fof(t9_msualg_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => r1_msualg_3(A,B,B,k2_msualg_3(u1_struct_0(A),u4_msualg_1(A,B))) ) ) ),
    inference(mizar_proof,[status(thm)],[d9_msualg_3,t7_msualg_3,d1_msualg_3,d10_msualg_1,t12_relset_1,d3_pboole,t46_relat_1,d5_msualg_1,d1_funct_2,t22_funct_1,d7_msualg_1,d1_funct_2,t12_relset_1,d5_funct_1,t35_funct_1,d1_funct_2,t60_relat_1,d4_funct_1,t7_msualg_3]),
    [file(msualg_3,t9_msualg_3),interesting(1.00)]).

fof(t17_msualg_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ( r6_msualg_3(A,B,C)
               => r6_msualg_3(A,C,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d13_msualg_3,t14_msualg_3,d13_msualg_3]),
    [file(msualg_3,t17_msualg_3),interesting(1.00)]).

fof(t16_msualg_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => ( r4_msualg_3(A,B,B,k2_msualg_3(u1_struct_0(A),u4_msualg_1(A,B)))
            & r5_msualg_3(A,B,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t9_msualg_3,d3_pboole,d1_msualg_3,d1_msualg_3,t71_relat_1,d3_msualg_3,d2_msualg_3,d11_msualg_3,d10_msualg_3,d12_msualg_3,d13_msualg_3,d12_msualg_3]),
    [file(msualg_3,t16_msualg_3),interesting(0.96)]).

fof(t18_msualg_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] : 
                  ( ( v5_msualg_1(D,A)
                    & l3_msualg_1(D,A) )
                 => ( ( r6_msualg_3(A,B,C)
                      & r6_msualg_3(A,C,D) )
                   => r6_msualg_3(A,B,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d13_msualg_3,d13_msualg_3,t15_msualg_3,d13_msualg_3]),
    [file(msualg_3,t18_msualg_3),interesting(0.91)]).

fof(t22_msualg_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( ( v5_msualg_1(C,A)
                & m1_msualg_2(C,A,B) )
             => ! [D] : 
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,B))
                 => ( r6_pboole(u1_struct_0(A),D,k2_msualg_3(u1_struct_0(A),u4_msualg_1(A,C)))
                   => r3_msualg_3(A,C,B,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t9_msualg_3,l39_msualg_3,d18_pboole,d1_msualg_3,t1_msualg_3,d11_msualg_3]),
    [file(msualg_3,t22_msualg_3),interesting(0.87)]).

fof(l27_msualg_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] : 
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ( r4_msualg_3(A,B,C,D)
                   => r1_msualg_3(A,C,B,k4_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t13_msualg_3,s3_funct_1,t6_msualg_3,t9_funct_1,t9_funct_1,d3_pboole,d1_funct_2,t12_relset_1,d1_funct_2,d5_msualg_1,d1_funct_2,t12_relset_1,d3_pboole,d10_msualg_1,t22_funct_1,d7_msualg_1,d5_msualg_3,d2_msualg_3,t61_funct_1,d9_msualg_3,t8_msualg_3,t5_msualg_3,t7_msualg_3,t22_funct_1,t35_funct_1,d9_msualg_3]),
    [file(msualg_3,l27_msualg_3),interesting(0.86)]).

fof(t4_msualg_3,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m3_pboole(D,A,B,C)
             => k13_pboole(D,k2_msualg_3(A,C)) = D ) ) ) ),
    inference(mizar_proof,[status(thm)],[d24_pboole,d3_pboole,d3_pboole,d3_pboole,d18_pboole,d18_pboole,d1_msualg_3,t2_msualg_3,t23_funct_2,d1_funct_2,t62_relat_1,t3_pboole]),
    [file(msualg_3,t4_msualg_3),interesting(0.84)]).

fof(t14_msualg_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] : 
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ! [E] : 
                      ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,B))
                     => ( ( r4_msualg_3(A,B,C,D)
                          & r6_pboole(u1_struct_0(A),E,k4_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D)) )
                       => r4_msualg_3(A,C,B,E) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d12_msualg_3,d11_msualg_3,d10_msualg_3,d3_pboole,d3_pboole,d18_pboole,d2_msualg_3,t62_funct_1,d5_msualg_3,d3_pboole,d18_pboole,d2_msualg_3,t55_funct_1,d16_pboole,d1_funct_2,d5_msualg_3,d3_msualg_3,d2_msualg_3,l27_msualg_3,d10_msualg_3,d11_msualg_3,d12_msualg_3]),
    [file(msualg_3,t14_msualg_3),interesting(0.80)]).

fof(t15_msualg_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] : 
                  ( ( v5_msualg_1(D,A)
                    & l3_msualg_1(D,A) )
                 => ! [E] : 
                      ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                     => ! [F] : 
                          ( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
                         => ( ( r4_msualg_3(A,B,C,E)
                              & r4_msualg_3(A,C,D,F) )
                           => r4_msualg_3(A,B,D,k3_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),u4_msualg_1(A,D),E,F)) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d12_msualg_3,d12_msualg_3,t11_msualg_3,t12_msualg_3,d12_msualg_3]),
    [file(msualg_3,t15_msualg_3),interesting(0.79)]).

