fof(t8_pre_circ,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B,C] : 
          ( ( v2_relat_1(C)
            & m1_pboole(C,A) )
         => ! [D] : 
              ( m3_pboole(D,A,k2_pre_circ(A,B),C)
             => k1_relat_1(k10_funct_6(D)) = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_pboole,t65_relat_1,d3_tarski,d5_funct_1,t13_funcop_1,d18_pboole,t57_partfun1,d1_tarski,t39_zfmisc_1,t15_funcop_1,d12_funct_6,t7_pre_circ,t49_funct_5,t60_relat_1,t6_pre_circ,t11_funct_2,d3_tarski,d5_funct_1,t13_funcop_1,d18_pboole,d16_pboole,d1_funct_2,t12_relset_1,d5_funct_1,t92_zfmisc_1,t1_xboole_1,d2_funct_2,d2_funct_2,t85_funct_6,t121_funct_2,d1_funct_2]),
    [file(pre_circ,t8_pre_circ),interesting(1.00)]).

fof(t7_pre_circ,theorem,(
    ! [A] : k4_funct_5(k2_pre_circ(A,k1_xboole_0)) = k1_xboole_0 ),
    inference(mizar_proof,[status(thm)],[t16_funcop_1,t50_funct_5,t64_relat_1,t14_funcop_1,t64_funct_5,t33_funct_5,t113_zfmisc_1,t64_relat_1]),
    [file(pre_circ,t7_pre_circ),interesting(0.89)]).

fof(t21_pre_circ,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => k1_card_1(A) = k1_card_1(k1_relat_1(A)) ) ),
    inference(mizar_proof,[status(thm)],[s3_funct_1,d4_wellord2,d8_funct_1,t33_zfmisc_1,d3_tarski,d5_funct_1,t8_funct_1,d10_xboole_0,d3_tarski,d1_relat_1,t8_funct_1,d5_funct_1,t21_card_1]),
    [file(pre_circ,t21_pre_circ),interesting(0.87)]).

fof(t3_pre_circ,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r1_tarski(A,B)
               => r1_tarski(k1_funct_4(A,C),k1_funct_4(B,C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t25_relat_1,d1_funct_4,t9_xboole_1,t13_funct_4,t14_funct_4,t14_funct_4,t12_funct_4,t12_funct_4,t8_grfunc_1,t8_grfunc_1]),
    [file(pre_circ,t3_pre_circ),interesting(0.86)]).

fof(t13_pre_circ,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( m1_trees_1(B,A)
         => r2_tarski(k4_trees_1(A,B),a_2_0_pre_circ(A,B)) ) ) ),
    inference(mizar_proof,[status(thm)],[s4_funct_1,d4_wellord2,d8_funct_1,t46_finseq_1,d3_tarski,d5_funct_1,d9_trees_1,t8_trees_1,d10_xboole_0,d3_tarski,t8_trees_1,t50_finseq_1,d9_trees_1,d5_funct_1]),
    [file(pre_circ,t13_pre_circ),interesting(0.85)]).

fof(t23_pre_circ,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A)
        & v3_trees_2(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finset_1(B)
            & v3_trees_2(B) )
         => ! [C] : 
              ( m1_trees_1(C,k1_relat_1(A))
             => k1_nat_1(k4_card_1(k8_trees_2(A,C,B)),k4_card_1(k5_trees_2(A,C))) = k1_nat_1(k4_card_1(A),k4_card_1(B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_trees_2,d12_trees_2,t21_pre_circ,t21_pre_circ,t22_pre_circ]),
    [file(pre_circ,t23_pre_circ),interesting(0.81)]).

fof(t4_pre_circ,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( ( r1_tarski(A,B)
                  & r1_xboole_0(k1_relat_1(A),k1_relat_1(C)) )
               => r1_tarski(A,k1_funct_4(B,C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t3_pre_circ,t33_funct_4,t1_xboole_1]),
    [file(pre_circ,t4_pre_circ),interesting(0.80)]).

fof(t6_pre_circ,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v2_relat_1(B)
            & m1_pboole(B,A) )
         => ~ v1_xboole_0(k3_tarski(k2_relat_1(B))) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_pboole,d5_funct_1,t91_orders_1]),
    [file(pre_circ,t6_pre_circ),interesting(0.80)]).

fof(t22_pre_circ,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_finset_1(B)
            & v1_trees_1(B) )
         => ! [C] : 
              ( m1_trees_1(C,A)
             => k1_nat_1(k4_card_1(k5_trees_1(A,C,B)),k4_card_1(k4_trees_1(A,C))) = k1_nat_1(k4_card_1(A),k4_card_1(B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s7_domain_1,s7_domain_1,t14_pre_circ,t4_xboole_0,d3_xboole_0,d3_xboole_0,t8_trees_1,d2_xboole_0,t4_xboole_0,d3_xboole_0,s4_funct_1,d4_wellord2,d8_funct_1,t46_finseq_1,d3_tarski,d5_funct_1,d5_trees_1,d10_xboole_0,d3_tarski,d5_funct_1,t68_card_1,t81_card_1,t13_pre_circ,t81_card_1,t53_card_2,t1_xcmplx_1,t53_card_2]),
    [file(pre_circ,t22_pre_circ),interesting(0.79)]).

fof(s1_pre_circ,theorem,(
    v1_finset_1(a_0_0_pre_circ) ),
    inference(mizar_proof,[status(thm)],[s21_fraenkel,d3_tarski,t13_finset_1]),
    [file(pre_circ,s1_pre_circ),interesting(0.77)]).

fof(t11_pre_circ,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ! [D] : 
              ( ( v1_relat_1(D)
                & v1_funct_1(D) )
             => ( r2_hidden(C,k4_card_3(B))
               => r2_hidden(k5_relat_1(D,C),k4_card_3(k5_relat_1(D,B))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_card_3,t3_funcop_1,t21_funct_1,t23_funct_1,d5_card_3]),
    [file(pre_circ,t11_pre_circ),interesting(0.70)]).

fof(t24_pre_circ,theorem,(
    ! [A] : k4_card_1(k1_trees_4(A)) = 1 ),
    inference(mizar_proof,[status(thm)],[t6_trees_4,t79_card_1]),
    [file(pre_circ,t24_pre_circ),interesting(0.68)]).

fof(t12_pre_circ,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : k4_card_3(k2_finseq_2(A,k1_tarski(B))) = k1_tarski(k2_finseq_2(A,B)) ) ),
    inference(mizar_proof,[status(thm)],[d5_card_3,t68_finseq_2,t70_finseq_2,d1_tarski,t17_funcop_1,d2_finseq_2,t68_finseq_2,t68_finseq_2,t68_finseq_2,t70_finseq_2,d1_tarski,t18_card_3,d1_tarski]),
    [file(pre_circ,t12_pre_circ),interesting(0.67)]).

