fof(t34_pua2mss1,theorem,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m3_pua2mss1(B,A)
         => ( B = k8_eqrel_1(u1_struct_0(A),k10_pua2mss1(A))
           => ! [C] : 
                ( ( ~ v3_struct_0(C)
                  & ~ v2_msualg_1(C)
                  & l1_msualg_1(C) )
               => ( r7_pua2mss1(A,C)
                 => r5_pua2mss1(k12_pua2mss1(A,B),C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d17_pua2mss1,d16_pua2mss1,d8_msualg_1,d16_pua2mss1,d3_pboole,d1_funct_2,t11_relset_1,d15_pua2mss1,d15_pua2mss1,t28_pua2mss1,d2_setfam_1,s1_wellord2,t4_funct_2,t46_relat_1,t47_relat_1,t4_funct_2,d14_pua2mss1,l2_pua2mss1,t4_pua2mss1,d11_finseq_1,d4_pua2mss1,d1_funct_2,d1_funct_2,d3_pboole,d16_pua2mss1,d3_pua2mss1,d4_pua2mss1,t148_relat_1,d12_funct_1,t25_relat_1,t23_funct_1,d19_pboole,t3_xboole_0,s1_wellord2,t4_funct_2,d1_funct_2,t12_relset_1,d13_pua2mss1,t21_funct_2,d5_funct_1,t23_funct_1,d11_finseq_1,d4_pua2mss1,d16_pua2mss1,d3_pua2mss1,d4_pua2mss1,d3_pboole,t148_relat_1,d12_funct_1,d1_funct_2,t25_relat_1,t3_xboole_0,d15_pua2mss1,t12_relset_1,t146_relat_1,t156_relat_1,t157_relat_1,t1_xboole_1,d5_funct_1,t1_xboole_1,t21_funct_2,t3_pua2mss1,t113_funct_2,l2_pua2mss1,t33_zfmisc_1,d15_pua2mss1,t21_funct_2,d19_pboole,t5_pua2mss1,t55_relat_1,t12_relset_1,d10_xboole_0,d3_tarski,d15_pua2mss1,d4_pua2mss1,t23_funct_1,d5_funct_1,d15_pua2mss1,d5_funct_1,t3_pua2mss1,d10_xboole_0,d3_tarski,t3_xboole_0,d5_card_3,l1_pua2mss1,t10_funct_6,d4_finseq_1,d2_funct_2,d6_eqrel_1,d4_card_3,t95_zfmisc_1,t1_xboole_1,d4_finseq_1,t7_pua2mss1,t18_card_3,d4_finseq_1,d11_pua2mss1,t18_card_3,d5_funct_1,d2_setfam_1,t3_pua2mss1,d10_pua2mss1,t38_card_3,t1_xboole_1,t33_pua2mss1,d1_funct_2,t23_funct_1,d19_pboole,d4_pua2mss1,t5_pua2mss1,d5_funct_1]),
    [file(pua2mss1,t34_pua2mss1),interesting(1.00)]).

fof(t26_pua2mss1,theorem,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => m3_pua2mss1(k8_eqrel_1(u1_struct_0(A),k10_pua2mss1(A)),A) ) ),
    inference(mizar_proof,[status(thm)],[t25_pua2mss1,d11_pua2mss1]),
    [file(pua2mss1,t26_pua2mss1),interesting(0.98)]).

fof(t28_pua2mss1,theorem,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m3_pua2mss1(B,A)
         => r1_setfam_1(B,k8_eqrel_1(u1_struct_0(A),k10_pua2mss1(A))) ) ) ),
    inference(mizar_proof,[status(thm)],[t43_eqrel_1,d2_setfam_1,d5_eqrel_1,d3_tarski,d3_relat_1,t106_zfmisc_1,d5_eqrel_1,t27_eqrel_1,t28_eqrel_1,d11_pua2mss1,d11_finseq_1,t7_pua2mss1,t3_xboole_0,d10_pua2mss1,t27_pua2mss1,d5_pua2mss1,t17_pua2mss1,d3_relat_1,t106_zfmisc_1,d5_eqrel_1,d11_finseq_1,t7_pua2mss1,d11_pua2mss1,d10_pua2mss1,d9_pua2mss1,t27_eqrel_1,t28_eqrel_1,t27_pua2mss1,d12_funct_1,d5_eqrel_1,t30_eqrel_1,d6_pua2mss1,t18_pua2mss1,s1_nat_1,d5_eqrel_1,t30_eqrel_1,d8_pua2mss1,t12_eqrel_1,t27_eqrel_1]),
    [file(pua2mss1,t28_pua2mss1),interesting(0.94)]).

fof(t32_pua2mss1,theorem,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m3_pua2mss1(B,A)
         => r7_pua2mss1(A,k12_pua2mss1(A,B)) ) ) ),
    inference(mizar_proof,[status(thm)],[d15_pua2mss1,t71_relat_1,d3_pboole,s5_pboole,s5_pboole,d3_pboole,d15_pua2mss1,d15_funct_1,d3_pboole,d6_eqrel_1,d4_finseq_1,t6_pua2mss1,d3_finseq_1,d2_finseq_1,d4_finseq_1,d11_finseq_1,t3_xboole_0,t7_mcart_1,d18_pboole,d1_funct_2,t12_relset_1,d4_finseq_1,d15_pua2mss1,d19_pboole,t79_relat_1,t23_funct_1,d15_pua2mss1,t7_mcart_1,t148_relat_1,d11_pua2mss1,d10_pua2mss1,t79_relat_1,t91_relat_1,t4_funct_2,t10_card_5,d3_pboole,d10_xboole_0,d3_tarski,d3_tarski,t10_card_5,d3_pboole,t3_xboole_0,t15_pua2mss1,d17_pua2mss1,t71_relat_1,d12_pua2mss1,d16_pua2mss1,d3_pboole,t9_pua2mss1,t11_pua2mss1,d5_funct_1,d3_pboole,d6_eqrel_1,t91_relat_1,d6_eqrel_1,t12_pua2mss1,d3_tarski,d5_funct_1,t90_relat_1,d3_xboole_0,d11_pua2mss1,t7_mcart_1,d10_pua2mss1,t28_xboole_1,t70_funct_1,t4_funct_2,d3_tarski,d11_pua2mss1,d10_pua2mss1,t28_xboole_1,t7_mcart_1,d3_pboole,t73_funct_1,d8_funct_1,t70_funct_1,t7_mcart_1,d11_pua2mss1,t7_mcart_1,d10_pua2mss1,t91_relat_1,t2_pua2mss1,t16_pua2mss1]),
    [file(pua2mss1,t32_pua2mss1),interesting(0.85)]).

fof(t11_pua2mss1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( r1_tarski(B,A)
         => ! [C] : 
              ( m1_eqrel_1(C,A)
             => m1_eqrel_1(a_3_1_pua2mss1(A,B,C),B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t26_xboole_1,t28_xboole_1,d10_xboole_0,d3_tarski,d6_eqrel_1,d4_tarski,t3_xboole_0,d3_xboole_0,d4_tarski,d7_xboole_0,d6_eqrel_1,t74_xboole_1,t74_xboole_1,t65_xboole_1,d6_eqrel_1]),
    [file(pua2mss1,t11_pua2mss1),interesting(0.84)]).

fof(t14_pua2mss1,theorem,(
    ! [A,B] : 
      ( m2_finseq_1(B,k3_pua2mss1(A))
     => ? [C] : 
          ( m2_finseq_1(C,A)
          & k4_card_3(B) = k1_tarski(C) ) ) ),
    inference(mizar_proof,[status(thm)],[t18_card_3,l1_pua2mss1,t10_funct_6,d4_finseq_1,d4_card_3,d2_funct_2,t95_zfmisc_1,t1_xboole_1,d6_eqrel_1,t2_zfmisc_1,d4_finseq_1,d3_tarski,d5_card_3,t18_card_3,d5_funct_1,d6_eqrel_1,t13_pua2mss1,d1_tarski,d1_tarski,t9_funct_1,d1_tarski,d10_xboole_0,t37_zfmisc_1]),
    [file(pua2mss1,t14_pua2mss1),interesting(0.83)]).