fof(t3_msualg_3,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m3_pboole(D,A,B,C)
             => k13_pboole(k2_msualg_3(A,B),D) = D ) ) ) ),
    inference(mizar_proof,[status(thm)],[d24_pboole,d3_pboole,d3_pboole,d3_pboole,d18_pboole,d18_pboole,t2_msualg_3,d1_msualg_3,d1_funct_2,t42_funct_1,d1_funct_2,t62_relat_1,t3_pboole]),
    [file(msualg_3,t3_msualg_3),interesting(0.77)]).

fof(t7_msualg_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] : 
              ( l3_msualg_1(C,A)
             => ( k3_msualg_1(A,B,C) != k1_xboole_0
               => ! [D] : 
                    ( m1_subset_1(D,k3_msualg_1(A,B,C))
                   => D = k5_msualg_3(A,C,C,B,k2_msualg_3(u1_struct_0(A),u4_msualg_1(A,C)),D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t10_pralg_2,d5_card_3,d5_card_3,t6_msualg_3,l14_msualg_3,d3_pboole,d4_finseq_1,t46_relat_1,d1_msualg_3,t6_msualg_3,t22_funct_1,d4_finseq_4,t35_funct_1,t9_funct_1]),
    [file(msualg_3,t7_msualg_3),interesting(0.72)]).

fof(t1_msualg_3,theorem,(
    ! [A,B] : 
      ( ( v1_funcop_1(B)
        & m1_pboole(B,A) )
     => ( v1_msualg_3(B)
      <=> ! [C] : 
            ( r2_hidden(C,A)
           => v2_funct_1(k1_funct_1(B,C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_pboole,d2_msualg_3,d2_msualg_3]),
    [file(msualg_3,t1_msualg_3),interesting(0.72)]).

fof(t11_msualg_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] : 
                  ( ( v5_msualg_1(D,A)
                    & l3_msualg_1(D,A) )
                 => ! [E] : 
                      ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                     => ! [F] : 
                          ( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
                         => ( ( r2_msualg_3(A,B,C,E)
                              & r2_msualg_3(A,C,D,F) )
                           => r2_msualg_3(A,B,D,k3_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),u4_msualg_1(A,D),E,F)) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d10_msualg_3,t10_msualg_3,d18_pboole,d18_pboole,d3_msualg_3,d3_msualg_3,d16_pboole,d1_funct_2,t47_relat_1,t2_msualg_3,d3_msualg_3,d10_msualg_3]),
    [file(msualg_3,t11_msualg_3),interesting(0.68)]).

fof(t5_msualg_3,theorem,(
    ! [A,B] : 
      ( ( v2_relat_1(B)
        & m1_pboole(B,A) )
     => ! [C] : 
          ( ( v2_relat_1(C)
            & m1_pboole(C,A) )
         => ! [D] : 
              ( m3_pboole(D,A,B,C)
             => ! [E] : 
                  ( m3_pboole(E,A,C,B)
                 => ( ( v1_msualg_3(D)
                      & v2_msualg_3(D,A,B,C)
                      & r6_pboole(A,E,k4_msualg_3(A,B,C,D)) )
                   => ( r6_pboole(A,k3_msualg_3(A,C,B,C,E,D),k2_msualg_3(A,C))
                      & r6_pboole(A,k3_msualg_3(A,B,C,B,D,E),k2_msualg_3(A,B)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_pboole,d18_pboole,d18_pboole,d5_msualg_3,d2_msualg_3,d16_pboole,d1_funct_2,t12_relset_1,t61_funct_1,t2_msualg_3,d3_pboole,d18_pboole,d18_pboole,d5_msualg_3,d2_msualg_3,t61_funct_1,d3_msualg_3,t2_msualg_3,d1_msualg_3]),
    [file(msualg_3,t5_msualg_3),interesting(0.67)]).

fof(t23_msualg_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] : 
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ~ ( r1_msualg_3(A,B,C,D)
                      & ! [E] : 
                          ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k7_msualg_3(A,B,C,D)))
                         => ! [F] : 
                              ( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,k7_msualg_3(A,B,C,D)),u4_msualg_1(A,C))
                             => ~ ( r2_msualg_3(A,B,k7_msualg_3(A,B,C,D),E)
                                  & r3_msualg_3(A,k7_msualg_3(A,B,C,D),C,F)
                                  & r6_pboole(u1_struct_0(A),D,k3_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k7_msualg_3(A,B,C,D)),u4_msualg_1(A,C),E,F)) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l36_msualg_3,d18_pboole,d18_pboole,d16_pboole,d1_funct_2,t12_relset_1,d14_msualg_3,d25_pboole,t146_relat_1,t9_funct_2,d18_pboole,t20_msualg_3,t22_msualg_3,t4_msualg_3]),
    [file(msualg_3,t23_msualg_3),interesting(0.65)]).

