( m2_finseq_2(D,C,k4_finseq_2(A,C))
                 => ! [E] : 
                      ( m2_finseq_2(E,C,k4_finseq_2(B,C))
                     => m2_finseq_2(k8_finseq_1(C,D,E),C,k4_finseq_2(k1_nat_1(A,B),C)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t125_finseq_2]),
    [file(finseq_2,t127_finseq_2),interesting(0.00)]).

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

fof(t12_finseq_2,theorem,(
    $true ),
    file(finseq_2,t12_finseq_2),
    [interesting(0.00)]).

fof(d21_ordinal2,definition,(
    ! [A] : 
      ( v4_ordinal2(A)
    <=> r2_hidden(A,k5_ordinal2) ) ),
    file(ordinal2,d21_ordinal2),
    [interesting(0.00)]).

fof(t71_relat_1,theorem,(
    ! [A] : 
      ( k1_relat_1(k6_relat_1(A)) = A
      & k2_relat_1(k6_relat_1(A)) = A ) ),
    file(relat_1,t71_relat_1),
    [interesting(0.00)]).

fof(t27_relset_1,theorem,(
    ! [A,B,C] : 
      ( m2_relset_1(C,B,A)
     => ( m2_relset_1(C,B,k1_xboole_0)
       => C = k1_xboole_0 ) ) ),
    file(relset_1,t27_relset_1),
    [interesting(0.00)]).

fof(t20_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( r1_tarski(k2_relat_1(B),k1_relat_1(A))
           => ( v1_relat_1(k5_relat_1(B,A))
              & v1_funct_1(k5_relat_1(B,A))
              & v1_finseq_1(k5_relat_1(B,A)) ) ) ) ) ),
    file(finseq_1,t20_finseq_1),
    [interesting(0.00)]).

fof(t33_finseq_2,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( ( r1_tarski(k2_relat_1(A),k1_relat_1(C))
                  & B = k5_relat_1(A,C) )
               => k3_finseq_1(B) = k3_finseq_1(A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t46_relat_1,d3_finseq_1,d3_finseq_1]),
    [file(finseq_2,t33_finseq_2),interesting(0.00)]).

fof(d3_funct_2,definition,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ( v2_funct_2(C,A,B)
      <=> k2_relat_1(C) = B ) ) ),
    file(funct_2,d3_funct_2),
    [interesting(0.00)]).

fof(t7_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( r1_xreal_0(A,B)
          <=> r1_tarski(k2_finseq_1(A),k2_finseq_1(B)) ) ) ) ),
    file(finseq_1,t7_finseq_1),
    [interesting(0.00)]).

fof(t67_funct_2,theorem,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & m2_relset_1(B,A,A) )
     => ( k4_relset_1(A,A,B) = A
        & r1_tarski(k2_relat_1(B),A) ) ) ),
    file(funct_2,t67_funct_2),
    [interesting(0.00)]).

fof(t46_finseq_2,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k4_finseq_1(A),k4_finseq_1(A))
                & m2_relset_1(C,k4_finseq_1(A),k4_finseq_1(A)) )
             => ( ( k2_relat_1(C) = k4_finseq_1(A)
                  & B = k5_relat_1(C,A) )
               => k3_finseq_1(B) = k3_finseq_1(A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_finseq_1,t45_finseq_2]),
    [file(finseq_2,t46_finseq_2),interesting(0.00)]).

fof(t126_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( m2_finseq_2(D,C,k4_finseq_2(k1_nat_1(A,B),C))
                 => ? [E] : 
                      ( m2_finseq_2(E,C,k4_finseq_2(A,C))
                      & ? [F] : 
                          ( m2_finseq_2(F,C,k4_finseq_2(B,C))
                          & D = k8_finseq_1(C,E,F) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t125_finseq_2]),
    [file(finseq_2,t126_finseq_2),interesting(0.00)]).

fof(t77_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(k1_relat_1(B),A)
       => k5_relat_1(k6_relat_1(A),B) = B ) ) ),
    file(relat_1,t77_relat_1),
    [interesting(0.00)]).

fof(t17_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( ( k4_finseq_1(A) = k4_finseq_1(B)
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r2_hidden(C,k4_finseq_1(A))
                   => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) )
           => A = B ) ) ) ),
    file(finseq_1,t17_finseq_1),
    [interesting(0.00)]).

