% Mizar problem: t96_cohsp_1,cohsp_1,3627,44 
fof(t96_cohsp_1,conjecture,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => k13_cohsp_1(k15_cohsp_1(A,B)) = k16_cohsp_1(k13_cohsp_1(A),k13_cohsp_1(B)) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_finseq_1,cc1_finset_1,cc1_finsub_1,cc1_nat_1,cc1_relset_1,cc2_finset_1,cc2_finsub_1,cc2_nat_1,cc3_cohsp_1,cc3_nat_1,cc4_cohsp_1,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k3_xboole_0,d10_xboole_0,d1_tarski,d22_cohsp_1,d23_cohsp_1,d24_cohsp_1,d25_cohsp_1,d3_tarski,d3_xboole_0,d4_tarski,d5_tarski,dt_k10_finseq_1,dt_k13_cohsp_1,dt_k14_cohsp_1,dt_k15_cohsp_1,dt_k16_cohsp_1,dt_k1_mcart_1,dt_k1_numbers,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_card_3,dt_k2_mcart_1,dt_k2_tarski,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_card_3,dt_k3_tarski,dt_k3_xboole_0,dt_k4_tarski,dt_k5_numbers,dt_k5_ordinal2,dt_m1_subset_1,existence_m1_subset_1,fc10_finset_1,fc11_finset_1,fc13_cohsp_1,fc14_cohsp_1,fc14_finset_1,fc15_cohsp_1,fc1_cohsp_1,fc1_finset_1,fc1_finsub_1,fc2_cohsp_1,fc2_finseq_1,fc2_finset_1,fc5_finseq_1,fc7_finseq_1,fc9_finset_1,fraenkel_a_1_2_cohsp_1,fraenkel_a_1_3_cohsp_1,fraenkel_a_1_4_cohsp_1,fraenkel_a_2_0_cohsp_1,idempotence_k2_xboole_0,idempotence_k3_xboole_0,rc1_cohsp_1,rc1_finseq_1,rc1_finset_1,rc1_finsub_1,rc1_nat_1,rc1_partfun1,rc2_cohsp_1,rc2_finset_1,rc2_nat_1,rc3_finseq_1,rc3_finset_1,rc3_nat_1,rc4_finset_1,rc5_cohsp_1,rc6_cohsp_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,redefinition_k5_numbers,reflexivity_r1_tarski,spc0_boole,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,t106_zfmisc_1,t1_boole,t1_coh_sp,t1_numerals,t1_subset,t1_xboole_1,t2_boole,t2_subset,t2_tarski,t2_xboole_1,t33_zfmisc_1,t3_subset,t4_coh_sp,t4_subset,t5_subset,t66_cohsp_1,t67_cohsp_1,t6_boole,t74_cohsp_1,t76_cohsp_1,t77_cohsp_1,t78_cohsp_1,t79_cohsp_1,t7_boole,t7_xboole_1,t80_cohsp_1,t83_cohsp_1,t84_cohsp_1,t86_cohsp_1,t87_cohsp_1,t88_cohsp_1,t8_boole,t92_zfmisc_1]),
    [file(cohsp_1,t96_cohsp_1)]).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

fof(cc1_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) ) ) ),
    file(finseq_1,cc1_finseq_1),
    []).

fof(cc1_finset_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_1),
    []).

fof(cc1_finsub_1,axiom,(
    ! [A] : 
      ( v4_finsub_1(A)
     => ( v1_finsub_1(A)
        & v3_finsub_1(A) ) ) ),
    file(finsub_1,cc1_finsub_1),
    []).

fof(cc1_nat_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(nat_1,cc1_nat_1),
    []).

fof(cc1_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    []).

fof(cc2_finset_1,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_finset_1(B) ) ) ),
    file(finset_1,cc2_finset_1),
    []).

