fof(t18_calcul_2,theorem,(
    ! [A] : 
      ( m2_finseq_1(A,k7_cqc_lang)
     => ! [B] : 
          ( m2_finseq_1(B,k7_cqc_lang)
         => r2_calcul_1(A,k8_finseq_1(k7_cqc_lang,B,A)) ) ) ),
    inference(mizar_proof,[status(thm)],[t16_calcul_2,t17_calcul_2,t11_calcul_2,t23_funct_1,t13_calcul_2,d7_finseq_1,t17_calcul_2,t17_finseq_1,d4_calcul_1]),
    [file(calcul_2,t18_calcul_2),interesting(1.00)]).

fof(t20_calcul_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] : 
          ( m2_finseq_1(B,k7_cqc_lang)
         => ! [C] : 
              ( m2_finseq_1(C,k7_cqc_lang)
             => ( r4_calcul_1(k8_finseq_1(k7_cqc_lang,B,k12_finseq_1(k7_cqc_lang,A)))
               => r4_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,C,B),k12_finseq_1(k7_cqc_lang,A))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t5_calcul_1,t18_calcul_2,t5_calcul_1,t36_calcul_1]),
    [file(calcul_2,t20_calcul_2),interesting(0.79)]).

fof(t6_calcul_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => r2_wellord2(k2_calcul_2(A,B),B) ) ) ),
    inference(mizar_proof,[status(thm)],[t2_calcul_2,t5_calcul_2,t52_card_1,d1_ordinal1,t48_card_1,t3_xboole_0,d1_tarski,t3_xboole_0,d1_tarski,t38_nat_1,t1_calcul_2,t58_card_1,s1_nat_1]),
    [file(calcul_2,t6_calcul_2),interesting(0.73)]).

fof(t4_calcul_2,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ! [C] : 
              ( v4_ordinal2(C)
             => ( r1_xreal_0(A,B)
              <=> r1_tarski(k2_calcul_2(C,A),k2_calcul_2(C,B)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t1_calcul_2,t8_xreal_1,t2_xreal_1,t3_calcul_2,t1_calcul_2,t8_xreal_1]),
    [file(calcul_2,t4_calcul_2),interesting(0.66)]).

fof(t10_calcul_2,theorem,(
    ! [A] : 
      ( m2_finseq_1(A,k7_cqc_lang)
     => ! [B] : 
          ( m2_finseq_1(B,k7_cqc_lang)
         => k3_finseq_1(k14_finseq_1(k2_calcul_2(k3_finseq_1(A),k3_finseq_1(B)))) = k3_finseq_1(B) ) ) ),
    inference(mizar_proof,[status(thm)],[t6_calcul_2,t81_card_1,t78_finseq_1,t7_calcul_2,t44_finseq_3]),
    [file(calcul_2,t10_calcul_2),interesting(0.66)]).

fof(t2_calcul_2,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => k2_calcul_2(A,0) = k1_xboole_0 ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t1_calcul_2,t38_nat_1]),
    [file(calcul_2,t2_calcul_2),interesting(0.65)]).

fof(t28_calcul_2,theorem,(
    ! [A] : 
      ( m2_finseq_1(A,k7_cqc_lang)
     => ! [B] : 
          ( m2_finseq_1(B,k7_cqc_lang)
         => ( ( r1_xreal_0(1,k3_finseq_1(A))
              & r4_calcul_1(k8_finseq_1(k7_cqc_lang,B,A)) )
           => r4_calcul_1(k8_finseq_1(k7_cqc_lang,B,k12_finseq_1(k7_cqc_lang,k5_calcul_2(k4_finseq_5(k7_cqc_lang,A))))) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_finseq_5,d4_calcul_2,d3_finseq_5,t6_calcul_1,t2_xreal_1,t28_nat_1,t23_finseq_1,d3_calcul_2,t65_finseq_5,t2_xreal_1,t27_finseq_3,t11_finseq_5,t27_finseq_3,t35_finseq_1,d7_finseq_1,d3_finseq_1,t98_relat_1,t98_relat_1,t29_nat_1,t38_nat_1,t29_nat_1,t11_xreal_1,t23_finseq_1,t29_nat_1,t27_finseq_3,t11_finseq_5,t27_finseq_3,t13_finseq_2,t13_finseq_2,t38_nat_1,t27_finseq_3,t60_finseq_5,t61_finseq_5,d3_finseq_5,t10_xreal_1,t16_int_1,t20_int_1,t29_nat_1,t22_xreal_1,t27_finseq_3,d7_finseq_1,t35_finseq_1,t27_finseq_3,t13_finseq_2,t27_calcul_2,s1_nat_1,d3_finseq_5,d3_finseq_5,t35_finseq_1,d3_finseq_1,t33_finseq_1]),
    [file(calcul_2,t28_calcul_2),interesting(0.63)]).

fof(t3_calcul_2,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( A = 0
            | r2_hidden(k2_xcmplx_0(A,B),k2_calcul_2(B,A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t22_nat_1,d21_ordinal2,t29_nat_1,t8_xreal_1]),
    [file(calcul_2,t3_calcul_2),interesting(0.61)]).

fof(t7_calcul_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => r1_tarski(k2_calcul_2(A,B),k2_finseq_1(k1_nat_1(A,B))) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t1_calcul_2,t29_nat_1,t2_xreal_1,t3_finseq_1]),
    [file(calcul_2,t7_calcul_2),interesting(0.58)]).

