% Mizar problem: t40_cohsp_1,cohsp_1,1780,53 
fof(t40_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) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & v9_cohsp_1(C)
                & m2_relset_1(C,A,B) )
             => ! [D] : 
                  ( m1_subset_1(D,A)
                 => k8_funct_2(A,B,C,D) = k9_relat_1(k8_cohsp_1(A,B,C),k3_cohsp_1(A,D)) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_cohsp_1,cc1_finseq_1,cc1_finset_1,cc1_finsub_1,cc1_relset_1,cc2_cohsp_1,cc2_finset_1,cc2_finsub_1,cc3_cohsp_1,cc3_finsub_1,cc4_cohsp_1,cc5_cohsp_1,cc7_cohsp_1,cc8_cohsp_1,commutativity_k2_tarski,commutativity_k2_xboole_0,d18_cohsp_1,d1_funct_2,d5_tarski,dt_k1_funct_1,dt_k1_mcart_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_mcart_1,dt_k2_tarski,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_cohsp_1,dt_k3_tarski,dt_k4_relset_1,dt_k4_tarski,dt_k5_finsub_1,dt_k7_cohsp_1,dt_k8_cohsp_1,dt_k8_funct_2,dt_k9_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc13_finset_1,fc14_finset_1,fc17_finseq_1,fc1_cohsp_1,fc1_finset_1,fc1_finsub_1,fc2_cohsp_1,fc2_finseq_1,fc2_finset_1,fc2_finsub_1,fc5_cohsp_1,fc6_cohsp_1,fc7_cohsp_1,fc9_cohsp_1,fc9_finset_1,idempotence_k2_xboole_0,l61_cohsp_1,rc1_cohsp_1,rc1_finseq_1,rc1_finset_1,rc1_finsub_1,rc1_partfun1,rc2_cohsp_1,rc2_partfun1,rc3_cohsp_1,rc3_finseq_1,rc3_finset_1,rc4_cohsp_1,rc4_finset_1,rc5_cohsp_1,rc6_cohsp_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,redefinition_k3_cohsp_1,redefinition_k4_relset_1,redefinition_k8_cohsp_1,redefinition_k8_funct_2,redefinition_m2_relset_1,reflexivity_r1_tarski,t1_boole,t1_subset,t2_subset,t34_cohsp_1,t35_cohsp_1,t36_cohsp_1,t38_cohsp_1,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t7_mcart_1,t8_boole]),
    [file(cohsp_1,t40_cohsp_1)]).

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

fof(cc1_cohsp_1,axiom,(
    ! [A] : 
      ( v1_cohsp_1(A)
     => ~ v1_xboole_0(A) ) ),
    file(cohsp_1,cc1_cohsp_1),
    []).

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_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_cohsp_1,axiom,(
    ! [A] : 
      ( v2_cohsp_1(A)
     => ~ v1_xboole_0(A) ) ),
    file(cohsp_1,cc2_cohsp_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(cc3_cohsp_1,axiom,(
    ! [A] : 
      ( v1_classes1(A)
     => v2_finsub_1(A) ) ),
    file(cohsp_1,cc3_cohsp_1),
    []).

fof(cc3_finsub_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k5_finsub_1(A))
     => v1_finset_1(B) ) ),
    file(finsub_1,cc3_finsub_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(cc5_cohsp_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_cohsp_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v6_cohsp_1(A) ) ) ),
    file(cohsp_1,cc5_cohsp_1),
    []).

fof(cc7_cohsp_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v8_cohsp_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_cohsp_1(A)
        & v6_cohsp_1(A) ) ) ),
    file(cohsp_1,cc7_cohsp_1),
    []).

fof(cc8_cohsp_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v9_cohsp_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v7_cohsp_1(A)
        & v8_cohsp_1(A) ) ) ),
    file(cohsp_1,cc8_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(d18_cohsp_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k7_cohsp_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D,E] : 
                  ( C = k4_tarski(D,E)
                  & r2_hidden(D,k1_relat_1(A))
                  & r2_hidden(E,k1_funct_1(A,D))
                  & ! [F] : 
                      ( ( r2_hidden(F,k1_relat_1(A))
                        & r1_tarski(F,D)
                        & r2_hidden(E,k1_funct_1(A,F)) )
                     => D = F ) ) ) ) ) ),
    file(cohsp_1,d18_cohsp_1),
    []).

fof(d1_funct_2,axiom,(
    ! [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),
    []).