fof(t14_pre_circ,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_finset_1(B)
            & v1_trees_1(B) )
         => ! [C] : 
              ( m1_trees_1(C,A)
             => k5_trees_1(A,C,B) = k2_xboole_0(a_2_1_pre_circ(A,C),a_3_0_pre_circ(A,B,C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s3_fraenkel,d8_xboole_0,d1_tarski,d1_tarski,d8_xboole_0,d2_xboole_0,t47_finseq_1,t47_trees_1,t64_trees_1,t4_xboole_1,t46_zfmisc_1]),
    [file(pre_circ,t14_pre_circ),interesting(0.67)]).

fof(t10_pre_circ,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v2_relat_1(C)
                & m1_pboole(C,A) )
             => ! [D] : 
                  ( m3_pboole(D,A,k2_pre_circ(A,B),C)
                 => ! [E] : 
                      ( m1_subset_1(E,B)
                     => ? [F] : 
                          ( m1_pboole(F,A)
                          & F = k1_funct_1(k10_funct_6(D),E)
                          & r3_pboole(A,F,C) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d12_funct_6,d3_pboole,d3_tarski,d4_funct_5,d16_pboole,d18_pboole,d1_funct_2,t13_funcop_1,t106_zfmisc_1,d10_xboole_0,d3_tarski,t23_mcart_1,t10_mcart_1,d16_pboole,d18_pboole,d1_funct_2,t13_funcop_1,t10_mcart_1,t45_funct_5,t39_funct_5,d3_pboole,d4_pboole,d16_pboole,t13_funcop_1,d18_pboole,d1_funct_2,t45_funct_5,t7_funct_2]),
    [file(pre_circ,t10_pre_circ),interesting(0.64)]).

fof(t15_pre_circ,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_finset_1(B)
            & v1_trees_1(B) )
         => ! [C] : 
              ( m1_trees_1(C,A)
             => ! [D] : 
                  ( m2_finseq_1(D,k5_numbers)
                 => ~ ( r2_hidden(D,k5_trees_1(A,C,B))
                      & r1_tarski(C,D)
                      & ! [E] : 
                          ( m1_trees_1(E,B)
                         => D != k8_finseq_1(k5_numbers,C,E) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t14_pre_circ,d2_xboole_0]),
    [file(pre_circ,t15_pre_circ),interesting(0.64)]).

fof(t20_pre_circ,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( m1_trees_1(B,A)
         => ~ ( B != k1_xboole_0
              & r1_xreal_0(k4_card_1(A),k4_card_1(k4_trees_1(A,B))) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_finseq_1,s4_funct_1,d4_wellord2,d8_funct_1,t46_finseq_1,d3_tarski,d5_funct_1,d5_trees_1,d10_xboole_0,d3_tarski,d5_funct_1,t68_card_1,d3_tarski,d9_trees_1,t47_trees_1,t48_finseq_1,d8_xboole_0,t81_card_1,t67_card_2]),
    [file(pre_circ,t20_pre_circ),interesting(0.62)]).

fof(t5_pre_circ,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => k1_funct_1(k6_pboole(A,B),k6_finseq_1(A)) = k1_tarski(k1_xboole_0) ) ),
    inference(mizar_proof,[status(thm)],[t66_finseq_1,d19_pboole,t19_card_3,t62_relat_1]),
    [file(pre_circ,t5_pre_circ),interesting(0.62)]).

fof(t2_pre_circ,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( ( k1_relat_1(A) = k1_tarski(B)
            & k2_relat_1(A) = k1_tarski(C) )
         => A = k1_tarski(k4_tarski(B,C)) ) ) ),
    inference(mizar_proof,[status(thm)],[t15_funcop_1,t35_zfmisc_1]),
    [file(pre_circ,t2_pre_circ),interesting(0.56)]).

fof(t9_pre_circ,theorem,(
    ! [A,B] : 
      ( ( v2_relat_1(B)
        & m1_pboole(B,A) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ! [D] : 
              ( m1_subset_1(D,k4_card_3(B))
             => ( ( r1_tarski(k1_relat_1(C),k1_relat_1(B))
                  & ! [E] : 
                      ( r2_hidden(E,k1_relat_1(C))
                     => r2_hidden(k1_funct_1(C,E),k1_funct_1(B,E)) ) )
               => m1_subset_1(k1_funct_4(D,C),k4_card_3(B)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_4,t18_card_3,t12_xboole_1,t14_funct_4,t12_funct_4,d5_card_3,t18_card_3]),
    [file(pre_circ,t9_pre_circ),interesting(0.56)]).

fof(s2_pre_circ,theorem,(
    ? [A] : 
      ( m1_pboole(A,f1_s2_pre_circ)
      & ! [B] : 
          ( m1_subset_1(B,f1_s2_pre_circ)
         => ( r2_hidden(B,f1_s2_pre_circ)
           => ( ( p1_s2_pre_circ(B)
               => k1_funct_1(A,B) = f2_s2_pre_circ(B) )
              & ( ~ p1_s2_pre_circ(B)
               => k1_funct_1(A,B) = f3_s2_pre_circ(B) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s3_pboole]),
    [file(pre_circ,s2_pre_circ),interesting(0.49)]).

fof(t16_pre_circ,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v4_trees_3(A) )
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r2_hidden(k1_nat_1(B,1),k4_finseq_1(A))
           => k4_trees_1(k13_trees_3(A),k12_finseq_1(k5_numbers,B)) = k1_funct_1(A,k1_nat_1(B,1)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t27_finseq_3,t38_nat_1,t52_trees_3]),
    [file(pre_circ,t16_pre_circ),interesting(0.39)]).

fof(t17_pre_circ,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v6_trees_3(A) )
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r2_hidden(k1_nat_1(B,1),k4_finseq_1(A))
           => r2_hidden(k12_finseq_1(k5_numbers,B),k13_trees_3(k2_funct_6(A))) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t27_finseq_3,t31_xreal_1,t2_xreal_1,t39_trees_3,t24_trees_3,t47_trees_1,d3_finseq_1,t8_finseq_1,t47_finseq_1,d15_trees_3]),
    [file(pre_circ,t17_pre_circ),interesting(0.36)]).