fof(t20_msualg_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] : 
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ! [E] : 
                      ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k7_msualg_3(A,B,C,D)))
                     => ( ( r6_pboole(u1_struct_0(A),D,E)
                          & r1_msualg_3(A,B,C,D) )
                       => r2_msualg_3(A,B,k7_msualg_3(A,B,C,D),E) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t6_msualg_3,t6_msualg_3,d8_msualg_3,t9_funct_1,d9_msualg_3,d10_msualg_2,d10_msualg_2,d7_msualg_2,d11_msualg_1,d9_msualg_2,d8_msualg_2,d9_msualg_1,t10_pralg_2,t10_pralg_2,d4_finseq_1,d3_pboole,t46_relat_1,d3_pboole,t46_relat_1,d5_funct_1,d1_funct_2,t12_relset_1,d14_msualg_3,t22_funct_1,d25_pboole,t146_relat_1,t22_funct_1,t38_card_3,d1_funct_2,d3_tarski,d3_xboole_0,t71_funct_1,d9_msualg_3,d14_msualg_3,d25_pboole,d1_funct_2,t146_relat_1,d3_msualg_3,d10_msualg_3]),
    [file(msualg_3,t20_msualg_3),interesting(0.64)]).

fof(l39_msualg_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] : 
                  ( ( v5_msualg_1(D,A)
                    & m1_msualg_2(D,A,C) )
                 => ! [E] : 
                      ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                     => ! [F] : 
                          ( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,D))
                         => ( ( r6_pboole(u1_struct_0(A),E,F)
                              & r1_msualg_3(A,B,D,F) )
                           => r1_msualg_3(A,B,C,E) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d18_pboole,d16_pboole,d10_msualg_2,d10_msualg_2,d23_pboole,d5_pboole,t9_funct_2,d18_pboole,t6_msualg_3,t6_msualg_3,d8_msualg_3,t9_funct_1,d9_msualg_3,d10_msualg_2,d10_msualg_2,d7_msualg_2,d11_msualg_1,d9_msualg_2,d8_msualg_2,d9_msualg_1,d1_funct_2,d3_xboole_0,t71_funct_1,d9_msualg_3]),
    [file(msualg_3,l39_msualg_3),interesting(0.64)]).

fof(t13_msualg_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => ! [C] : 
              ( l3_msualg_1(C,A)
             => ! [D] : 
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ( r4_msualg_3(A,B,C,D)
                  <=> ( r1_msualg_3(A,B,C,D)
                      & v2_msualg_3(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                      & v1_msualg_3(D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d12_msualg_3,d10_msualg_3,d11_msualg_3,d10_msualg_3,d11_msualg_3,d12_msualg_3]),
    [file(msualg_3,t13_msualg_3),interesting(0.60)]).

fof(t21_msualg_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] : 
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ~ ( r1_msualg_3(A,B,C,D)
                      & ! [E] : 
                          ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k7_msualg_3(A,B,C,D)))
                         => ~ ( r6_pboole(u1_struct_0(A),D,E)
                              & r2_msualg_3(A,B,k7_msualg_3(A,B,C,D),E) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l36_msualg_3,t20_msualg_3]),
    [file(msualg_3,t21_msualg_3),interesting(0.56)]).

fof(t19_msualg_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( ( v4_msualg_1(C,A)
                & v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] : 
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ( r1_msualg_3(A,B,C,D)
                   => ( r2_msualg_3(A,B,C,D)
                    <=> k7_msualg_3(A,B,C,D) = C ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d10_msualg_3,d18_pboole,d3_msualg_3,d25_pboole,d16_pboole,d1_funct_2,t146_relat_1,t3_pboole,t6_msualg_2,d14_msualg_3,d14_msualg_3,d25_pboole,d1_funct_2,t146_relat_1,d3_msualg_3,d10_msualg_3]),
    [file(msualg_3,t19_msualg_3),interesting(0.46)]).

fof(t8_msualg_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] : 
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] : 
                  ( ( v5_msualg_1(D,A)
                    & l3_msualg_1(D,A) )
                 => ! [E] : 
                      ( ( v5_msualg_1(E,A)
                        & l3_msualg_1(E,A) )
                     => ! [F] : 
                          ( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
                         => ! [G] : 
                              ( m3_pboole(G,u1_struct_0(A),u4_msualg_1(A,D),u4_msualg_1(A,E))
                             => ! [H] : 
                                  ( m1_subset_1(H,k3_msualg_1(A,B,C))
                                 => k6_msualg_3(A,C,E,B,k3_msualg_3(u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D),u4_msualg_1(A,E),F,G),H) = k6_msualg_3(A,D,E,B,G,k6_msualg_3(A,C,D,B,F,H)) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t6_msualg_3,d8_msualg_3,d4_finseq_1,d3_pboole,t46_relat_1,d4_finseq_4,d1_funct_2,t12_relset_1,d1_funct_2,t22_funct_1,t6_msualg_3,t2_msualg_3,t22_funct_1,d8_msualg_3,d8_msualg_3,t9_funct_1]),
    [file(msualg_3,t8_msualg_3),interesting(0.45)]).