fof(t5_calcul_2,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => k2_xboole_0(k2_calcul_2(A,B),k1_tarski(k2_xcmplx_0(k2_xcmplx_0(A,B),1))) = k2_calcul_2(A,k2_xcmplx_0(B,1)) ) ) ),
    inference(mizar_proof,[status(thm)],[t9_xreal_1,t4_calcul_2,d3_tarski,d2_xboole_0,d1_tarski,t3_calcul_2,d10_xboole_0,d3_tarski,t1_calcul_2,t26_nat_1,d1_tarski,d2_xboole_0]),
    [file(calcul_2,t5_calcul_2),interesting(0.58)]).

fof(t11_calcul_2,theorem,(
    ! [A] : 
      ( m2_finseq_1(A,k7_cqc_lang)
     => ! [B] : 
          ( m2_finseq_1(B,k7_cqc_lang)
         => k4_relset_1(k5_numbers,k5_numbers,k14_finseq_1(k2_calcul_2(k3_finseq_1(A),k3_finseq_1(B)))) = k4_relset_1(k5_numbers,k7_cqc_lang,B) ) ) ),
    inference(mizar_proof,[status(thm)],[t10_calcul_2,t31_finseq_3]),
    [file(calcul_2,t11_calcul_2),interesting(0.57)]).

fof(t31_calcul_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( r1_xreal_0(1,A)
         => k2_relat_1(k2_finseq_2(A,B)) = k2_relat_1(k9_finseq_1(B)) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t11_finseq_2,d3_finseq_1,t69_finseq_2,t70_finseq_2,d1_tarski,t55_finseq_1,d10_xboole_0,d3_tarski,t55_finseq_1,d1_tarski,t69_finseq_2,t27_finseq_3,t3_finseq_1,t70_finseq_2,d5_funct_1]),
    [file(calcul_2,t31_calcul_2),interesting(0.56)]).

fof(t32_calcul_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] : 
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] : 
                  ( m2_finseq_1(D,k7_cqc_lang)
                 => ( ( r1_xreal_0(1,C)
                      & r4_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,D,k6_calcul_2(k7_cqc_lang,C,A)),k12_finseq_1(k7_cqc_lang,B))) )
                   => r4_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,D,k12_finseq_1(k7_cqc_lang,A)),k12_finseq_1(k7_cqc_lang,B))) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t20_calcul_2,t45_finseq_1,t10_calcul_1,t28_calcul_2,d3_finseq_5,d4_calcul_2,d3_finseq_5,t27_finseq_3,t13_finseq_2,t60_finseq_5,t61_finseq_5,t38_nat_1,t38_nat_1,t27_finseq_3,t60_finseq_5,d3_finseq_5,t10_xreal_1,t16_int_1,t38_nat_1,t31_xreal_1,t10_xreal_1,t61_finseq_5,t38_nat_1,t27_finseq_3,t60_finseq_5,t61_finseq_5,d3_finseq_5,t31_xreal_1,t10_xreal_1,t35_finseq_1,t56_finseq_1,t38_nat_1,t27_finseq_3,t72_funct_1,t33_finseq_1,t12_funct_1,t44_finseq_1,t31_calcul_2,t44_finseq_1,t5_calcul_1,t11_finseq_2,t5_calcul_1,d3_calcul_1,t33_calcul_1,t56_calcul_1,t27_finseq_3,t60_finseq_5,t61_finseq_5,s1_nat_1,d3_finseq_5,d3_finseq_5,t65_finseq_5,d3_calcul_2,t65_finseq_5,t35_finseq_1,t56_finseq_1,t59_finseq_1]),
    [file(calcul_2,t32_calcul_2),interesting(0.56)]).

fof(t1_calcul_2,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ! [C] : 
              ( v4_ordinal2(C)
             => ( r2_hidden(A,k2_calcul_2(B,C))
              <=> ( r1_xreal_0(k2_xcmplx_0(1,B),A)
                  & r1_xreal_0(A,k2_xcmplx_0(C,B)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d21_ordinal2]),
    [file(calcul_2,t1_calcul_2),interesting(0.55)]).

fof(t21_calcul_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] : 
          ( m2_finseq_1(B,k7_cqc_lang)
         => r4_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,B,k12_finseq_1(k7_cqc_lang,A)),k12_finseq_1(k7_cqc_lang,A))) ) ) ),
    inference(mizar_proof,[status(thm)],[t10_calcul_1,t35_finseq_1,t56_finseq_1,t59_finseq_1,d3_calcul_1,t5_calcul_1,t5_calcul_1,t33_calcul_1]),
    [file(calcul_2,t21_calcul_2),interesting(0.55)]).

fof(t27_calcul_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] : 
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] : 
              ( m2_finseq_1(C,k7_cqc_lang)
             => ( r4_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,A)),k12_finseq_1(k7_cqc_lang,B)))
               => r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,k12_cqc_lang(A,B)))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t21_calcul_2,t22_calcul_2,t5_calcul_1,t5_calcul_1,t10_calcul_1,t13_calcul_1,t5_calcul_1,t36_calcul_1,t24_calcul_2,t23_calcul_2,t25_calcul_2,t21_calcul_2,t26_calcul_2,d2_qc_lang2]),
    [file(calcul_2,t27_calcul_2),interesting(0.52)]).

fof(t14_calcul_2,theorem,(
    ! [A] : 
      ( m2_finseq_1(A,k7_cqc_lang)
     => ! [B] : 
          ( m2_finseq_1(B,k7_cqc_lang)
         => r1_tarski(k2_calcul_2(k3_finseq_1(A),k3_finseq_1(B)),k4_relset_1(k5_numbers,k7_cqc_lang,k8_finseq_1(k7_cqc_lang,A,B))) ) ) ),
    inference(mizar_proof,[status(thm)],[t1_calcul_2,t29_nat_1,t2_xreal_1,t35_finseq_1,t27_finseq_3,d3_tarski]),
    [file(calcul_2,t14_calcul_2),interesting(0.51)]).