fof(t25_pua2mss1,theorem,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m1_pua2mss1(B,k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),k1_pua2mss1(u1_struct_0(A),u1_unialg_1(A)))
         => r2_pua2mss1(u1_struct_0(A),B,k8_eqrel_1(u1_struct_0(A),k10_pua2mss1(A))) ) ) ),
    inference(mizar_proof,[status(thm)],[t3_xboole_0,t27_partfun1,d5_eqrel_1,d3_tarski,d12_funct_1,t10_funct_6,d2_funct_2,d3_finseq_1,d2_finseq_1,d3_finseq_1,t28_eqrel_1,t27_eqrel_1,t23_pua2mss1,t106_zfmisc_1,d5_pua2mss1,d5_funct_1,t12_relset_1,d8_pua2mss1,t18_pua2mss1,d6_pua2mss1,t22_pua2mss1,t12_eqrel_1,d8_pua2mss1,t13_eqrel_1,t27_eqrel_1,d4_finseq_1,d5_funct_1,d5_card_3,d5_eqrel_1,t30_eqrel_1,s4_pua2mss1,d7_xboole_0,t145_relat_1,t149_relat_1,t2_xboole_1,d9_pua2mss1,d10_pua2mss1,t3_xboole_0,d3_tarski,t10_funct_6,d2_funct_2,d3_finseq_1,d2_finseq_1,d3_finseq_1,t23_pua2mss1,t106_zfmisc_1,d5_pua2mss1,d4_finseq_1,d5_funct_1,d5_card_3,d5_eqrel_1,t30_eqrel_1,s4_pua2mss1]),
    [file(pua2mss1,t25_pua2mss1),interesting(0.83)]).

fof(t9_pua2mss1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_eqrel_1(B,A)
         => m1_eqrel_1(a_2_0_pua2mss1(A,B),k3_finseq_2(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d3_tarski,d5_card_3,d3_finseq_1,d2_finseq_1,d3_tarski,d5_funct_1,d4_finseq_1,d5_funct_1,d4_finseq_1,d11_finseq_1,d10_xboole_0,d3_tarski,d11_finseq_1,d6_eqrel_1,d4_finseq_1,t6_pua2mss1,d3_finseq_1,d2_finseq_1,d4_finseq_1,d11_finseq_1,d4_tarski,t3_xboole_0,d5_card_3,d5_card_3,d4_finseq_1,d5_funct_1,t3_xboole_0,d6_eqrel_1,t9_funct_1,d6_eqrel_1]),
    [file(pua2mss1,t9_pua2mss1),interesting(0.82)]).

fof(t7_pua2mss1,theorem,(
    ! [A,B] : 
      ( m1_eqrel_1(B,A)
     => ! [C] : 
          ( m2_finseq_1(C,A)
         => ? [D] : 
              ( m2_finseq_1(D,B)
              & r2_hidden(C,k4_card_3(D)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_eqrel_1,d4_finseq_1,t2_zfmisc_1,t6_pua2mss1,d3_finseq_1,d2_finseq_1,d4_finseq_1]),
    [file(pua2mss1,t7_pua2mss1),interesting(0.80)]).

fof(t12_pua2mss1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( m1_eqrel_1(B,k1_relat_1(A))
         => m1_eqrel_1(a_2_1_pua2mss1(A,B),A) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t88_relat_1,d10_xboole_0,d3_tarski,d1_relat_1,d6_eqrel_1,d4_relat_1,d4_tarski,d11_relat_1,d4_tarski,d4_funct_1,d11_relat_1,d6_eqrel_1,t3_xboole_0,d1_relat_1,d11_relat_1,t3_xboole_0,d6_eqrel_1]),
    [file(pua2mss1,t12_pua2mss1),interesting(0.78)]).

fof(t13_pua2mss1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => k3_pua2mss1(A) = a_1_0_pua2mss1(A) ) ),
    inference(mizar_proof,[status(thm)],[d5_eqrel_1,t33_eqrel_1,d10_xboole_0,d3_tarski,d3_tarski,t33_eqrel_1,d5_eqrel_1]),
    [file(pua2mss1,t13_pua2mss1),interesting(0.76)]).

fof(t23_pua2mss1,theorem,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => r1_tarski(k10_pua2mss1(A),k7_pua2mss1(A)) ) ),
    inference(mizar_proof,[status(thm)],[d3_relat_1,t106_zfmisc_1,d8_pua2mss1,t17_pua2mss1]),
    [file(pua2mss1,t23_pua2mss1),interesting(0.76)]).

fof(t4_pua2mss1,theorem,(
    ! [A,B] : 
      ( r1_setfam_1(A,B)
     => ! [C] : 
          ( m2_finseq_1(C,A)
         => ? [D] : 
              ( m2_finseq_1(D,B)
              & r1_tarski(k4_card_3(C),k4_card_3(D)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_setfam_1,d4_finseq_1,d5_funct_1,s1_wellord2,d3_finseq_1,d2_finseq_1,t38_card_3,d4_finseq_1]),
    [file(pua2mss1,t4_pua2mss1),interesting(0.76)]).

fof(t3_pua2mss1,theorem,(
    ! [A,B] : 
      ( m1_eqrel_1(B,A)
     => ! [C,D,E] : 
          ( ( r2_hidden(C,D)
            & r2_hidden(D,B)
            & r2_hidden(C,E)
            & r2_hidden(E,B) )
         => D = E ) ) ),
    inference(mizar_proof,[status(thm)],[t3_xboole_0,d6_eqrel_1]),
    [file(pua2mss1,t3_pua2mss1),interesting(0.76)]).

fof(t2_pua2mss1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v2_relat_1(B)
            & v1_funct_1(B) )
         => ( k4_card_3(A) = k4_card_3(B)
           => A = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_card_3,t1_pua2mss1,d10_xboole_0,t9_funct_1]),
    [file(pua2mss1,t2_pua2mss1),interesting(0.74)]).

fof(l2_pua2mss1,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( m2_finseq_1(C,A)
         => ! [D] : 
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,B)
                & m2_relset_1(D,A,B) )
             => m2_finseq_1(k1_partfun1(k5_numbers,A,A,B,C,D),B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_finseq_1,d1_funct_2,t45_relat_1,t46_relat_1,t12_relset_1,l1_pua2mss1,t1_xboole_1,d4_finseq_1]),
    [file(pua2mss1,l2_pua2mss1),interesting(0.73)]).

fof(t21_pua2mss1,theorem,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => r1_tarski(k8_pua2mss1(A,B),B) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_relat_1,t106_zfmisc_1,d6_pua2mss1]),
    [file(pua2mss1,t21_pua2mss1),interesting(0.72)]).

fof(t31_pua2mss1,theorem,(
    ! [A] : 
      ( l1_msualg_1(A)
     => ! [B] : 
          ( l1_msualg_1(B)
         => ! [C] : 
              ( l1_msualg_1(C)
             => ( ( r4_pua2mss1(A,B)
                  & r4_pua2mss1(B,C) )
               => r4_pua2mss1(A,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d14_pua2mss1,d14_pua2mss1,d14_pua2mss1,t30_pua2mss1,d13_pua2mss1,t47_relat_1]),
    [file(pua2mss1,t31_pua2mss1),interesting(0.69)]).

fof(l1_pua2mss1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( k1_relat_1(B) = k4_finseq_1(A)
           => ( v1_relat_1(B)
              & v1_funct_1(B)
              & v1_finseq_1(B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_finseq_1,d2_finseq_1]),
    [file(pua2mss1,l1_pua2mss1),interesting(0.66)]).