fof(t19_pre_circ,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A)
        & v3_trees_2(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finset_1(B)
            & v3_trees_2(B) )
         => ! [C,D] : 
              ( m2_subset_1(D,k1_numbers,k5_numbers)
             => ! [E] : 
                  ( ( v1_relat_1(E)
                    & v1_funct_1(E)
                    & v1_finseq_1(E)
                    & v6_trees_3(E) )
                 => ~ ( r2_hidden(k12_finseq_1(k5_numbers,D),k1_relat_1(A))
                      & A = k4_trees_4(C,E)
                      & ! [F] : 
                          ( ( v1_relat_1(F)
                            & v1_funct_1(F)
                            & v1_finseq_1(F)
                            & v6_trees_3(F) )
                         => ~ ( k8_trees_2(A,k12_finseq_1(k5_numbers,D),B) = k4_trees_4(C,F)
                              & k3_finseq_1(F) = k3_finseq_1(E)
                              & k1_funct_1(F,k1_nat_1(D,1)) = B
                              & ! [G] : 
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ( r2_hidden(G,k4_finseq_1(E))
                                   => ( G = k1_nat_1(D,1)
                                      | k1_funct_1(F,G) = k1_funct_1(E,G) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s2_finseq_1,d3_finseq_1,t31_finseq_3,d1_cqc_lang,t26_trees_3,t26_trees_3,t11_trees_4,t6_trees_1,d8_finseq_1,d8_finseq_1,t29_nat_1,t38_nat_1,t27_finseq_3,d3_finseq_1,d1_cqc_lang,d4_trees_4,d4_trees_4,t40_trees_3,t40_trees_3,t39_trees_3,d1_cqc_lang,t26_trees_3,t31_funct_6,t31_funct_6,t31_funct_6,t18_pre_circ,d4_trees_4,d4_trees_4,t50_finseq_1,t8_trees_1,t2_xcmplx_1,t40_trees_3,t29_nat_1,t38_nat_1,t27_finseq_3,d4_trees_4,t39_trees_3,t39_trees_3,d1_cqc_lang,t26_trees_3,t16_pre_circ,d4_trees_4,t16_pre_circ,t31_funct_6,t31_funct_6,d11_trees_2,d4_trees_4,d11_trees_2,d15_trees_3,d4_trees_4,t66_trees_1,d11_trees_2,t15_pre_circ,d12_trees_2,d1_cqc_lang]),
    [file(pre_circ,t19_pre_circ),interesting(0.28)]).

fof(s4_pre_circ,theorem,
    ( ! [A] : 
        ( m1_subset_1(A,f1_s4_pre_circ)
       => ( r2_hidden(A,f2_s4_pre_circ)
         => ( v1_funct_1(f5_s4_pre_circ(A))
            & v1_funct_2(f5_s4_pre_circ(A),k1_funct_1(f3_s4_pre_circ,A),k1_funct_1(f4_s4_pre_circ,A))
            & m2_relset_1(f5_s4_pre_circ(A),k1_funct_1(f3_s4_pre_circ,A),k1_funct_1(f4_s4_pre_circ,A)) ) ) )
   => ? [A] : 
        ( m3_pboole(A,f2_s4_pre_circ,f3_s4_pre_circ,f4_s4_pre_circ)
        & ! [B] : 
            ( m1_subset_1(B,f1_s4_pre_circ)
           => ( r2_hidden(B,f2_s4_pre_circ)
             => k1_funct_1(A,B) = f5_s4_pre_circ(B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s4_pboole,d6_funcop_1,d3_pboole,d18_pboole]),
    [file(pre_circ,s4_pre_circ),interesting(0.27)]).

fof(t18_pre_circ,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v4_trees_3(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B)
            & v4_trees_3(B) )
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( k3_finseq_1(A) = k3_finseq_1(B)
                  & r2_hidden(k1_nat_1(C,1),k4_finseq_1(A))
                  & ! [D] : 
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r2_hidden(D,k4_finseq_1(A))
                       => ( D = k1_nat_1(C,1)
                          | k1_funct_1(A,D) = k1_funct_1(B,D) ) ) ) )
               => ! [D] : 
                    ( ( ~ v1_xboole_0(D)
                      & v1_trees_1(D) )
                   => ( k1_funct_1(B,k1_nat_1(C,1)) = D
                     => k13_trees_3(B) = k5_trees_1(k13_trees_3(A),k12_finseq_1(k5_numbers,C),D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t27_finseq_3,t38_nat_1,t24_trees_3,t47_trees_1,t47_finseq_1,d15_trees_3,t25_trees_1,t47_trees_1,t50_finseq_1,t2_xcmplx_1,t29_nat_1,t38_nat_1,t27_finseq_3,d15_trees_3,d8_xboole_0,t8_trees_1,t58_finseq_1,t58_finseq_1,d15_trees_3,t47_trees_1,t29_nat_1,t38_nat_1,t27_finseq_3,t24_trees_3,t47_trees_1,d15_trees_3,t8_trees_1,t5_trees_1,d8_xboole_0,t2_xcmplx_1,t29_nat_1,t38_nat_1,t27_finseq_3,d15_trees_3,d15_trees_3,d15_trees_3,d12_trees_1]),
    [file(pre_circ,t18_pre_circ),interesting(0.21)]).

fof(s21_fraenkel,theorem,
    ( v1_finset_1(f2_s21_fraenkel)
   => v1_finset_1(a_0_38_fraenkel) ),
    file(fraenkel,s21_fraenkel),
    [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(t13_finset_1,theorem,(
    ! [A,B] : 
      ( ( r1_tarski(A,B)
        & v1_finset_1(B) )
     => v1_finset_1(A) ) ),
    file(finset_1,t13_finset_1),
    [interesting(0.00)]).

fof(s3_pboole,theorem,
    ( ! [A] : ~ ( r2_hidden(A,f1_s3_pboole)
        & ! [B] : ~ p1_s3_pboole(A,B) )
   => ? [A] : 
        ( m1_pboole(A,f1_s3_pboole)
        & ! [B] : 
            ( r2_hidden(B,f1_s3_pboole)
           => p1_s3_pboole(B,k1_funct_1(A,B)) ) ) ),
    file(pboole,s3_pboole),
    [interesting(0.00)]).

fof(s4_recdef_1,theorem,(
    ? [A] : 
      ( v1_funct_1(A)
      & v1_funct_2(A,k5_numbers,f1_s4_recdef_1)
      & m2_relset_1(A,k5_numbers,f1_s4_recdef_1)
      & k8_funct_2(k5_numbers,f1_s4_recdef_1,A,0) = f2_s4_recdef_1
      & ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => k8_funct_2(k5_numbers,f1_s4_recdef_1,A,k1_nat_1(B,1)) = f3_s4_recdef_1(B,k8_funct_2(k5_numbers,f1_s4_recdef_1,A,B)) ) ) ),
    file(recdef_1,s4_recdef_1),
    [interesting(0.00)]).

fof(s12_recdef_1,theorem,
    ( ( k8_funct_2(k5_numbers,f1_s12_recdef_1,f4_s12_recdef_1,0) = f2_s12_recdef_1
      & ! [A] : 
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => k8_funct_2(k5_numbers,f1_s12_recdef_1,f4_s12_recdef_1,k1_nat_1(A,1)) = f3_s12_recdef_1(A,k8_funct_2(k5_numbers,f1_s12_recdef_1,f4_s12_recdef_1,A)) )
      & k8_funct_2(k5_numbers,f1_s12_recdef_1,f5_s12_recdef_1,0) = f2_s12_recdef_1
      & ! [A] : 
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => k8_funct_2(k5_numbers,f1_s12_recdef_1,f5_s12_recdef_1,k1_nat_1(A,1)) = f3_s12_recdef_1(A,k8_funct_2(k5_numbers,f1_s12_recdef_1,f5_s12_recdef_1,A)) ) )
   => f4_s12_recdef_1 = f5_s12_recdef_1 ),
    file(recdef_1,s12_recdef_1),
    [interesting(0.00)]).

