fof(t37_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m4_pboole(C,A,k1_mboolean(A,B))
         => ! [D] : 
              ( m4_pboole(D,A,k1_mboolean(A,B))
             => m4_pboole(k5_pboole(A,C,D),A,k1_mboolean(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t36_mssubfam,t34_mssubfam]),
    [file(mssubfam,t37_mssubfam),interesting(1.00)]).

fof(t24_mssubfam,theorem,(
    ! [A,B] : 
      ( ( v1_funcop_1(B)
        & m1_pboole(B,A) )
     => ( v1_pre_circ(k1_mssubfam(A,B),A)
       => v1_pre_circ(k2_mssubfam(A,B),A) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_pre_circ,d3_pre_circ,t14_mssubfam,t26_finset_1,t13_mssubfam]),
    [file(mssubfam,t24_mssubfam),interesting(0.97)]).

fof(t17_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( ( v1_funcop_1(D)
                & m1_pboole(D,A) )
             => ( ( r1_pzfmisc1(A,B,C)
                  & m3_pboole(D,A,B,C) )
               => ( r6_pboole(A,k1_mssubfam(A,D),B)
                  & r2_pboole(A,k2_mssubfam(A,D),C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d18_pboole,d3_pzfmisc1,t14_mssubfam,d1_funct_2,t3_pboole,d5_pboole,d18_pboole,t12_relset_1,t13_mssubfam]),
    [file(mssubfam,t17_mssubfam),interesting(0.95)]).

fof(t40_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m4_pboole(C,A,k1_mboolean(A,B))
         => r2_pboole(A,k2_mboolean(A,C),B) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_pboole,t32_mssubfam,d2_mboolean]),
    [file(mssubfam,t40_mssubfam),interesting(0.88)]).

fof(t39_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( ( r2_pboole(A,B,C)
                  & r2_pboole(A,D,C) )
               => m4_pboole(k2_pzfmisc1(A,B,D),A,k1_mboolean(A,C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t38_mssubfam,t34_mssubfam,t11_pzfmisc1]),
    [file(mssubfam,t39_mssubfam),interesting(0.87)]).

fof(l62_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v1_mssubfam(k3_mssubfam(A,B),A,B)
        & v2_mssubfam(k3_mssubfam(A,B),A,B)
        & v3_mssubfam(k3_mssubfam(A,B),A,B)
        & v4_mssubfam(k3_mssubfam(A,B),A,B)
        & v5_mssubfam(k3_mssubfam(A,B),A,B)
        & v6_mssubfam(k3_mssubfam(A,B),A,B) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_mssubfam,t1_mboolean,t18_pboole,t1_mboolean,d4_mssubfam,t40_mssubfam,t19_mboolean,d5_mssubfam,t1_mboolean,t15_mboolean,t1_mboolean,d6_mssubfam,d23_pboole,t19_mboolean,t19_mboolean,d7_mssubfam,t5_mboolean,t1_mboolean,d8_mssubfam]),
    [file(mssubfam,l62_mssubfam),interesting(0.81)]).

fof(t30_mssubfam,theorem,(
    ! [A,B] : 
      ( ( v1_funcop_1(B)
        & m1_pboole(B,A) )
     => ! [C] : 
          ( m1_pboole(C,A)
         => ~ ( v1_pre_circ(C,A)
              & r2_pboole(A,C,k2_mssubfam(A,B))
              & ! [D] : 
                  ( m1_pboole(D,A)
                 => ~ ( r2_pboole(A,D,k1_mssubfam(A,B))
                      & v1_pre_circ(D,A)
                      & r6_pboole(A,k14_pboole(A,D,B),C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_pre_circ,t13_mssubfam,d5_pboole,t195_orders_1,t14_mssubfam,s3_pboole,d5_pboole,d3_pre_circ,d25_pboole,t3_pboole]),
    [file(mssubfam,t30_mssubfam),interesting(0.81)]).

fof(t36_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m4_pboole(D,A,k1_mboolean(A,C))
             => m4_pboole(k4_pboole(A,D,B),A,k1_mboolean(A,C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d23_pboole,t59_pboole,t62_pboole,t15_pboole,d23_pboole]),
    [file(mssubfam,t36_mssubfam),interesting(0.80)]).

fof(t16_mssubfam,theorem,(
    ! [A,B] : 
      ( ( v2_relat_1(B)
        & m1_pboole(B,A) )
     => ! [C] : 
          ( m3_pboole(C,A,B,k1_pboole(A))
         => r6_pboole(A,C,k1_pboole(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[d18_pboole,d16_pboole,t5_pboole,d1_funct_2,t5_pboole,t3_pboole]),
    [file(mssubfam,t16_mssubfam),interesting(0.69)]).

fof(t38_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r2_pboole(A,B,C)
           => m4_pboole(k1_pzfmisc1(A,B),A,k1_mboolean(A,C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t19_mboolean,t36_pzfmisc1,d23_pboole]),
    [file(mssubfam,t38_mssubfam),interesting(0.68)]).

fof(t11_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r1_pboole(A,B,C)
           => m2_pboole(B,A,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d17_pboole,d4_pboole]),
    [file(mssubfam,t11_mssubfam),interesting(0.65)]).

fof(t22_mssubfam,theorem,(
    ! [A,B] : 
      ( ( v2_relat_1(B)
        & m1_pboole(B,A) )
     => ( ( v1_pre_circ(B,A)
          & ! [C] : 
              ( m1_pboole(C,A)
             => ( r1_pboole(A,C,B)
               => v1_pre_circ(C,A) ) ) )
       => v1_pre_circ(k2_mboolean(A,B),A) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_pre_circ,d3_pre_circ,t146_pboole,t5_cqc_lang,t1_pzfmisc1,d3_pboole,d1_tarski,t14_funct_4,t6_cqc_lang,d4_pboole,d1_tarski,t12_funct_4,d4_pboole,d3_pre_circ,t25_finset_1,d2_mboolean]),
    [file(mssubfam,t22_mssubfam),interesting(0.65)]).

fof(t34_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m4_pboole(C,A,k1_mboolean(A,B))
         => ! [D] : 
              ( m4_pboole(D,A,k1_mboolean(A,B))
             => m4_pboole(k2_pboole(A,C,D),A,k1_mboolean(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d23_pboole,d23_pboole,t18_pboole,d23_pboole]),
    [file(mssubfam,t34_mssubfam),interesting(0.64)]).

fof(t21_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v1_pre_circ(B,A)
      <=> v1_pre_circ(k1_mboolean(A,B),A) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_pre_circ,d3_pre_circ,t24_finset_1,d1_mboolean,d3_pre_circ,d3_pre_circ,d1_mboolean,t24_finset_1]),
    [file(mssubfam,t21_mssubfam),interesting(0.63)]).