fof(t5_pua2mss1,theorem,(
    ! [A,B] : 
      ( m1_eqrel_1(B,A)
     => ! [C] : 
          ( m1_eqrel_1(C,A)
         => ! [D] : 
              ( ( v1_funct_1(D)
                & v1_funct_2(D,B,C)
                & m2_relset_1(D,B,C) )
             => ( ! [E] : 
                    ( r2_hidden(E,B)
                   => r1_tarski(E,k1_funct_1(D,E)) )
               => ! [E] : 
                    ( m2_finseq_1(E,B)
                   => ! [F] : 
                        ( m2_finseq_1(F,C)
                       => ( r1_tarski(k4_card_3(E),k4_card_3(F))
                        <=> k1_partfun1(k5_numbers,B,B,C,E,D) = F ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_finseq_1,d6_eqrel_1,d1_funct_2,t12_relset_1,t46_relat_1,t1_pua2mss1,d5_funct_1,d6_eqrel_1,t7_funct_2,t3_pua2mss1,t23_funct_1,t9_funct_1,t23_funct_1,d5_funct_1,t38_card_3]),
    [file(pua2mss1,t5_pua2mss1),interesting(0.66)]).

fof(t8_pua2mss1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m1_eqrel_1(C,A)
             => ! [D] : 
                  ( m1_eqrel_1(D,B)
                 => m1_eqrel_1(a_4_0_pua2mss1(A,B,C,D),k2_zfmisc_1(A,B)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d10_xboole_0,d3_tarski,d2_zfmisc_1,d6_eqrel_1,d4_tarski,d6_eqrel_1,d4_tarski,t106_zfmisc_1,d4_tarski,d6_eqrel_1,d7_xboole_0,t123_zfmisc_1,t113_zfmisc_1,d7_xboole_0,d6_eqrel_1]),
    [file(pua2mss1,t8_pua2mss1),interesting(0.66)]).

fof(t10_pua2mss1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( m1_eqrel_1(C,A)
             => m1_eqrel_1(a_3_0_pua2mss1(A,B,C),k4_finseq_2(B,A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d3_tarski,d5_card_3,d3_finseq_1,d2_finseq_1,d3_tarski,d5_funct_1,d4_finseq_1,d5_funct_1,d3_finseq_1,d4_finseq_1,t109_finseq_2,t110_finseq_2,d10_xboole_0,d3_tarski,d6_eqrel_1,d4_finseq_1,t6_pua2mss1,d3_finseq_1,d2_finseq_1,d4_finseq_1,d3_finseq_1,t109_finseq_2,t110_finseq_2,d4_tarski,t3_xboole_0,d5_card_3,d5_card_3,d4_finseq_1,d5_funct_1,t3_xboole_0,d6_eqrel_1,t9_funct_1,d6_eqrel_1]),
    [file(pua2mss1,t10_pua2mss1),interesting(0.65)]).

fof(t29_pua2mss1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => r3_pua2mss1(A,A,k6_partfun1(u1_struct_0(A)),k6_partfun1(u1_msualg_1(A))) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,t12_relset_1,t79_relat_1,t42_funct_1,t71_relat_1,d13_pua2mss1,t34_funct_1,t7_funct_2,d11_finseq_1,d4_finseq_1,t79_relat_1]),
    [file(pua2mss1,t29_pua2mss1),interesting(0.64)]).

fof(t6_pua2mss1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ~ ( r1_tarski(k2_relat_1(B),k3_tarski(A))
          & ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ~ ( k1_relat_1(C) = k1_relat_1(B)
                  & r1_tarski(k2_relat_1(C),A)
                  & r2_hidden(B,k4_card_3(C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_funct_1,d4_tarski,s1_wellord2,d5_card_3]),
    [file(pua2mss1,t6_pua2mss1),interesting(0.63)]).

fof(t15_pua2mss1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v2_relat_1(B)
        & v1_funct_1(B) )
     => ( ( k3_card_3(B) = A
          & ! [C,D] : 
              ( ( r2_hidden(C,k1_relat_1(B))
                & r2_hidden(D,k1_relat_1(B)) )
             => ( C = D
                | r1_xboole_0(k1_funct_1(B,C),k1_funct_1(B,D)) ) ) )
       => m2_pua2mss1(B,A) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t92_zfmisc_1,d4_card_3,d4_card_3,d5_funct_1,d15_funct_1,d5_funct_1,d5_funct_1,d15_funct_1,d4_tarski,d4_card_3,d6_eqrel_1,d3_pua2mss1,d8_funct_1,d15_funct_1,t3_xboole_0]),
    [file(pua2mss1,t15_pua2mss1),interesting(0.62)]).

fof(t24_pua2mss1,theorem,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m1_pua2mss1(B,k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),k1_pua2mss1(u1_struct_0(A),u1_unialg_1(A)))
         => r2_pua2mss1(u1_struct_0(A),B,k3_pua2mss1(u1_struct_0(A))) ) ) ),
    inference(mizar_proof,[status(thm)],[t14_pua2mss1,d5_funct_1,t12_relset_1,t13_pua2mss1,d3_tarski,d12_funct_1,d1_tarski,d1_tarski,d9_pua2mss1,d10_pua2mss1,t14_pua2mss1,t3_xboole_0,d3_tarski,d1_tarski]),
    [file(pua2mss1,t24_pua2mss1),interesting(0.61)]).

fof(t16_pua2mss1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m1_eqrel_1(C,B)
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,C)
                    & m2_relset_1(D,A,C) )
                 => ( ( r1_tarski(C,k2_relat_1(D))
                      & v2_funct_1(D) )
                   => m2_pua2mss1(D,B) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t12_relset_1,d10_xboole_0,d3_pua2mss1]),
    [file(pua2mss1,t16_pua2mss1),interesting(0.61)]).

fof(t17_pua2mss1,theorem,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( k9_pua2mss1(A,B,0) = B
            & k9_pua2mss1(A,B,1) = k8_pua2mss1(A,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_pua2mss1,d7_pua2mss1]),
    [file(pua2mss1,t17_pua2mss1),interesting(0.59)]).

fof(t20_pua2mss1,theorem,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( v3_relat_2(B)
            & v8_relat_2(B)
            & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( r1_tarski(B,k7_pua2mss1(A))
           => ( v1_partfun1(k8_pua2mss1(A,B),u1_struct_0(A),u1_struct_0(A))
              & v3_relat_2(k8_pua2mss1(A,B))
              & v8_relat_2(k8_pua2mss1(A,B)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t11_eqrel_1,d5_funct_1,t12_relset_1,t11_eqrel_1,d6_pua2mss1,d1_relat_2,t98_orders_1,d4_partfun1,d6_pua2mss1,t12_eqrel_1,d6_pua2mss1,t12_eqrel_1,d6_pua2mss1,d3_relat_2,d11_relat_2,d6_pua2mss1,d5_pua2mss1,d6_pua2mss1,t13_eqrel_1,d6_pua2mss1,t13_eqrel_1,d6_pua2mss1,d8_relat_2,d16_relat_2]),
    [file(pua2mss1,t20_pua2mss1),interesting(0.56)]).

fof(t27_pua2mss1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_eqrel_1(B,A)
         => ! [C] : 
              ( m2_finseq_1(C,B)
             => ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D) )
                 => ! [E] : 
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E)
                        & v1_finseq_1(E) )
                     => ! [F,G] : 
                          ( r2_hidden(k7_finseq_1(k7_finseq_1(D,k9_finseq_1(F)),E),k4_card_3(C))
                         => ( ! [H] : 
                                ( m2_subset_1(H,k1_zfmisc_1(A),B)
                               => ~ ( r2_hidden(F,H)
                                    & r2_hidden(G,H) ) )
                            | r2_hidden(k7_finseq_1(k7_finseq_1(D,k9_finseq_1(G)),E),k4_card_3(C)) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_card_3,d3_finseq_1,t35_finseq_1,t35_finseq_1,t57_finseq_1,t57_finseq_1,t35_finseq_1,t35_finseq_1,d3_finseq_1,t55_finseq_1,t57_finseq_1,t35_finseq_1,d3_finseq_1,t38_finseq_1,t39_finseq_1,d7_finseq_1,d7_finseq_1,t4_finseq_1,d1_tarski,t6_finseq_1,t59_finseq_1,d7_finseq_1,d4_finseq_1,d5_funct_1,t3_xboole_0,d6_eqrel_1,d7_finseq_1,t38_finseq_1,d5_card_3]),
    [file(pua2mss1,t27_pua2mss1),interesting(0.54)]).