fof(t6_msualg_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] : 
              ( l3_msualg_1(C,A)
             => ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( r2_hidden(D,k3_msualg_1(A,B,C))
                   => ( k1_relat_1(D) = k4_finseq_1(k1_msualg_1(A,B))
                      & ! [E] : 
                          ( r2_hidden(E,k1_relat_1(k5_relat_1(k1_msualg_1(A,B),u4_msualg_1(A,C))))
                         => r2_hidden(k1_funct_1(D,E),k1_funct_1(k5_relat_1(k1_msualg_1(A,B),u4_msualg_1(A,C)),E)) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t10_pralg_2,t18_card_3,d3_pboole,d4_finseq_1,t18_card_3,t46_relat_1]),
    [file(msualg_3,t6_msualg_3),interesting(0.39)]).

fof(l14_msualg_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => ! [C] : 
              ( l3_msualg_1(C,A)
             => ! [D] : 
                  ( m1_subset_1(D,u1_msualg_1(A))
                 => ! [E] : 
                      ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                     => ! [F] : 
                          ( m1_subset_1(F,k3_msualg_1(A,D,B))
                         => ! [G] : 
                              ( ( v1_relat_1(G)
                                & v1_funct_1(G) )
                             => ! [H] : 
                                  ( ( v1_relat_1(H)
                                    & v1_funct_1(H) )
                                 => ( ( F = G
                                      & r2_hidden(F,k3_msualg_1(A,D,B))
                                      & r2_hidden(H,k3_msualg_1(A,D,C)) )
                                   => ( ( H = k5_msualg_3(A,B,C,D,E,F)
                                       => ! [I] : 
                                            ( m2_subset_1(I,k1_numbers,k5_numbers)
                                           => ( r2_hidden(I,k1_relat_1(G))
                                             => k1_funct_1(H,I) = k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),E,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,D),I)),k1_funct_1(G,I)) ) ) )
                                      & ( ! [I] : 
                                            ( m2_subset_1(I,k1_numbers,k5_numbers)
                                           => ( r2_hidden(I,k1_relat_1(G))
                                             => k1_funct_1(H,I) = k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),E,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,D),I)),k1_funct_1(G,I)) ) )
                                       => H = k5_msualg_3(A,B,C,D,E,F) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_finseq_1,d3_pboole,t10_pralg_2,t18_card_3,t46_relat_1,d3_pboole,t18_card_3,t46_relat_1,t21_funct_1,t21_funct_1,d3_pboole,d3_pboole,t21_funct_1,t28_funct_6,d3_tarski,d10_xboole_0,d3_tarski,t28_funct_6,t21_funct_1,t13_finseq_2,d3_pboole,t21_funct_1,t28_funct_6,t21_funct_1,t13_finseq_2,d18_pboole,t23_funct_1,d5_funct_1,t37_card_3,d1_funct_2,t21_funct_5,t23_funct_1,d2_funct_6,d7_msualg_3,t13_finseq_2,d3_pboole,t21_funct_1,t22_funct_1,d4_finseq_4,d8_pralg_2,d17_pralg_1,d3_pboole,t10_pralg_2,d7_msualg_3,d8_pralg_2,d17_pralg_1,t46_relat_1,t13_finseq_2,d3_pboole,t21_funct_1,t22_funct_1,d4_finseq_4,d17_pralg_1,d8_pralg_2,t9_funct_1]),
    [file(msualg_3,l14_msualg_3),interesting(0.07)]).

fof(d9_msualg_3,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => ! [C] : 
              ( l3_msualg_1(C,A)
             => ! [D] : 
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ( r1_msualg_3(A,B,C,D)
                  <=> ! [E] : 
                        ( m1_subset_1(E,u1_msualg_1(A))
                       => ( k3_msualg_1(A,E,B) != k1_xboole_0
                         => ! [F] : 
                              ( m1_subset_1(F,k3_msualg_1(A,E,B))
                             => k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D,k2_msualg_1(A,E)),k1_funct_1(k5_msualg_1(A,E,B),F)) = k1_funct_1(k5_msualg_1(A,E,C),k5_msualg_3(A,B,C,E,D,F)) ) ) ) ) ) ) ) ) ),
    file(msualg_3,d9_msualg_3),
    [interesting(0.00)]).

fof(t10_pralg_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => ! [C] : 
              ( m1_subset_1(C,u1_msualg_1(A))
             => ( k3_msualg_1(A,C,B) = k4_card_3(k5_relat_1(k1_msualg_1(A,C),u4_msualg_1(A,B)))
                & k1_relat_1(k5_relat_1(k1_msualg_1(A,C),u4_msualg_1(A,B))) = k1_relat_1(k1_msualg_1(A,C))
                & k4_msualg_1(A,C,B) = k1_funct_1(u4_msualg_1(A,B),k2_msualg_1(A,C)) ) ) ) ) ),
    file(pralg_2,t10_pralg_2),
    [interesting(0.00)]).

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

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

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

fof(t46_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(k2_relat_1(A),k1_relat_1(B))
           => k1_relat_1(k5_relat_1(A,B)) = k1_relat_1(A) ) ) ) ),
    file(relat_1,t46_relat_1),
    [interesting(0.00)]).