fof(t12_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( ( v2_relat_1(C)
            & m1_pboole(C,A) )
         => ( m2_pboole(B,A,C)
           => r1_pboole(A,B,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_pboole,d17_pboole,d16_pboole]),
    [file(mssubfam,t12_mssubfam),interesting(0.62)]).

fof(t33_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m4_pboole(D,A,k1_mboolean(A,C))
             => ( r1_pboole(A,B,D)
               => m4_pboole(B,A,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d23_pboole,t9_pboole,t19_mboolean,d23_pboole]),
    [file(mssubfam,t33_mssubfam),interesting(0.62)]).

fof(t41_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m4_pboole(C,A,k1_mboolean(A,B))
         => ( r6_pboole(A,C,k1_pboole(A))
           => r6_pboole(A,k6_mssubfam(A,B,C),B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_mssubfam,t5_pboole,d10_setfam_1,t3_pboole]),
    [file(mssubfam,t41_mssubfam),interesting(0.61)]).

fof(t44_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m4_pboole(C,A,k1_mboolean(A,B))
         => ( r1_pboole(A,k1_pboole(A),C)
           => r6_pboole(A,k6_mssubfam(A,B,C),k1_pboole(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_mssubfam,d4_pboole,d10_setfam_1,d4_pboole,t5_pboole,t5_setfam_1,t5_pboole,t3_pboole]),
    [file(mssubfam,t44_mssubfam),interesting(0.61)]).

fof(t18_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( ( r2_pboole(A,B,C)
              & v1_pre_circ(C,A) )
           => v1_pre_circ(B,A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_pre_circ,d5_pboole,d3_pre_circ,t13_finset_1]),
    [file(mssubfam,t18_mssubfam),interesting(0.59)]).

fof(t42_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( ( v2_relat_1(C)
            & m4_pboole(C,A,k1_mboolean(A,B)) )
         => r2_pboole(A,k6_mssubfam(A,B,C),k2_mboolean(A,C)) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_pboole,d2_mssubfam,t3_setfam_1,d16_pboole,d10_setfam_1,d2_mboolean]),
    [file(mssubfam,t42_mssubfam),interesting(0.59)]).

fof(t43_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m4_pboole(D,A,k1_mboolean(A,B))
             => ( r1_pboole(A,C,D)
               => r2_pboole(A,k6_mssubfam(A,B,D),C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_pboole,d2_mssubfam,d4_pboole,d10_setfam_1,t4_setfam_1]),
    [file(mssubfam,t43_mssubfam),interesting(0.59)]).

fof(t32_mssubfam,theorem,(
    ! [A,B,C] : 
      ( m1_pboole(C,B)
     => ! [D] : 
          ( m4_pboole(D,B,k1_mboolean(B,C))
         => ( r2_hidden(A,B)
           => m1_subset_1(k1_funct_1(D,A),k1_zfmisc_1(k1_zfmisc_1(k1_funct_1(C,A)))) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d23_pboole,d5_pboole,d1_mboolean]),
    [file(mssubfam,t32_mssubfam),interesting(0.58)]).

fof(t19_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( ( v2_relat_1(B)
              & v1_pre_circ(k11_pboole(A,C,B),A) )
           => v1_pre_circ(C,A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_pre_circ,d3_pre_circ,d16_pboole,d21_pboole,t22_finset_1]),
    [file(mssubfam,t19_mssubfam),interesting(0.58)]).

fof(t20_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( ( v2_relat_1(B)
              & v1_pre_circ(k11_pboole(A,B,C),A) )
           => v1_pre_circ(C,A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_pre_circ,d3_pre_circ,d16_pboole,d21_pboole,t23_finset_1]),
    [file(mssubfam,t20_mssubfam),interesting(0.58)]).

fof(t23_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v1_pre_circ(k2_mboolean(A,B),A)
       => ( v1_pre_circ(B,A)
          & ! [C] : 
              ( m1_pboole(C,A)
             => ( r1_pboole(A,C,B)
               => v1_pre_circ(C,A) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_pre_circ,d3_pre_circ,d2_mboolean,t25_finset_1,d3_pre_circ,d3_pre_circ,d2_mboolean,d4_pboole,t25_finset_1]),
    [file(mssubfam,t23_mssubfam),interesting(0.57)]).

fof(t45_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( ( v2_relat_1(D)
                & m4_pboole(D,A,k1_mboolean(A,C)) )
             => ( ! [E] : 
                    ( m1_pboole(E,A)
                   => ( r1_pboole(A,E,D)
                     => r2_pboole(A,B,E) ) )
               => r2_pboole(A,B,k6_mssubfam(A,C,D)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_pboole,d2_mssubfam,d16_pboole,d10_setfam_1,t146_pboole,t5_cqc_lang,t1_pzfmisc1,d3_pboole,d1_tarski,t14_funct_4,t6_cqc_lang,d4_pboole,d1_tarski,t12_funct_4,d4_pboole,d5_pboole,t6_setfam_1]),
    [file(mssubfam,t45_mssubfam),interesting(0.57)]).

fof(t50_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m4_pboole(C,A,k1_mboolean(A,B))
         => ! [D] : 
              ( m4_pboole(D,A,B)
             => ( r6_pboole(A,C,k1_pzfmisc1(A,D))
               => r6_pboole(A,k6_mssubfam(A,B,C),D) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_mssubfam,d16_pboole,d10_setfam_1,d1_pzfmisc1,t11_setfam_1,t3_pboole]),
    [file(mssubfam,t50_mssubfam),interesting(0.57)]).

fof(t35_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m4_pboole(C,A,k1_mboolean(A,B))
         => ! [D] : 
              ( m4_pboole(D,A,k1_mboolean(A,B))
             => m4_pboole(k3_pboole(A,C,D),A,k1_mboolean(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d23_pboole,d23_pboole,t23_pboole,d23_pboole]),
    [file(mssubfam,t35_mssubfam),interesting(0.56)]).

fof(t53_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( ( v2_relat_1(D)
                & m4_pboole(D,A,k1_mboolean(A,C)) )
             => ( ( r1_pboole(A,B,C)
                  & ! [E] : 
                      ( m1_pboole(E,A)
                     => ( r1_pboole(A,E,D)
                       => r1_pboole(A,B,E) ) ) )
               => r1_pboole(A,B,k6_mssubfam(A,C,D)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_pboole,d2_mssubfam,d4_pboole,t146_pboole,t5_cqc_lang,t1_pzfmisc1,d3_pboole,d1_tarski,t14_funct_4,t6_cqc_lang,d4_pboole,d1_tarski,t12_funct_4,d4_pboole,d4_pboole,t58_setfam_1]),
    [file(mssubfam,t53_mssubfam),interesting(0.54)]).