fof(t8_calcul_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => r1_xboole_0(k2_finseq_1(A),k2_calcul_2(A,B)) ) ) ),
    inference(mizar_proof,[status(thm)],[t3_xboole_0,t1_calcul_2,t3_finseq_1,t38_nat_1]),
    [file(calcul_2,t8_calcul_2),interesting(0.51)]).

fof(t12_calcul_2,theorem,(
    ! [A] : 
      ( m2_finseq_1(A,k7_cqc_lang)
     => ! [B] : 
          ( m2_finseq_1(B,k7_cqc_lang)
         => k5_relset_1(k5_numbers,k5_numbers,k14_finseq_1(k2_calcul_2(k3_finseq_1(A),k3_finseq_1(B)))) = k2_calcul_2(k3_finseq_1(A),k3_finseq_1(B)) ) ) ),
    inference(mizar_proof,[status(thm)],[t7_calcul_2,d13_finseq_1]),
    [file(calcul_2,t12_calcul_2),interesting(0.50)]).

fof(t17_calcul_2,theorem,(
    ! [A] : 
      ( m2_finseq_1(A,k7_cqc_lang)
     => ! [B] : 
          ( m2_finseq_1(B,k7_cqc_lang)
         => k4_finseq_1(k15_finseq_1(k8_relset_1(k5_numbers,k7_cqc_lang,k8_finseq_1(k7_cqc_lang,A,B),k2_calcul_2(k3_finseq_1(A),k3_finseq_1(B))))) = k4_relset_1(k5_numbers,k7_cqc_lang,B) ) ) ),
    inference(mizar_proof,[status(thm)],[t12_calcul_2,t14_calcul_2,t16_calcul_2,t46_relat_1,t11_calcul_2]),
    [file(calcul_2,t17_calcul_2),interesting(0.49)]).

fof(t15_calcul_2,theorem,(
    ! [A] : 
      ( m2_finseq_1(A,k7_cqc_lang)
     => ! [B] : 
          ( m2_finseq_1(B,k7_cqc_lang)
         => k4_relset_1(k5_numbers,k7_cqc_lang,k8_relset_1(k5_numbers,k7_cqc_lang,k8_finseq_1(k7_cqc_lang,A,B),k2_calcul_2(k3_finseq_1(A),k3_finseq_1(B)))) = k2_calcul_2(k3_finseq_1(A),k3_finseq_1(B)) ) ) ),
    inference(mizar_proof,[status(thm)],[t90_relat_1,t14_calcul_2,t28_xboole_1]),
    [file(calcul_2,t15_calcul_2),interesting(0.43)]).

fof(t13_calcul_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_finseq_1(B,k7_cqc_lang)
         => ! [C] : 
              ( m2_finseq_1(C,k7_cqc_lang)
             => ( r2_hidden(A,k4_relset_1(k5_numbers,k5_numbers,k14_finseq_1(k2_calcul_2(k3_finseq_1(B),k3_finseq_1(C)))))
               => k1_funct_1(k14_finseq_1(k2_calcul_2(k3_finseq_1(B),k3_finseq_1(C))),A) = k1_nat_1(k3_finseq_1(B),A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t11_calcul_2,t27_finseq_3,t2_xreal_1,t38_nat_1,t11_calcul_2,t27_finseq_3,t12_funct_1,t1_calcul_2,t12_calcul_2,t2_xreal_1,t27_finseq_3,t11_calcul_2,t12_funct_1,t38_nat_1,t2_xreal_1,t10_calcul_2,t38_nat_1,t7_calcul_2,t38_nat_1,d13_finseq_1,t29_nat_1,t8_xreal_1,t12_calcul_2,t11_finseq_2,t38_nat_1,t2_xreal_1,t38_nat_1,t27_finseq_3,t26_nat_1,t27_finseq_3,t29_nat_1,t7_calcul_2,d13_finseq_1,t1_xreal_1,t26_nat_1,s1_nat_1]),
    [file(calcul_2,t13_calcul_2),interesting(0.43)]).

fof(t30_calcul_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] : 
          ( m2_finseq_1(B,k7_cqc_lang)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k4_relset_1(k5_numbers,k7_cqc_lang,B),k4_relset_1(k5_numbers,k7_cqc_lang,B))
                & v3_funct_2(C,k4_relset_1(k5_numbers,k7_cqc_lang,B),k4_relset_1(k5_numbers,k7_cqc_lang,B))
                & m2_relset_1(C,k4_relset_1(k5_numbers,k7_cqc_lang,B),k4_relset_1(k5_numbers,k7_cqc_lang,B)) )
             => ( r4_calcul_1(k8_finseq_1(k7_cqc_lang,B,k12_finseq_1(k7_cqc_lang,A)))
               => r4_calcul_1(k8_finseq_1(k7_cqc_lang,k3_calcul_2(k7_cqc_lang,B,C),k12_finseq_1(k7_cqc_lang,A))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t20_calcul_2,t45_finseq_1,t10_calcul_1,t28_calcul_2,t29_calcul_2]),
    [file(calcul_2,t30_calcul_2),interesting(0.35)]).