fof(s3_pre_circ,theorem,
    ( ? [A] : 
        ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,f1_s3_pre_circ)
        & m2_relset_1(A,k5_numbers,f1_s3_pre_circ)
        & k8_funct_2(k5_numbers,f1_s3_pre_circ,A,0) = f2_s3_pre_circ
        & ! [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => k8_funct_2(k5_numbers,f1_s3_pre_circ,A,k1_nat_1(B,1)) = f3_s3_pre_circ(B,k8_funct_2(k5_numbers,f1_s3_pre_circ,A,B)) ) )
    & ! [A] : 
        ( ( v1_funct_1(A)
          & v1_funct_2(A,k5_numbers,f1_s3_pre_circ)
          & m2_relset_1(A,k5_numbers,f1_s3_pre_circ) )
       => ! [B] : 
            ( ( v1_funct_1(B)
              & v1_funct_2(B,k5_numbers,f1_s3_pre_circ)
              & m2_relset_1(B,k5_numbers,f1_s3_pre_circ) )
           => ( ( k8_funct_2(k5_numbers,f1_s3_pre_circ,A,0) = f2_s3_pre_circ
                & ! [C] : 
                    ( m2_subset_1(C,k1_numbers,k5_numbers)
                   => k8_funct_2(k5_numbers,f1_s3_pre_circ,A,k1_nat_1(C,1)) = f3_s3_pre_circ(C,k8_funct_2(k5_numbers,f1_s3_pre_circ,A,C)) )
                & k8_funct_2(k5_numbers,f1_s3_pre_circ,B,0) = f2_s3_pre_circ
                & ! [C] : 
                    ( m2_subset_1(C,k1_numbers,k5_numbers)
                   => k8_funct_2(k5_numbers,f1_s3_pre_circ,B,k1_nat_1(C,1)) = f3_s3_pre_circ(C,k8_funct_2(k5_numbers,f1_s3_pre_circ,B,C)) ) )
             => A = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[s4_recdef_1,s12_recdef_1]),
    [file(pre_circ,s3_pre_circ),interesting(0.00)]).

fof(s4_pboole,theorem,(
    ? [A] : 
      ( m1_pboole(A,f1_s4_pboole)
      & ! [B] : 
          ( r2_hidden(B,f1_s4_pboole)
         => k1_funct_1(A,B) = f2_s4_pboole(B) ) ) ),
    file(pboole,s4_pboole),
    [interesting(0.00)]).

fof(d6_funcop_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_funcop_1(A)
      <=> ! [B] : 
            ( r2_hidden(B,k1_relat_1(A))
           => ( v1_relat_1(k1_funct_1(A,B))
              & v1_funct_1(k1_funct_1(A,B)) ) ) ) ) ),
    file(funcop_1,d6_funcop_1),
    [interesting(0.00)]).

fof(d3_pboole,definition,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( m1_pboole(B,A)
      <=> k1_relat_1(B) = A ) ) ),
    file(pboole,d3_pboole),
    [interesting(0.00)]).

fof(d18_pboole,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( m3_pboole(D,A,B,C)
              <=> ! [E] : 
                    ( r2_hidden(E,A)
                   => ( v1_funct_1(k1_funct_1(D,E))
                      & v1_funct_2(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E))
                      & m2_relset_1(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ) ),
    file(pboole,d18_pboole),
    [interesting(0.00)]).

fof(d12_funct_6,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => k10_funct_6(A) = k5_funct_5(k4_funct_5(A)) ) ),
    file(funct_6,d12_funct_6),
    [interesting(0.00)]).

fof(d4_funct_5,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( B = k4_funct_5(A)
          <=> ( ! [C] : 
                  ( r2_hidden(C,k1_relat_1(B))
                <=> ? [D,E] : 
                      ( v1_relat_1(E)
                      & v1_funct_1(E)
                      & ? [F] : 
                          ( C = k4_tarski(D,F)
                          & r2_hidden(D,k1_relat_1(A))
                          & E = k1_funct_1(A,D)
                          & r2_hidden(F,k1_relat_1(E)) ) ) )
              & ! [C,D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( ( r2_hidden(C,k1_relat_1(B))
                      & D = k1_funct_1(A,k1_mcart_1(C)) )
                   => k1_funct_1(B,C) = k1_funct_1(D,k2_mcart_1(C)) ) ) ) ) ) ) ),
    file(funct_5,d4_funct_5),
    [interesting(0.00)]).

fof(d16_pboole,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v2_relat_1(B)
      <=> ! [C] : ~ ( r2_hidden(C,A)
            & v1_xboole_0(k1_funct_1(B,C)) ) ) ) ),
    file(pboole,d16_pboole),
    [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(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(t106_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D))
    <=> ( r2_hidden(A,C)
        & r2_hidden(B,D) ) ) ),
    file(zfmisc_1,t106_zfmisc_1),
    [interesting(0.00)]).

fof(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(t23_mcart_1,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(A,k2_zfmisc_1(B,C))
     => A = k4_tarski(k1_mcart_1(A),k2_mcart_1(A)) ) ),
    file(mcart_1,t23_mcart_1),
    [interesting(0.00)]).

fof(t10_mcart_1,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(A,k2_zfmisc_1(B,C))
     => ( r2_hidden(k1_mcart_1(A),B)
        & r2_hidden(k2_mcart_1(A),C) ) ) ),
    file(mcart_1,t10_mcart_1),
    [interesting(0.00)]).

fof(t45_funct_5,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ! [D] : 
          ( ( v1_relat_1(D)
            & v1_funct_1(D) )
         => ( ( r2_hidden(A,k1_relat_1(C))
              & D = k1_funct_1(C,A)
              & r2_hidden(B,k1_relat_1(D)) )
           => ( r2_hidden(k4_tarski(A,B),k1_relat_1(k4_funct_5(C)))
              & k1_funct_1(k4_funct_5(C),k4_tarski(A,B)) = k1_funct_1(D,B)
              & r2_hidden(k1_funct_1(D,B),k2_relat_1(k4_funct_5(C))) ) ) ) ) ),
    file(funct_5,t45_funct_5),
    [interesting(0.00)]).

fof(t39_funct_5,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_relat_1(D)
        & v1_funct_1(D) )
     => ~ ( k2_zfmisc_1(A,B) != k1_xboole_0
          & k1_relat_1(D) = k2_zfmisc_1(A,B)
          & r2_hidden(C,B)
          & ! [E] : 
              ( ( v1_relat_1(E)
                & v1_funct_1(E) )
             => ~ ( k1_funct_1(k5_funct_5(D),C) = E
                  & k1_relat_1(E) = A
                  & r1_tarski(k2_relat_1(E),k2_relat_1(D))
                  & ! [F] : 
                      ( r2_hidden(F,A)
                     => k1_funct_1(E,F) = k1_funct_1(D,k4_tarski(F,C)) ) ) ) ) ) ),
    file(funct_5,t39_funct_5),
    [interesting(0.00)]).