fof(t15_mssubfam,theorem,(
    ! [A,B] : 
      ( ( v1_funcop_1(B)
        & m1_pboole(B,A) )
     => ! [C] : 
          ( ( v1_funcop_1(C)
            & m1_pboole(C,A) )
         => ( v1_funcop_1(k13_pboole(B,C))
            & m1_pboole(k13_pboole(B,C),A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d24_pboole,d3_pboole,d3_pboole,d3_pboole]),
    [file(mssubfam,t15_mssubfam),interesting(0.52)]).

fof(t2_mssubfam,theorem,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( r2_hidden(B,C)
       => r1_tarski(k8_setfam_1(A,C),B) ) ) ),
    inference(mizar_proof,[status(thm)],[d10_setfam_1,t4_setfam_1]),
    [file(mssubfam,t2_mssubfam),interesting(0.52)]).

fof(t47_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ! [E] : 
                  ( m4_pboole(E,A,k1_mboolean(A,B))
                 => ( ( r1_pboole(A,C,E)
                      & r2_pboole(A,C,D) )
                   => r2_pboole(A,k6_mssubfam(A,B,E),D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_pboole,d2_mssubfam,d4_pboole,d10_setfam_1,d5_pboole,t8_setfam_1]),
    [file(mssubfam,t47_mssubfam),interesting(0.52)]).

fof(t51_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m4_pboole(C,A,k1_mboolean(A,B))
         => ! [D] : 
              ( m4_pboole(D,A,B)
             => ! [E] : 
                  ( m4_pboole(E,A,B)
                 => ( r6_pboole(A,C,k2_pzfmisc1(A,D,E))
                   => r6_pboole(A,k6_mssubfam(A,B,C),k3_pboole(A,D,E)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_mssubfam,d16_pboole,d10_setfam_1,d2_pzfmisc1,t12_setfam_1,d8_pboole,t3_pboole]),
    [file(mssubfam,t51_mssubfam),interesting(0.52)]).

fof(t46_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m4_pboole(C,A,k1_mboolean(A,B))
         => ! [D] : 
              ( m4_pboole(D,A,k1_mboolean(A,B))
             => ( r2_pboole(A,C,D)
               => r2_pboole(A,k6_mssubfam(A,B,D),k6_mssubfam(A,B,C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_pboole,d2_mssubfam,d2_mssubfam,d5_pboole,t59_setfam_1]),
    [file(mssubfam,t46_mssubfam),interesting(0.51)]).

fof(t52_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m4_pboole(D,A,k1_mboolean(A,B))
             => ( r1_pboole(A,C,k6_mssubfam(A,B,D))
               => ! [E] : 
                    ( m1_pboole(E,A)
                   => ( r1_pboole(A,E,D)
                     => r1_pboole(A,C,E) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_pboole,d2_mssubfam,d4_pboole,d4_pboole,t58_setfam_1]),
    [file(mssubfam,t52_mssubfam),interesting(0.51)]).

fof(t6_mssubfam,theorem,(
    ! [A,B,C,D] : 
      ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( r2_hidden(B,D)
          & r1_tarski(B,C) )
       => r1_tarski(k8_setfam_1(A,D),C) ) ) ),
    inference(mizar_proof,[status(thm)],[d10_setfam_1,t8_setfam_1]),
    [file(mssubfam,t6_mssubfam),interesting(0.50)]).

fof(t7_mssubfam,theorem,(
    ! [A,B,C,D] : 
      ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( r2_hidden(B,D)
          & r1_xboole_0(B,C) )
       => r1_xboole_0(k8_setfam_1(A,D),C) ) ) ),
    inference(mizar_proof,[status(thm)],[d10_setfam_1,t9_setfam_1]),
    [file(mssubfam,t7_mssubfam),interesting(0.50)]).

fof(t3_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( r2_hidden(k1_xboole_0,B)
       => k8_setfam_1(A,B) = k1_xboole_0 ) ) ),
    inference(mizar_proof,[status(thm)],[d10_setfam_1,t5_setfam_1]),
    [file(mssubfam,t3_mssubfam),interesting(0.49)]).

fof(t25_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( ( v1_funcop_1(C)
            & m1_pboole(C,A) )
         => ( ( r2_pboole(A,B,k2_mssubfam(A,C))
              & ! [D,E] : 
                  ( ( v1_relat_1(E)
                    & v1_funct_1(E) )
                 => ( ( r2_hidden(D,A)
                      & E = k1_funct_1(C,D) )
                   => v1_finset_1(k10_relat_1(E,k1_funct_1(B,D))) ) ) )
           => v1_pre_circ(B,A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_pre_circ,t13_mssubfam,d5_pboole,t27_finset_1]),
    [file(mssubfam,t25_mssubfam),interesting(0.48)]).

fof(t27_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ~ ( v1_pre_circ(B,A)
                  & v1_pre_circ(C,A)
                  & r2_pboole(A,B,k11_pboole(A,D,C))
                  & ! [E] : 
                      ( m1_pboole(E,A)
                     => ~ ( v1_pre_circ(E,A)
                          & r2_pboole(A,E,D)
                          & r2_pboole(A,B,k11_pboole(A,E,C)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_pre_circ,d3_pre_circ,d5_pboole,d21_pboole,t14_cqc_the1,s3_pboole,d3_pre_circ,d5_pboole,d5_pboole,d21_pboole]),
    [file(mssubfam,t27_mssubfam),interesting(0.46)]).

fof(t31_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v3_relat_1(k1_pboole(A))
        & v1_pre_circ(k1_pboole(A),A)
        & m4_pboole(k1_pboole(A),A,k1_mboolean(A,B)) ) ) ),
    inference(mizar_proof,[status(thm)],[t49_pboole,d23_pboole]),
    [file(mssubfam,t31_mssubfam),interesting(0.46)]).

fof(t4_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( ! [D] : 
                ( r2_hidden(D,B)
               => r1_tarski(C,D) )
           => r1_tarski(C,k8_setfam_1(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d10_setfam_1,t6_setfam_1,d10_setfam_1]),
    [file(mssubfam,t4_mssubfam),interesting(0.46)]).

