% Mizar problem: t1_groeb_3,groeb_3,39,49 
fof(t1_groeb_3,conjecture,(
    ! [A,B] : 
      ( ( v7_seqm_3(B)
        & v1_polynom1(B)
        & m1_pboole(B,A) )
     => ! [C] : 
          ( ( v7_seqm_3(C)
            & v1_polynom1(C)
            & m1_pboole(C,A) )
         => k1_groeb_2(A,k9_polynom1(A,B,C),C) = B ) ) ),
    inference(mizar_bg_added,[status(thm)],[cc3_polynom1,commutativity_k9_polynom1,d1_groeb_2,dt_k10_polynom1,dt_k1_groeb_2,dt_k9_polynom1,dt_m1_pboole,existence_m1_pboole,fc17_polynom1,fc18_polynom1,fc19_polynom1,fc23_polynom1,fc24_polynom1,rc10_polynom1,rc13_polynom1,rc7_polynom1,rc8_polynom1,rc9_polynom1,redefinition_r6_pboole,reflexivity_r3_polynom1,reflexivity_r6_pboole,symmetry_r6_pboole,t52_polynom1,t54_polynom1]),
    [file(groeb_3,t1_groeb_3)]).

fof(cc3_polynom1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v7_seqm_3(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) ) ) ),
    file(polynom1,cc3_polynom1),
    []).

fof(commutativity_k9_polynom1,axiom,(
    ! [A,B,C] : 
      ( ( v1_seq_1(B)
        & m1_pboole(B,A)
        & v1_seq_1(C)
        & m1_pboole(C,A) )
     => k9_polynom1(A,B,C) = k9_polynom1(A,C,B) ) ),
    file(polynom1,k9_polynom1),
    []).

fof(d1_groeb_2,axiom,(
    ! [A,B] : 
      ( ( v7_seqm_3(B)
        & v1_polynom1(B)
        & m1_pboole(B,A) )
     => ! [C] : 
          ( ( v7_seqm_3(C)
            & v1_polynom1(C)
            & m1_pboole(C,A) )
         => ( r3_polynom1(A,C,B)
           => ! [D] : 
                ( ( v7_seqm_3(D)
                  & v1_polynom1(D)
                  & m1_pboole(D,A) )
               => ( D = k1_groeb_2(A,B,C)
                <=> r6_pboole(A,k9_polynom1(A,C,D),B) ) ) ) ) ) ),
    file(groeb_2,d1_groeb_2),
    []).

fof(dt_k10_polynom1,axiom,(
    ! [A,B,C] : 
      ( ( v7_seqm_3(B)
        & m1_pboole(B,A)
        & v7_seqm_3(C)
        & m1_pboole(C,A) )
     => m1_pboole(k10_polynom1(A,B,C),A) ) ),
    file(polynom1,k10_polynom1),
    []).

fof(dt_k1_groeb_2,axiom,(
    ! [A,B,C] : 
      ( ( v7_seqm_3(B)
        & v1_polynom1(B)
        & m1_pboole(B,A)
        & v7_seqm_3(C)
        & v1_polynom1(C)
        & m1_pboole(C,A) )
     => ( v7_seqm_3(k1_groeb_2(A,B,C))
        & v1_polynom1(k1_groeb_2(A,B,C))
        & m1_pboole(k1_groeb_2(A,B,C),A) ) ) ),
    file(groeb_2,k1_groeb_2),
    []).

fof(dt_k9_polynom1,axiom,(
    ! [A,B,C] : 
      ( ( v1_seq_1(B)
        & m1_pboole(B,A)
        & v1_seq_1(C)
        & m1_pboole(C,A) )
     => m1_pboole(k9_polynom1(A,B,C),A) ) ),
    file(polynom1,k9_polynom1),
    []).

fof(dt_m1_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B) ) ) ),
    file(pboole,m1_pboole),
    []).

fof(existence_m1_pboole,axiom,(
    ! [A] : 
    ? [B] : m1_pboole(B,A) ),
    file(pboole,m1_pboole),
    []).

fof(fc17_polynom1,axiom,(
    ! [A,B,C] : 
      ( ( v1_seq_1(B)
        & m1_pboole(B,A)
        & v1_seq_1(C)
        & m1_pboole(C,A) )
     => ( v1_relat_1(k9_polynom1(A,B,C))
        & v1_funct_1(k9_polynom1(A,B,C))
        & v1_seq_1(k9_polynom1(A,B,C)) ) ) ),
    file(polynom1,fc17_polynom1),
    []).

fof(fc18_polynom1,axiom,(
    ! [A,B,C] : 
      ( ( v7_seqm_3(B)
        & m1_pboole(B,A)
        & v7_seqm_3(C)
        & m1_pboole(C,A) )
     => ( v1_relat_1(k9_polynom1(A,B,C))
        & v1_funct_1(k9_polynom1(A,B,C))
        & v1_seq_1(k9_polynom1(A,B,C))
        & v7_seqm_3(k9_polynom1(A,B,C)) ) ) ),
    file(polynom1,fc18_polynom1),
    []).