fof(t22_pua2mss1,theorem,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( v3_relat_2(B)
            & v8_relat_2(B)
            & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( r1_tarski(B,k7_pua2mss1(A))
           => ! [C] : 
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ( v1_partfun1(k9_pua2mss1(A,B,C),u1_struct_0(A),u1_struct_0(A))
                  & v3_relat_2(k9_pua2mss1(A,B,C))
                  & v8_relat_2(k9_pua2mss1(A,B,C)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t17_pua2mss1,t18_pua2mss1,t21_pua2mss1,t20_pua2mss1,t1_xboole_1,s1_nat_1]),
    [file(pua2mss1,t22_pua2mss1),interesting(0.53)]).

fof(t18_pua2mss1,theorem,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
             => k9_pua2mss1(A,C,k1_nat_1(B,1)) = k8_pua2mss1(A,k9_pua2mss1(A,C,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_pua2mss1,d7_pua2mss1]),
    [file(pua2mss1,t18_pua2mss1),interesting(0.52)]).

fof(t19_pua2mss1,theorem,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] : 
                  ( m2_relset_1(D,u1_struct_0(A),u1_struct_0(A))
                 => k9_pua2mss1(A,D,k1_nat_1(B,C)) = k9_pua2mss1(A,k9_pua2mss1(A,D,B),C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t17_pua2mss1,t18_pua2mss1,t18_pua2mss1,s1_nat_1]),
    [file(pua2mss1,t19_pua2mss1),interesting(0.43)]).

fof(s4_pua2mss1,theorem,
    ( ( p1_s4_pua2mss1(f1_s4_pua2mss1)
      & k3_finseq_1(f1_s4_pua2mss1) = k3_finseq_1(f2_s4_pua2mss1)
      & ! [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,D] : 
                  ( ( p1_s4_pua2mss1(k7_finseq_1(k7_finseq_1(A,k9_finseq_1(C)),B))
                    & p2_s4_pua2mss1(C,D) )
                 => p1_s4_pua2mss1(k7_finseq_1(k7_finseq_1(A,k9_finseq_1(D)),B)) ) ) )
      & ! [A] : 
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ( r2_hidden(A,k4_finseq_1(f1_s4_pua2mss1))
           => p2_s4_pua2mss1(k1_funct_1(f1_s4_pua2mss1,A),k1_funct_1(f2_s4_pua2mss1,A)) ) ) )
   => p1_s4_pua2mss1(f2_s4_pua2mss1) ),
    inference(mizar_proof,[status(thm)],[t25_finseq_1,t25_finseq_1,t63_finseq_1,t63_finseq_1,d3_finseq_1,t57_finseq_1,t35_finseq_1,t6_finseq_1,t39_finseq_1,t45_finseq_1,t59_finseq_1,d7_finseq_1,t45_finseq_1,s1_nat_1,t47_finseq_1]),
    [file(pua2mss1,s4_pua2mss1),interesting(0.37)]).

fof(s1_pua2mss1,theorem,(
    ? [A] : 
      ( m2_relset_1(A,f1_s1_pua2mss1,f2_s1_pua2mss1)
      & ? [B] : 
          ( m1_pboole(B,k5_numbers)
          & A = k1_funct_1(B,f3_s1_pua2mss1)
          & k1_funct_1(B,0) = f4_s1_pua2mss1
          & ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] : 
                  ( m2_relset_1(D,f1_s1_pua2mss1,f2_s1_pua2mss1)
                 => ( D = k1_funct_1(B,C)
                   => k1_funct_1(B,k1_nat_1(C,1)) = f5_s1_pua2mss1(D,C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s3_recdef_1,d3_pboole,s1_nat_1]),
    [file(pua2mss1,s1_pua2mss1),interesting(0.23)]).

fof(t33_pua2mss1,theorem,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] : 
              ( l3_msualg_1(C,B)
             => ! [D] : 
                  ( m2_pua2mss1(D,u1_msualg_1(B))
                 => ( r6_pua2mss1(A,B,C,D)
                   => ! [E] : 
                        ( m1_subset_1(E,k4_finseq_1(u1_unialg_1(A)))
                       => ! [F] : 
                            ( m2_finseq_1(F,k2_relat_1(u4_msualg_1(B,C)))
                           => ~ ( r1_tarski(k4_card_3(F),k4_relset_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),k2_pua2mss1(A,E)))
                                & ! [G] : 
                                    ( m1_subset_1(G,u1_msualg_1(B))
                                   => ~ ( k5_relat_1(k1_msualg_1(B,G),u4_msualg_1(B,C)) = F
                                        & r2_hidden(G,k1_funct_1(D,E)) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d16_pua2mss1,d3_pboole,d1_funct_2,t11_relset_1,d11_finseq_1,d4_funct_1,d4_pua2mss1,d5_funct_1,d3_pboole,t91_relat_1,t91_relat_1,l2_pua2mss1,d11_finseq_1,t9_pua2mss1,d1_funct_2,t23_funct_1,d19_pboole,t70_funct_1,d4_relat_1,t3_pua2mss1,t2_pua2mss1]),
    [file(pua2mss1,t33_pua2mss1),interesting(0.17)]).

fof(s3_recdef_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_relat_1(A) = k5_numbers
      & k1_funct_1(A,0) = f1_s3_recdef_1
      & ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => k1_funct_1(A,k1_nat_1(B,1)) = f2_s3_recdef_1(B,k1_funct_1(A,B)) ) ) ),
    file(recdef_1,s3_recdef_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(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(d2_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( A = B
          <=> ! [C,D] : 
                ( r2_hidden(k4_tarski(C,D),A)
              <=> r2_hidden(k4_tarski(C,D),B) ) ) ) ) ),
    file(relat_1,d2_relat_1),
    [interesting(0.00)]).

fof(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(s2_pua2mss1,theorem,(
    ! [A] : 
      ( m2_relset_1(A,f1_s2_pua2mss1,f2_s2_pua2mss1)
     => ! [B] : 
          ( m2_relset_1(B,f1_s2_pua2mss1,f2_s2_pua2mss1)
         => ( ( ! [C] : 
                  ( m1_subset_1(C,f1_s2_pua2mss1)
                 => ! [D] : 
                      ( m1_subset_1(D,f2_s2_pua2mss1)
                     => ( r2_hidden(k4_tarski(C,D),A)
                      <=> p1_s2_pua2mss1(C,D) ) ) )
              & ! [C] : 
                  ( m1_subset_1(C,f1_s2_pua2mss1)
                 => ! [D] : 
                      ( m1_subset_1(D,f2_s2_pua2mss1)
                     => ( r2_hidden(k4_tarski(C,D),B)
                      <=> p1_s2_pua2mss1(C,D) ) ) ) )
           => A = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_relat_1,t106_zfmisc_1,t106_zfmisc_1,t106_zfmisc_1,t106_zfmisc_1]),
    [file(pua2mss1,s2_pua2mss1),interesting(0.00)]).

fof(s3_pua2mss1,theorem,(
    ! [A] : 
      ( m2_relset_1(A,f1_s3_pua2mss1,f2_s3_pua2mss1)
     => ! [B] : 
          ( m2_relset_1(B,f1_s3_pua2mss1,f2_s3_pua2mss1)
         => ~ ( ? [C] : 
                  ( m1_pboole(C,k5_numbers)
                  & A = k1_funct_1(C,f3_s3_pua2mss1)
                  & k1_funct_1(C,0) = f4_s3_pua2mss1
                  & ! [D] : 
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ! [E] : 
                          ( m2_relset_1(E,f1_s3_pua2mss1,f2_s3_pua2mss1)
                         => ( E = k1_funct_1(C,D)
                           => k1_funct_1(C,k1_nat_1(D,1)) = f5_s3_pua2mss1(E,D) ) ) ) )
              & ? [C] : 
                  ( m1_pboole(C,k5_numbers)
                  & B = k1_funct_1(C,f3_s3_pua2mss1)
                  & k1_funct_1(C,0) = f4_s3_pua2mss1
                  & ! [D] : 
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ! [E] : 
                          ( m2_relset_1(E,f1_s3_pua2mss1,f2_s3_pua2mss1)
                         => ( E = k1_funct_1(C,D)
                           => k1_funct_1(C,k1_nat_1(D,1)) = f5_s3_pua2mss1(E,D) ) ) ) )
              & A != B ) ) ) ),
    inference(mizar_proof,[status(thm)],[s1_nat_1]),
    [file(pua2mss1,s3_pua2mss1),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(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(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(d2_finseq_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v1_finseq_1(A)
      <=> ? [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
            & k1_relat_1(A) = k2_finseq_1(B) ) ) ) ),
    file(finseq_1,d2_finseq_1),
    [interesting(0.00)]).

fof(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(d4_finseq_1,definition,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( m1_finseq_1(B,A)
      <=> r1_tarski(k2_relat_1(B),A) ) ) ),
    file(finseq_1,d4_finseq_1),
    [interesting(0.00)]).