fof(t28_mssubfam,theorem,(
    ! [A,B] : 
      ( ( v2_relat_1(B)
        & v1_pre_circ(B,A)
        & m1_pboole(B,A) )
     => ~ ( ! [C] : 
              ( m1_pboole(C,A)
             => ! [D] : 
                  ( m1_pboole(D,A)
                 => ~ ( r1_pboole(A,C,B)
                      & r1_pboole(A,D,B)
                      & ~ r2_pboole(A,C,D)
                      & ~ r2_pboole(A,D,C) ) ) )
          & ! [C] : 
              ( m1_pboole(C,A)
             => ~ ( r1_pboole(A,C,B)
                  & ! [D] : 
                      ( m1_pboole(D,A)
                     => ( r1_pboole(A,D,B)
                       => r2_pboole(A,C,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_pre_circ,d16_pboole,d9_ordinal1,d9_xboole_0,t146_pboole,t146_pboole,t1_pzfmisc1,d3_pboole,t1_pzfmisc1,d3_pboole,t5_cqc_lang,d1_tarski,t14_funct_4,t6_cqc_lang,t5_cqc_lang,d1_tarski,t14_funct_4,t6_cqc_lang,d4_pboole,d1_tarski,t12_funct_4,d4_pboole,d4_pboole,d1_tarski,t12_funct_4,d4_pboole,d5_pboole,t30_finset_1,s3_pboole,d4_pboole,d5_pboole,d4_pboole]),
    [file(mssubfam,t28_mssubfam),interesting(0.45)]).

fof(t29_mssubfam,theorem,(
    ! [A,B] : 
      ( ( v2_relat_1(B)
        & v1_pre_circ(B,A)
        & m1_pboole(B,A) )
     => ~ ( ! [C] : 
              ( m1_pboole(C,A)
             => ! [D] : 
                  ( m1_pboole(D,A)
                 => ~ ( r1_pboole(A,C,B)
                      & r1_pboole(A,D,B)
                      & ~ r2_pboole(A,C,D)
                      & ~ r2_pboole(A,D,C) ) ) )
          & ! [C] : 
              ( m1_pboole(C,A)
             => ~ ( r1_pboole(A,C,B)
                  & ! [D] : 
                      ( m1_pboole(D,A)
                     => ( r1_pboole(A,D,B)
                       => r2_pboole(A,D,C) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_pre_circ,d16_pboole,d9_ordinal1,d9_xboole_0,t146_pboole,t146_pboole,t1_pzfmisc1,d3_pboole,t1_pzfmisc1,d3_pboole,t5_cqc_lang,d1_tarski,t14_funct_4,t6_cqc_lang,t5_cqc_lang,d1_tarski,t14_funct_4,t6_cqc_lang,d4_pboole,d1_tarski,t12_funct_4,d4_pboole,d4_pboole,d1_tarski,t12_funct_4,d4_pboole,d5_pboole,t31_finset_1,s3_pboole,d4_pboole,d5_pboole,d4_pboole]),
    [file(mssubfam,t29_mssubfam),interesting(0.45)]).

fof(t9_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( B = k1_tarski(C)
           => k8_setfam_1(A,B) = C ) ) ) ),
    inference(mizar_proof,[status(thm)],[d10_setfam_1,t11_setfam_1]),
    [file(mssubfam,t9_mssubfam),interesting(0.45)]).

fof(t1_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( B != k1_xboole_0
       => r1_tarski(k8_setfam_1(A,B),k5_setfam_1(A,B)) ) ) ),
    inference(mizar_proof,[status(thm)],[d10_setfam_1,t3_setfam_1]),
    [file(mssubfam,t1_mssubfam),interesting(0.44)]).

fof(t49_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m4_pboole(C,A,k1_mboolean(A,B))
         => ! [D] : 
              ( m4_pboole(D,A,k1_mboolean(A,B))
             => ! [E] : 
                  ( m4_pboole(E,A,k1_mboolean(A,B))
                 => ( r6_pboole(A,C,k2_pboole(A,D,E))
                   => r6_pboole(A,k6_mssubfam(A,B,C),k3_pboole(A,k6_mssubfam(A,B,D),k6_mssubfam(A,B,E))) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_mssubfam,d2_mssubfam,d2_mssubfam,d7_pboole,t15_xboole_1,d10_setfam_1,t10_setfam_1,d10_setfam_1,d10_setfam_1,d8_pboole,t28_xboole_1,d10_setfam_1,d8_pboole,t28_xboole_1,d10_setfam_1,d8_pboole,d8_pboole,t3_pboole]),
    [file(mssubfam,t49_mssubfam),interesting(0.44)]).

fof(t5_mssubfam,theorem,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ! [D] : 
            ( r2_hidden(D,C)
           => r1_tarski(B,D) )
       => ( C = k1_xboole_0
          | r1_tarski(B,k8_setfam_1(A,C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d10_setfam_1,t6_setfam_1]),
    [file(mssubfam,t5_mssubfam),interesting(0.44)]).

fof(t26_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ~ ( v1_pre_circ(B,A)
                  & r2_pboole(A,B,k11_pboole(A,C,D))
                  & ! [E] : 
                      ( m1_pboole(E,A)
                     => ! [F] : 
                          ( m1_pboole(F,A)
                         => ~ ( v1_pre_circ(E,A)
                              & r2_pboole(A,E,C)
                              & v1_pre_circ(F,A)
                              & r2_pboole(A,F,D)
                              & r2_pboole(A,B,k11_pboole(A,E,F)) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_pre_circ,d5_pboole,d21_pboole,t13_cqc_the1,s3_pboole,s3_pboole,d3_pre_circ,d5_pboole,d3_pre_circ,d5_pboole,d5_pboole,d21_pboole]),
    [file(mssubfam,t26_mssubfam),interesting(0.43)]).

fof(t48_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ! [E] : 
                  ( m4_pboole(E,A,k1_mboolean(A,B))
                 => ( ( r1_pboole(A,C,E)
                      & r6_pboole(A,k3_pboole(A,C,D),k1_pboole(A)) )
                   => r6_pboole(A,k3_pboole(A,k6_mssubfam(A,B,E),D),k1_pboole(A)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_mssubfam,d4_pboole,d10_setfam_1,d8_pboole,t5_pboole,d7_xboole_0,t9_setfam_1,d7_xboole_0,t5_pboole,d8_pboole,t3_pboole]),
    [file(mssubfam,t48_mssubfam),interesting(0.43)]).

fof(t10_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ! [D] : 
              ( m1_subset_1(D,k1_zfmisc_1(A))
             => ( B = k2_tarski(C,D)
               => k8_setfam_1(A,B) = k5_subset_1(A,C,D) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d10_setfam_1,t12_setfam_1]),
    [file(mssubfam,t10_mssubfam),interesting(0.37)]).