fof(fc19_polynom1,axiom,(
    ! [A,B,C] : 
      ( ( v7_seqm_3(B)
        & m1_pboole(B,A)
        & v7_seqm_3(C)
        & m1_pboole(C,A) )
     => ( v1_relat_1(k10_polynom1(A,B,C))
        & v1_funct_1(k10_polynom1(A,B,C))
        & v1_seq_1(k10_polynom1(A,B,C))
        & v7_seqm_3(k10_polynom1(A,B,C)) ) ) ),
    file(polynom1,fc19_polynom1),
    []).

fof(fc23_polynom1,axiom,(
    ! [A,B,C] : 
      ( ( v7_seqm_3(B)
        & v1_polynom1(B)
        & m1_pboole(B,A)
        & v7_seqm_3(C)
        & v1_polynom1(C)
        & m1_pboole(C,A) )
     => ( v1_relat_1(k9_polynom1(A,B,C))
        & v1_funct_1(k9_polynom1(A,B,C))
        & v1_seq_1(k9_polynom1(A,B,C))
        & v7_seqm_3(k9_polynom1(A,B,C))
        & v1_polynom1(k9_polynom1(A,B,C)) ) ) ),
    file(polynom1,fc23_polynom1),
    []).

fof(fc24_polynom1,axiom,(
    ! [A,B,C] : 
      ( ( v7_seqm_3(B)
        & v1_polynom1(B)
        & m1_pboole(B,A)
        & v7_seqm_3(C)
        & v1_polynom1(C)
        & m1_pboole(C,A) )
     => ( v1_relat_1(k10_polynom1(A,B,C))
        & v1_funct_1(k10_polynom1(A,B,C))
        & v1_seq_1(k10_polynom1(A,B,C))
        & v7_seqm_3(k10_polynom1(A,B,C))
        & v1_polynom1(k10_polynom1(A,B,C)) ) ) ),
    file(polynom1,fc24_polynom1),
    []).

fof(rc10_polynom1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_seq_1(B) ) ),
    file(polynom1,rc10_polynom1),
    []).

fof(rc13_polynom1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_seq_1(B)
      & v7_seqm_3(B)
      & v1_polynom1(B) ) ),
    file(polynom1,rc13_polynom1),
    []).

fof(rc7_polynom1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_seq_1(A)
      & v7_seqm_3(A) ) ),
    file(polynom1,rc7_polynom1),
    []).

fof(rc8_polynom1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_seq_1(B)
      & v7_seqm_3(B) ) ),
    file(polynom1,rc8_polynom1),
    []).

fof(rc9_polynom1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_seq_1(B) ) ),
    file(polynom1,rc9_polynom1),
    []).

fof(redefinition_r6_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ( r6_pboole(A,B,C)
      <=> B = C ) ) ),
    file(pboole,r6_pboole),
    []).

fof(reflexivity_r3_polynom1,axiom,(
    ! [A,B,C] : 
      ( ( v7_seqm_3(B)
        & v1_polynom1(B)
        & m1_pboole(B,A)
        & v7_seqm_3(C)
        & v1_polynom1(C)
        & m1_pboole(C,A) )
     => r3_polynom1(A,B,B) ) ),
    file(polynom1,r3_polynom1),
    []).

fof(reflexivity_r6_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => r6_pboole(A,B,B) ) ),
    file(pboole,r6_pboole),
    []).

fof(symmetry_r6_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ( r6_pboole(A,B,C)
       => r6_pboole(A,C,B) ) ) ),
    file(pboole,r6_pboole),
    []).

fof(t52_polynom1,axiom,(
    ! [A,B] : 
      ( ( v7_seqm_3(B)
        & v1_polynom1(B)
        & m1_pboole(B,A) )
     => ! [C] : 
          ( ( v7_seqm_3(C)
            & v1_polynom1(C)
            & m1_pboole(C,A) )
         => r6_pboole(A,k10_polynom1(A,k9_polynom1(A,C,B),B),C) ) ) ),
    file(polynom1,t52_polynom1),
    []).

fof(t54_polynom1,axiom,(
    ! [A,B] : 
      ( ( v7_seqm_3(B)
        & v1_polynom1(B)
        & m1_pboole(B,A) )
     => ! [C] : 
          ( ( v7_seqm_3(C)
            & v1_polynom1(C)
            & m1_pboole(C,A) )
         => ! [D] : 
              ( ( v7_seqm_3(D)
                & v1_polynom1(D)
                & m1_pboole(D,A) )
             => ( r6_pboole(A,B,k9_polynom1(A,C,D))
               => r3_polynom1(A,C,B) ) ) ) ) ),
    file(polynom1,t54_polynom1),
    []).