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

fof(t110_finseq_2,theorem,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
     => m1_subset_1(B,k4_finseq_2(k3_finseq_1(B),A)) ) ),
    file(finseq_2,t110_finseq_2),
    [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(d6_eqrel_1,definition,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( A != k1_xboole_0
         => ( m1_eqrel_1(B,A)
          <=> ( k5_setfam_1(A,B) = A
              & ! [C] : 
                  ( m1_subset_1(C,k1_zfmisc_1(A))
                 => ( r2_hidden(C,B)
                   => ( C != k1_xboole_0
                      & ! [D] : 
                          ( m1_subset_1(D,k1_zfmisc_1(A))
                         => ~ ( r2_hidden(D,B)
                              & C != D
                              & ~ r1_xboole_0(C,D) ) ) ) ) ) ) ) )
        & ( A = k1_xboole_0
         => ( m1_eqrel_1(B,A)
          <=> B = k1_xboole_0 ) ) ) ) ),
    file(eqrel_1,d6_eqrel_1),
    [interesting(0.00)]).

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

fof(s1_wellord2,theorem,
    ( ! [A] : ~ ( r2_hidden(A,f1_s1_wellord2)
        & ! [B] : ~ ( r2_hidden(B,f2_s1_wellord2)
            & p1_s1_wellord2(A,B) ) )
   => ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & k1_relat_1(A) = f1_s1_wellord2
        & r1_tarski(k2_relat_1(A),f2_s1_wellord2)
        & ! [B] : 
            ( r2_hidden(B,f1_s1_wellord2)
           => p1_s1_wellord2(B,k1_funct_1(A,B)) ) ) ),
    file(wellord2,s1_wellord2),
    [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(t9_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) ) )
           => A = B ) ) ) ),
    file(funct_1,t9_funct_1),
    [interesting(0.00)]).

fof(d7_pua2mss1,definition,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] : 
                  ( m2_relset_1(D,u1_struct_0(A),u1_struct_0(A))
                 => ( D = k9_pua2mss1(A,B,C)
                  <=> ? [E] : 
                        ( m1_pboole(E,k5_numbers)
                        & D = k1_funct_1(E,C)
                        & k1_funct_1(E,0) = B
                        & ! [F] : 
                            ( m2_subset_1(F,k1_numbers,k5_numbers)
                           => ! [G] : 
                                ( m2_relset_1(G,u1_struct_0(A),u1_struct_0(A))
                               => ( G = k1_funct_1(E,F)
                                 => k1_funct_1(E,k1_nat_1(F,1)) = k8_pua2mss1(A,G) ) ) ) ) ) ) ) ) ) ),
    file(pua2mss1,d7_pua2mss1),
    [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(t10_funct_6,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => r1_tarski(k4_card_3(A),k1_funct_2(k1_relat_1(A),k3_card_3(A))) ) ),
    file(funct_6,t10_funct_6),
    [interesting(0.00)]).

fof(d4_card_3,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => k3_card_3(A) = k3_tarski(k2_relat_1(A)) ) ),
    file(card_3,d4_card_3),
    [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(t95_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => r1_tarski(k3_tarski(A),k3_tarski(B)) ) ),
    file(zfmisc_1,t95_zfmisc_1),
    [interesting(0.00)]).

fof(t1_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_1),
    [interesting(0.00)]).

fof(t2_zfmisc_1,theorem,(
    k3_tarski(k1_xboole_0) = k1_xboole_0 ),
    file(zfmisc_1,t2_zfmisc_1),
    [interesting(0.00)]).

fof(d5_eqrel_1,definition,(
    ! [A,B] : 
      ( ( v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
         => ( C = k7_eqrel_1(A,B)
          <=> ! [D] : 
                ( m1_subset_1(D,k1_zfmisc_1(A))
               => ( r2_hidden(D,C)
                <=> ? [E] : 
                      ( r2_hidden(E,A)
                      & D = k6_eqrel_1(A,B,E) ) ) ) ) ) ) ),
    file(eqrel_1,d5_eqrel_1),
    [interesting(0.00)]).

fof(t33_eqrel_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(B,A)
     => k6_eqrel_1(A,k6_partfun1(A),B) = k1_tarski(B) ) ),
    file(eqrel_1,t33_eqrel_1),
    [interesting(0.00)]).

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

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

fof(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(d12_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( C = k9_relat_1(A,B)
        <=> ! [D] : 
              ( r2_hidden(D,C)
            <=> ? [E] : 
                  ( r2_hidden(E,k1_relat_1(A))
                  & r2_hidden(E,B)
                  & D = k1_funct_1(A,E) ) ) ) ) ),
    file(funct_1,d12_funct_1),
    [interesting(0.00)]).

fof(d9_pua2mss1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k3_finseq_2(A),A) )
         => ! [C] : 
              ( m1_eqrel_1(C,A)
             => ( r1_pua2mss1(A,B,C)
              <=> ! [D] : 
                    ( m2_finseq_1(D,C)
                   => ? [E] : 
                        ( m2_subset_1(E,k1_zfmisc_1(A),C)
                        & r1_tarski(k9_relat_1(B,k4_card_3(D)),E) ) ) ) ) ) ) ),
    file(pua2mss1,d9_pua2mss1),
    [interesting(0.00)]).

fof(d10_pua2mss1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k3_finseq_2(A),A) )
         => ! [C] : 
              ( m1_eqrel_1(C,A)
             => ( r2_pua2mss1(A,B,C)
              <=> ( r1_pua2mss1(A,B,C)
                  & ! [D] : 
                      ( m2_finseq_1(D,C)
                     => ( ~ r1_xboole_0(k4_card_3(D),k4_relset_1(k3_finseq_2(A),A,B))
                       => r1_tarski(k4_card_3(D),k4_relset_1(k3_finseq_2(A),A,B)) ) ) ) ) ) ) ) ),
    file(pua2mss1,d10_pua2mss1),
    [interesting(0.00)]).

fof(t27_partfun1,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & m2_relset_1(D,A,B) )
     => ( r2_hidden(C,k4_relset_1(A,B,D))
       => r2_hidden(k1_funct_1(D,C),B) ) ) ),
    file(partfun1,t27_partfun1),
    [interesting(0.00)]).

fof(t28_eqrel_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_2(B)
        & v3_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,k6_eqrel_1(A,B,C)) ) ) ),
    file(eqrel_1,t28_eqrel_1),
    [interesting(0.00)]).

fof(t27_eqrel_1,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_relat_2(D)
        & v3_relat_2(D)
        & v1_partfun1(D,A,A)
        & m2_relset_1(D,A,A) )
     => ( r2_hidden(B,k6_eqrel_1(A,D,C))
      <=> r2_hidden(k4_tarski(B,C),D) ) ) ),
    file(eqrel_1,t27_eqrel_1),
    [interesting(0.00)]).