fof(t14_mssubfam,theorem,(
    ! [A,B,C] : 
      ( ( v1_funcop_1(C)
        & m1_pboole(C,B) )
     => ! [D] : 
          ( ( v1_relat_1(D)
            & v1_funct_1(D) )
         => ( ( r2_hidden(A,B)
              & D = k1_funct_1(C,A) )
           => k1_funct_1(k1_mssubfam(B,C),A) = k1_relat_1(D) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_pboole,t31_funct_6]),
    [file(mssubfam,t14_mssubfam),interesting(0.28)]).

fof(t13_mssubfam,theorem,(
    ! [A,B,C] : 
      ( ( v1_funcop_1(C)
        & m1_pboole(C,B) )
     => ! [D] : 
          ( ( v1_relat_1(D)
            & v1_funct_1(D) )
         => ( ( r2_hidden(A,B)
              & D = k1_funct_1(C,A) )
           => k1_funct_1(k2_mssubfam(B,C),A) = k2_relat_1(D) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_pboole,t31_funct_6]),
    [file(mssubfam,t13_mssubfam),interesting(0.28)]).

fof(d3_mssubfam,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m4_pboole(C,A,k1_mboolean(A,B))
         => ( v1_mssubfam(C,A,B)
          <=> ! [D] : 
                ( m1_pboole(D,A)
               => ! [E] : 
                    ( m1_pboole(E,A)
                   => ( ( r1_pboole(A,D,C)
                        & r1_pboole(A,E,C) )
                     => r1_pboole(A,k2_pboole(A,D,E),C) ) ) ) ) ) ) ),
    file(mssubfam,d3_mssubfam),
    [interesting(0.00)]).

fof(t1_mboolean,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r6_pboole(A,B,k1_mboolean(A,C))
          <=> ! [D] : 
                ( m1_pboole(D,A)
               => ( r1_pboole(A,D,B)
                <=> r2_pboole(A,D,C) ) ) ) ) ) ),
    file(mboolean,t1_mboolean),
    [interesting(0.00)]).

fof(t18_pboole,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( ( r2_pboole(A,B,C)
                  & r2_pboole(A,D,C) )
               => r2_pboole(A,k2_pboole(A,B,D),C) ) ) ) ) ),
    file(pboole,t18_pboole),
    [interesting(0.00)]).

fof(d4_mssubfam,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m4_pboole(C,A,k1_mboolean(A,B))
         => ( v2_mssubfam(C,A,B)
          <=> ! [D] : 
                ( m4_pboole(D,A,k1_mboolean(A,B))
               => ( r2_pboole(A,D,C)
                 => r1_pboole(A,k2_mboolean(A,D),C) ) ) ) ) ) ),
    file(mssubfam,d4_mssubfam),
    [interesting(0.00)]).

fof(d5_pboole,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r2_pboole(A,B,C)
          <=> ! [D] : 
                ( r2_hidden(D,A)
               => r1_tarski(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) ) ),
    file(pboole,d5_pboole),
    [interesting(0.00)]).

fof(d23_pboole,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( m4_pboole(C,A,B)
          <=> r2_pboole(A,C,B) ) ) ) ),
    file(pboole,d23_pboole),
    [interesting(0.00)]).

fof(d1_mboolean,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( C = k1_mboolean(A,B)
          <=> ! [D] : 
                ( r2_hidden(D,A)
               => k1_funct_1(C,D) = k1_zfmisc_1(k1_funct_1(B,D)) ) ) ) ) ),
    file(mboolean,d1_mboolean),
    [interesting(0.00)]).

fof(d2_mboolean,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( C = k2_mboolean(A,B)
          <=> ! [D] : 
                ( r2_hidden(D,A)
               => k1_funct_1(C,D) = k3_tarski(k1_funct_1(B,D)) ) ) ) ) ),
    file(mboolean,d2_mboolean),
    [interesting(0.00)]).

fof(t19_mboolean,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r2_pboole(A,B,C)
          <=> r1_pboole(A,B,k1_mboolean(A,C)) ) ) ) ),
    file(mboolean,t19_mboolean),
    [interesting(0.00)]).

fof(d5_mssubfam,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m4_pboole(C,A,k1_mboolean(A,B))
         => ( v3_mssubfam(C,A,B)
          <=> ! [D] : 
                ( m1_pboole(D,A)
               => ! [E] : 
                    ( m1_pboole(E,A)
                   => ( ( r1_pboole(A,D,C)
                        & r1_pboole(A,E,C) )
                     => r1_pboole(A,k3_pboole(A,D,E),C) ) ) ) ) ) ) ),
    file(mssubfam,d5_mssubfam),
    [interesting(0.00)]).

fof(t15_mboolean,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( ( r2_pboole(A,B,C)
                  | r2_pboole(A,D,C) )
               => r2_pboole(A,k3_pboole(A,B,D),C) ) ) ) ) ),
    file(mboolean,t15_mboolean),
    [interesting(0.00)]).

fof(d6_mssubfam,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m4_pboole(C,A,k1_mboolean(A,B))
         => ( v4_mssubfam(C,A,B)
          <=> ! [D] : 
                ( m4_pboole(D,A,k1_mboolean(A,B))
               => ( r2_pboole(A,D,C)
                 => r1_pboole(A,k6_mssubfam(A,B,D),C) ) ) ) ) ) ),
    file(mssubfam,d6_mssubfam),
    [interesting(0.00)]).

fof(d7_mssubfam,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m4_pboole(C,A,k1_mboolean(A,B))
         => ( v5_mssubfam(C,A,B)
          <=> r1_pboole(A,B,C) ) ) ) ),
    file(mssubfam,d7_mssubfam),
    [interesting(0.00)]).

fof(t5_mboolean,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => r2_pboole(A,k1_pboole(A),B) ) ),
    file(mboolean,t5_mboolean),
    [interesting(0.00)]).

fof(d8_mssubfam,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m4_pboole(C,A,k1_mboolean(A,B))
         => ( v6_mssubfam(C,A,B)
          <=> r1_pboole(A,k1_pboole(A),C) ) ) ) ),
    file(mssubfam,d8_mssubfam),
    [interesting(0.00)]).

fof(s1_funct_2,theorem,
    ( ! [A] : ~ ( r2_hidden(A,f1_s1_funct_2)
        & ! [B] : ~ ( r2_hidden(B,f2_s1_funct_2)
            & p1_s1_funct_2(A,B) ) )
   => ? [A] : 
        ( v1_funct_1(A)
        & v1_funct_2(A,f1_s1_funct_2,f2_s1_funct_2)
        & m2_relset_1(A,f1_s1_funct_2,f2_s1_funct_2)
        & ! [B] : 
            ( r2_hidden(B,f1_s1_funct_2)
           => p1_s1_funct_2(B,k1_funct_1(A,B)) ) ) ),
    file(funct_2,s1_funct_2),
    [interesting(0.00)]).

fof(d1_xboole_0,definition,(
    ! [A] : 
      ( A = k1_xboole_0
    <=> ! [B] : ~ r2_hidden(B,A) ) ),
    file(xboole_0,d1_xboole_0),
    [interesting(0.00)]).

fof(t55_funct_2,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( k1_relat_1(B) = k1_xboole_0
       => ( v1_funct_1(B)
          & v1_funct_2(B,k1_xboole_0,A)
          & m2_relset_1(B,k1_xboole_0,A) ) ) ) ),
    file(funct_2,t55_funct_2),
    [interesting(0.00)]).