fof(d4_pboole,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r1_pboole(A,B,C)
          <=> ! [D] : 
                ( r2_hidden(D,A)
               => r2_hidden(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) ) ),
    file(pboole,d4_pboole),
    [interesting(0.00)]).

fof(t7_funct_2,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( r2_hidden(C,A)
       => ( B = k1_xboole_0
          | r2_hidden(k1_funct_1(D,C),B) ) ) ) ),
    file(funct_2,t7_funct_2),
    [interesting(0.00)]).

fof(d5_card_3,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k4_card_3(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( v1_relat_1(D)
                  & v1_funct_1(D)
                  & C = D
                  & k1_relat_1(D) = k1_relat_1(A)
                  & ! [E] : 
                      ( r2_hidden(E,k1_relat_1(A))
                     => r2_hidden(k1_funct_1(D,E),k1_funct_1(A,E)) ) ) ) ) ) ),
    file(card_3,d5_card_3),
    [interesting(0.00)]).

fof(t3_funcop_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( k1_relat_1(A) = k1_relat_1(B)
               => k1_relat_1(k5_relat_1(C,A)) = k1_relat_1(k5_relat_1(C,B)) ) ) ) ) ),
    file(funcop_1,t3_funcop_1),
    [interesting(0.00)]).

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

fof(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(t68_finseq_2,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : k4_finseq_1(k2_finseq_2(A,B)) = k2_finseq_1(A) ) ),
    file(finseq_2,t68_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(d1_tarski,definition,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    [interesting(0.00)]).

fof(t17_funcop_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ! [C] : 
              ( r2_hidden(C,k1_relat_1(A))
             => k1_funct_1(A,C) = B )
         => A = k2_funcop_1(k1_relat_1(A),B) ) ) ),
    file(funcop_1,t17_funcop_1),
    [interesting(0.00)]).

fof(d2_finseq_2,definition,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : k2_finseq_2(A,B) = k2_funcop_1(k2_finseq_1(A),B) ) ),
    file(finseq_2,d2_finseq_2),
    [interesting(0.00)]).

fof(t18_card_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r2_hidden(A,k4_card_3(B))
          <=> ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(B))
                 => r2_hidden(k1_funct_1(A,C),k1_funct_1(B,C)) ) ) ) ) ) ),
    file(card_3,t18_card_3),
    [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(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(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(t39_trees_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v6_trees_3(A) )
     => ( k1_relat_1(k2_funct_6(A)) = k1_relat_1(A)
        & v4_trees_3(k2_funct_6(A)) ) ) ),
    file(trees_3,t39_trees_3),
    [interesting(0.00)]).

fof(t24_trees_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v4_trees_3(A)
      <=> ! [B] : 
            ( r2_hidden(B,k1_relat_1(A))
           => ( ~ v1_xboole_0(k1_funct_1(A,B))
              & v1_trees_1(k1_funct_1(A,B)) ) ) ) ) ),
    file(trees_3,t24_trees_3),
    [interesting(0.00)]).

fof(t47_trees_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ( r2_hidden(k1_xboole_0,A)
        & r2_hidden(k6_finseq_1(k5_numbers),A) ) ) ),
    file(trees_1,t47_trees_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(t8_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( k2_finseq_1(A) = k2_finseq_1(B)
           => A = B ) ) ) ),
    file(finseq_1,t8_finseq_1),
    [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(d15_trees_3,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v4_trees_3(A)
       => ! [B] : 
            ( ( ~ v1_xboole_0(B)
              & v1_trees_1(B) )
           => ( B = k13_trees_3(A)
            <=> ! [C] : 
                  ( r2_hidden(C,B)
                <=> ~ ( C != k1_xboole_0
                      & ! [D] : 
                          ( m2_subset_1(D,k1_numbers,k5_numbers)
                         => ! [E] : 
                              ( ( v1_relat_1(E)
                                & v1_funct_1(E)
                                & v1_finseq_1(E) )
                             => ~ ( ~ r1_xreal_0(k3_finseq_1(A),D)
                                  & r2_hidden(E,k1_funct_1(A,k1_nat_1(D,1)))
                                  & C = k7_finseq_1(k12_finseq_1(k5_numbers,D),E) ) ) ) ) ) ) ) ) ) ),
    file(trees_3,d15_trees_3),
    [interesting(0.00)]).

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(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(d1_cqc_lang,definition,(
    ! [A,B,C,D] : 
      ( ( A = B
       => k1_cqc_lang(A,B,C,D) = C )
      & ( A != B
       => k1_cqc_lang(A,B,C,D) = D ) ) ),
    file(cqc_lang,d1_cqc_lang),
    [interesting(0.00)]).

fof(t26_trees_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v6_trees_3(A)
      <=> ! [B] : 
            ( r2_hidden(B,k1_relat_1(A))
           => ( v1_relat_1(k1_funct_1(A,B))
              & v1_funct_1(k1_funct_1(A,B))
              & v3_trees_2(k1_funct_1(A,B)) ) ) ) ) ),
    file(trees_3,t26_trees_3),
    [interesting(0.00)]).

fof(t11_trees_4,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C)
        & v1_finseq_1(C)
        & v6_trees_3(C) )
     => ( r2_hidden(A,k1_relat_1(k4_trees_4(B,C)))
      <=> ~ ( A != k1_xboole_0
            & ! [D] : 
                ( m2_subset_1(D,k1_numbers,k5_numbers)
               => ! [E] : 
                    ( ( v1_relat_1(E)
                      & v1_funct_1(E)
                      & v3_trees_2(E) )
                   => ! [F] : 
                        ( m1_trees_1(F,k1_relat_1(E))
                       => ~ ( ~ r1_xreal_0(k3_finseq_1(C),D)
                            & E = k1_funct_1(C,k1_nat_1(D,1))
                            & A = k8_finseq_1(k5_numbers,k12_finseq_1(k5_numbers,D),F) ) ) ) ) ) ) ) ),
    file(trees_4,t11_trees_4),
    [interesting(0.00)]).

fof(t6_trees_1,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) )
         => ~ ( k7_finseq_1(B,C) = k9_finseq_1(A)
              & ~ ( B = k9_finseq_1(A)
                  & C = k1_xboole_0 )
              & ~ ( B = k1_xboole_0
                  & C = k9_finseq_1(A) ) ) ) ) ),
    file(trees_1,t6_trees_1),
    [interesting(0.00)]).

fof(d8_finseq_1,definition,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( B = k9_finseq_1(A)
      <=> ( k1_relat_1(B) = k2_finseq_1(1)
          & k1_funct_1(B,1) = A ) ) ) ),
    file(finseq_1,d8_finseq_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(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(d4_trees_4,definition,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( v6_trees_3(B)
       => ! [C] : 
            ( ( v1_relat_1(C)
              & v1_funct_1(C)
              & v3_trees_2(C) )
           => ( C = k4_trees_4(A,B)
            <=> ( ? [D] : 
                    ( v1_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D)
                    & v6_trees_3(D)
                    & B = D
                    & k1_relat_1(C) = k13_trees_3(k2_funct_6(D)) )
                & k1_funct_1(C,k1_xboole_0) = A
                & ! [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( ~ r1_xreal_0(k3_finseq_1(B),D)
                     => k5_trees_2(C,k12_finseq_1(k5_numbers,D)) = k1_funct_1(B,k1_nat_1(D,1)) ) ) ) ) ) ) ) ),
    file(trees_4,d4_trees_4),
    [interesting(0.00)]).

