fof(t49_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_analmetr(A,B,C)
               => ( ~ v3_struct_0(k7_geomtrap(A,B,C))
                  & v2_geomtrap(k7_geomtrap(A,B,C))
                  & l1_geomtrap(k7_geomtrap(A,B,C)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l81_geomtrap,l82_geomtrap,l83_geomtrap,l84_geomtrap,l85_geomtrap,l86_geomtrap,l87_geomtrap,l88_geomtrap,l89_geomtrap,l90_geomtrap,l91_geomtrap,l92_geomtrap,l93_geomtrap,l94_geomtrap,d13_geomtrap]),
    [file(geomtrap,t49_geomtrap),interesting(1.00)]).

fof(l106_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_geomtrap(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => r2_analoaf(A,B,C,B,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d14_geomtrap,d14_geomtrap,d14_geomtrap,d14_geomtrap,d14_geomtrap,d14_geomtrap,d14_geomtrap]),
    [file(geomtrap,l106_geomtrap),interesting(0.82)]).

fof(t25_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( r1_analmetr(A,B,C)
                              & r2_geomtrap(A,B,C,D,E,D,F) )
                           => E = F ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_geomtrap,t9_geomtrap,t21_analoaf,t14_geomtrap,t17_analoaf,t18_analoaf,t20_analoaf,t18_analoaf,t20_analoaf,t18_analoaf,d1_geomtrap,d1_geomtrap,d1_geomtrap,d1_geomtrap,l37_geomtrap,l27_geomtrap,l25_geomtrap,l37_geomtrap,l27_geomtrap,l25_geomtrap]),
    [file(geomtrap,t25_geomtrap),interesting(0.73)]).

fof(t20_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( r1_analmetr(A,B,C)
                              & r2_geomtrap(A,B,C,D,E,E,F) )
                           => ( D = E
                              & E = F ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_geomtrap,t9_geomtrap,t15_geomtrap,l17_geomtrap,d1_geomtrap,t14_geomtrap,d1_geomtrap,t9_geomtrap,l27_geomtrap,l27_geomtrap,l25_geomtrap,t9_geomtrap,l27_geomtrap,l27_geomtrap,l25_geomtrap,t19_geomtrap]),
    [file(geomtrap,t20_geomtrap),interesting(0.71)]).

fof(l107_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_geomtrap(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k2_diraf(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k2_diraf(A)))
             => r2_analoaf(k2_diraf(A),B,C,C,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t50_geomtrap,l106_geomtrap,t51_geomtrap]),
    [file(geomtrap,l107_geomtrap),interesting(0.69)]).

fof(t27_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ! [H] : 
                                  ( m1_subset_1(H,u1_struct_0(A))
                                 => ( ( r1_analmetr(A,B,C)
                                      & r2_geomtrap(A,B,C,D,E,F,G) )
                                   => ( D = E
                                      | ( ~ r2_geomtrap(A,B,C,D,E,F,H)
                                        & ~ r2_geomtrap(A,B,C,D,E,H,F) )
                                      | G = H ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t21_geomtrap,t20_geomtrap,t26_geomtrap]),
    [file(geomtrap,t27_geomtrap),interesting(0.68)]).

fof(l20_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r1_analoaf(A,B,C,D,E)
                       => r1_geomtrap(A,B,C,k1_geomtrap(A,B,E),k1_geomtrap(A,C,D)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t18_analoaf,d1_geomtrap,t10_geomtrap,d1_geomtrap,d1_analoaf,t81_vectsp_1,t39_rlvect_1,t39_rlvect_1,t38_rlvect_1,d9_rlvect_1,t48_rlvect_1,d9_rlvect_1,d9_rlvect_1,d9_rlvect_1,d2_geomtrap,d6_rlvect_1,d9_rlvect_1,d9_rlvect_1,d9_rlvect_1,d2_geomtrap,t41_rlvect_1,d6_rlvect_1,d6_rlvect_1,d9_rlvect_1,d9_rlvect_1,t18_analmetr,d1_geomtrap]),
    [file(geomtrap,l20_geomtrap),interesting(0.68)]).

fof(t50_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_geomtrap(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
        <=> m1_subset_1(B,u1_struct_0(k2_diraf(A))) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_diraf]),
    [file(geomtrap,t50_geomtrap),interesting(0.67)]).

fof(t26_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ! [H] : 
                                  ( m1_subset_1(H,u1_struct_0(A))
                                 => ~ ( r1_analmetr(A,B,C)
                                      & r2_geomtrap(A,B,C,D,E,F,G)
                                      & r2_geomtrap(A,B,C,D,E,F,H)
                                      & D != E
                                      & G != H ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t21_geomtrap,t25_geomtrap]),
    [file(geomtrap,t26_geomtrap),interesting(0.64)]).