fof(t16_calcul_2,theorem,(
    ! [A] : 
      ( m2_finseq_1(A,k7_cqc_lang)
     => ! [B] : 
          ( m2_finseq_1(B,k7_cqc_lang)
         => k15_finseq_1(k8_relset_1(k5_numbers,k7_cqc_lang,k8_finseq_1(k7_cqc_lang,A,B),k2_calcul_2(k3_finseq_1(A),k3_finseq_1(B)))) = k7_relset_1(k5_numbers,k5_numbers,k5_numbers,k7_cqc_lang,k14_finseq_1(k2_calcul_2(k3_finseq_1(A),k3_finseq_1(B))),k8_finseq_1(k7_cqc_lang,A,B)) ) ) ),
    inference(mizar_proof,[status(thm)],[d14_finseq_1,t15_calcul_2,t12_calcul_2,t2_funct_4]),
    [file(calcul_2,t16_calcul_2),interesting(0.33)]).

fof(t9_calcul_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) )
         => k2_finseq_1(k3_finseq_1(k7_finseq_1(A,B))) = k4_subset_1(k5_numbers,k2_finseq_1(k3_finseq_1(A)),k2_calcul_2(k3_finseq_1(A),k3_finseq_1(B))) ) ) ),
    inference(mizar_proof,[status(thm)],[t3_finseq_1,t3_finseq_1,t7_xboole_1,t35_finseq_1,t38_nat_1,t7_xboole_1,d3_tarski,d10_xboole_0,d3_tarski,t3_finseq_1,t6_calcul_1,t2_xreal_1,t3_finseq_1,t1_calcul_2,t35_finseq_1,t29_nat_1,t2_xreal_1,t3_finseq_1,d2_xboole_0]),
    [file(calcul_2,t9_calcul_2),interesting(0.33)]).

fof(t19_calcul_2,theorem,(
    ! [A] : 
      ( m2_finseq_1(A,k7_cqc_lang)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k4_relset_1(k5_numbers,k7_cqc_lang,A),k4_relset_1(k5_numbers,k7_cqc_lang,A))
            & v3_funct_2(B,k4_relset_1(k5_numbers,k7_cqc_lang,A),k4_relset_1(k5_numbers,k7_cqc_lang,A))
            & m2_relset_1(B,k4_relset_1(k5_numbers,k7_cqc_lang,A),k4_relset_1(k5_numbers,k7_cqc_lang,A)) )
         => k4_relset_1(k5_numbers,k7_cqc_lang,k3_calcul_2(k7_cqc_lang,A,B)) = k4_relset_1(k5_numbers,k7_cqc_lang,A) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_funct_2,d3_funct_2,t46_relat_1,t67_funct_2]),
    [file(calcul_2,t19_calcul_2),interesting(0.28)]).

fof(t5_calcul_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] : 
          ( m2_finseq_1(B,k7_cqc_lang)
         => ( k2_calcul_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,B,k12_finseq_1(k7_cqc_lang,A))) = A
            & k1_calcul_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,B,k12_finseq_1(k7_cqc_lang,A))) = B ) ) ) ),
    file(calcul_1,t5_calcul_1),
    [interesting(0.00)]).

fof(d14_finseq_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_finseq_1(A) )
     => k15_finseq_1(A) = k5_relat_1(k14_finseq_1(k1_relat_1(A)),A) ) ),
    file(finseq_1,d14_finseq_1),
    [interesting(0.00)]).

fof(t90_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => k1_relat_1(k7_relat_1(B,A)) = k3_xboole_0(k1_relat_1(B),A) ) ),
    file(relat_1,t90_relat_1),
    [interesting(0.00)]).

fof(d21_ordinal2,definition,(
    ! [A] : 
      ( v4_ordinal2(A)
    <=> r2_hidden(A,k5_ordinal2) ) ),
    file(ordinal2,d21_ordinal2),
    [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(t2_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(B,C) )
               => r1_xreal_0(A,C) ) ) ) ) ),
    file(xreal_1,t2_xreal_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(t27_finseq_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( r2_hidden(B,k4_finseq_1(A))
          <=> ( r1_xreal_0(1,B)
              & r1_xreal_0(B,k3_finseq_1(A)) ) ) ) ) ),
    file(finseq_3,t27_finseq_3),
    [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(t28_xboole_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => k3_xboole_0(A,B) = A ) ),
    file(xboole_1,t28_xboole_1),
    [interesting(0.00)]).

fof(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(d13_finseq_1,definition,(
    ! [A] : 
      ( ? [B] : 
          ( v4_ordinal2(B)
          & r1_tarski(A,k2_finseq_1(B)) )
     => ! [B] : 
          ( m2_finseq_1(B,k5_numbers)
         => ( B = k14_finseq_1(A)
          <=> ( k2_relat_1(B) = A
              & ! [C] : 
                  ( v4_ordinal2(C)
                 => ! [D] : 
                      ( v4_ordinal2(D)
                     => ! [E] : 
                          ( v4_ordinal2(E)
                         => ! [F] : 
                              ( v4_ordinal2(F)
                             => ~ ( r1_xreal_0(1,C)
                                  & ~ r1_xreal_0(D,C)
                                  & r1_xreal_0(D,k3_finseq_1(B))
                                  & E = k1_funct_1(B,C)
                                  & F = k1_funct_1(B,D)
                                  & r1_xreal_0(F,E) ) ) ) ) ) ) ) ) ) ),
    file(finseq_1,d13_finseq_1),
    [interesting(0.00)]).

fof(t2_funct_4,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => k5_relat_1(B,A) = k5_relat_1(B,k7_relat_1(A,k2_relat_1(B))) ) ) ),
    file(funct_4,t2_funct_4),
    [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(t38_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( ~ r1_xreal_0(k2_xcmplx_0(B,1),A)
          <=> r1_xreal_0(A,B) ) ) ) ),
    file(nat_1,t38_nat_1),
    [interesting(0.00)]).

fof(t9_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ! [D] : 
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => r1_xreal_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,D)) ) ) ) ) ) ),
    file(xreal_1,t9_xreal_1),
    [interesting(0.00)]).

fof(t8_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(k2_xcmplx_0(A,C),k2_xcmplx_0(B,C)) ) ) ) ) ),
    file(xreal_1,t8_xreal_1),
    [interesting(0.00)]).

fof(t22_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ~ ( A != 0
          & ! [B] : 
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => A != k1_nat_1(B,1) ) ) ) ),
    file(nat_1,t22_nat_1),
    [interesting(0.00)]).

fof(d2_xboole_0,definition,(
    ! [A,B,C] : 
      ( C = k2_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            | r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d2_xboole_0),
    [interesting(0.00)]).