fof(t40_trees_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v6_trees_3(A) )
     => k3_finseq_1(k2_funct_6(A)) = k3_finseq_1(A) ) ),
    file(trees_3,t40_trees_3),
    [interesting(0.00)]).

fof(t31_funct_6,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))
              & C = k1_funct_1(B,A) )
           => ( r2_hidden(A,k1_relat_1(k2_funct_6(B)))
              & k1_funct_1(k2_funct_6(B),A) = k1_relat_1(C)
              & r2_hidden(A,k1_relat_1(k3_funct_6(B)))
              & k1_funct_1(k3_funct_6(B),A) = k2_relat_1(C) ) ) ) ) ),
    file(funct_6,t31_funct_6),
    [interesting(0.00)]).

fof(t25_trees_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( ~ r2_xboole_0(B,k1_xboole_0)
            & ~ r2_xboole_0(B,k6_finseq_1(A)) ) ) ) ),
    file(trees_1,t25_trees_1),
    [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(t2_xcmplx_1,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => ! [C] : 
              ( v1_xcmplx_0(C)
             => ( k2_xcmplx_0(A,B) = k2_xcmplx_0(C,B)
               => A = C ) ) ) ) ),
    file(xcmplx_1,t2_xcmplx_1),
    [interesting(0.00)]).

fof(d8_xboole_0,definition,(
    ! [A,B] : 
      ( r2_xboole_0(A,B)
    <=> ( r1_tarski(A,B)
        & A != B ) ) ),
    file(xboole_0,d8_xboole_0),
    [interesting(0.00)]).

fof(t8_trees_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(A,B)
          <=> ? [C] : 
                ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C)
                & B = k7_finseq_1(A,C) ) ) ) ) ),
    file(trees_1,t8_trees_1),
    [interesting(0.00)]).

fof(t58_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => k1_funct_1(k7_finseq_1(k9_finseq_1(A),B),1) = A ) ),
    file(finseq_1,t58_finseq_1),
    [interesting(0.00)]).

fof(t5_trees_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_finseq_1(A,B)
              | A = k7_finseq_1(B,A) )
           => B = k1_xboole_0 ) ) ) ),
    file(trees_1,t5_trees_1),
    [interesting(0.00)]).

fof(d12_trees_1,definition,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( m2_finseq_1(B,k5_numbers)
         => ! [C] : 
              ( ( ~ v1_xboole_0(C)
                & v1_trees_1(C) )
             => ( r2_hidden(B,A)
               => ! [D] : 
                    ( ( ~ v1_xboole_0(D)
                      & v1_trees_1(D) )
                   => ( D = k5_trees_1(A,B,C)
                    <=> ! [E] : 
                          ( m2_finseq_1(E,k5_numbers)
                         => ( r2_hidden(E,D)
                          <=> ~ ( ~ ( r2_hidden(E,A)
                                    & ~ r2_xboole_0(B,E) )
                                & ! [F] : 
                                    ( m2_finseq_1(F,k5_numbers)
                                   => ~ ( r2_hidden(F,C)
                                        & E = k8_finseq_1(k5_numbers,B,F) ) ) ) ) ) ) ) ) ) ) ) ),
    file(trees_1,d12_trees_1),
    [interesting(0.00)]).

fof(t52_trees_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v4_trees_3(A)
       => ( k2_trees_2(k13_trees_3(A),1) = a_1_0_trees_3(A)
          & ! [B] : 
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => ( ~ r1_xreal_0(k3_finseq_1(A),B)
               => k4_trees_1(k13_trees_3(A),k12_finseq_1(k5_numbers,B)) = k1_funct_1(A,k1_nat_1(B,1)) ) ) ) ) ) ),
    file(trees_3,t52_trees_3),
    [interesting(0.00)]).

fof(d11_trees_2,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A) )
     => ! [B] : 
          ( m2_finseq_1(B,k5_numbers)
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v3_trees_2(C) )
             => ( C = k5_trees_2(A,B)
              <=> ( k1_relat_1(C) = k4_trees_1(k1_relat_1(A),B)
                  & ! [D] : 
                      ( m2_finseq_1(D,k5_numbers)
                     => ( r2_hidden(D,k4_trees_1(k1_relat_1(A),B))
                       => k1_funct_1(C,D) = k1_funct_1(A,k8_finseq_1(k5_numbers,B,D)) ) ) ) ) ) ) ) ),
    file(trees_2,d11_trees_2),
    [interesting(0.00)]).

fof(t66_trees_1,theorem,(
    ! [A] : 
      ( m2_finseq_1(A,k5_numbers)
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_trees_1(B) )
         => ! [C] : 
              ( ( ~ v1_xboole_0(C)
                & v1_trees_1(C) )
             => ( r2_hidden(A,B)
               => C = k4_trees_1(k5_trees_1(B,A,C),A) ) ) ) ) ),
    file(trees_1,t66_trees_1),
    [interesting(0.00)]).

fof(s3_fraenkel,theorem,
    ( ! [A] : 
        ( m1_subset_1(A,f1_s3_fraenkel)
       => ( p1_s3_fraenkel(A)
        <=> p2_s3_fraenkel(A) ) )
   => a_0_4_fraenkel = a_0_5_fraenkel ),
    file(fraenkel,s3_fraenkel),
    [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(t64_trees_1,theorem,(
    ! [A] : 
      ( m2_finseq_1(A,k5_numbers)
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_trees_1(B) )
         => ! [C] : 
              ( ( ~ v1_xboole_0(C)
                & v1_trees_1(C) )
             => ( r2_hidden(A,B)
               => k5_trees_1(B,A,C) = k2_xboole_0(a_2_0_trees_1(A,B),a_2_1_trees_1(A,C)) ) ) ) ) ),
    file(trees_1,t64_trees_1),
    [interesting(0.00)]).

fof(t4_xboole_1,theorem,(
    ! [A,B,C] : k2_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(A,k2_xboole_0(B,C)) ),
    file(xboole_1,t4_xboole_1),
    [interesting(0.00)]).

fof(t46_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => k2_xboole_0(k1_tarski(A),B) = B ) ),
    file(zfmisc_1,t46_zfmisc_1),
    [interesting(0.00)]).