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

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

fof(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(s1_mssubfam,theorem,
    ( ! [A] : 
        ( r2_hidden(A,f1_s1_mssubfam)
       => ! [B] : ~ ( r2_hidden(B,k1_funct_1(f2_s1_mssubfam,A))
            & ! [C] : ~ ( r2_hidden(C,k1_funct_1(f3_s1_mssubfam,A))
                & p1_s1_mssubfam(C,B,A) ) ) )
   => ? [A] : 
        ( m3_pboole(A,f1_s1_mssubfam,f2_s1_mssubfam,f3_s1_mssubfam)
        & ! [B] : ~ ( r2_hidden(B,f1_s1_mssubfam)
            & ! [C] : 
                ( ( v1_funct_1(C)
                  & v1_funct_2(C,k1_funct_1(f2_s1_mssubfam,B),k1_funct_1(f3_s1_mssubfam,B))
                  & m2_relset_1(C,k1_funct_1(f2_s1_mssubfam,B),k1_funct_1(f3_s1_mssubfam,B)) )
               => ~ ( C = k1_funct_1(A,B)
                    & ! [D] : 
                        ( r2_hidden(D,k1_funct_1(f2_s1_mssubfam,B))
                       => p1_s1_mssubfam(k1_funct_1(C,D),D,B) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s1_funct_2,d1_xboole_0,t55_funct_2,t60_relat_1,s3_pboole,d18_pboole]),
    [file(mssubfam,s1_mssubfam),interesting(0.00)]).

fof(d10_setfam_1,definition,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( B != k1_xboole_0
         => k8_setfam_1(A,B) = k6_setfam_1(A,B) )
        & ( B = k1_xboole_0
         => k8_setfam_1(A,B) = A ) ) ) ),
    file(setfam_1,d10_setfam_1),
    [interesting(0.00)]).

fof(t12_setfam_1,theorem,(
    ! [A,B] : k1_setfam_1(k2_tarski(A,B)) = k3_xboole_0(A,B) ),
    file(setfam_1,t12_setfam_1),
    [interesting(0.00)]).

fof(d17_pboole,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( m2_pboole(C,A,B)
          <=> ! [D] : 
                ( r2_hidden(D,A)
               => m1_subset_1(k1_funct_1(C,D),k1_funct_1(B,D)) ) ) ) ) ),
    file(pboole,d17_pboole),
    [interesting(0.00)]).

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

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

fof(d24_pboole,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_funcop_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_funcop_1(C) )
             => ( C = k13_pboole(A,B)
              <=> ( k1_relat_1(C) = k3_xboole_0(k1_relat_1(A),k1_relat_1(B))
                  & ! [D] : 
                      ( r2_hidden(D,k1_relat_1(C))
                     => k1_funct_1(C,D) = k5_relat_1(k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) ) ) ),
    file(pboole,d24_pboole),
    [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(t5_pboole,theorem,(
    ! [A,B] : k1_funct_1(k1_pboole(B),A) = k1_xboole_0 ),
    file(pboole,t5_pboole),
    [interesting(0.00)]).

fof(d1_funct_2,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( ( ( B = k1_xboole_0
           => A = k1_xboole_0 )
         => ( v1_funct_2(C,A,B)
          <=> A = k4_relset_1(A,B,C) ) )
        & ( B = k1_xboole_0
         => ( A = k1_xboole_0
            | ( v1_funct_2(C,A,B)
            <=> C = k1_xboole_0 ) ) ) ) ) ),
    file(funct_2,d1_funct_2),
    [interesting(0.00)]).

fof(t3_pboole,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( ! [D] : 
                ( r2_hidden(D,A)
               => k1_funct_1(B,D) = k1_funct_1(C,D) )
           => B = C ) ) ) ),
    file(pboole,t3_pboole),
    [interesting(0.00)]).

fof(d3_pzfmisc1,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r1_pzfmisc1(A,B,C)
          <=> ! [D] : 
                ( ( r2_hidden(D,A)
                  & k1_funct_1(C,D) = k1_xboole_0 )
               => k1_funct_1(B,D) = k1_xboole_0 ) ) ) ) ),
    file(pzfmisc1,d3_pzfmisc1),
    [interesting(0.00)]).

fof(t31_funct_6,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( ( r2_hidden(A,k1_relat_1(B))
              & C = k1_funct_1(B,A) )
           => ( r2_hidden(A,k1_relat_1(k2_funct_6(B)))
              & k1_funct_1(k2_funct_6(B),A) = k1_relat_1(C)
              & r2_hidden(A,k1_relat_1(k3_funct_6(B)))
              & k1_funct_1(k3_funct_6(B),A) = k2_relat_1(C) ) ) ) ) ),
    file(funct_6,t31_funct_6),
    [interesting(0.00)]).

fof(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(d3_pre_circ,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v1_pre_circ(B,A)
      <=> ! [C] : 
            ( r2_hidden(C,A)
           => v1_finset_1(k1_funct_1(B,C)) ) ) ) ),
    file(pre_circ,d3_pre_circ),
    [interesting(0.00)]).