fof(t10_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( ( k3_finseq_1(B) = A
                  & k3_finseq_1(C) = A
                  & ! [D] : 
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r2_hidden(D,k2_finseq_1(A))
                       => k1_funct_1(B,D) = k1_funct_1(C,D) ) ) )
               => B = C ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_finseq_1,t17_finseq_1]),
    [file(finseq_2,t10_finseq_2),interesting(0.00)]).

fof(t139_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m2_finseq_2(C,B,k4_finseq_2(A,B))
             => ! [D] : 
                  ( m2_finseq_2(D,B,k4_finseq_2(A,B))
                 => ( ! [E] : 
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ( r2_hidden(E,k2_finseq_1(A))
                         => k1_funct_1(C,E) = k1_funct_1(D,E) ) )
                   => C = D ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t109_finseq_2,t10_finseq_2]),
    [file(finseq_2,t139_finseq_2),interesting(0.00)]).

fof(d3_funcop_1,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) )
             => k3_funcop_1(A,B,C) = k5_relat_1(k13_funct_3(B,C),A) ) ) ) ),
    file(funcop_1,d3_funcop_1),
    [interesting(0.00)]).

fof(t38_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( k1_square_1(A,B) = A
            | k1_square_1(A,B) = B ) ) ) ),
    file(square_1,t38_square_1),
    [interesting(0.00)]).

fof(t9_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( r1_xreal_0(A,B)
           => k2_finseq_1(A) = k5_subset_1(k5_numbers,k2_finseq_1(B),k2_finseq_1(A)) ) ) ) ),
    file(finseq_1,t9_finseq_1),
    [interesting(0.00)]).

fof(d1_square_1,definition,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
             => k1_square_1(A,B) = A )
            & ( ~ r1_xreal_0(A,B)
             => k1_square_1(A,B) = B ) ) ) ) ),
    file(square_1,d1_square_1),
    [interesting(0.00)]).

fof(t2_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( A = k3_square_1(B,C)
               => k5_subset_1(k5_numbers,k2_finseq_1(B),k2_finseq_1(C)) = k2_finseq_1(A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t9_finseq_1,d1_square_1]),
    [file(finseq_2,t2_finseq_2),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(l83_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( ( r1_tarski(k2_zfmisc_1(k2_relat_1(B),k2_relat_1(C)),k1_relat_1(D))
                      & A = k3_square_1(k3_finseq_1(B),k3_finseq_1(C)) )
                   => k1_relat_1(k3_funcop_1(D,B,C)) = k2_finseq_1(A) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_finseq_1,t71_funct_3,t2_finseq_2,d3_funcop_1,d8_funct_3,t1_xboole_1,t46_relat_1]),
    [file(finseq_2,l83_finseq_2),interesting(0.00)]).

fof(t78_finseq_2,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r1_tarski(k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B)),k1_relat_1(C))
               => ( v1_relat_1(k3_funcop_1(C,A,B))
                  & v1_funct_1(k3_funcop_1(C,A,B))
                  & v1_finseq_1(k3_funcop_1(C,A,B)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t38_square_1,l83_finseq_2,d2_finseq_1]),
    [file(finseq_2,t78_finseq_2),interesting(0.00)]).

fof(t79_finseq_2,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( ( r1_tarski(k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B)),k1_relat_1(D))
                      & C = k3_funcop_1(D,A,B) )
                   => k3_finseq_1(C) = k3_square_1(k3_finseq_1(A),k3_finseq_1(B)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t38_square_1,l83_finseq_2,d3_finseq_1]),
    [file(finseq_2,t79_finseq_2),interesting(0.00)]).

fof(t86_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D) )
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(A,B),C)
                        & m2_relset_1(E,k2_zfmisc_1(A,B),C) )
                     => ! [F] : 
                          ( m2_finseq_1(F,A)
                         => ! [G] : 
                              ( m2_finseq_1(G,B)
                             => ( ( k3_finseq_1(F) = k3_finseq_1(G)
                                  & D = k3_funcop_1(E,F,G) )
                               => ( k3_finseq_1(D) = k3_finseq_1(F)
                                  & k3_finseq_1(D) = k3_finseq_1(G) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t85_finseq_2]),
    [file(finseq_2,t86_finseq_2),interesting(0.00)]).