fof(d12_trees_2,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A) )
     => ! [B] : 
          ( m2_finseq_1(B,k5_numbers)
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v3_trees_2(C) )
             => ( r2_hidden(B,k1_relat_1(A))
               => ! [D] : 
                    ( ( v1_relat_1(D)
                      & v1_funct_1(D)
                      & v3_trees_2(D) )
                   => ( D = k8_trees_2(A,B,C)
                    <=> ( k1_relat_1(D) = k5_trees_1(k1_relat_1(A),B,k1_relat_1(C))
                        & ! [E] : 
                            ( m2_finseq_1(E,k5_numbers)
                           => ~ ( r2_hidden(E,k5_trees_1(k1_relat_1(A),B,k1_relat_1(C)))
                                & ~ ( ~ r1_tarski(B,E)
                                    & k1_funct_1(D,E) = k1_funct_1(A,E) )
                                & ! [F] : 
                                    ( m2_finseq_1(F,k5_numbers)
                                   => ~ ( r2_hidden(F,k1_relat_1(C))
                                        & E = k8_finseq_1(k5_numbers,B,F)
                                        & k1_funct_1(D,E) = k1_funct_1(C,F) ) ) ) ) ) ) ) ) ) ) ) ),
    file(trees_2,d12_trees_2),
    [interesting(0.00)]).

fof(t1_pre_circ,theorem,(
    $true ),
    file(pre_circ,t1_pre_circ),
    [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(s4_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_relat_1(A) = f1_s4_funct_1
      & ! [B] : 
          ( m1_subset_1(B,f1_s4_funct_1)
         => k1_funct_1(A,B) = f2_s4_funct_1(B) ) ) ),
    file(funct_1,s4_funct_1),
    [interesting(0.00)]).

fof(d4_wellord2,definition,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
    <=> ? [C] : 
          ( v1_relat_1(C)
          & v1_funct_1(C)
          & v2_funct_1(C)
          & k1_relat_1(C) = A
          & k2_relat_1(C) = B ) ) ),
    file(wellord2,d4_wellord2),
    [interesting(0.00)]).

fof(d8_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
      <=> ! [B,C] : 
            ( ( r2_hidden(B,k1_relat_1(A))
              & r2_hidden(C,k1_relat_1(A))
              & k1_funct_1(A,B) = k1_funct_1(A,C) )
           => B = C ) ) ) ),
    file(funct_1,d8_funct_1),
    [interesting(0.00)]).

fof(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(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(d5_trees_1,definition,(
    ! [A] : 
      ( v1_trees_1(A)
    <=> ( r1_tarski(A,k13_finseq_1(k5_numbers))
        & ! [B] : 
            ( m2_finseq_1(B,k5_numbers)
           => ( r2_hidden(B,A)
             => r1_tarski(k1_trees_1(B),A) ) )
        & ! [B] : 
            ( m2_finseq_1(B,k5_numbers)
           => ! [C] : 
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ! [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( ( r2_hidden(k8_finseq_1(k5_numbers,B,k12_finseq_1(k5_numbers,C)),A)
                        & r1_xreal_0(D,C) )
                     => r2_hidden(k8_finseq_1(k5_numbers,B,k12_finseq_1(k5_numbers,D)),A) ) ) ) ) ) ) ),
    file(trees_1,d5_trees_1),
    [interesting(0.00)]).

fof(t68_card_1,theorem,(
    ! [A,B] : 
      ( ( r2_wellord2(A,B)
        & v1_finset_1(A) )
     => v1_finset_1(B) ) ),
    file(card_1,t68_card_1),
    [interesting(0.00)]).

fof(d9_trees_1,definition,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( m2_finseq_1(B,k5_numbers)
         => ( r2_hidden(B,A)
           => ! [C] : 
                ( ( ~ v1_xboole_0(C)
                  & v1_trees_1(C) )
               => ( C = k4_trees_1(A,B)
                <=> ! [D] : 
                      ( m2_finseq_1(D,k5_numbers)
                     => ( r2_hidden(D,C)
                      <=> r2_hidden(k8_finseq_1(k5_numbers,B,D),A) ) ) ) ) ) ) ) ),
    file(trees_1,d9_trees_1),
    [interesting(0.00)]).

fof(t48_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) )
         => ( k7_finseq_1(A,B) = k1_xboole_0
           => ( A = k1_xboole_0
              & B = k1_xboole_0 ) ) ) ) ),
    file(finseq_1,t48_finseq_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(t67_card_2,theorem,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( v1_finset_1(B)
         => ( r2_xboole_0(A,B)
           => ( ~ r1_xreal_0(k4_card_1(B),k4_card_1(A))
              & r2_hidden(k1_card_1(A),k1_card_1(B)) ) ) ) ) ),
    file(card_2,t67_card_2),
    [interesting(0.00)]).

fof(s3_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_relat_1(A) = f1_s3_funct_1
      & ! [B] : 
          ( r2_hidden(B,f1_s3_funct_1)
         => k1_funct_1(A,B) = f2_s3_funct_1(B) ) ) ),
    file(funct_1,s3_funct_1),
    [interesting(0.00)]).

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

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

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

fof(t21_card_1,theorem,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
    <=> k1_card_1(A) = k1_card_1(B) ) ),
    file(card_1,t21_card_1),
    [interesting(0.00)]).

fof(s7_domain_1,theorem,(
    m1_subset_1(a_0_0_domain_1,k1_zfmisc_1(f1_s7_domain_1)) ),
    file(domain_1,s7_domain_1),
    [interesting(0.00)]).

fof(t4_xboole_0,theorem,(
    ! [A,B] : 
      ( ~ ( ~ r1_xboole_0(A,B)
          & ! [C] : ~ r2_hidden(C,k3_xboole_0(A,B)) )
      & ~ ( ? [C] : r2_hidden(C,k3_xboole_0(A,B))
          & r1_xboole_0(A,B) ) ) ),
    file(xboole_0,t4_xboole_0),
    [interesting(0.00)]).

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

fof(t53_card_2,theorem,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( v1_finset_1(B)
         => ( r1_xboole_0(A,B)
           => k4_card_1(k2_xboole_0(A,B)) = k1_nat_1(k4_card_1(A),k4_card_1(B)) ) ) ) ),
    file(card_2,t53_card_2),
    [interesting(0.00)]).

fof(t1_xcmplx_1,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => ! [C] : 
              ( v1_xcmplx_0(C)
             => k2_xcmplx_0(A,k2_xcmplx_0(B,C)) = k2_xcmplx_0(k2_xcmplx_0(A,B),C) ) ) ) ),
    file(xcmplx_1,t1_xcmplx_1),
    [interesting(0.00)]).

fof(t6_trees_4,theorem,(
    ! [A] : k1_trees_4(A) = k1_tarski(k4_tarski(k1_xboole_0,A)) ),
    file(trees_4,t6_trees_4),
    [interesting(0.00)]).

fof(t79_card_1,theorem,(
    ! [A] : k4_card_1(k1_tarski(A)) = 1 ),
    file(card_1,t79_card_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(t35_zfmisc_1,theorem,(
    ! [A,B] : k2_zfmisc_1(k1_tarski(A),k1_tarski(B)) = k1_tarski(k4_tarski(A,B)) ),
    file(zfmisc_1,t35_zfmisc_1),
    [interesting(0.00)]).