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

fof(t28_funct_6,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r2_hidden(A,k10_relat_1(B,k1_funct_6(k2_relat_1(B))))
      <=> ( r2_hidden(A,k1_relat_1(B))
          & v1_relat_1(k1_funct_1(B,A))
          & v1_funct_1(k1_funct_1(B,A)) ) ) ) ),
    file(funct_6,t28_funct_6),
    [interesting(0.00)]).

fof(d3_tarski,definition,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    [interesting(0.00)]).

fof(d10_xboole_0,definition,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    [interesting(0.00)]).

fof(t13_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B,C] : 
          ( m2_finseq_1(C,B)
         => ( r2_hidden(A,k4_finseq_1(C))
           => r2_hidden(k1_funct_1(C,A),B) ) ) ) ),
    file(finseq_2,t13_finseq_2),
    [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(t23_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(B))
           => k1_funct_1(k5_relat_1(B,C),A) = k1_funct_1(C,k1_funct_1(B,A)) ) ) ) ),
    file(funct_1,t23_funct_1),
    [interesting(0.00)]).

fof(d5_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( r2_hidden(D,k1_relat_1(A))
                  & C = k1_funct_1(A,D) ) ) ) ) ),
    file(funct_1,d5_funct_1),
    [interesting(0.00)]).

fof(t37_card_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( k4_card_3(A) = k1_xboole_0
      <=> r2_hidden(k1_xboole_0,k2_relat_1(A)) ) ) ),
    file(card_3,t37_card_3),
    [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(t21_funct_5,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( k1_funct_5(A) = k1_relat_1(A)
        & k2_funct_5(A) = k2_relat_1(A) ) ) ),
    file(funct_5,t21_funct_5),
    [interesting(0.00)]).

fof(d2_funct_6,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( B = k2_funct_6(A)
          <=> ( k1_relat_1(B) = k10_relat_1(A,k1_funct_6(k2_relat_1(A)))
              & ! [C] : 
                  ( r2_hidden(C,k10_relat_1(A,k1_funct_6(k2_relat_1(A))))
                 => k1_funct_1(B,C) = k1_funct_5(k1_funct_1(A,C)) ) ) ) ) ) ),
    file(funct_6,d2_funct_6),
    [interesting(0.00)]).

fof(d7_msualg_3,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => ! [C] : 
              ( l3_msualg_1(C,A)
             => ! [D] : 
                  ( m1_subset_1(D,u1_msualg_1(A))
                 => ! [E] : 
                      ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                     => ! [F] : 
                          ( m1_subset_1(F,k3_msualg_1(A,D,B))
                         => ~ ( k3_msualg_1(A,D,B) != k1_xboole_0
                              & k3_msualg_1(A,D,C) != k1_xboole_0
                              & k5_msualg_3(A,B,C,D,E,F) != k1_funct_1(k3_pralg_2(k5_relat_1(k1_msualg_1(A,D),E)),F) ) ) ) ) ) ) ) ),
    file(msualg_3,d7_msualg_3),
    [interesting(0.00)]).

fof(t22_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(k5_relat_1(C,B)))
           => k1_funct_1(k5_relat_1(C,B),A) = k1_funct_1(B,k1_funct_1(C,A)) ) ) ) ),
    file(funct_1,t22_funct_1),
    [interesting(0.00)]).

fof(d4_finseq_4,definition,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => ! [D] : 
          ( r2_hidden(D,k1_relat_1(C))
         => k4_finseq_4(A,B,C,D) = k1_funct_1(C,D) ) ) ),
    file(finseq_4,d4_finseq_4),
    [interesting(0.00)]).

fof(d8_pralg_2,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => ! [B] : 
          ( ( v1_funcop_1(B)
            & m1_pboole(B,k4_card_3(k2_funct_6(A))) )
         => ( B = k3_pralg_2(A)
          <=> ! [C] : 
                ( ( v1_relat_1(C)
                  & v1_funct_1(C) )
               => ( r2_hidden(C,k4_card_3(k2_funct_6(A)))
                 => k1_funct_1(B,C) = k15_pralg_1(A,C) ) ) ) ) ) ),
    file(pralg_2,d8_pralg_2),
    [interesting(0.00)]).

fof(d17_pralg_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( C = k15_pralg_1(A,B)
              <=> ( k1_relat_1(C) = k1_relat_1(A)
                  & ! [D] : 
                      ( r2_hidden(D,k1_relat_1(A))
                     => k1_funct_1(C,D) = k1_funct_1(k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) ) ) ),
    file(pralg_1,d17_pralg_1),
    [interesting(0.00)]).

fof(t9_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) ) )
           => A = B ) ) ) ),
    file(funct_1,t9_funct_1),
    [interesting(0.00)]).

fof(d1_msualg_3,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m3_pboole(C,A,B,B)
         => ( C = k2_msualg_3(A,B)
          <=> ! [D] : 
                ( r2_hidden(D,A)
               => k1_funct_1(C,D) = k6_partfun1(k1_funct_1(B,D)) ) ) ) ) ),
    file(msualg_3,d1_msualg_3),
    [interesting(0.00)]).