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

fof(d8_pua2mss1,definition,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( B = k10_pua2mss1(A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_hidden(k4_tarski(C,D),B)
                    <=> ! [E] : 
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => r2_hidden(k4_tarski(C,D),k9_pua2mss1(A,k7_pua2mss1(A),E)) ) ) ) ) ) ) ) ),
    file(pua2mss1,d8_pua2mss1),
    [interesting(0.00)]).

fof(d5_pua2mss1,definition,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( B = k7_pua2mss1(A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_hidden(k4_tarski(C,D),B)
                    <=> ! [E] : 
                          ( m1_pua2mss1(E,k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),k1_pua2mss1(u1_struct_0(A),u1_unialg_1(A)))
                         => ! [F] : 
                              ( ( v1_relat_1(F)
                                & v1_funct_1(F)
                                & v1_finseq_1(F) )
                             => ! [G] : 
                                  ( ( v1_relat_1(G)
                                    & v1_funct_1(G)
                                    & v1_finseq_1(G) )
                                 => ( r2_hidden(k7_finseq_1(k7_finseq_1(F,k12_finseq_1(u1_struct_0(A),C)),G),k4_relset_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),E))
                                  <=> r2_hidden(k7_finseq_1(k7_finseq_1(F,k12_finseq_1(u1_struct_0(A),D)),G),k4_relset_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),E)) ) ) ) ) ) ) ) ) ) ) ),
    file(pua2mss1,d5_pua2mss1),
    [interesting(0.00)]).

fof(d6_pua2mss1,definition,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ! [C] : 
              ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
             => ( C = k8_pua2mss1(A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( r2_hidden(k4_tarski(D,E),C)
                        <=> ( r2_hidden(k4_tarski(D,E),B)
                            & ! [F] : 
                                ( m1_pua2mss1(F,k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),k1_pua2mss1(u1_struct_0(A),u1_unialg_1(A)))
                               => ! [G] : 
                                    ( ( v1_relat_1(G)
                                      & v1_funct_1(G)
                                      & v1_finseq_1(G) )
                                   => ! [H] : 
                                        ( ( v1_relat_1(H)
                                          & v1_funct_1(H)
                                          & v1_finseq_1(H) )
                                       => ( ( r2_hidden(k7_finseq_1(k7_finseq_1(G,k12_finseq_1(u1_struct_0(A),D)),H),k4_relset_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),F))
                                            & r2_hidden(k7_finseq_1(k7_finseq_1(G,k12_finseq_1(u1_struct_0(A),E)),H),k4_relset_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),F)) )
                                         => r2_hidden(k4_tarski(k1_funct_1(F,k7_finseq_1(k7_finseq_1(G,k12_finseq_1(u1_struct_0(A),D)),H)),k1_funct_1(F,k7_finseq_1(k7_finseq_1(G,k12_finseq_1(u1_struct_0(A),E)),H))),B) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(pua2mss1,d6_pua2mss1),
    [interesting(0.00)]).

fof(t11_eqrel_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_2(C)
        & v1_partfun1(C,A,A)
        & m2_relset_1(C,A,A) )
     => ( r2_hidden(B,A)
       => r2_hidden(k4_tarski(B,B),C) ) ) ),
    file(eqrel_1,t11_eqrel_1),
    [interesting(0.00)]).

fof(d1_relat_2,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r1_relat_2(A,B)
        <=> ! [C] : 
              ( r2_hidden(C,B)
             => r2_hidden(k4_tarski(C,C),A) ) ) ) ),
    file(relat_2,d1_relat_2),
    [interesting(0.00)]).

fof(t98_orders_1,theorem,(
    ! [A,B] : 
      ( m2_relset_1(B,A,A)
     => ( r1_relat_2(B,A)
       => ( k4_relset_1(A,A,B) = A
          & k3_relat_1(B) = A ) ) ) ),
    file(orders_1,t98_orders_1),
    [interesting(0.00)]).

fof(d4_partfun1,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( v1_partfun1(C,A,B)
      <=> k4_relset_1(A,B,C) = A ) ) ),
    file(partfun1,d4_partfun1),
    [interesting(0.00)]).

fof(t12_eqrel_1,theorem,(
    ! [A,B,C,D] : 
      ( ( v3_relat_2(D)
        & v1_partfun1(D,A,A)
        & m2_relset_1(D,A,A) )
     => ( r2_hidden(k4_tarski(B,C),D)
       => r2_hidden(k4_tarski(C,B),D) ) ) ),
    file(eqrel_1,t12_eqrel_1),
    [interesting(0.00)]).

fof(d3_relat_2,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r3_relat_2(A,B)
        <=> ! [C,D] : 
              ( ( r2_hidden(C,B)
                & r2_hidden(D,B)
                & r2_hidden(k4_tarski(C,D),A) )
             => r2_hidden(k4_tarski(D,C),A) ) ) ) ),
    file(relat_2,d3_relat_2),
    [interesting(0.00)]).

fof(d11_relat_2,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v3_relat_2(A)
      <=> r3_relat_2(A,k3_relat_1(A)) ) ) ),
    file(relat_2,d11_relat_2),
    [interesting(0.00)]).

fof(t13_eqrel_1,theorem,(
    ! [A,B,C,D,E] : 
      ( ( v8_relat_2(E)
        & v1_partfun1(E,A,A)
        & m2_relset_1(E,A,A) )
     => ( ( r2_hidden(k4_tarski(B,C),E)
          & r2_hidden(k4_tarski(C,D),E) )
       => r2_hidden(k4_tarski(B,D),E) ) ) ),
    file(eqrel_1,t13_eqrel_1),
    [interesting(0.00)]).

fof(d8_relat_2,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r8_relat_2(A,B)
        <=> ! [C,D,E] : 
              ( ( r2_hidden(C,B)
                & r2_hidden(D,B)
                & r2_hidden(E,B)
                & r2_hidden(k4_tarski(C,D),A)
                & r2_hidden(k4_tarski(D,E),A) )
             => r2_hidden(k4_tarski(C,E),A) ) ) ) ),
    file(relat_2,d8_relat_2),
    [interesting(0.00)]).

fof(d16_relat_2,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v8_relat_2(A)
      <=> r8_relat_2(A,k3_relat_1(A)) ) ) ),
    file(relat_2,d16_relat_2),
    [interesting(0.00)]).

fof(t30_eqrel_1,theorem,(
    ! [A,B,C,D,E] : 
      ( ( v1_relat_2(E)
        & v3_relat_2(E)
        & v8_relat_2(E)
        & v1_partfun1(E,A,A)
        & m2_relset_1(E,A,A) )
     => ( ( r2_hidden(B,k6_eqrel_1(A,E,C))
          & r2_hidden(D,k6_eqrel_1(A,E,C)) )
       => r2_hidden(k4_tarski(B,D),E) ) ) ),
    file(eqrel_1,t30_eqrel_1),
    [interesting(0.00)]).

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

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

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

fof(t35_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(t6_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => r2_hidden(k2_xcmplx_0(A,1),k2_finseq_1(k2_xcmplx_0(A,1))) ) ),
    file(finseq_1,t6_finseq_1),
    [interesting(0.00)]).

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

fof(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(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(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(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(d7_xboole_0,definition,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
    <=> k3_xboole_0(A,B) = k1_xboole_0 ) ),
    file(xboole_0,d7_xboole_0),
    [interesting(0.00)]).

fof(t145_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => k9_relat_1(B,A) = k9_relat_1(B,k3_xboole_0(k1_relat_1(B),A)) ) ),
    file(relat_1,t145_relat_1),
    [interesting(0.00)]).

fof(t149_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => k9_relat_1(A,k1_xboole_0) = k1_xboole_0 ) ),
    file(relat_1,t149_relat_1),
    [interesting(0.00)]).