fof(cc2_finsub_1,axiom,(
    ! [A] : 
      ( ( v1_finsub_1(A)
        & v3_finsub_1(A) )
     => v4_finsub_1(A) ) ),
    file(finsub_1,cc2_finsub_1),
    []).

fof(cc2_nat_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc2_nat_1),
    []).

fof(cc3_cohsp_1,axiom,(
    ! [A] : 
      ( v1_classes1(A)
     => v2_finsub_1(A) ) ),
    file(cohsp_1,cc3_cohsp_1),
    []).

fof(cc3_nat_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc3_nat_1),
    []).

fof(cc4_cohsp_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ( ~ v1_xboole_0(A)
        & v2_finsub_1(A)
        & v1_classes1(A)
        & v1_coh_sp(A)
        & v3_cohsp_1(A) ) ) ),
    file(cohsp_1,cc4_cohsp_1),
    []).

fof(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

fof(commutativity_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    []).

fof(commutativity_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file(xboole_0,k3_xboole_0),
    []).

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

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

fof(d22_cohsp_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => k13_cohsp_1(A) = a_1_2_cohsp_1(A) ) ),
    file(cohsp_1,d22_cohsp_1),
    []).

fof(d23_cohsp_1,axiom,(
    ! [A,B] : k14_cohsp_1(A,B) = k3_card_3(k2_card_3(k10_finseq_1(A,B))) ),
    file(cohsp_1,d23_cohsp_1),
    []).

fof(d24_cohsp_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => k15_cohsp_1(A,B) = a_2_0_cohsp_1(A,B) ) ) ),
    file(cohsp_1,d24_cohsp_1),
    []).

fof(d25_cohsp_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => k16_cohsp_1(A,B) = k2_xboole_0(a_1_3_cohsp_1(A),a_1_4_cohsp_1(B)) ) ) ),
    file(cohsp_1,d25_cohsp_1),
    []).

fof(d3_tarski,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    []).

fof(d3_xboole_0,axiom,(
    ! [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),
    []).

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

fof(d5_tarski,axiom,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    []).

fof(dt_k10_finseq_1,axiom,(
    $true ),
    file(finseq_1,k10_finseq_1),
    []).

fof(dt_k13_cohsp_1,axiom,(
    $true ),
    file(cohsp_1,k13_cohsp_1),
    []).

fof(dt_k14_cohsp_1,axiom,(
    $true ),
    file(cohsp_1,k14_cohsp_1),
    []).

fof(dt_k15_cohsp_1,axiom,(
    $true ),
    file(cohsp_1,k15_cohsp_1),
    []).

fof(dt_k16_cohsp_1,axiom,(
    $true ),
    file(cohsp_1,k16_cohsp_1),
    []).

fof(dt_k1_mcart_1,axiom,(
    $true ),
    file(mcart_1,k1_mcart_1),
    []).

fof(dt_k1_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    []).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

fof(dt_k2_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k2_card_3(A))
        & v1_funct_1(k2_card_3(A)) ) ) ),
    file(card_3,k2_card_3),
    []).

fof(dt_k2_mcart_1,axiom,(
    $true ),
    file(mcart_1,k2_mcart_1),
    []).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_k3_card_3,axiom,(
    $true ),
    file(card_3,k3_card_3),
    []).

fof(dt_k3_tarski,axiom,(
    $true ),
    file(tarski,k3_tarski),
    []).

fof(dt_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    []).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

fof(dt_k5_numbers,axiom,(
    m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ),
    file(numbers,k5_numbers),
    []).

fof(dt_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(fc10_finset_1,axiom,(
    ! [A,B] : 
      ( v1_finset_1(B)
     => v1_finset_1(k3_xboole_0(A,B)) ) ),
    file(finset_1,fc10_finset_1),
    []).

fof(fc11_finset_1,axiom,(
    ! [A,B] : 
      ( v1_finset_1(A)
     => v1_finset_1(k3_xboole_0(A,B)) ) ),
    file(finset_1,fc11_finset_1),
    []).