fof(l81_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k7_geomtrap(A,B,C)))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(k7_geomtrap(A,B,C)))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(k7_geomtrap(A,B,C)))
                         => ( ( r1_analmetr(A,B,C)
                              & r2_analoaf(k7_geomtrap(A,B,C),D,E,E,F) )
                           => ( D = E
                              & E = F ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t47_geomtrap,t20_geomtrap]),
    [file(geomtrap,l81_geomtrap),interesting(0.64)]).

fof(t28_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ( ( r1_analmetr(A,B,C)
                                  & r2_geomtrap(A,B,C,D,E,F,G) )
                               => r2_geomtrap(A,B,C,D,E,k1_geomtrap(A,D,F),k1_geomtrap(A,E,G)) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_geomtrap,t8_geomtrap,t14_geomtrap,d1_geomtrap,t16_geomtrap,d1_geomtrap,t21_analoaf,t16_geomtrap,d1_geomtrap,t8_geomtrap,l26_geomtrap,l27_geomtrap,l27_geomtrap,l27_geomtrap,l26_geomtrap,d3_geomtrap]),
    [file(geomtrap,t28_geomtrap),interesting(0.63)]).

fof(t22_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ~ ( r1_analmetr(A,B,C)
                              & ! [G] : 
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ( ~ r2_geomtrap(A,B,C,D,E,F,G)
                                    & ~ r2_geomtrap(A,B,C,D,E,G,F) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l23_geomtrap,t18_analoaf,l22_geomtrap,d3_geomtrap,t9_geomtrap,t35_rlvect_1,t17_analmetr,t12_geomtrap,t78_rlsub_2,d9_rlvect_1,d9_rlvect_1,d9_rlvect_1,d2_geomtrap,t41_rlvect_1,t41_rlvect_1,t41_rlvect_1,t11_analmetr,d3_analmetr,l22_geomtrap,l22_geomtrap,t43_rlvect_1,t28_rlvect_1,t10_rlvect_1,t12_geomtrap,d9_rlvect_1,d9_rlvect_1,t23_rlvect_1,t26_rlvect_1,d9_rlvect_1,d9_rlvect_1,d9_rlvect_1,t78_rlsub_2,t18_analoaf,l23_geomtrap,l22_geomtrap,d3_geomtrap,t11_analmetr,d3_analmetr,l22_geomtrap,l22_geomtrap,l22_geomtrap,d9_rlvect_1,t18_analmetr,t21_analoaf,d3_geomtrap]),
    [file(geomtrap,t22_geomtrap),interesting(0.61)]).

fof(t13_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => r1_analoaf(A,B,k1_geomtrap(A,B,C),k1_geomtrap(A,B,C),C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t12_geomtrap,t12_geomtrap,d1_analoaf]),
    [file(geomtrap,t13_geomtrap),interesting(0.59)]).

fof(t39_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_analmetr(A,B,C)
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] : 
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ! [H] : 
                                    ( m1_subset_1(H,u1_struct_0(A))
                                   => ! [I] : 
                                        ( m1_subset_1(I,u1_struct_0(A))
                                       => ! [J] : 
                                            ( m1_subset_1(J,u1_struct_0(A))
                                           => ! [K] : 
                                                ( m1_subset_1(K,u1_struct_0(A))
                                               => ! [L] : 
                                                    ( m1_subset_1(L,u1_struct_0(A))
                                                   => ! [M] : 
                                                        ( m1_subset_1(M,u1_struct_0(A))
                                                       => ( ( r2_geomtrap(A,B,C,D,E,F,J)
                                                            & r2_geomtrap(A,B,C,D,E,G,K)
                                                            & r2_geomtrap(A,B,C,D,E,H,L)
                                                            & r2_geomtrap(A,B,C,D,E,I,M)
                                                            & r1_analoaf(A,F,G,H,I) )
                                                         => ( D = E
                                                            | r1_analoaf(A,J,K,L,M) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t38_geomtrap,t38_geomtrap,t26_geomtrap,d1_analoaf,t26_geomtrap,d1_analoaf,t16_analoaf,t33_geomtrap,t33_geomtrap,l64_geomtrap,t4_xcmplx_1,l64_geomtrap,l64_geomtrap,l64_geomtrap,d9_rlvect_1,d9_rlvect_1,d9_rlvect_1,d9_rlvect_1,d1_analoaf]),
    [file(geomtrap,t39_geomtrap),interesting(0.54)]).