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

fof(d11_pua2mss1,definition,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m1_eqrel_1(B,u1_struct_0(A))
         => ( m3_pua2mss1(B,A)
          <=> ! [C] : 
                ( m1_pua2mss1(C,k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),k1_pua2mss1(u1_struct_0(A),u1_unialg_1(A)))
               => r2_pua2mss1(u1_struct_0(A),C,B) ) ) ) ) ),
    file(pua2mss1,d11_pua2mss1),
    [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(t79_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(k2_relat_1(B),A)
       => k5_relat_1(B,k6_relat_1(A)) = B ) ) ),
    file(relat_1,t79_relat_1),
    [interesting(0.00)]).

fof(t42_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( k5_relat_1(k6_relat_1(k1_relat_1(A)),A) = A
        & k5_relat_1(A,k6_relat_1(k2_relat_1(A))) = A ) ) ),
    file(funct_1,t42_funct_1),
    [interesting(0.00)]).

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

fof(d13_pua2mss1,definition,(
    ! [A] : 
      ( l1_msualg_1(A)
     => ! [B] : 
          ( l1_msualg_1(B)
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( r3_pua2mss1(A,B,C,D)
                  <=> ( k1_relat_1(C) = u1_struct_0(A)
                      & k1_relat_1(D) = u1_msualg_1(A)
                      & r1_tarski(k2_relat_1(C),u1_struct_0(B))
                      & r1_tarski(k2_relat_1(D),u1_msualg_1(B))
                      & k5_relat_1(u3_msualg_1(A),C) = k5_relat_1(D,u3_msualg_1(B))
                      & ! [E,F] : 
                          ( ( v1_relat_1(F)
                            & v1_funct_1(F) )
                         => ( ( r2_hidden(E,u1_msualg_1(A))
                              & F = k1_funct_1(u2_msualg_1(A),E) )
                           => k5_relat_1(F,C) = k1_funct_1(u2_msualg_1(B),k1_funct_1(D,E)) ) ) ) ) ) ) ) ) ),
    file(pua2mss1,d13_pua2mss1),
    [interesting(0.00)]).

fof(t34_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( B = k6_relat_1(A)
      <=> ( k1_relat_1(B) = A
          & ! [C] : 
              ( r2_hidden(C,A)
             => k1_funct_1(B,C) = C ) ) ) ) ),
    file(funct_1,t34_funct_1),
    [interesting(0.00)]).

fof(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(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(d14_pua2mss1,definition,(
    ! [A] : 
      ( l1_msualg_1(A)
     => ! [B] : 
          ( l1_msualg_1(B)
         => ( r4_pua2mss1(A,B)
          <=> ? [C] : 
                ( v1_relat_1(C)
                & v1_funct_1(C)
                & ? [D] : 
                    ( v1_relat_1(D)
                    & v1_funct_1(D)
                    & r3_pua2mss1(B,A,C,D)
                    & k2_relat_1(C) = u1_struct_0(A)
                    & k2_relat_1(D) = u1_msualg_1(A) ) ) ) ) ) ),
    file(pua2mss1,d14_pua2mss1),
    [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(t45_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => r1_tarski(k2_relat_1(k5_relat_1(A,B)),k2_relat_1(B)) ) ) ),
    file(relat_1,t45_relat_1),
    [interesting(0.00)]).

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

fof(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(t30_pua2mss1,theorem,(
    ! [A] : 
      ( l1_msualg_1(A)
     => ! [B] : 
          ( l1_msualg_1(B)
         => ! [C] : 
              ( l1_msualg_1(C)
             => ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ! [E] : 
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E) )
                     => ! [F] : 
                          ( ( v1_relat_1(F)
                            & v1_funct_1(F) )
                         => ! [G] : 
                              ( ( v1_relat_1(G)
                                & v1_funct_1(G) )
                             => ( ( r3_pua2mss1(A,B,D,F)
                                  & r3_pua2mss1(B,C,E,G) )
                               => r3_pua2mss1(A,C,k5_relat_1(D,E),k5_relat_1(F,G)) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d13_pua2mss1,t46_relat_1,d13_pua2mss1,t45_relat_1,t1_xboole_1,t55_relat_1,t55_relat_1,t55_relat_1,d5_funct_1,t23_funct_1,t55_relat_1]),
    [file(pua2mss1,t30_pua2mss1),interesting(0.00)]).

fof(t47_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(k1_relat_1(A),k2_relat_1(B))
           => k2_relat_1(k5_relat_1(B,A)) = k2_relat_1(A) ) ) ) ),
    file(relat_1,t47_relat_1),
    [interesting(0.00)]).

fof(d15_pua2mss1,definition,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m3_pua2mss1(B,A)
         => ! [C] : 
              ( ( v1_msualg_1(C)
                & l1_msualg_1(C) )
             => ( C = k12_pua2mss1(A,B)
              <=> ( u1_struct_0(C) = B
                  & u1_msualg_1(C) = a_2_2_pua2mss1(A,B)
                  & ! [D] : 
                      ( m1_subset_1(D,k4_finseq_1(u1_unialg_1(A)))
                     => ! [E] : 
                          ( m2_finseq_2(E,B,k3_finseq_2(B))
                         => ( ~ r2_subset_1(k4_card_3(E),k4_relset_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),k2_pua2mss1(A,D)))
                           => ( k1_funct_1(u2_msualg_1(C),k4_tarski(D,E)) = E
                              & r1_tarski(k9_relat_1(k2_pua2mss1(A,D),k4_card_3(E)),k1_funct_1(u3_msualg_1(C),k4_tarski(D,E))) ) ) ) ) ) ) ) ) ) ),
    file(pua2mss1,d15_pua2mss1),
    [interesting(0.00)]).

fof(s5_pboole,theorem,(
    ? [A] : 
      ( m1_pboole(A,f1_s5_pboole)
      & ! [B] : 
          ( m1_subset_1(B,f1_s5_pboole)
         => k1_funct_1(A,B) = f2_s5_pboole(B) ) ) ),
    file(pboole,s5_pboole),
    [interesting(0.00)]).

fof(d15_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_relat_1(A)
      <=> ! [B] : ~ ( r2_hidden(B,k1_relat_1(A))
            & v1_xboole_0(k1_funct_1(A,B)) ) ) ) ),
    file(funct_1,d15_funct_1),
    [interesting(0.00)]).

fof(t7_mcart_1,theorem,(
    ! [A,B] : 
      ( k1_mcart_1(k4_tarski(A,B)) = A
      & k2_mcart_1(k4_tarski(A,B)) = B ) ),
    file(mcart_1,t7_mcart_1),
    [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(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(t148_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => k2_relat_1(k7_relat_1(B,A)) = k9_relat_1(B,A) ) ),
    file(relat_1,t148_relat_1),
    [interesting(0.00)]).

fof(t91_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(A,k1_relat_1(B))
       => k1_relat_1(k7_relat_1(B,A)) = A ) ) ),
    file(relat_1,t91_relat_1),
    [interesting(0.00)]).

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

fof(t10_card_5,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r2_hidden(A,k3_card_3(B))
      <=> ? [C] : 
            ( r2_hidden(C,k1_relat_1(B))
            & r2_hidden(A,k1_funct_1(B,C)) ) ) ) ),
    file(card_5,t10_card_5),
    [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(d3_pua2mss1,definition,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( m2_pua2mss1(B,A)
      <=> ( m1_eqrel_1(k2_relat_1(B),A)
          & v2_funct_1(B) ) ) ) ),
    file(pua2mss1,d3_pua2mss1),
    [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(d17_pua2mss1,definition,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ( r7_pua2mss1(A,B)
          <=> ? [C] : 
                ( l3_msualg_1(C,B)
                & ? [D] : 
                    ( m2_pua2mss1(D,u1_msualg_1(B))
                    & r6_pua2mss1(A,B,C,D) ) ) ) ) ) ),
    file(pua2mss1,d17_pua2mss1),
    [interesting(0.00)]).

fof(d12_pua2mss1,definition,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m2_pua2mss1(B,u1_struct_0(A))
         => ( m4_pua2mss1(B,A)
          <=> m3_pua2mss1(k4_pua2mss1(u1_struct_0(A),B),A) ) ) ) ),
    file(pua2mss1,d12_pua2mss1),
    [interesting(0.00)]).