fof(fc13_cohsp_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ( ~ v1_xboole_0(k13_cohsp_1(A))
        & v2_finsub_1(k13_cohsp_1(A))
        & v1_classes1(k13_cohsp_1(A))
        & v1_coh_sp(k13_cohsp_1(A))
        & v3_cohsp_1(k13_cohsp_1(A)) ) ) ),
    file(cohsp_1,fc13_cohsp_1),
    []).

fof(fc14_cohsp_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A)
        & ~ v1_xboole_0(B)
        & v1_classes1(B)
        & v1_coh_sp(B) )
     => ( ~ v1_xboole_0(k15_cohsp_1(A,B))
        & v2_finsub_1(k15_cohsp_1(A,B))
        & v1_classes1(k15_cohsp_1(A,B))
        & v1_coh_sp(k15_cohsp_1(A,B))
        & v3_cohsp_1(k15_cohsp_1(A,B)) ) ) ),
    file(cohsp_1,fc14_cohsp_1),
    []).

fof(fc14_finset_1,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_zfmisc_1(A,B)) ) ),
    file(finset_1,fc14_finset_1),
    []).

fof(fc15_cohsp_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A)
        & ~ v1_xboole_0(B)
        & v1_classes1(B)
        & v1_coh_sp(B) )
     => ( ~ v1_xboole_0(k16_cohsp_1(A,B))
        & v2_finsub_1(k16_cohsp_1(A,B))
        & v1_classes1(k16_cohsp_1(A,B))
        & v1_coh_sp(k16_cohsp_1(A,B))
        & v3_cohsp_1(k16_cohsp_1(A,B)) ) ) ),
    file(cohsp_1,fc15_cohsp_1),
    []).

fof(fc1_cohsp_1,axiom,
    ( ~ v1_xboole_0(k1_tarski(k1_xboole_0))
    & v1_classes1(k1_tarski(k1_xboole_0))
    & v1_finset_1(k1_tarski(k1_xboole_0))
    & v1_coh_sp(k1_tarski(k1_xboole_0)) ),
    file(cohsp_1,fc1_cohsp_1),
    []).

fof(fc1_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A)) ) ),
    file(finset_1,fc1_finset_1),
    []).

fof(fc1_finsub_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_zfmisc_1(A))
      & v1_finsub_1(k1_zfmisc_1(A))
      & v3_finsub_1(k1_zfmisc_1(A))
      & v4_finsub_1(k1_zfmisc_1(A)) ) ),
    file(finsub_1,fc1_finsub_1),
    []).

fof(fc2_cohsp_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_zfmisc_1(A))
      & v1_finsub_1(k1_zfmisc_1(A))
      & v3_finsub_1(k1_zfmisc_1(A))
      & v4_finsub_1(k1_zfmisc_1(A))
      & v1_classes1(k1_zfmisc_1(A))
      & v1_coh_sp(k1_zfmisc_1(A)) ) ),
    file(cohsp_1,fc2_cohsp_1),
    []).

fof(fc2_finseq_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0) ),
    file(finseq_1,fc2_finseq_1),
    []).

fof(fc2_finset_1,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(k2_tarski(A,B))
      & v1_finset_1(k2_tarski(A,B)) ) ),
    file(finset_1,fc2_finset_1),
    []).

fof(fc5_finseq_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(k10_finseq_1(A,B))
      & v1_funct_1(k10_finseq_1(A,B)) ) ),
    file(finseq_1,fc5_finseq_1),
    []).

fof(fc7_finseq_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(k10_finseq_1(A,B))
      & v1_funct_1(k10_finseq_1(A,B))
      & v1_finset_1(k10_finseq_1(A,B))
      & v1_finseq_1(k10_finseq_1(A,B)) ) ),
    file(finseq_1,fc7_finseq_1),
    []).

fof(fc9_finset_1,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_xboole_0(A,B)) ) ),
    file(finset_1,fc9_finset_1),
    []).