fof(t140_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( ~ v1_xboole_0(D)
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(B,C),D)
                        & m2_relset_1(E,k2_zfmisc_1(B,C),D) )
                     => ! [F] : 
                          ( m2_finseq_2(F,B,k4_finseq_2(A,B))
                         => ! [G] : 
                              ( m2_finseq_2(G,C,k4_finseq_2(A,C))
                             => m2_finseq_2(k3_funcop_1(E,F,G),D,k4_finseq_2(A,D)) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t84_finseq_2,t109_finseq_2,t86_finseq_2,t110_finseq_2]),
    [file(finseq_2,t140_finseq_2),interesting(0.00)]).

fof(d5_funcop_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => k5_funcop_1(A,B,C) = k5_relat_1(k13_funct_3(k2_funcop_1(k1_relat_1(C),B),C),A) ) ) ),
    file(funcop_1,d5_funcop_1),
    [interesting(0.00)]).

fof(t80_finseq_2,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r1_tarski(k2_zfmisc_1(k1_tarski(A),k2_relat_1(B)),k1_relat_1(C))
           => ( v1_relat_1(k5_funcop_1(C,A,B))
              & v1_funct_1(k5_funcop_1(C,A,B))
              & v1_finseq_1(k5_funcop_1(C,A,B)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l86_finseq_2,d3_finseq_1,d2_finseq_1]),
    [file(finseq_2,t80_finseq_2),interesting(0.00)]).

fof(t81_finseq_2,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C)
            & v1_finseq_1(C) )
         => ! [D] : 
              ( ( v1_relat_1(D)
                & v1_funct_1(D) )
             => ( ( r1_tarski(k2_zfmisc_1(k1_tarski(A),k2_relat_1(B)),k1_relat_1(D))
                  & C = k5_funcop_1(D,A,B) )
               => k3_finseq_1(C) = k3_finseq_1(B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l86_finseq_2,d3_finseq_1,d3_finseq_1]),
    [file(finseq_2,t81_finseq_2),interesting(0.00)]).

fof(t141_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( ~ v1_xboole_0(D)
                 => ! [E] : 
                      ( m1_subset_1(E,B)
                     => ! [F] : 
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(B,C),D)
                            & m2_relset_1(F,k2_zfmisc_1(B,C),D) )
                         => ! [G] : 
                              ( m2_finseq_2(G,C,k4_finseq_2(A,C))
                             => m2_finseq_2(k5_funcop_1(F,E,G),D,k4_finseq_2(A,D)) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t91_finseq_2,t109_finseq_2,t92_finseq_2,t110_finseq_2]),
    [file(finseq_2,t141_finseq_2),interesting(0.00)]).

fof(t142_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( ~ v1_xboole_0(D)
                 => ! [E] : 
                      ( m1_subset_1(E,C)
                     => ! [F] : 
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(B,C),D)
                            & m2_relset_1(F,k2_zfmisc_1(B,C),D) )
                         => ! [G] : 
                              ( m2_finseq_2(G,B,k4_finseq_2(A,B))
                             => m2_finseq_2(k4_funcop_1(F,G,E),D,k4_finseq_2(A,D)) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t97_finseq_2,t109_finseq_2,t98_finseq_2,t110_finseq_2]),
    [file(finseq_2,t142_finseq_2),interesting(0.00)]).

fof(t6_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => r2_hidden(k2_xcmplx_0(A,1),k2_finseq_1(k2_xcmplx_0(A,1))) ) ),
    file(finseq_1,t6_finseq_1),
    [interesting(0.00)]).

fof(t13_funcop_1,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(B,A)
     => k1_funct_1(k2_funcop_1(A,C),B) = C ) ),
    file(funcop_1,t13_funcop_1),
    [interesting(0.00)]).

fof(t42_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => r1_tarski(k2_relat_1(A),k2_relat_1(k7_finseq_1(A,B))) ) ) ),
    file(finseq_1,t42_finseq_1),
    [interesting(0.00)]).

fof(t14_funcop_1,theorem,(
    ! [A,B] : 
      ( A != k1_xboole_0
     => k2_relat_1(k2_funcop_1(A,B)) = k1_tarski(B) ) ),
    file(funcop_1,t14_funcop_1),
    [interesting(0.00)]).

fof(t39_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,k1_tarski(B))
    <=> ( A = k1_xboole_0
        | A = k1_tarski(B) ) ) ),
    file(zfmisc_1,t39_zfmisc_1),
    [interesting(0.00)]).