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_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    []).

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

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    []).

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_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_cohsp_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & m1_subset_1(B,A) )
     => ( ~ v1_xboole_0(k3_cohsp_1(A,B))
        & v4_finsub_1(k3_cohsp_1(A,B))
        & m1_subset_1(k3_cohsp_1(A,B),k1_zfmisc_1(A)) ) ) ),
    file(cohsp_1,k3_cohsp_1),
    []).

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

fof(dt_k4_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(relset_1,k4_relset_1),
    []).

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

fof(dt_k5_finsub_1,axiom,(
    ! [A] : v4_finsub_1(k5_finsub_1(A)) ),
    file(finsub_1,k5_finsub_1),
    []).

fof(dt_k7_cohsp_1,axiom,(
    $true ),
    file(cohsp_1,k7_cohsp_1),
    []).

fof(dt_k8_cohsp_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k8_cohsp_1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(A,k3_tarski(B)))) ) ),
    file(cohsp_1,k8_cohsp_1),
    []).

fof(dt_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ),
    file(funct_2,k8_funct_2),
    []).

fof(dt_k9_relat_1,axiom,(
    $true ),
    file(relat_1,k9_relat_1),
    []).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    []).

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

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

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

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    []).

fof(fc13_finset_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k9_relat_1(A,B)) ) ),
    file(finset_1,fc13_finset_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(fc17_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k1_relat_1(A)) ) ),
    file(finseq_1,fc17_finseq_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(fc2_finsub_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k5_finsub_1(A))
      & v1_finsub_1(k5_finsub_1(A))
      & v3_finsub_1(k5_finsub_1(A))
      & v4_finsub_1(k5_finsub_1(A)) ) ),
    file(finsub_1,fc2_finsub_1),
    []).

fof(fc5_cohsp_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k5_finsub_1(A))
      & v1_finsub_1(k5_finsub_1(A))
      & v3_finsub_1(k5_finsub_1(A))
      & v4_finsub_1(k5_finsub_1(A))
      & v1_cohsp_1(k5_finsub_1(A))
      & v2_cohsp_1(k5_finsub_1(A)) ) ),
    file(cohsp_1,fc5_cohsp_1),
    []).

fof(fc6_cohsp_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v8_cohsp_1(A) )
     => v3_cohsp_1(k1_relat_1(A)) ) ),
    file(cohsp_1,fc6_cohsp_1),
    []).

fof(fc7_cohsp_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v9_cohsp_1(A) )
     => ( v2_finsub_1(k1_relat_1(A))
        & v3_cohsp_1(k1_relat_1(A)) ) ) ),
    file(cohsp_1,fc7_cohsp_1),
    []).

fof(fc9_cohsp_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => v1_relat_1(k7_cohsp_1(A)) ) ),
    file(cohsp_1,fc9_cohsp_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(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

fof(l61_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] : 
              ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k3_tarski(B))))
             => ~ ( ! [D] : 
                      ( r2_hidden(D,C)
                     => v1_finset_1(k1_mcart_1(D)) )
                  & ! [D] : 
                      ( m1_subset_1(D,A)
                     => ! [E] : 
                          ( m1_subset_1(E,A)
                         => ( r2_hidden(k2_xboole_0(D,E),A)
                           => ! [F,G] : 
                                ( ( r2_hidden(k4_tarski(D,F),C)
                                  & r2_hidden(k4_tarski(E,G),C) )
                               => r2_hidden(k2_tarski(F,G),B) ) ) ) )
                  & ! [D] : 
                      ( m1_subset_1(D,A)
                     => ! [E] : 
                          ( m1_subset_1(E,A)
                         => ( r2_hidden(k2_xboole_0(D,E),A)
                           => ! [F] : 
                                ( ( r2_hidden(k4_tarski(D,F),C)
                                  & r2_hidden(k4_tarski(E,F),C) )
                               => D = E ) ) ) )
                  & ! [D] : 
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,A,B)
                        & v9_cohsp_1(D)
                        & m2_relset_1(D,A,B) )
                     => ~ ( C = k8_cohsp_1(A,B,D)
                          & ! [E] : 
                              ( m1_subset_1(E,A)
                             => k8_funct_2(A,B,D,E) = k9_relat_1(C,k3_cohsp_1(A,E)) ) ) ) ) ) ) ) ),
    file(cohsp_1,l61_cohsp_1),
    []).