fof(fraenkel_a_1_2_cohsp_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & v1_classes1(B)
        & v1_coh_sp(B) )
     => ( r2_hidden(A,a_1_2_cohsp_1(B))
      <=> ? [C] : 
            ( m1_subset_1(C,k1_zfmisc_1(k3_tarski(B)))
            & A = C
            & ! [D] : 
                ( m1_subset_1(D,B)
               => ? [E] : r1_tarski(k3_xboole_0(C,D),k1_tarski(E)) ) ) ) ) ),
    file(cohsp_1,a_1_2_cohsp_1),
    []).

fof(fraenkel_a_1_3_cohsp_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & v1_classes1(B)
        & v1_coh_sp(B) )
     => ( r2_hidden(A,a_1_3_cohsp_1(B))
      <=> ? [C] : 
            ( m1_subset_1(C,B)
            & A = k14_cohsp_1(C,k1_xboole_0) ) ) ) ),
    file(cohsp_1,a_1_3_cohsp_1),
    []).

fof(fraenkel_a_1_4_cohsp_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & v1_classes1(B)
        & v1_coh_sp(B) )
     => ( r2_hidden(A,a_1_4_cohsp_1(B))
      <=> ? [C] : 
            ( m1_subset_1(C,B)
            & A = k14_cohsp_1(k1_xboole_0,C) ) ) ) ),
    file(cohsp_1,a_1_4_cohsp_1),
    []).

fof(fraenkel_a_2_0_cohsp_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & v1_classes1(B)
        & v1_coh_sp(B)
        & ~ v1_xboole_0(C)
        & v1_classes1(C)
        & v1_coh_sp(C) )
     => ( r2_hidden(A,a_2_0_cohsp_1(B,C))
      <=> ? [D,E] : 
            ( m1_subset_1(D,B)
            & m1_subset_1(E,C)
            & A = k14_cohsp_1(D,E) ) ) ) ),
    file(cohsp_1,a_2_0_cohsp_1),
    []).

fof(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

fof(idempotence_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,A) = A ),
    file(xboole_0,k3_xboole_0),
    []).

fof(rc1_cohsp_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_classes1(A)
      & v1_finset_1(A)
      & v1_coh_sp(A) ) ),
    file(cohsp_1,rc1_cohsp_1),
    []).

fof(rc1_finseq_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc1_finseq_1),
    []).

fof(rc1_finset_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A) ) ),
    file(finset_1,rc1_finset_1),
    []).

fof(rc1_finsub_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finsub_1(A)
      & v2_finsub_1(A)
      & v3_finsub_1(A)
      & v4_finsub_1(A) ) ),
    file(finsub_1,rc1_finsub_1),
    []).

fof(rc1_nat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc1_nat_1),
    []).

fof(rc1_partfun1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A) ) ),
    file(partfun1,rc1_partfun1),
    []).

fof(rc2_cohsp_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ? [B] : 
          ( m1_subset_1(B,A)
          & v1_finset_1(B) ) ) ),
    file(cohsp_1,rc2_cohsp_1),
    []).

fof(rc2_finset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_ordinal1(B)
      & v2_ordinal1(B)
      & v3_ordinal1(B)
      & v4_ordinal2(B)
      & v1_finset_1(B) ) ),
    file(finset_1,rc2_finset_1),
    []).

fof(rc2_nat_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v3_ordinal1(A) ) ),
    file(nat_1,rc2_nat_1),
    []).

fof(rc3_finseq_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc3_finseq_1),
    []).

fof(rc3_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc3_finset_1),
    []).

fof(rc3_nat_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k5_numbers)
      & ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc3_nat_1),
    []).

fof(rc4_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc4_finset_1),
    []).

fof(rc5_cohsp_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finsub_1(B)
          & v3_finsub_1(B)
          & v4_finsub_1(B) ) ) ),
    file(cohsp_1,rc5_cohsp_1),
    []).