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) ) ) ),
    file(funcop_1,t15_funcop_1),
    [interesting(0.00)]).

fof(t45_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => k7_finseq_1(k7_finseq_1(A,B),C) = k7_finseq_1(A,k7_finseq_1(B,C)) ) ) ) ),
    file(finseq_1,t45_finseq_1),
    [interesting(0.00)]).

fof(t12_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r2_hidden(A,k1_relat_1(B))
       => r2_hidden(k1_funct_1(B,A),k2_relat_1(B)) ) ) ),
    file(funct_1,t12_funct_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(t38_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(k2_tarski(A,B),C)
    <=> ( r2_hidden(A,C)
        & r2_hidden(B,C) ) ) ),
    file(zfmisc_1,t38_zfmisc_1),
    [interesting(0.00)]).

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

fof(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(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(t41_finseq_2,theorem,(
    ! [A,B,C,D] : 
      ( ~ v1_xboole_0(D)
     => ! [E] : 
          ( ~ v1_xboole_0(E)
         => ! [F] : 
              ( m2_finseq_1(F,D)
             => ! [G] : 
                  ( ( v1_funct_1(G)
                    & v1_funct_2(G,D,E)
                    & m2_relset_1(G,D,E) )
                 => ( F = k11_finseq_1(A,B,C)
                   => k1_partfun1(k5_numbers,D,D,E,F,G) = k11_finseq_1(k1_funct_1(G,A),k1_funct_1(G,B),k1_funct_1(G,C)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t36_finseq_2,t62_finseq_1,t37_finseq_2,t62_finseq_1,d3_finseq_1,t22_funct_1,t62_finseq_1]),
    [file(finseq_2,t41_finseq_2),interesting(0.00)]).

fof(t146_finseq_2,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C,D] : 
          ( ( r2_hidden(B,k1_relat_1(A))
            & r2_hidden(C,k1_relat_1(A))
            & r2_hidden(D,k1_relat_1(A)) )
         => k5_relat_1(k11_finseq_1(B,C,D),A) = k11_finseq_1(k1_funct_1(A,B),k1_funct_1(A,C),k1_funct_1(A,D)) ) ) ),
    inference(mizar_proof,[status(thm)],[t12_funct_1,d1_funct_2,t11_relset_1,l18_finseq_2,t43_enumset1,t37_zfmisc_1,t38_zfmisc_1,t8_xboole_1,d4_finseq_1,t41_finseq_2]),
    [file(finseq_2,t146_finseq_2),interesting(0.00)]).

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) ) ) ) ) ) ),
    file(grfunc_1,t8_grfunc_1),
    [interesting(0.00)]).

fof(t149_finseq_2,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( ( r1_tarski(A,C)
                  & r1_tarski(B,C)
                  & k3_finseq_1(A) = k3_finseq_1(B) )
               => A = B ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_finseq_1,d3_finseq_1,t8_grfunc_1,t8_grfunc_1,t10_finseq_2]),
    [file(finseq_2,t149_finseq_2),interesting(0.00)]).

fof(t17_finseq_2,theorem,(
    $true ),
    file(finseq_2,t17_finseq_2),
    [interesting(0.00)]).

fof(t49_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( k2_square_1(A,B) = A
            | k2_square_1(A,B) = B ) ) ) ),
    file(square_1,t49_square_1),
    [interesting(0.00)]).

fof(t46_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( ( k7_finseq_1(A,B) = k7_finseq_1(C,B)
                  | k7_finseq_1(B,A) = k7_finseq_1(B,C) )
               => A = C ) ) ) ) ),
    file(finseq_1,t46_finseq_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(t23_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( ( B = k7_relat_1(C,k2_finseq_1(A))
                  & r1_xreal_0(k3_finseq_1(C),A) )
               => C = B ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t7_finseq_1,d3_finseq_1,t97_relat_1]),
    [file(finseq_2,t23_finseq_2),interesting(0.00)]).

fof(t24_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( B = k7_relat_1(C,k2_finseq_1(A))
               => k3_finseq_1(B) = k3_square_1(A,k3_finseq_1(C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t21_finseq_1,t23_finseq_2,d1_square_1]),
    [file(finseq_2,t24_finseq_2),interesting(0.00)]).