fof(t35_funct_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(B,A)
     => k1_funct_1(k6_relat_1(A),B) = B ) ),
    file(funct_1,t35_funct_1),
    [interesting(0.00)]).

fof(d10_msualg_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] : 
              ( l3_msualg_1(C,A)
             => k4_msualg_1(A,B,C) = k1_funct_1(k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,C)),B) ) ) ) ),
    file(msualg_1,d10_msualg_1),
    [interesting(0.00)]).

fof(t12_relset_1,theorem,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( r1_tarski(k1_relat_1(C),A)
        & r1_tarski(k2_relat_1(C),B) ) ) ),
    file(relset_1,t12_relset_1),
    [interesting(0.00)]).

fof(d5_msualg_1,definition,(
    ! [A] : 
      ( l1_msualg_1(A)
     => ( v2_msualg_1(A)
      <=> u1_msualg_1(A) = k1_xboole_0 ) ) ),
    file(msualg_1,d5_msualg_1),
    [interesting(0.00)]).

fof(d7_msualg_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_msualg_1(A))
         => k2_msualg_1(A,B) = k1_funct_1(u3_msualg_1(A),B) ) ) ),
    file(msualg_1,d7_msualg_1),
    [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(d4_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( ( r2_hidden(B,k1_relat_1(A))
           => ( C = k1_funct_1(A,B)
            <=> r2_hidden(k4_tarski(B,C),A) ) )
          & ( ~ r2_hidden(B,k1_relat_1(A))
           => ( C = k1_funct_1(A,B)
            <=> C = k1_xboole_0 ) ) ) ) ),
    file(funct_1,d4_funct_1),
    [interesting(0.00)]).

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

fof(d3_msualg_3,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m3_pboole(D,A,B,C)
             => ( v2_msualg_3(D,A,B,C)
              <=> ! [E] : 
                    ( r2_hidden(E,A)
                   => k2_relat_1(k1_funct_1(D,E)) = k1_funct_1(C,E) ) ) ) ) ) ),
    file(msualg_3,d3_msualg_3),
    [interesting(0.00)]).

fof(d2_msualg_3,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_msualg_3(A)
      <=> ! [B,C] : 
            ( ( v1_relat_1(C)
              & v1_funct_1(C) )
           => ( ( r2_hidden(B,k1_relat_1(A))
                & k1_funct_1(A,B) = C )
             => v2_funct_1(C) ) ) ) ) ),
    file(msualg_3,d2_msualg_3),
    [interesting(0.00)]).

fof(d11_msualg_3,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => ! [C] : 
              ( l3_msualg_1(C,A)
             => ! [D] : 
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ( r3_msualg_3(A,B,C,D)
                  <=> ( r1_msualg_3(A,B,C,D)
                      & v1_msualg_3(D) ) ) ) ) ) ) ),
    file(msualg_3,d11_msualg_3),
    [interesting(0.00)]).

fof(d10_msualg_3,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => ! [C] : 
              ( l3_msualg_1(C,A)
             => ! [D] : 
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ( r2_msualg_3(A,B,C,D)
                  <=> ( r1_msualg_3(A,B,C,D)
                      & v2_msualg_3(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) ) ) ) ) ) ) ),
    file(msualg_3,d10_msualg_3),
    [interesting(0.00)]).

fof(d12_msualg_3,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => ! [C] : 
              ( l3_msualg_1(C,A)
             => ! [D] : 
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ( r4_msualg_3(A,B,C,D)
                  <=> ( r2_msualg_3(A,B,C,D)
                      & r3_msualg_3(A,B,C,D) ) ) ) ) ) ) ),
    file(msualg_3,d12_msualg_3),
    [interesting(0.00)]).

fof(d13_msualg_3,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => ! [C] : 
              ( l3_msualg_1(C,A)
             => ( r5_msualg_3(A,B,C)
              <=> ? [D] : 
                    ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                    & r4_msualg_3(A,B,C,D) ) ) ) ) ) ),
    file(msualg_3,d13_msualg_3),
    [interesting(0.00)]).

fof(t62_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
       => v2_funct_1(k2_funct_1(A)) ) ) ),
    file(funct_1,t62_funct_1),
    [interesting(0.00)]).

fof(d5_msualg_3,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m3_pboole(D,A,B,C)
             => ( ( v1_msualg_3(D)
                  & v2_msualg_3(D,A,B,C) )
               => ! [E] : 
                    ( m3_pboole(E,A,C,B)
                   => ( E = k4_msualg_3(A,B,C,D)
                    <=> ! [F] : 
                          ( r2_hidden(F,A)
                         => k1_funct_1(E,F) = k2_funct_1(k1_funct_1(D,F)) ) ) ) ) ) ) ) ),
    file(msualg_3,d5_msualg_3),
    [interesting(0.00)]).