fof(rc6_cohsp_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v2_finsub_1(A)
      & v1_classes1(A)
      & v1_coh_sp(A)
      & v3_cohsp_1(A) ) ),
    file(cohsp_1,rc6_cohsp_1),
    []).

fof(rc6_finseq_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc6_finseq_1),
    []).

fof(rc7_finseq_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc7_finseq_1),
    []).

fof(rc8_finseq_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc8_finseq_1),
    []).

fof(redefinition_k5_numbers,axiom,(
    k5_numbers = k5_ordinal2 ),
    file(numbers,k5_numbers),
    []).

fof(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(spc0_boole,axiom,(
    v1_xboole_0(0) ),
    file(boole,spc0_boole),
    []).

fof(spc1_boole,axiom,(
    ~ v1_xboole_0(1) ),
    file(boole,spc1_boole),
    []).

fof(spc1_numerals,axiom,
    ( v2_xreal_0(1)
    & m1_subset_1(1,k5_numbers) ),
    file(numerals,spc1_numerals),
    []).

fof(spc2_boole,axiom,(
    ~ v1_xboole_0(2) ),
    file(boole,spc2_boole),
    []).

fof(spc2_numerals,axiom,
    ( v2_xreal_0(2)
    & m1_subset_1(2,k5_numbers) ),
    file(numerals,spc2_numerals),
    []).

fof(t106_zfmisc_1,axiom,(
    ! [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),
    []).

fof(t1_boole,axiom,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    []).

fof(t1_coh_sp,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => r2_hidden(k1_xboole_0,A) ) ),
    file(coh_sp,t1_coh_sp),
    []).

fof(t1_numerals,axiom,(
    m1_subset_1(0,k5_numbers) ),
    file(numerals,t1_numerals),
    []).

fof(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

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

fof(t2_boole,axiom,(
    ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ),
    file(boole,t2_boole),
    []).

fof(t2_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    []).

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

fof(t2_xboole_1,axiom,(
    ! [A] : r1_tarski(k1_xboole_0,A) ),
    file(xboole_1,t2_xboole_1),
    []).

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

fof(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).

fof(t4_coh_sp,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & v1_classes1(B)
        & v1_coh_sp(B) )
     => ( r2_hidden(A,k3_tarski(B))
       => r2_hidden(k1_tarski(A),B) ) ) ),
    file(coh_sp,t4_coh_sp),
    []).

fof(t4_subset,axiom,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    []).

fof(t5_subset,axiom,(
    ! [A,B,C] : ~ ( r2_hidden(A,B)
      & m1_subset_1(B,k1_zfmisc_1(C))
      & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    []).

fof(t66_cohsp_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] : 
          ( r2_hidden(B,k13_cohsp_1(A))
        <=> ( r1_tarski(B,k3_tarski(A))
            & ! [C] : 
                ( m1_subset_1(C,A)
               => ? [D] : r1_tarski(k3_xboole_0(B,C),k1_tarski(D)) ) ) ) ) ),
    file(cohsp_1,t66_cohsp_1),
    []).

fof(t67_cohsp_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => k3_tarski(k13_cohsp_1(A)) = k3_tarski(A) ) ),
    file(cohsp_1,t67_cohsp_1),
    []).

fof(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

fof(t74_cohsp_1,axiom,(
    ! [A,B] : k14_cohsp_1(A,B) = k2_xboole_0(k2_zfmisc_1(A,k1_tarski(1)),k2_zfmisc_1(B,k1_tarski(2))) ),
    file(cohsp_1,t74_cohsp_1),
    []).

fof(t76_cohsp_1,axiom,(
    ! [A,B,C] : 
      ( r2_hidden(C,k14_cohsp_1(A,B))
     => ( C = k4_tarski(k1_mcart_1(C),k2_mcart_1(C))
        & ( ( k2_mcart_1(C) = 1
            & r2_hidden(k1_mcart_1(C),A) )
          | ( k2_mcart_1(C) = 2
            & r2_hidden(k1_mcart_1(C),B) ) ) ) ) ),
    file(cohsp_1,t76_cohsp_1),
    []).