fof(t29_finseq_2,theorem,(
    $true ),
    file(finseq_2,t29_finseq_2),
    [interesting(0.00)]).

fof(t4_funct_2,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r1_tarski(k2_relat_1(B),A)
       => ( v1_funct_1(B)
          & v1_funct_2(B,k1_relat_1(B),A)
          & m2_relset_1(B,k1_relat_1(B),A) ) ) ) ),
    file(funct_2,t4_funct_2),
    [interesting(0.00)]).

fof(t38_funct_2,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( r1_tarski(C,A)
       => ( ( B = k1_xboole_0
            & A != k1_xboole_0 )
          | ( v1_funct_1(k2_partfun1(A,B,D,C))
            & v1_funct_2(k2_partfun1(A,B,D,C),C,B)
            & m2_relset_1(k2_partfun1(A,B,D,C),C,B) ) ) ) ) ),
    file(funct_2,t38_funct_2),
    [interesting(0.00)]).

fof(t35_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ( B = k2_finseq_1(A)
               => ! [D] : 
                    ( m2_finseq_1(D,C)
                   => ! [E] : 
                        ( m2_finseq_1(E,B)
                       => ( r1_xreal_0(A,k3_finseq_1(D))
                         => m2_finseq_1(k1_partfun1(k5_numbers,B,k5_numbers,C,E,D),C) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t34_finseq_2,d4_finseq_1,t45_relat_1,t1_xboole_1,d4_finseq_1]),
    [file(finseq_2,t35_finseq_2),interesting(0.00)]).

fof(t44_finseq_2,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k4_finseq_1(A),k4_finseq_1(A))
            & m2_relset_1(B,k4_finseq_1(A),k4_finseq_1(A)) )
         => ( v1_relat_1(k5_relat_1(B,A))
            & v1_funct_1(k5_relat_1(B,A))
            & v1_finseq_1(k5_relat_1(B,A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_finseq_1,t43_finseq_2]),
    [file(finseq_2,t44_finseq_2),interesting(0.00)]).

fof(t47_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A))
                    & v3_funct_2(D,k2_finseq_1(A),k2_finseq_1(A))
                    & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) )
                 => ( ( r1_xreal_0(A,k3_finseq_1(B))
                      & C = k5_relat_1(D,B) )
                   => k3_finseq_1(C) = A ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_funct_2,t45_finseq_2]),
    [file(finseq_2,t47_finseq_2),interesting(0.00)]).

fof(t48_finseq_2,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k4_finseq_1(A),k4_finseq_1(A))
                & v3_funct_2(C,k4_finseq_1(A),k4_finseq_1(A))
                & m2_relset_1(C,k4_finseq_1(A),k4_finseq_1(A)) )
             => ( B = k5_relat_1(C,A)
               => k3_finseq_1(B) = k3_finseq_1(A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_finseq_1,t47_finseq_2]),
    [file(finseq_2,t48_finseq_2),interesting(0.00)]).

fof(t53_finseq_2,theorem,(
    $true ),
    file(finseq_2,t53_finseq_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(t11_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( r1_xreal_0(A,B)
              <=> r1_xreal_0(k6_xcmplx_0(A,C),k6_xcmplx_0(B,C)) ) ) ) ) ),
    file(xreal_1,t11_xreal_1),
    [interesting(0.00)]).

fof(t26_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
          <=> r1_xreal_0(k4_xcmplx_0(B),k4_xcmplx_0(A)) ) ) ) ),
    file(xreal_1,t26_xreal_1),
    [interesting(0.00)]).

fof(d2_square_1,definition,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(B,A)
             => k2_square_1(A,B) = A )
            & ( ~ r1_xreal_0(B,A)
             => k2_square_1(A,B) = B ) ) ) ) ),
    file(square_1,d2_square_1),
    [interesting(0.00)]).

fof(d5_real_1,definition,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
          <=> ~ ( r1_xreal_0(B,A)
                & B != A ) ) ) ) ),
    file(real_1,d5_real_1),
    [interesting(0.00)]).

fof(t61_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( r1_xreal_0(A,B)
           => m2_subset_1(k6_xcmplx_0(B,A),k1_numbers,k5_numbers) ) ) ) ),
    file(nat_1,t61_nat_1),
    [interesting(0.00)]).