fof(t25_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(A,B)
           => ( r1_tarski(k1_relat_1(A),k1_relat_1(B))
              & r1_tarski(k2_relat_1(A),k2_relat_1(B)) ) ) ) ) ),
    file(relat_1,t25_relat_1),
    [interesting(0.00)]).

fof(d1_funct_4,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 = k1_funct_4(A,B)
              <=> ( k1_relat_1(C) = k2_xboole_0(k1_relat_1(A),k1_relat_1(B))
                  & ! [D] : 
                      ( r2_hidden(D,k2_xboole_0(k1_relat_1(A),k1_relat_1(B)))
                     => ( ( r2_hidden(D,k1_relat_1(B))
                         => k1_funct_1(C,D) = k1_funct_1(B,D) )
                        & ( ~ r2_hidden(D,k1_relat_1(B))
                         => k1_funct_1(C,D) = k1_funct_1(A,D) ) ) ) ) ) ) ) ) ),
    file(funct_4,d1_funct_4),
    [interesting(0.00)]).

fof(t9_xboole_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(A,B)
     => r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,C)) ) ),
    file(xboole_1,t9_xboole_1),
    [interesting(0.00)]).

fof(t13_funct_4,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(k1_funct_4(B,C)))
          <=> ( r2_hidden(A,k1_relat_1(B))
              | r2_hidden(A,k1_relat_1(C)) ) ) ) ) ),
    file(funct_4,t13_funct_4),
    [interesting(0.00)]).

fof(t14_funct_4,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(k1_funct_4(C,B),A) = k1_funct_1(B,A) ) ) ) ),
    file(funct_4,t14_funct_4),
    [interesting(0.00)]).

fof(t12_funct_4,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(k1_funct_4(C,B),A) = k1_funct_1(C,A) ) ) ) ),
    file(funct_4,t12_funct_4),
    [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(t33_funct_4,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_xboole_0(k1_relat_1(A),k1_relat_1(B))
           => r1_tarski(A,k1_funct_4(A,B)) ) ) ) ),
    file(funct_4,t33_funct_4),
    [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(t66_finseq_1,theorem,(
    ! [A] : r2_hidden(k1_xboole_0,k13_finseq_1(A)) ),
    file(finseq_1,t66_finseq_1),
    [interesting(0.00)]).

fof(d19_pboole,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,k3_finseq_2(A))
         => ( C = k6_pboole(A,B)
          <=> ! [D] : 
                ( m2_finseq_2(D,A,k3_finseq_2(A))
               => k1_funct_1(C,D) = k4_card_3(k5_relat_1(D,B)) ) ) ) ) ),
    file(pboole,d19_pboole),
    [interesting(0.00)]).

fof(t19_card_3,theorem,(
    k4_card_3(k1_xboole_0) = k1_tarski(k1_xboole_0) ),
    file(card_3,t19_card_3),
    [interesting(0.00)]).

fof(t62_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( k5_relat_1(k1_xboole_0,A) = k1_xboole_0
        & k5_relat_1(A,k1_xboole_0) = k1_xboole_0 ) ) ),
    file(relat_1,t62_relat_1),
    [interesting(0.00)]).

fof(t65_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( k1_relat_1(A) = k1_xboole_0
      <=> k2_relat_1(A) = k1_xboole_0 ) ) ),
    file(relat_1,t65_relat_1),
    [interesting(0.00)]).

fof(t57_partfun1,theorem,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k1_xboole_0,A) )
     => B = k1_xboole_0 ) ),
    file(partfun1,t57_partfun1),
    [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(t16_funcop_1,theorem,(
    ! [A] : 
      ( k1_relat_1(k2_funcop_1(k1_xboole_0,A)) = k1_xboole_0
      & k2_relat_1(k2_funcop_1(k1_xboole_0,A)) = k1_xboole_0 ) ),
    file(funcop_1,t16_funcop_1),
    [interesting(0.00)]).

fof(t50_funct_5,theorem,
    ( k4_funct_5(k1_xboole_0) = k1_xboole_0
    & k6_funct_5(k1_xboole_0) = k1_xboole_0 ),
    file(funct_5,t50_funct_5),
    [interesting(0.00)]).

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

fof(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(t64_funct_5,theorem,(
    ! [A] : k1_funct_2(k1_xboole_0,A) = k1_tarski(k1_xboole_0) ),
    file(funct_5,t64_funct_5),
    [interesting(0.00)]).

fof(t33_funct_5,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r1_tarski(k2_relat_1(C),k1_funct_2(A,B))
       => ( k1_relat_1(k4_funct_5(C)) = k2_zfmisc_1(k1_relat_1(C),A)
          & k1_relat_1(k6_funct_5(C)) = k2_zfmisc_1(A,k1_relat_1(C)) ) ) ) ),
    file(funct_5,t33_funct_5),
    [interesting(0.00)]).

fof(t113_zfmisc_1,theorem,(
    ! [A,B] : 
      ( k2_zfmisc_1(A,B) = k1_xboole_0
    <=> ( A = k1_xboole_0
        | B = k1_xboole_0 ) ) ),
    file(zfmisc_1,t113_zfmisc_1),
    [interesting(0.00)]).

fof(t49_funct_5,theorem,
    ( k3_funct_5(k1_xboole_0) = k1_xboole_0
    & k5_funct_5(k1_xboole_0) = k1_xboole_0 ),
    file(funct_5,t49_funct_5),
    [interesting(0.00)]).

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

fof(t91_orders_1,theorem,(
    ! [A] : 
      ( ~ ( ? [B] : 
              ( B != k1_xboole_0
              & r2_hidden(B,A) )
          & k3_tarski(A) = k1_xboole_0 )
      & ~ ( k3_tarski(A) != k1_xboole_0
          & ! [B] : ~ ( B != k1_xboole_0
              & r2_hidden(B,A) ) ) ) ),
    file(orders_1,t91_orders_1),
    [interesting(0.00)]).

fof(t11_funct_2,theorem,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ( ( B = k1_xboole_0
         => A = k1_xboole_0 )
       => r2_hidden(C,k1_funct_2(A,B)) ) ) ),
    file(funct_2,t11_funct_2),
    [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(t92_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => r1_tarski(A,k3_tarski(B)) ) ),
    file(zfmisc_1,t92_zfmisc_1),
    [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(t85_funct_6,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_relat_1(D)
        & v1_funct_1(D) )
     => ( r2_hidden(D,k1_funct_2(A,k1_funct_2(B,C)))
       => ( A = k1_xboole_0
          | B = k1_xboole_0
          | r2_hidden(k10_funct_6(D),k1_funct_2(B,k1_funct_2(A,C))) ) ) ) ),
    file(funct_6,t85_funct_6),
    [interesting(0.00)]).

fof(t121_funct_2,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(C,k1_funct_2(A,B))
     => ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) ) ) ),
    file(funct_2,t121_funct_2),
    [interesting(0.00)]).

fof(t12_xboole_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => k2_xboole_0(A,B) = B ) ),
    file(xboole_1,t12_xboole_1),
    [interesting(0.00)]).