fof(t77_cohsp_1,axiom,(
    ! [A,B,C] : 
      ( r2_hidden(k4_tarski(C,1),k14_cohsp_1(A,B))
    <=> r2_hidden(C,A) ) ),
    file(cohsp_1,t77_cohsp_1),
    []).

fof(t78_cohsp_1,axiom,(
    ! [A,B,C] : 
      ( r2_hidden(k4_tarski(C,2),k14_cohsp_1(A,B))
    <=> r2_hidden(C,B) ) ),
    file(cohsp_1,t78_cohsp_1),
    []).

fof(t79_cohsp_1,axiom,(
    ! [A,B,C,D] : 
      ( r1_tarski(k14_cohsp_1(A,B),k14_cohsp_1(C,D))
    <=> ( r1_tarski(A,C)
        & r1_tarski(B,D) ) ) ),
    file(cohsp_1,t79_cohsp_1),
    []).

fof(t7_boole,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    []).

fof(t7_xboole_1,axiom,(
    ! [A,B] : r1_tarski(A,k2_xboole_0(A,B)) ),
    file(xboole_1,t7_xboole_1),
    []).

fof(t80_cohsp_1,axiom,(
    ! [A,B,C] : ~ ( r1_tarski(C,k14_cohsp_1(A,B))
      & ! [D,E] : ~ ( C = k14_cohsp_1(D,E)
          & r1_tarski(D,A)
          & r1_tarski(E,B) ) ) ),
    file(cohsp_1,t80_cohsp_1),
    []).

fof(t83_cohsp_1,axiom,(
    ! [A,B,C,D] : k3_xboole_0(k14_cohsp_1(A,B),k14_cohsp_1(C,D)) = k14_cohsp_1(k3_xboole_0(A,C),k3_xboole_0(B,D)) ),
    file(cohsp_1,t83_cohsp_1),
    []).

fof(t84_cohsp_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C] : 
              ( r2_hidden(C,k15_cohsp_1(A,B))
            <=> ? [D] : 
                  ( m1_subset_1(D,A)
                  & ? [E] : 
                      ( m1_subset_1(E,B)
                      & C = k14_cohsp_1(D,E) ) ) ) ) ) ),
    file(cohsp_1,t84_cohsp_1),
    []).

fof(t86_cohsp_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => k3_tarski(k15_cohsp_1(A,B)) = k14_cohsp_1(k3_tarski(A),k3_tarski(B)) ) ) ),
    file(cohsp_1,t86_cohsp_1),
    []).

fof(t87_cohsp_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C,D] : 
              ( r2_hidden(k14_cohsp_1(C,D),k16_cohsp_1(A,B))
            <=> ( ( r2_hidden(C,A)
                  & D = k1_xboole_0 )
                | ( C = k1_xboole_0
                  & r2_hidden(D,B) ) ) ) ) ) ),
    file(cohsp_1,t87_cohsp_1),
    []).

fof(t88_cohsp_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & v1_coh_sp(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_classes1(B)
            & v1_coh_sp(B) )
         => ! [C] : ~ ( r2_hidden(C,k16_cohsp_1(A,B))
              & ! [D] : 
                  ( m1_subset_1(D,A)
                 => ! [E] : 
                      ( m1_subset_1(E,B)
                     => ~ ( C = k14_cohsp_1(D,E)
                          & ( D = k1_xboole_0
                            | E = k1_xboole_0 ) ) ) ) ) ) ) ),
    file(cohsp_1,t88_cohsp_1),
    []).

fof(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).

fof(t92_zfmisc_1,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => r1_tarski(A,k3_tarski(B)) ) ),
    file(zfmisc_1,t92_zfmisc_1),
    []).