fof(t34_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( B = k6_relat_1(A)
      <=> ( k1_relat_1(B) = A
          & ! [C] : 
              ( r2_hidden(C,A)
             => k1_funct_1(B,C) = C ) ) ) ) ),
    file(funct_1,t34_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(t65_finseq_2,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v1_funct_1(k1_finseq_2(A))
        & v1_funct_2(k1_finseq_2(A),k2_finseq_1(A),k2_finseq_1(A))
        & v3_funct_2(k1_finseq_2(A),k2_finseq_1(A),k2_finseq_1(A))
        & m2_relset_1(k1_finseq_2(A),k2_finseq_1(A),k2_finseq_1(A)) ) ) ),
    file(finseq_2,t65_finseq_2),
    [interesting(0.00)]).

fof(t67_finseq_2,theorem,(
    $true ),
    file(finseq_2,t67_finseq_2),
    [interesting(0.00)]).

fof(t7_finseq_2,theorem,(
    $true ),
    file(finseq_2,t7_finseq_2),
    [interesting(0.00)]).

fof(t6_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( k3_square_1(0,A) = 0
        & k3_square_1(A,0) = 0
        & k4_square_1(0,A) = A
        & k4_square_1(A,0) = A ) ) ),
    inference(mizar_proof,[status(thm)],[d1_square_1,d2_square_1]),
    [file(finseq_2,t6_finseq_2),interesting(0.00)]).

fof(t87_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(A,B),C)
                    & m2_relset_1(D,k2_zfmisc_1(A,B),C) )
                 => ! [E] : 
                      ( m2_finseq_1(E,A)
                     => ! [F] : 
                          ( m2_finseq_1(F,B)
                         => ( k3_funcop_1(D,k6_finseq_1(A),F) = k6_finseq_1(C)
                            & k3_funcop_1(D,E,k6_finseq_1(B)) = k6_finseq_1(C) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t84_finseq_2,t32_finseq_1,t85_finseq_2,t6_finseq_2,t32_finseq_1]),
    [file(finseq_2,t87_finseq_2),interesting(0.00)]).

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)) ) ) ) ) ),
    file(funcop_1,t28_funcop_1),
    [interesting(0.00)]).

fof(t88_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( m1_subset_1(D,A)
                 => ! [E] : 
                      ( m1_subset_1(E,B)
                     => ! [F] : 
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(A,B),C)
                            & m2_relset_1(F,k2_zfmisc_1(A,B),C) )
                         => ! [G] : 
                              ( m2_finseq_1(G,A)
                             => ! [H] : 
                                  ( m2_finseq_1(H,B)
                                 => ( ( G = k12_finseq_1(A,D)
                                      & H = k12_finseq_1(B,E) )
                                   => k3_funcop_1(F,G,H) = k12_finseq_1(C,k2_binop_1(A,B,C,F,D,E)) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t84_finseq_2,t56_finseq_1,t86_finseq_2,t57_finseq_1,d3_finseq_1,t28_funcop_1,t57_finseq_1]),
    [file(finseq_2,t88_finseq_2),interesting(0.00)]).

fof(t89_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( m1_subset_1(D,A)
                 => ! [E] : 
                      ( m1_subset_1(E,A)
                     => ! [F] : 
                          ( m1_subset_1(F,B)
                         => ! [G] : 
                              ( m1_subset_1(G,B)
                             => ! [H] : 
                                  ( ( v1_funct_1(H)
                                    & v1_funct_2(H,k2_zfmisc_1(A,B),C)
                                    & m2_relset_1(H,k2_zfmisc_1(A,B),C) )
                                 => ! [I] : 
                                      ( m2_finseq_1(I,A)
                                     => ! [J] : 
                                          ( m2_finseq_1(J,B)
                                         => ( ( I = k10_finseq_1(D,E)
                                              & J = k10_finseq_1(F,G) )
                                           => k3_funcop_1(H,I,J) = k10_finseq_1(k2_binop_1(A,B,C,H,D,F),k2_binop_1(A,B,C,H,E,G)) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t84_finseq_2,t61_finseq_1,t86_finseq_2,t61_finseq_1,d3_finseq_1,t28_funcop_1,t61_finseq_1]),
    [file(finseq_2,t89_finseq_2),interesting(0.00)]).