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_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_partfun1,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C) ) ),
    file(partfun1,rc2_partfun1),
    []).

fof(rc3_cohsp_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A)
      & v1_cohsp_1(A)
      & v2_cohsp_1(A) ) ),
    file(cohsp_1,rc3_cohsp_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(rc4_cohsp_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B)
          & v1_cohsp_1(B)
          & v2_cohsp_1(B) ) ) ),
    file(cohsp_1,rc4_cohsp_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_k3_cohsp_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes1(A)
        & m1_subset_1(B,A) )
     => k3_cohsp_1(A,B) = k5_finsub_1(B) ) ),
    file(cohsp_1,k3_cohsp_1),
    []).

fof(redefinition_k4_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k4_relset_1(A,B,C) = k1_relat_1(C) ) ),
    file(relset_1,k4_relset_1),
    []).

fof(redefinition_k8_cohsp_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => k8_cohsp_1(A,B,C) = k7_cohsp_1(C) ) ),
    file(cohsp_1,k8_cohsp_1),
    []).

fof(redefinition_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(funct_2,k8_funct_2),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

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

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

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

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

fof(t34_cohsp_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v8_cohsp_1(A) )
     => ( v1_classes1(k1_relat_1(A))
       => ! [B,C] : 
            ( r2_hidden(k4_tarski(B,C),k7_cohsp_1(A))
           => v1_finset_1(B) ) ) ) ),
    file(cohsp_1,t34_cohsp_1),
    []).

fof(t35_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] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & v6_cohsp_1(C)
                & m2_relset_1(C,A,B) )
             => ! [D,E] : 
                  ( r2_hidden(k2_xboole_0(D,E),A)
                 => ! [F,G] : 
                      ( ( r2_hidden(k4_tarski(D,F),k8_cohsp_1(A,B,C))
                        & r2_hidden(k4_tarski(E,G),k8_cohsp_1(A,B,C)) )
                     => r2_hidden(k2_tarski(F,G),B) ) ) ) ) ) ),
    file(cohsp_1,t35_cohsp_1),
    []).

fof(t36_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] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & v7_cohsp_1(C)
                & m2_relset_1(C,A,B) )
             => ! [D,E] : 
                  ( r2_hidden(k2_xboole_0(D,E),A)
                 => ! [F] : 
                      ( ( r2_hidden(k4_tarski(D,F),k8_cohsp_1(A,B,C))
                        & r2_hidden(k4_tarski(E,F),k8_cohsp_1(A,B,C)) )
                     => D = E ) ) ) ) ) ),
    file(cohsp_1,t36_cohsp_1),
    []).

fof(t38_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] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & v9_cohsp_1(C)
                & m2_relset_1(C,A,B) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & v9_cohsp_1(D)
                    & m2_relset_1(D,A,B) )
                 => ( k8_cohsp_1(A,B,C) = k8_cohsp_1(A,B,D)
                   => C = D ) ) ) ) ) ),
    file(cohsp_1,t38_cohsp_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_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(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

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

fof(t7_mcart_1,axiom,(
    ! [A,B] : 
      ( k1_mcart_1(k4_tarski(A,B)) = A
      & k2_mcart_1(k4_tarski(A,B)) = B ) ),
    file(mcart_1,t7_mcart_1),
    []).

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