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

fof(d10_xboole_0,definition,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    [interesting(0.00)]).

fof(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(t52_card_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k1_ordinal1(A) = k1_nat_1(A,1) ) ),
    file(card_1,t52_card_1),
    [interesting(0.00)]).

fof(d1_ordinal1,definition,(
    ! [A] : k1_ordinal1(A) = k2_xboole_0(A,k1_tarski(A)) ),
    file(ordinal1,d1_ordinal1),
    [interesting(0.00)]).

fof(t48_card_1,theorem,(
    ! [A,B] : 
      ( r2_wellord2(A,k1_tarski(B))
    <=> ? [C] : A = k1_tarski(C) ) ),
    file(card_1,t48_card_1),
    [interesting(0.00)]).

fof(t3_xboole_0,theorem,(
    ! [A,B] : 
      ( ~ ( ~ r1_xboole_0(A,B)
          & ! [C] : ~ ( r2_hidden(C,A)
              & r2_hidden(C,B) ) )
      & ~ ( ? [C] : 
              ( r2_hidden(C,A)
              & r2_hidden(C,B) )
          & r1_xboole_0(A,B) ) ) ),
    file(xboole_0,t3_xboole_0),
    [interesting(0.00)]).

fof(t58_card_1,theorem,(
    ! [A,B,C,D] : 
      ( ( r1_xboole_0(A,B)
        & r1_xboole_0(C,D)
        & r2_wellord2(A,C)
        & r2_wellord2(B,D) )
     => r2_wellord2(k2_xboole_0(A,B),k2_xboole_0(C,D)) ) ),
    file(card_1,t58_card_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(t81_card_1,theorem,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( v1_finset_1(B)
         => ( r2_wellord2(A,B)
           => k4_card_1(A) = k4_card_1(B) ) ) ) ),
    file(card_1,t81_card_1),
    [interesting(0.00)]).

fof(t78_finseq_1,theorem,
    ( ! [A] : 
        ( v4_ordinal2(A)
       => k4_card_1(k2_finseq_1(A)) = A )
    & ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ( k4_card_1(A) = A
          & k4_card_1(k1_card_1(A)) = A ) ) ),
    file(finseq_1,t78_finseq_1),
    [interesting(0.00)]).

fof(t44_finseq_3,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v1_finset_1(B)
         => ( r1_tarski(B,k2_finseq_1(A))
           => k3_finseq_1(k14_finseq_1(B)) = k4_card_1(B) ) ) ) ),
    file(finseq_3,t44_finseq_3),
    [interesting(0.00)]).

fof(t31_finseq_3,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(A) = k3_finseq_1(B)
          <=> k4_finseq_1(A) = k4_finseq_1(B) ) ) ) ),
    file(finseq_3,t31_finseq_3),
    [interesting(0.00)]).

fof(t23_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(B))
           => k1_funct_1(k5_relat_1(B,C),A) = k1_funct_1(C,k1_funct_1(B,A)) ) ) ) ),
    file(funct_1,t23_funct_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_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 ) ) ) ) ),
    file(finseq_2,t11_finseq_2),
    [interesting(0.00)]).

fof(t1_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & r1_xreal_0(B,A) )
           => A = B ) ) ) ),
    file(xreal_1,t1_xreal_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(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(d4_calcul_1,definition,(
    ! [A] : 
      ( m2_finseq_1(A,k7_cqc_lang)
     => ! [B] : 
          ( m2_finseq_1(B,k7_cqc_lang)
         => ( r2_calcul_1(A,B)
          <=> ? [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(k5_numbers))
                & r1_tarski(A,k15_finseq_1(k8_relset_1(k5_numbers,k7_cqc_lang,B,C))) ) ) ) ) ),
    file(calcul_1,d4_calcul_1),
    [interesting(0.00)]).

fof(t36_calcul_1,theorem,(
    ! [A] : 
      ( m2_finseq_1(A,k7_cqc_lang)
     => ! [B] : 
          ( m2_finseq_1(B,k7_cqc_lang)
         => ( ( r2_calcul_1(k1_calcul_1(k7_cqc_lang,A),k1_calcul_1(k7_cqc_lang,B))
              & k2_calcul_1(k7_cqc_lang,A) = k2_calcul_1(k7_cqc_lang,B)
              & r4_calcul_1(A) )
           => r4_calcul_1(B) ) ) ) ),
    file(calcul_1,t36_calcul_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(t10_calcul_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( r1_xreal_0(1,k3_finseq_1(k7_finseq_1(B,k9_finseq_1(A))))
        & r2_hidden(k3_finseq_1(k7_finseq_1(B,k9_finseq_1(A))),k1_relat_1(k7_finseq_1(B,k9_finseq_1(A)))) ) ) ),
    file(calcul_1,t10_calcul_1),
    [interesting(0.00)]).