fof(t3_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( r2_hidden(A,k2_finseq_1(B))
          <=> ( r1_xreal_0(1,A)
              & r1_xreal_0(A,B) ) ) ) ) ),
    file(finseq_1,t3_finseq_1),
    [interesting(0.00)]).

fof(t26_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ~ ( r1_xreal_0(A,k2_xcmplx_0(B,1))
              & ~ r1_xreal_0(A,B)
              & A != k2_xcmplx_0(B,1) ) ) ) ),
    file(nat_1,t26_nat_1),
    [interesting(0.00)]).

fof(t8_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ~ ( r2_hidden(A,k2_finseq_1(k1_nat_1(B,1)))
              & ~ r2_hidden(A,k2_finseq_1(B))
              & A != k1_nat_1(B,1) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t3_finseq_1,t26_nat_1]),
    [file(finseq_2,t8_finseq_2),interesting(0.00)]).

fof(t90_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( m1_subset_1(D,A)
                 => ! [E] : 
                      ( m1_subset_1(E,A)
                     => ! [F] : 
                          ( m1_subset_1(F,A)
                         => ! [G] : 
                              ( m1_subset_1(G,B)
                             => ! [H] : 
                                  ( m1_subset_1(H,B)
                                 => ! [I] : 
                                      ( m1_subset_1(I,B)
                                     => ! [J] : 
                                          ( ( v1_funct_1(J)
                                            & v1_funct_2(J,k2_zfmisc_1(A,B),C)
                                            & m2_relset_1(J,k2_zfmisc_1(A,B),C) )
                                         => ! [K] : 
                                              ( m2_finseq_1(K,A)
                                             => ! [L] : 
                                                  ( m2_finseq_1(L,B)
                                                 => ( ( K = k11_finseq_1(D,E,F)
                                                      & L = k11_finseq_1(G,H,I) )
                                                   => k3_funcop_1(J,K,L) = k11_finseq_1(k2_binop_1(A,B,C,J,D,G),k2_binop_1(A,B,C,J,E,H),k2_binop_1(A,B,C,J,F,I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t84_finseq_2,t62_finseq_1,t86_finseq_2,t62_finseq_1,d3_finseq_1,t28_funcop_1,t62_finseq_1]),
    [file(finseq_2,t90_finseq_2),interesting(0.00)]).

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)) ) ) ) ),
    file(funcop_1,t42_funcop_1),
    [interesting(0.00)]).

fof(t95_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( m1_subset_1(D,A)
                 => ! [E] : 
                      ( m1_subset_1(E,B)
                     => ! [F] : 
                          ( m1_subset_1(F,B)
                         => ! [G] : 
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,k2_zfmisc_1(A,B),C)
                                & m2_relset_1(G,k2_zfmisc_1(A,B),C) )
                             => ! [H] : 
                                  ( m2_finseq_1(H,B)
                                 => ( H = k10_finseq_1(E,F)
                                   => k5_funcop_1(G,D,H) = k10_finseq_1(k2_binop_1(A,B,C,G,D,E),k2_binop_1(A,B,C,G,D,F)) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t91_finseq_2,t61_finseq_1,t92_finseq_2,t61_finseq_1,d3_finseq_1,t42_funcop_1,t61_finseq_1]),
    [file(finseq_2,t95_finseq_2),interesting(0.00)]).

fof(t96_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( m1_subset_1(D,A)
                 => ! [E] : 
                      ( m1_subset_1(E,B)
                     => ! [F] : 
                          ( m1_subset_1(F,B)
                         => ! [G] : 
                              ( m1_subset_1(G,B)
                             => ! [H] : 
                                  ( ( v1_funct_1(H)
                                    & v1_funct_2(H,k2_zfmisc_1(A,B),C)
                                    & m2_relset_1(H,k2_zfmisc_1(A,B),C) )
                                 => ! [I] : 
                                      ( m2_finseq_1(I,B)
                                     => ( I = k11_finseq_1(E,F,G)
                                       => k5_funcop_1(H,D,I) = k11_finseq_1(k2_binop_1(A,B,C,H,D,E),k2_binop_1(A,B,C,H,D,F),k2_binop_1(A,B,C,H,D,G)) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t91_finseq_2,t62_finseq_1,t92_finseq_2,t62_finseq_1,d3_finseq_1,t42_funcop_1,t62_finseq_1]),
    [file(finseq_2,t96_finseq_2),interesting(0.00)]).