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

fof(d21_pboole,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( D = k11_pboole(A,B,C)
              <=> ! [E] : 
                    ( r2_hidden(E,A)
                   => k1_funct_1(D,E) = k2_zfmisc_1(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ),
    file(pboole,d21_pboole),
    [interesting(0.00)]).

fof(t22_finset_1,theorem,(
    ! [A,B] : 
      ( v1_finset_1(k2_zfmisc_1(B,A))
     => ( A = k1_xboole_0
        | v1_finset_1(B) ) ) ),
    file(finset_1,t22_finset_1),
    [interesting(0.00)]).

fof(t3_setfam_1,theorem,(
    ! [A] : r1_tarski(k1_setfam_1(A),k3_tarski(A)) ),
    file(setfam_1,t3_setfam_1),
    [interesting(0.00)]).

fof(t23_finset_1,theorem,(
    ! [A,B] : 
      ( v1_finset_1(k2_zfmisc_1(A,B))
     => ( A = k1_xboole_0
        | v1_finset_1(B) ) ) ),
    file(finset_1,t23_finset_1),
    [interesting(0.00)]).

fof(t24_finset_1,theorem,(
    ! [A] : 
      ( v1_finset_1(A)
    <=> v1_finset_1(k1_zfmisc_1(A)) ) ),
    file(finset_1,t24_finset_1),
    [interesting(0.00)]).

fof(t146_pboole,theorem,(
    ! [A,B] : 
      ( ( v2_relat_1(B)
        & m1_pboole(B,A) )
     => ? [C] : 
          ( m1_pboole(C,A)
          & r1_pboole(A,C,B) ) ) ),
    file(pboole,t146_pboole),
    [interesting(0.00)]).

fof(t5_cqc_lang,theorem,(
    ! [A,B] : 
      ( k1_relat_1(k3_cqc_lang(A,B)) = k1_tarski(A)
      & k2_relat_1(k3_cqc_lang(A,B)) = k1_tarski(B) ) ),
    file(cqc_lang,t5_cqc_lang),
    [interesting(0.00)]).

fof(t1_pzfmisc1,theorem,(
    ! [A,B,C,D] : 
      ( m1_pboole(D,A)
     => ( r2_hidden(B,A)
       => k1_relat_1(k1_funct_4(D,k3_cqc_lang(B,C))) = A ) ) ),
    file(pzfmisc1,t1_pzfmisc1),
    [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(t14_funct_4,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(B))
           => k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(B,A) ) ) ) ),
    file(funct_4,t14_funct_4),
    [interesting(0.00)]).

fof(t6_cqc_lang,theorem,(
    ! [A,B] : k1_funct_1(k3_cqc_lang(A,B),A) = B ),
    file(cqc_lang,t6_cqc_lang),
    [interesting(0.00)]).

fof(t12_funct_4,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( ~ r2_hidden(A,k1_relat_1(B))
           => k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(C,A) ) ) ) ),
    file(funct_4,t12_funct_4),
    [interesting(0.00)]).

fof(t25_finset_1,theorem,(
    ! [A] : 
      ( ( v1_finset_1(A)
        & ! [B] : 
            ( r2_hidden(B,A)
           => v1_finset_1(B) ) )
    <=> v1_finset_1(k3_tarski(A)) ) ),
    file(finset_1,t25_finset_1),
    [interesting(0.00)]).

fof(t26_finset_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_finset_1(k1_relat_1(A))
       => v1_finset_1(k2_relat_1(A)) ) ) ),
    file(finset_1,t26_finset_1),
    [interesting(0.00)]).

fof(t27_finset_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( ( r1_tarski(A,k2_relat_1(B))
          & v1_finset_1(k10_relat_1(B,A)) )
       => v1_finset_1(A) ) ) ),
    file(finset_1,t27_finset_1),
    [interesting(0.00)]).

fof(t13_cqc_the1,theorem,(
    ! [A,B,C] : ~ ( v1_finset_1(A)
      & r1_tarski(A,k2_zfmisc_1(B,C))
      & ! [D,E] : ~ ( v1_finset_1(D)
          & r1_tarski(D,B)
          & v1_finset_1(E)
          & r1_tarski(E,C)
          & r1_tarski(A,k2_zfmisc_1(D,E)) ) ) ),
    file(cqc_the1,t13_cqc_the1),
    [interesting(0.00)]).

fof(t14_cqc_the1,theorem,(
    ! [A,B,C] : ~ ( v1_finset_1(A)
      & v1_finset_1(B)
      & r1_tarski(A,k2_zfmisc_1(C,B))
      & ! [D] : ~ ( v1_finset_1(D)
          & r1_tarski(D,C)
          & r1_tarski(A,k2_zfmisc_1(D,B)) ) ) ),
    file(cqc_the1,t14_cqc_the1),
    [interesting(0.00)]).

fof(d9_ordinal1,definition,(
    ! [A] : 
      ( v6_ordinal1(A)
    <=> ! [B,C] : 
          ( ( r2_hidden(B,A)
            & r2_hidden(C,A) )
         => r3_xboole_0(B,C) ) ) ),
    file(ordinal1,d9_ordinal1),
    [interesting(0.00)]).

fof(d9_xboole_0,definition,(
    ! [A,B] : 
      ( r3_xboole_0(A,B)
    <=> ( r1_tarski(A,B)
        | r1_tarski(B,A) ) ) ),
    file(xboole_0,d9_xboole_0),
    [interesting(0.00)]).

fof(t30_finset_1,theorem,(
    ! [A] : ~ ( v1_finset_1(A)
      & A != k1_xboole_0
      & v6_ordinal1(A)
      & ! [B] : ~ ( r2_hidden(B,A)
          & ! [C] : 
              ( r2_hidden(C,A)
             => r1_tarski(B,C) ) ) ) ),
    file(finset_1,t30_finset_1),
    [interesting(0.00)]).

fof(t31_finset_1,theorem,(
    ! [A] : ~ ( v1_finset_1(A)
      & A != k1_xboole_0
      & v6_ordinal1(A)
      & ! [B] : ~ ( r2_hidden(B,A)
          & ! [C] : 
              ( r2_hidden(C,A)
             => r1_tarski(C,B) ) ) ) ),
    file(finset_1,t31_finset_1),
    [interesting(0.00)]).

fof(t4_setfam_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => r1_tarski(k1_setfam_1(B),A) ) ),
    file(setfam_1,t4_setfam_1),
    [interesting(0.00)]).

fof(t195_orders_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : ~ ( v1_finset_1(B)
          & r1_tarski(B,k2_relat_1(A))
          & ! [C] : ~ ( r1_tarski(C,k1_relat_1(A))
              & v1_finset_1(C)
              & k9_relat_1(A,C) = B ) ) ) ),
    file(orders_1,t195_orders_1),
    [interesting(0.00)]).

fof(d25_pboole,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( ( v1_funcop_1(C)
            & m1_pboole(C,A) )
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( D = k14_pboole(A,B,C)
              <=> ! [E] : 
                    ( r2_hidden(E,A)
                   => k1_funct_1(D,E) = k9_relat_1(k1_funct_1(C,E),k1_funct_1(B,E)) ) ) ) ) ) ),
    file(pboole,d25_pboole),
    [interesting(0.00)]).

fof(t49_pboole,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => r2_pboole(A,k1_pboole(A),B) ) ),
    file(pboole,t49_pboole),
    [interesting(0.00)]).