fof(d3_finseq_5,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) )
         => ( B = k3_finseq_5(A)
          <=> ( k3_finseq_1(B) = k3_finseq_1(A)
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r2_hidden(C,k4_finseq_1(B))
                   => k1_funct_1(B,C) = k1_funct_1(A,k2_xcmplx_0(k6_xcmplx_0(k3_finseq_1(A),C),1)) ) ) ) ) ) ) ),
    file(finseq_5,d3_finseq_5),
    [interesting(0.00)]).

fof(d4_calcul_2,definition,(
    ! [A] : 
      ( m2_finseq_1(A,k7_cqc_lang)
     => ( r1_xreal_0(1,k3_finseq_1(A))
       => ! [B] : 
            ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
           => ( B = k5_calcul_2(A)
            <=> ? [C] : 
                  ( m2_finseq_1(C,k7_cqc_lang)
                  & B = k1_funct_1(C,k3_finseq_1(A))
                  & k3_finseq_1(C) = k3_finseq_1(A)
                  & ( k1_funct_1(C,1) = k4_calcul_2(A)
                    | k3_finseq_1(A) = 0 )
                  & ! [D] : 
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ~ ( r1_xreal_0(1,D)
                          & ~ r1_xreal_0(k3_finseq_1(A),D)
                          & ! [E] : 
                              ( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
                             => ! [F] : 
                                  ( m2_subset_1(F,k8_qc_lang1,k7_cqc_lang)
                                 => ~ ( E = k1_funct_1(A,k1_nat_1(D,1))
                                      & F = k1_funct_1(C,D)
                                      & k1_funct_1(C,k1_nat_1(D,1)) = k12_cqc_lang(E,F) ) ) ) ) ) ) ) ) ) ) ),
    file(calcul_2,d4_calcul_2),
    [interesting(0.00)]).

fof(t6_calcul_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_xreal_0(k3_finseq_1(A),k3_finseq_1(k7_finseq_1(A,B)))
            & r1_xreal_0(k3_finseq_1(B),k3_finseq_1(k7_finseq_1(A,B)))
            & ( A != k1_xboole_0
             => ( r1_xreal_0(1,k3_finseq_1(A))
                & ~ r1_xreal_0(k3_finseq_1(k7_finseq_1(B,A)),k3_finseq_1(B)) ) ) ) ) ) ),
    file(calcul_1,t6_calcul_1),
    [interesting(0.00)]).

fof(t28_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ~ ( r1_xreal_0(A,B)
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => B != k2_xcmplx_0(A,C) ) ) ) ) ),
    file(nat_1,t28_nat_1),
    [interesting(0.00)]).

fof(t23_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B,C] : 
          ( m2_finseq_1(C,B)
         => m2_finseq_1(k7_relat_1(C,k2_finseq_1(A)),B) ) ) ),
    file(finseq_1,t23_finseq_1),
    [interesting(0.00)]).

fof(d3_calcul_2,definition,(
    ! [A] : 
      ( m2_finseq_1(A,k7_cqc_lang)
     => ! [B] : 
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ( ( r1_xreal_0(1,k3_finseq_1(A))
             => ( B = k4_calcul_2(A)
              <=> B = k1_funct_1(A,1) ) )
            & ( ~ r1_xreal_0(1,k3_finseq_1(A))
             => ( B = k4_calcul_2(A)
              <=> B = k9_cqc_lang ) ) ) ) ) ),
    file(calcul_2,d3_calcul_2),
    [interesting(0.00)]).

fof(t65_finseq_5,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( k1_funct_1(A,1) = k1_funct_1(k3_finseq_5(A),k3_finseq_1(A))
        & k1_funct_1(A,k3_finseq_1(A)) = k1_funct_1(k3_finseq_5(A),1) ) ) ),
    file(finseq_5,t65_finseq_5),
    [interesting(0.00)]).

fof(t11_finseq_5,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(k1_nat_1(A,1),k4_finseq_1(B))
                  & C = k7_relat_1(B,k2_finseq_1(A)) )
               => k7_relat_1(B,k2_finseq_1(k1_nat_1(A,1))) = k7_finseq_1(C,k9_finseq_1(k1_funct_1(B,k1_nat_1(A,1)))) ) ) ) ) ),
    file(finseq_5,t11_finseq_5),
    [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(t98_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => k7_relat_1(A,k1_relat_1(A)) = A ) ),
    file(relat_1,t98_relat_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(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) ) ) ) ),
    file(finseq_2,t13_finseq_2),
    [interesting(0.00)]).

fof(t60_finseq_5,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( k4_finseq_1(A) = k4_finseq_1(k3_finseq_5(A))
        & k2_relat_1(A) = k2_relat_1(k3_finseq_5(A)) ) ) ),
    file(finseq_5,t60_finseq_5),
    [interesting(0.00)]).

fof(t61_finseq_5,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( r2_hidden(A,k4_finseq_1(B))
           => k1_funct_1(k3_finseq_5(B),A) = k1_funct_1(B,k2_xcmplx_0(k6_xcmplx_0(k3_finseq_1(B),A),1)) ) ) ) ),
    file(finseq_5,t61_finseq_5),
    [interesting(0.00)]).

fof(t10_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ! [D] : 
                  ( v1_xreal_0(D)
                 => ~ ( ~ r1_xreal_0(B,A)
                      & r1_xreal_0(C,D)
                      & r1_xreal_0(k2_xcmplx_0(B,D),k2_xcmplx_0(A,C)) ) ) ) ) ) ),
    file(xreal_1,t10_xreal_1),
    [interesting(0.00)]).

fof(t16_int_1,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ( r1_xreal_0(0,A)
       => r2_hidden(A,k5_numbers) ) ) ),
    file(int_1,t16_int_1),
    [interesting(0.00)]).