fof(t55_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
       => ( k2_relat_1(A) = k1_relat_1(k2_funct_1(A))
          & k1_relat_1(A) = k2_relat_1(k2_funct_1(A)) ) ) ) ),
    file(funct_1,t55_funct_1),
    [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(s3_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_relat_1(A) = f1_s3_funct_1
      & ! [B] : 
          ( r2_hidden(B,f1_s3_funct_1)
         => k1_funct_1(A,B) = f2_s3_funct_1(B) ) ) ),
    file(funct_1,s3_funct_1),
    [interesting(0.00)]).

fof(t61_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
       => ( k5_relat_1(A,k2_funct_1(A)) = k6_relat_1(k1_relat_1(A))
          & k5_relat_1(k2_funct_1(A),A) = k6_relat_1(k2_relat_1(A)) ) ) ) ),
    file(funct_1,t61_funct_1),
    [interesting(0.00)]).

fof(d8_msualg_3,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] : 
                  ( m1_subset_1(D,u1_msualg_1(A))
                 => ! [E] : 
                      ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                     => ! [F] : 
                          ( m1_subset_1(F,k3_msualg_1(A,D,B))
                         => ! [G] : 
                              ( m1_subset_1(G,k3_msualg_1(A,D,C))
                             => ( G = k6_msualg_3(A,B,C,D,E,F)
                              <=> ! [H] : 
                                    ( m2_subset_1(H,k1_numbers,k5_numbers)
                                   => ( r2_hidden(H,k1_relat_1(F))
                                     => k1_funct_1(G,H) = k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),E,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,D),H)),k1_funct_1(F,H)) ) ) ) ) ) ) ) ) ) ) ),
    file(msualg_3,d8_msualg_3),
    [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(t2_msualg_3,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ! [E] : 
                  ( m3_pboole(E,A,B,C)
                 => ! [F] : 
                      ( m3_pboole(F,A,C,D)
                     => ( k1_relat_1(k13_pboole(E,F)) = A
                        & ! [G] : 
                            ( r2_hidden(G,A)
                           => k1_funct_1(k13_pboole(E,F),G) = k5_relat_1(k1_funct_1(E,G),k1_funct_1(F,G)) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_pboole,d24_pboole,d24_pboole]),
    [file(msualg_3,t2_msualg_3),interesting(0.00)]).

fof(t10_msualg_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] : 
                  ( ( v5_msualg_1(D,A)
                    & l3_msualg_1(D,A) )
                 => ! [E] : 
                      ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                     => ! [F] : 
                          ( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
                         => ( ( r1_msualg_3(A,B,C,E)
                              & r1_msualg_3(A,C,D,F) )
                           => r1_msualg_3(A,B,D,k3_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),u4_msualg_1(A,D),E,F)) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d9_msualg_3,d9_msualg_3,d9_msualg_3,t2_msualg_3,d1_funct_2,d10_msualg_1,t12_relset_1,d3_pboole,t46_relat_1,d5_msualg_1,d1_funct_2,t22_funct_1,d7_msualg_1,t22_funct_1,t8_msualg_3]),
    [file(msualg_3,t10_msualg_3),interesting(0.00)]).

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

fof(t46_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( v2_funct_1(A)
              & v2_funct_1(B) )
           => v2_funct_1(k5_relat_1(A,B)) ) ) ) ),
    file(funct_1,t46_funct_1),
    [interesting(0.00)]).

fof(t12_msualg_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] : 
                  ( ( v5_msualg_1(D,A)
                    & l3_msualg_1(D,A) )
                 => ! [E] : 
                      ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                     => ! [F] : 
                          ( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
                         => ( ( r3_msualg_3(A,B,C,E)
                              & r3_msualg_3(A,C,D,F) )
                           => r3_msualg_3(A,B,D,k3_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),u4_msualg_1(A,D),E,F)) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_msualg_3,t10_msualg_3,d3_pboole,d3_pboole,d3_pboole,d18_pboole,d18_pboole,d2_msualg_3,d2_msualg_3,t46_funct_1,t2_msualg_3,d2_msualg_3,d11_msualg_3]),
    [file(msualg_3,t12_msualg_3),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(t146_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => k9_relat_1(A,k1_relat_1(A)) = k2_relat_1(A) ) ),
    file(relat_1,t146_relat_1),
    [interesting(0.00)]).

fof(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(t6_msualg_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => m1_msualg_2(B,A,B) ) ) ),
    file(msualg_2,t6_msualg_2),
    [interesting(0.00)]).

fof(d14_msualg_3,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] : 
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ( r1_msualg_3(A,B,C,D)
                   => ! [E] : 
                        ( ( v4_msualg_1(E,A)
                          & v5_msualg_1(E,A)
                          & m1_msualg_2(E,A,C) )
                       => ( E = k7_msualg_3(A,B,C,D)
                        <=> r6_pboole(u1_struct_0(A),u4_msualg_1(A,E),k14_pboole(u1_struct_0(A),u4_msualg_1(A,B),D)) ) ) ) ) ) ) ) ),
    file(msualg_3,d14_msualg_3),
    [interesting(0.00)]).

fof(t3_funct_2,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_funct_1(A)
        & v1_funct_2(A,k1_relat_1(A),k2_relat_1(A))
        & m2_relset_1(A,k1_relat_1(A),k2_relat_1(A)) ) ) ),
    file(funct_2,t3_funct_2),
    [interesting(0.00)]).