fof(t9_pboole,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( ( r1_pboole(A,B,C)
                  & r2_pboole(A,C,D) )
               => r1_pboole(A,B,D) ) ) ) ) ),
    file(pboole,t9_pboole),
    [interesting(0.00)]).

fof(t23_pboole,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ! [E] : 
                  ( m1_pboole(E,A)
                 => ( ( r2_pboole(A,B,C)
                      & r2_pboole(A,D,E) )
                   => r2_pboole(A,k3_pboole(A,B,D),k3_pboole(A,C,E)) ) ) ) ) ) ),
    file(pboole,t23_pboole),
    [interesting(0.00)]).

fof(t59_pboole,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( r2_pboole(A,B,C)
               => r2_pboole(A,k4_pboole(A,B,D),k4_pboole(A,C,D)) ) ) ) ) ),
    file(pboole,t59_pboole),
    [interesting(0.00)]).

fof(t62_pboole,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => r2_pboole(A,k4_pboole(A,B,C),B) ) ) ),
    file(pboole,t62_pboole),
    [interesting(0.00)]).

fof(t15_pboole,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( ( r2_pboole(A,B,C)
                  & r2_pboole(A,C,D) )
               => r2_pboole(A,B,D) ) ) ) ) ),
    file(pboole,t15_pboole),
    [interesting(0.00)]).

fof(t36_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r2_pboole(A,k1_pzfmisc1(A,B),C)
          <=> r1_pboole(A,B,C) ) ) ) ),
    file(pzfmisc1,t36_pzfmisc1),
    [interesting(0.00)]).

fof(t11_pzfmisc1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => r6_pboole(A,k2_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C)),k2_pzfmisc1(A,B,C)) ) ) ),
    file(pzfmisc1,t11_pzfmisc1),
    [interesting(0.00)]).

fof(t5_setfam_1,theorem,(
    ! [A] : 
      ( r2_hidden(k1_xboole_0,A)
     => k1_setfam_1(A) = k1_xboole_0 ) ),
    file(setfam_1,t5_setfam_1),
    [interesting(0.00)]).

fof(d2_mssubfam,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m4_pboole(C,A,k1_mboolean(A,B))
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( D = k5_mssubfam(A,B,C)
              <=> ! [E] : ~ ( r2_hidden(E,A)
                    & ! [F] : 
                        ( m1_subset_1(F,k1_zfmisc_1(k1_zfmisc_1(k1_funct_1(B,E))))
                       => ~ ( F = k1_funct_1(C,E)
                            & k1_funct_1(D,E) = k8_setfam_1(k1_funct_1(B,E),F) ) ) ) ) ) ) ) ),
    file(mssubfam,d2_mssubfam),
    [interesting(0.00)]).

fof(t6_setfam_1,theorem,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
         => r1_tarski(B,C) )
     => ( A = k1_xboole_0
        | r1_tarski(B,k1_setfam_1(A)) ) ) ),
    file(setfam_1,t6_setfam_1),
    [interesting(0.00)]).

fof(t59_setfam_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
         => ( r1_tarski(B,C)
           => r1_tarski(k8_setfam_1(A,C),k8_setfam_1(A,B)) ) ) ) ),
    file(setfam_1,t59_setfam_1),
    [interesting(0.00)]).

fof(t8_setfam_1,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & r1_tarski(A,C) )
     => r1_tarski(k1_setfam_1(B),C) ) ),
    file(setfam_1,t8_setfam_1),
    [interesting(0.00)]).

fof(d8_pboole,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( D = k3_pboole(A,B,C)
              <=> ! [E] : 
                    ( r2_hidden(E,A)
                   => k1_funct_1(D,E) = k3_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ),
    file(pboole,d8_pboole),
    [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(t9_setfam_1,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & r1_xboole_0(A,C) )
     => r1_xboole_0(k1_setfam_1(B),C) ) ),
    file(setfam_1,t9_setfam_1),
    [interesting(0.00)]).

fof(d7_pboole,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( D = k2_pboole(A,B,C)
              <=> ! [E] : 
                    ( r2_hidden(E,A)
                   => k1_funct_1(D,E) = k2_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ),
    file(pboole,d7_pboole),
    [interesting(0.00)]).

fof(t15_xboole_1,theorem,(
    ! [A,B] : 
      ( k2_xboole_0(A,B) = k1_xboole_0
     => A = k1_xboole_0 ) ),
    file(xboole_1,t15_xboole_1),
    [interesting(0.00)]).

fof(t10_setfam_1,theorem,(
    ! [A,B] : ~ ( A != k1_xboole_0
      & B != k1_xboole_0
      & k1_setfam_1(k2_xboole_0(A,B)) != k3_xboole_0(k1_setfam_1(A),k1_setfam_1(B)) ) ),
    file(setfam_1,t10_setfam_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(d1_pzfmisc1,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( C = k1_pzfmisc1(A,B)
          <=> ! [D] : 
                ( r2_hidden(D,A)
               => k1_funct_1(C,D) = k1_tarski(k1_funct_1(B,D)) ) ) ) ) ),
    file(pzfmisc1,d1_pzfmisc1),
    [interesting(0.00)]).

fof(t11_setfam_1,theorem,(
    ! [A] : k1_setfam_1(k1_tarski(A)) = A ),
    file(setfam_1,t11_setfam_1),
    [interesting(0.00)]).

fof(d2_pzfmisc1,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( D = k2_pzfmisc1(A,B,C)
              <=> ! [E] : 
                    ( r2_hidden(E,A)
                   => k1_funct_1(D,E) = k2_tarski(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ),
    file(pzfmisc1,d2_pzfmisc1),
    [interesting(0.00)]).

fof(t58_setfam_1,theorem,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( r2_hidden(B,A)
       => ( r2_hidden(B,k8_setfam_1(A,C))
        <=> ! [D] : 
              ( r2_hidden(D,C)
             => r2_hidden(B,D) ) ) ) ) ),
    file(setfam_1,t58_setfam_1),
    [interesting(0.00)]).

fof(t8_mssubfam,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
         => ! [D] : 
              ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A)))
             => ( B = k4_subset_1(k1_zfmisc_1(A),C,D)
               => k8_setfam_1(A,B) = k5_subset_1(A,k8_setfam_1(A,C),k8_setfam_1(A,D)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d10_setfam_1,t28_xboole_1,d10_setfam_1,d10_setfam_1,d10_setfam_1,t28_xboole_1,d10_setfam_1,d10_setfam_1,t15_xboole_1,d10_setfam_1,d10_setfam_1,t10_setfam_1]),
    [file(mssubfam,t8_mssubfam),interesting(0.00)]).