fof(t20_int_1,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ! [B] : 
          ( v1_int_1(B)
         => ( ~ r1_xreal_0(B,A)
           => r1_xreal_0(k2_xcmplx_0(A,1),B) ) ) ) ),
    file(int_1,t20_int_1),
    [interesting(0.00)]).

fof(t22_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( r1_xreal_0(A,k2_xcmplx_0(B,C))
              <=> r1_xreal_0(k6_xcmplx_0(A,B),C) ) ) ) ) ),
    file(xreal_1,t22_xreal_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(d3_calcul_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ! [C] : 
              ( m2_finseq_1(C,A)
             => ( r1_calcul_1(A,B,C)
              <=> ? [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                    & r2_hidden(D,k4_relset_1(k5_numbers,A,C))
                    & k1_funct_1(C,D) = B ) ) ) ) ) ),
    file(calcul_1,d3_calcul_1),
    [interesting(0.00)]).

fof(t33_calcul_1,theorem,(
    ! [A] : 
      ( m2_finseq_1(A,k7_cqc_lang)
     => ( r1_calcul_1(k7_cqc_lang,k2_calcul_1(k7_cqc_lang,A),k1_calcul_1(k7_cqc_lang,A))
       => r4_calcul_1(A) ) ) ),
    file(calcul_1,t33_calcul_1),
    [interesting(0.00)]).

fof(t40_calcul_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] : 
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] : 
              ( m2_finseq_1(C,k7_cqc_lang)
             => ( ( k11_cqc_lang(A,B) = k2_calcul_1(k7_cqc_lang,C)
                  & r4_calcul_1(C) )
               => r4_calcul_1(k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,C),k12_finseq_1(k7_cqc_lang,A))) ) ) ) ) ),
    file(calcul_1,t40_calcul_1),
    [interesting(0.00)]).

fof(t22_calcul_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] : 
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] : 
              ( m2_finseq_1(C,k7_cqc_lang)
             => ( r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,k11_cqc_lang(A,B))))
               => r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,A))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t5_calcul_1,t40_calcul_1,t5_calcul_1]),
    [file(calcul_2,t22_calcul_2),interesting(0.00)]).

fof(t13_calcul_1,theorem,(
    ! [A] : 
      ( m2_finseq_1(A,k7_cqc_lang)
     => ! [B] : 
          ( m2_finseq_1(B,k7_cqc_lang)
         => ( ~ r1_xreal_0(k3_finseq_1(A),0)
           => r2_calcul_1(A,k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,A),B),k12_finseq_1(k7_cqc_lang,k2_calcul_1(k7_cqc_lang,A)))) ) ) ) ),
    file(calcul_1,t13_calcul_1),
    [interesting(0.00)]).

fof(t45_calcul_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] : 
          ( m2_finseq_1(B,k7_cqc_lang)
         => ( ( r1_xreal_0(1,k3_finseq_1(B))
              & r4_calcul_1(B)
              & r4_calcul_1(k8_finseq_1(k7_cqc_lang,B,k12_finseq_1(k7_cqc_lang,A))) )
           => r4_calcul_1(k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,B),k12_finseq_1(k7_cqc_lang,A))) ) ) ) ),
    file(calcul_1,t45_calcul_1),
    [interesting(0.00)]).

fof(t24_calcul_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] : 
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] : 
              ( m2_finseq_1(C,k7_cqc_lang)
             => ( ( r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,A)))
                  & r4_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,A)),k12_finseq_1(k7_cqc_lang,B))) )
               => r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,B))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t10_calcul_1,t45_calcul_1,t5_calcul_1]),
    [file(calcul_2,t24_calcul_2),interesting(0.00)]).

fof(t41_calcul_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] : 
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] : 
              ( m2_finseq_1(C,k7_cqc_lang)
             => ( ( k11_cqc_lang(A,B) = k2_calcul_1(k7_cqc_lang,C)
                  & r4_calcul_1(C) )
               => r4_calcul_1(k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,C),k12_finseq_1(k7_cqc_lang,B))) ) ) ) ) ),
    file(calcul_1,t41_calcul_1),
    [interesting(0.00)]).

fof(t23_calcul_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] : 
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] : 
              ( m2_finseq_1(C,k7_cqc_lang)
             => ( r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,k11_cqc_lang(A,B))))
               => r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,B))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t5_calcul_1,t41_calcul_1,t5_calcul_1]),
    [file(calcul_2,t23_calcul_2),interesting(0.00)]).

fof(t44_calcul_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] : 
          ( m2_finseq_1(B,k7_cqc_lang)
         => ( ( r4_calcul_1(B)
              & r4_calcul_1(k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,B),k12_finseq_1(k7_cqc_lang,k10_cqc_lang(k2_calcul_1(k7_cqc_lang,B))))) )
           => r4_calcul_1(k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,B),k12_finseq_1(k7_cqc_lang,A))) ) ) ) ),
    file(calcul_1,t44_calcul_1),
    [interesting(0.00)]).

fof(t25_calcul_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] : 
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] : 
              ( m2_finseq_1(C,k7_cqc_lang)
             => ( ( r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,A)))
                  & r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,k10_cqc_lang(A)))) )
               => r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,B))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t5_calcul_1,t44_calcul_1]),
    [file(calcul_2,t25_calcul_2),interesting(0.00)]).

fof(t9_calcul_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C)
        & v1_finseq_1(C) )
     => ~ r1_xreal_0(k3_finseq_1(k7_finseq_1(k7_finseq_1(C,k9_finseq_1(A)),k9_finseq_1(B))),1) ) ),
    file(calcul_1,t9_calcul_1),
    [interesting(0.00)]).