fof(l36_msualg_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] : 
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ( r1_msualg_3(A,B,C,D)
                   => m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k7_msualg_3(A,B,C,D))) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d18_pboole,d16_pboole,d1_funct_2,t12_relset_1,d14_msualg_3,d25_pboole,t146_relat_1,t3_funct_2,d18_pboole]),
    [file(msualg_3,l36_msualg_3),interesting(0.00)]).

fof(d10_msualg_2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => ! [C] : 
              ( l3_msualg_1(C,A)
             => ( m1_msualg_2(C,A,B)
              <=> ( m4_pboole(u4_msualg_1(A,C),u1_struct_0(A),u4_msualg_1(A,B))
                  & ! [D] : 
                      ( m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B))
                     => ( r6_pboole(u1_struct_0(A),D,u4_msualg_1(A,C))
                       => ( v3_msualg_2(D,A,B)
                          & r6_pboole(u1_msualg_1(A),u5_msualg_1(A,C),k4_msualg_2(A,B,D)) ) ) ) ) ) ) ) ) ),
    file(msualg_2,d10_msualg_2),
    [interesting(0.00)]).

fof(d7_msualg_2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => ! [C] : 
              ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
             => ( v3_msualg_2(C,A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,u1_msualg_1(A))
                   => r1_msualg_2(A,B,D,C) ) ) ) ) ) ),
    file(msualg_2,d7_msualg_2),
    [interesting(0.00)]).

fof(d11_msualg_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] : 
              ( l3_msualg_1(C,A)
             => k5_msualg_1(A,B,C) = k1_funct_1(u5_msualg_1(A,C),B) ) ) ) ),
    file(msualg_1,d11_msualg_1),
    [interesting(0.00)]).

fof(d9_msualg_2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => ! [C] : 
              ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
             => ! [D] : 
                  ( m3_pboole(D,u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),C)),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),C))
                 => ( D = k4_msualg_2(A,B,C)
                  <=> ! [E] : 
                        ( m1_subset_1(E,u1_msualg_1(A))
                       => k1_funct_1(D,E) = k3_msualg_2(A,B,E,C) ) ) ) ) ) ) ),
    file(msualg_2,d9_msualg_2),
    [interesting(0.00)]).

fof(d8_msualg_2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => ! [C] : 
              ( m1_subset_1(C,u1_msualg_1(A))
             => ! [D] : 
                  ( m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B))
                 => ( r1_msualg_2(A,B,C,D)
                   => k3_msualg_2(A,B,C,D) = k7_relat_1(k5_msualg_1(A,C,B),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),D)),C)) ) ) ) ) ) ),
    file(msualg_2,d8_msualg_2),
    [interesting(0.00)]).

fof(d9_msualg_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] : 
              ( l3_msualg_1(C,A)
             => k3_msualg_1(A,B,C) = k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),u4_msualg_1(A,C))),B) ) ) ) ),
    file(msualg_1,d9_msualg_1),
    [interesting(0.00)]).

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

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

fof(t71_funct_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(B,k3_xboole_0(k1_relat_1(C),A))
       => k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B) ) ) ),
    file(funct_1,t71_funct_1),
    [interesting(0.00)]).

fof(t9_funct_2,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( r1_tarski(B,C)
       => ( ( B = k1_xboole_0
            & A != k1_xboole_0 )
          | ( v1_funct_1(D)
            & v1_funct_2(D,A,C)
            & m2_relset_1(D,A,C) ) ) ) ) ),
    file(funct_2,t9_funct_2),
    [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(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(t23_funct_2,theorem,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( k7_relset_1(A,A,A,B,k6_partfun1(A),C) = C
        & k7_relset_1(A,B,B,B,C,k6_partfun1(B)) = C ) ) ),
    file(funct_2,t23_funct_2),
    [interesting(0.00)]).

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

fof(t24_msualg_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => ! [C] : 
              ( l3_msualg_1(C,A)
             => ! [D] : 
                  ( m1_subset_1(D,u1_msualg_1(A))
                 => ! [E] : 
                      ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                     => ! [F] : 
                          ( m1_subset_1(F,k3_msualg_1(A,D,B))
                         => ! [G] : 
                              ( ( v1_relat_1(G)
                                & v1_funct_1(G) )
                             => ! [H] : 
                                  ( ( v1_relat_1(H)
                                    & v1_funct_1(H) )
                                 => ( ( F = G
                                      & r2_hidden(F,k3_msualg_1(A,D,B))
                                      & r2_hidden(H,k3_msualg_1(A,D,C)) )
                                   => ( H = k5_msualg_3(A,B,C,D,E,F)
                                    <=> ! [I] : 
                                          ( m2_subset_1(I,k1_numbers,k5_numbers)
                                         => ( r2_hidden(I,k1_relat_1(G))
                                           => k1_funct_1(H,I) = k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),E,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,D),I)),k1_funct_1(G,I)) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l14_msualg_3]),
    [file(msualg_3,t24_msualg_3),interesting(0.00)]).

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