fof(t29_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ~ ( r1_analmetr(A,B,C)
                                  & r2_geomtrap(A,B,C,D,E,F,G)
                                  & ~ r2_geomtrap(A,B,C,D,E,k1_geomtrap(A,D,G),k1_geomtrap(A,E,F))
                                  & ~ r2_geomtrap(A,B,C,D,E,k1_geomtrap(A,E,F),k1_geomtrap(A,D,G)) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_geomtrap,t8_geomtrap,t14_geomtrap,d1_geomtrap,l20_geomtrap,d1_geomtrap,l26_geomtrap,l26_geomtrap,d3_geomtrap,l27_geomtrap,l27_geomtrap,l22_geomtrap,l22_geomtrap,l27_geomtrap,d3_geomtrap,t28_geomtrap]),
    [file(geomtrap,t29_geomtrap),interesting(0.53)]).

fof(t40_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_analmetr(A,B,C)
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] : 
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ! [H] : 
                                    ( m1_subset_1(H,u1_struct_0(A))
                                   => ! [I] : 
                                        ( m1_subset_1(I,u1_struct_0(A))
                                       => ! [J] : 
                                            ( m1_subset_1(J,u1_struct_0(A))
                                           => ! [K] : 
                                                ( m1_subset_1(K,u1_struct_0(A))
                                               => ( ( r2_geomtrap(A,B,C,D,E,F,I)
                                                    & r2_geomtrap(A,B,C,D,E,G,J)
                                                    & r2_geomtrap(A,B,C,D,E,H,K)
                                                    & H = k1_geomtrap(A,F,G) )
                                                 => ( D = E
                                                    | K = k1_geomtrap(A,I,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t38_geomtrap,d6_rlvect_1,d6_rlvect_1,d6_rlvect_1,d9_rlvect_1,d2_geomtrap,d6_rlvect_1,d6_rlvect_1,d6_rlvect_1,d9_rlvect_1,t32_geomtrap,d2_geomtrap,t32_geomtrap,d2_geomtrap]),
    [file(geomtrap,t40_geomtrap),interesting(0.51)]).

fof(t41_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_analmetr(A,B,C)
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] : 
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ! [H] : 
                                    ( m1_subset_1(H,u1_struct_0(A))
                                   => ! [I] : 
                                        ( m1_subset_1(I,u1_struct_0(A))
                                       => ( ( r2_geomtrap(A,B,C,D,E,F,H)
                                            & r2_geomtrap(A,B,C,D,E,G,I) )
                                         => ( D = E
                                            | r2_geomtrap(A,B,C,D,E,k1_geomtrap(A,F,G),k1_geomtrap(A,H,I)) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t21_geomtrap,t28_geomtrap,t23_geomtrap,t21_geomtrap,t23_geomtrap,t21_geomtrap,t18_analoaf,l23_geomtrap,l22_geomtrap,d3_geomtrap,d3_analmetr,d9_rlvect_1,d9_rlvect_1,d9_rlvect_1,d2_geomtrap,d9_rlvect_1,d9_rlvect_1,d9_rlvect_1,l53_geomtrap,d9_rlvect_1,d9_rlvect_1,t48_rlvect_1,d6_rlvect_1,d6_rlvect_1,d6_rlvect_1,d9_rlvect_1,t11_analmetr,t14_analmetr,d3_analmetr,d3_geomtrap]),
    [file(geomtrap,t41_geomtrap),interesting(0.50)]).

fof(l50_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,k1_numbers)
                     => ! [F] : 
                          ( m1_subset_1(F,k1_numbers)
                         => ( ( r1_analmetr(A,B,C)
                              & D = k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F)) )
                           => ( E = k2_geomtrap(A,B,C,D)
                              & F = k3_geomtrap(A,B,C,D) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l49_geomtrap,l46_geomtrap]),
    [file(geomtrap,l50_geomtrap),interesting(0.49)]).

fof(t36_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_analmetr(A,B,C)
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(A))
                           => k4_real_1(2,k4_geomtrap(A,B,C,D,k1_geomtrap(A,E,F))) = k3_real_1(k4_geomtrap(A,B,C,D,E),k4_geomtrap(A,B,C,D,F)) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l52_geomtrap,l52_geomtrap]),
    [file(geomtrap,t36_geomtrap),interesting(0.49)]).

fof(l49_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_analmetr(A,B,C)
                   => D = k4_rlvect_1(A,k3_rlvect_1(A,B,k2_geomtrap(A,B,C,D)),k3_rlvect_1(A,C,k3_geomtrap(A,B,C,D))) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_geomtrap,d5_geomtrap]),
    [file(geomtrap,l49_geomtrap),interesting(0.47)]).

fof(t1_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_analmetr(A,B,C)
               => ( ~ v3_struct_0(k2_analoaf(A))
                  & ~ v3_realset2(k2_analoaf(A))
                  & v2_analoaf(k2_analoaf(A))
                  & l1_analoaf(k2_analoaf(A)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_analmetr,t38_analoaf]),
    [file(geomtrap,t1_geomtrap),interesting(0.47)]).