fof(d16_pua2mss1,definition,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] : 
              ( l3_msualg_1(C,B)
             => ! [D] : 
                  ( m2_pua2mss1(D,u1_msualg_1(B))
                 => ( r6_pua2mss1(A,B,C,D)
                  <=> ( m4_pua2mss1(u4_msualg_1(B,C),A)
                      & k1_relat_1(D) = k4_finseq_1(u1_unialg_1(A))
                      & ! [E] : 
                          ( m1_subset_1(E,k4_finseq_1(u1_unialg_1(A)))
                         => m2_pua2mss1(k7_relat_1(u5_msualg_1(B,C),k1_funct_1(D,E)),k2_pua2mss1(A,E)) ) ) ) ) ) ) ) ),
    file(pua2mss1,d16_pua2mss1),
    [interesting(0.00)]).

fof(t26_xboole_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(A,B)
     => r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,C)) ) ),
    file(xboole_1,t26_xboole_1),
    [interesting(0.00)]).

fof(t28_xboole_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => k3_xboole_0(A,B) = A ) ),
    file(xboole_1,t28_xboole_1),
    [interesting(0.00)]).

fof(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(t74_xboole_1,theorem,(
    ! [A,B,C] : ~ ( ~ r1_xboole_0(A,k3_xboole_0(B,C))
      & r1_xboole_0(A,B) ) ),
    file(xboole_1,t74_xboole_1),
    [interesting(0.00)]).

fof(t65_xboole_1,theorem,(
    ! [A] : r1_xboole_0(A,k1_xboole_0) ),
    file(xboole_1,t65_xboole_1),
    [interesting(0.00)]).

fof(t88_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => r1_tarski(k7_relat_1(B,A),B) ) ),
    file(relat_1,t88_relat_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(d4_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( B = k1_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : r2_hidden(k4_tarski(C,D),A) ) ) ) ),
    file(relat_1,d4_relat_1),
    [interesting(0.00)]).

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

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

fof(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(t70_funct_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(B,k1_relat_1(k7_relat_1(C,A)))
       => k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B) ) ) ),
    file(funct_1,t70_funct_1),
    [interesting(0.00)]).

fof(t73_funct_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( ( r2_hidden(B,k1_relat_1(C))
          & r2_hidden(B,A) )
       => r2_hidden(k1_funct_1(C,B),k2_relat_1(k7_relat_1(C,A))) ) ) ),
    file(funct_1,t73_funct_1),
    [interesting(0.00)]).

fof(s1_partfun1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_relat_1(A) = f1_s1_partfun1
      & ! [B] : 
          ( r2_hidden(B,f1_s1_partfun1)
         => ( ( p1_s1_partfun1(B)
             => k1_funct_1(A,B) = f2_s1_partfun1(B) )
            & ( ~ p1_s1_partfun1(B)
             => k1_funct_1(A,B) = f3_s1_partfun1(B) ) ) ) ) ),
    file(partfun1,s1_partfun1),
    [interesting(0.00)]).

fof(t1_pua2mss1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v2_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_tarski(k4_card_3(A),k4_card_3(B))
           => ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => r1_tarski(k1_funct_1(A,C),k1_funct_1(B,C)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_card_3,d3_tarski,s1_partfun1,t18_card_3,t18_card_3,t18_card_3]),
    [file(pua2mss1,t1_pua2mss1),interesting(0.00)]).

fof(d8_msualg_1,definition,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( l2_msualg_1(B,A)
         => ( v5_msualg_1(B,A)
          <=> v2_relat_1(u4_msualg_1(A,B)) ) ) ) ),
    file(msualg_1,d8_msualg_1),
    [interesting(0.00)]).

fof(t11_relset_1,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( ( r1_tarski(k1_relat_1(C),A)
          & r1_tarski(k2_relat_1(C),B) )
       => m2_relset_1(C,A,B) ) ) ),
    file(relset_1,t11_relset_1),
    [interesting(0.00)]).

fof(t43_eqrel_1,theorem,(
    ! [A,B] : 
      ( m1_eqrel_1(B,A)
     => ? [C] : 
          ( v3_relat_2(C)
          & v8_relat_2(C)
          & v1_partfun1(C,A,A)
          & m2_relset_1(C,A,A)
          & B = k7_eqrel_1(A,C) ) ) ),
    file(eqrel_1,t43_eqrel_1),
    [interesting(0.00)]).

fof(d2_setfam_1,definition,(
    ! [A,B] : 
      ( r1_setfam_1(A,B)
    <=> ! [C] : ~ ( r2_hidden(C,A)
          & ! [D] : ~ ( r2_hidden(D,B)
              & r1_tarski(C,D) ) ) ) ),
    file(setfam_1,d2_setfam_1),
    [interesting(0.00)]).

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

fof(t38_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_subset_1(C,k1_numbers,k5_numbers)
             => ~ ( r2_hidden(C,k4_finseq_1(k7_finseq_1(A,B)))
                  & ~ r2_hidden(C,k4_finseq_1(A))
                  & ! [D] : 
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ~ ( r2_hidden(D,k4_finseq_1(B))
                          & C = k1_nat_1(k3_finseq_1(A),D) ) ) ) ) ) ) ),
    file(finseq_1,t38_finseq_1),
    [interesting(0.00)]).

fof(t4_finseq_1,theorem,
    ( k2_finseq_1(0) = k1_xboole_0
    & k2_finseq_1(1) = k1_tarski(1)
    & k2_finseq_1(2) = k2_tarski(1,2) ),
    file(finseq_1,t4_finseq_1),
    [interesting(0.00)]).

fof(t38_card_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => r1_tarski(k1_funct_1(A,C),k1_funct_1(B,C)) ) )
           => r1_tarski(k4_card_3(A),k4_card_3(B)) ) ) ) ),
    file(card_3,t38_card_3),
    [interesting(0.00)]).

fof(d4_pua2mss1,definition,(
    ! [A,B] : 
      ( m2_pua2mss1(B,A)
     => ! [C] : 
          ( r2_hidden(C,A)
         => ! [D] : 
              ( D = k6_pua2mss1(A,B,C)
            <=> ( r2_hidden(D,k1_relat_1(B))
                & r2_hidden(C,k1_funct_1(B,D)) ) ) ) ) ),
    file(pua2mss1,d4_pua2mss1),
    [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(t21_funct_2,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ! [E] : 
          ( ( v1_relat_1(E)
            & v1_funct_1(E) )
         => ( r2_hidden(C,A)
           => ( B = k1_xboole_0
              | k1_funct_1(k5_relat_1(D,E),C) = k1_funct_1(E,k1_funct_1(D,C)) ) ) ) ) ),
    file(funct_2,t21_funct_2),
    [interesting(0.00)]).

fof(t146_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => k9_relat_1(A,k1_relat_1(A)) = k2_relat_1(A) ) ),
    file(relat_1,t146_relat_1),
    [interesting(0.00)]).

fof(t156_relat_1,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( r1_tarski(A,B)
       => r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B)) ) ) ),
    file(relat_1,t156_relat_1),
    [interesting(0.00)]).

fof(t157_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ! [C] : 
          ( v1_relat_1(C)
         => ( r1_tarski(B,C)
           => r1_tarski(k9_relat_1(B,A),k9_relat_1(C,A)) ) ) ) ),
    file(relat_1,t157_relat_1),
    [interesting(0.00)]).

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

fof(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(d2_zfmisc_1,definition,(
    ! [A,B,C] : 
      ( C = k2_zfmisc_1(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ? [E,F] : 
              ( r2_hidden(E,A)
              & r2_hidden(F,B)
              & D = k4_tarski(E,F) ) ) ) ),
    file(zfmisc_1,d2_zfmisc_1),
    [interesting(0.00)]).

fof(t123_zfmisc_1,theorem,(
    ! [A,B,C,D] : k2_zfmisc_1(k3_xboole_0(A,B),k3_xboole_0(C,D)) = k3_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) ),
    file(zfmisc_1,t123_zfmisc_1),
    [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)]).