fof(t37_calcul_1,theorem,(
    ! [A] : 
      ( m2_finseq_1(A,k7_cqc_lang)
     => ! [B] : 
          ( m2_finseq_1(B,k7_cqc_lang)
         => ( ( k1_calcul_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,A)) = k1_calcul_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,B))
              & k10_cqc_lang(k2_calcul_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,A))) = k2_calcul_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,B))
              & k2_calcul_1(k7_cqc_lang,A) = k2_calcul_1(k7_cqc_lang,B)
              & r4_calcul_1(A)
              & r4_calcul_1(B) )
           => ( r1_xreal_0(k3_finseq_1(A),1)
              | r1_xreal_0(k3_finseq_1(B),1)
              | r4_calcul_1(k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,A)),k12_finseq_1(k7_cqc_lang,k2_calcul_1(k7_cqc_lang,A)))) ) ) ) ) ),
    file(calcul_1,t37_calcul_1),
    [interesting(0.00)]).

fof(t26_calcul_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] : 
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] : 
              ( m2_finseq_1(C,k7_cqc_lang)
             => ( ( r4_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,A)),k12_finseq_1(k7_cqc_lang,B)))
                  & r4_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,k10_cqc_lang(A))),k12_finseq_1(k7_cqc_lang,B))) )
               => r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,B))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t5_calcul_1,t5_calcul_1,t5_calcul_1,t5_calcul_1,t9_calcul_1,t5_calcul_1,t37_calcul_1]),
    [file(calcul_2,t26_calcul_2),interesting(0.00)]).

fof(d2_qc_lang2,definition,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] : 
          ( m1_subset_1(B,k8_qc_lang1)
         => k2_qc_lang2(A,B) = k12_qc_lang1(k13_qc_lang1(A,k12_qc_lang1(B))) ) ) ),
    file(qc_lang2,d2_qc_lang2),
    [interesting(0.00)]).

fof(t33_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) )
         => A = k7_relat_1(k7_finseq_1(A,B),k4_finseq_1(A)) ) ) ),
    file(finseq_1,t33_finseq_1),
    [interesting(0.00)]).

fof(t31_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,0)
              & r1_xreal_0(k2_xcmplx_0(B,A),B) ) ) ) ),
    file(xreal_1,t31_xreal_1),
    [interesting(0.00)]).

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

fof(d4_funct_2,definition,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ( v3_funct_2(C,A,B)
      <=> ( v2_funct_1(C)
          & v2_funct_2(C,A,B) ) ) ) ),
    file(funct_2,d4_funct_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(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(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(t56_calcul_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] : 
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] : 
              ( m2_finseq_1(C,k7_cqc_lang)
             => ( ( r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,k12_cqc_lang(A,B))))
                  & r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,A))) )
               => r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,B))) ) ) ) ) ),
    file(calcul_1,t56_calcul_1),
    [interesting(0.00)]).

fof(t29_calcul_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] : 
          ( m2_finseq_1(B,k7_cqc_lang)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k4_relset_1(k5_numbers,k7_cqc_lang,B),k4_relset_1(k5_numbers,k7_cqc_lang,B))
                & v3_funct_2(C,k4_relset_1(k5_numbers,k7_cqc_lang,B),k4_relset_1(k5_numbers,k7_cqc_lang,B))
                & m2_relset_1(C,k4_relset_1(k5_numbers,k7_cqc_lang,B),k4_relset_1(k5_numbers,k7_cqc_lang,B)) )
             => ( r4_calcul_1(k8_finseq_1(k7_cqc_lang,k3_calcul_2(k7_cqc_lang,B,C),k12_finseq_1(k7_cqc_lang,k5_calcul_2(k4_finseq_5(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,B,k12_finseq_1(k7_cqc_lang,A)))))))
               => r4_calcul_1(k8_finseq_1(k7_cqc_lang,k3_calcul_2(k7_cqc_lang,B,C),k12_finseq_1(k7_cqc_lang,A))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t10_calcul_1,d3_finseq_5,d4_calcul_2,d3_finseq_5,t27_finseq_3,t13_finseq_2,t60_finseq_5,t61_finseq_5,t38_nat_1,t38_nat_1,t27_finseq_3,t60_finseq_5,d3_finseq_5,t10_xreal_1,t16_int_1,t38_nat_1,t31_xreal_1,t10_xreal_1,t61_finseq_5,t38_nat_1,t27_finseq_3,t60_finseq_5,t61_finseq_5,d3_finseq_5,t31_xreal_1,t10_xreal_1,t35_finseq_1,t56_finseq_1,t38_nat_1,t27_finseq_3,t72_funct_1,d4_funct_2,d3_funct_2,d5_funct_1,d3_finseq_1,t19_calcul_2,t5_calcul_1,t33_finseq_1,t23_funct_1,t5_calcul_1,t5_calcul_1,d3_calcul_1,t33_calcul_1,t56_calcul_1,t27_finseq_3,t60_finseq_5,t61_finseq_5,s1_nat_1,d3_finseq_5,d3_finseq_5,t65_finseq_5,d3_calcul_2,t65_finseq_5,t35_finseq_1,t56_finseq_1,t59_finseq_1]),
    [file(calcul_2,t29_calcul_2),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(t69_finseq_2,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : k3_finseq_1(k2_finseq_2(A,B)) = A ) ),
    file(finseq_2,t69_finseq_2),
    [interesting(0.00)]).

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 ) ) ),
    file(finseq_2,t70_finseq_2),
    [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(t7_xboole_1,theorem,(
    ! [A,B] : r1_tarski(A,k2_xboole_0(A,B)) ),
    file(xboole_1,t7_xboole_1),
    [interesting(0.00)]).