fof(t35_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_analmetr(A,B,C)
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] : 
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ( r3_analmetr(A,D,E,F,G,B,C)
                                <=> k4_geomtrap(A,B,C,k6_rlvect_1(A,E,D),k6_rlvect_1(A,G,F)) = 0 ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_analmetr,t34_geomtrap]),
    [file(geomtrap,t35_geomtrap),interesting(0.45)]).

fof(t33_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_analmetr(A,B,C)
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] : 
                            ( m1_subset_1(F,k1_numbers)
                           => ( k4_geomtrap(A,B,C,k3_rlvect_1(A,D,F),E) = k4_real_1(F,k4_geomtrap(A,B,C,D,E))
                              & k4_geomtrap(A,B,C,D,k3_rlvect_1(A,E,F)) = k4_real_1(F,k4_geomtrap(A,B,C,D,E))
                              & k4_geomtrap(A,B,C,k3_rlvect_1(A,D,F),E) = k4_real_1(k4_geomtrap(A,B,C,D,E),F)
                              & k4_geomtrap(A,B,C,D,k3_rlvect_1(A,E,F)) = k4_real_1(k4_geomtrap(A,B,C,D,E),F) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l51_geomtrap,l51_geomtrap]),
    [file(geomtrap,t33_geomtrap),interesting(0.44)]).

fof(l93_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k7_geomtrap(A,B,C)))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(k7_geomtrap(A,B,C)))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(k7_geomtrap(A,B,C)))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(k7_geomtrap(A,B,C)))
                             => ! [H] : 
                                  ( m1_subset_1(H,u1_struct_0(k7_geomtrap(A,B,C)))
                                 => ! [I] : 
                                      ( m1_subset_1(I,u1_struct_0(k7_geomtrap(A,B,C)))
                                     => ! [J] : 
                                          ( m1_subset_1(J,u1_struct_0(k7_geomtrap(A,B,C)))
                                         => ! [K] : 
                                              ( m1_subset_1(K,u1_struct_0(k7_geomtrap(A,B,C)))
                                             => ! [L] : 
                                                  ( m1_subset_1(L,u1_struct_0(k7_geomtrap(A,B,C)))
                                                 => ( ( r1_analmetr(A,B,C)
                                                      & r2_analoaf(k7_geomtrap(A,B,C),D,E,F,G)
                                                      & k9_geomtrap(k7_geomtrap(A,B,C),D,H) = I
                                                      & k9_geomtrap(k7_geomtrap(A,B,C),E,J) = I
                                                      & k9_geomtrap(k7_geomtrap(A,B,C),F,K) = I
                                                      & k9_geomtrap(k7_geomtrap(A,B,C),G,L) = I )
                                                   => r2_analoaf(k7_geomtrap(A,B,C),H,J,K,L) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t47_geomtrap,t48_geomtrap,t30_geomtrap,t47_geomtrap]),
    [file(geomtrap,l93_geomtrap),interesting(0.44)]).

fof(l52_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r1_analmetr(A,B,C)
                       => ( k4_real_1(2,k2_geomtrap(A,B,C,k1_geomtrap(A,D,E))) = k3_real_1(k2_geomtrap(A,B,C,D),k2_geomtrap(A,B,C,E))
                          & k4_real_1(2,k3_geomtrap(A,B,C,k1_geomtrap(A,D,E))) = k3_real_1(k3_geomtrap(A,B,C,D),k3_geomtrap(A,B,C,E)) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d9_rlvect_1,d9_rlvect_1,d9_rlvect_1,d2_geomtrap,l51_geomtrap,l51_geomtrap]),
    [file(geomtrap,l52_geomtrap),interesting(0.42)]).

fof(t32_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_analmetr(A,B,C)
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( k4_geomtrap(A,B,C,D,k4_rlvect_1(A,E,F)) = k3_real_1(k4_geomtrap(A,B,C,D,E),k4_geomtrap(A,B,C,D,F))
                              & k4_geomtrap(A,B,C,D,k6_rlvect_1(A,E,F)) = k5_real_1(k4_geomtrap(A,B,C,D,E),k4_geomtrap(A,B,C,D,F))
                              & k4_geomtrap(A,B,C,k6_rlvect_1(A,E,F),D) = k5_real_1(k4_geomtrap(A,B,C,E,D),k4_geomtrap(A,B,C,F,D))
                              & k4_geomtrap(A,B,C,k4_rlvect_1(A,E,F),D) = k3_real_1(k4_geomtrap(A,B,C,E,D),k4_geomtrap(A,B,C,F,D)) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l51_geomtrap,l51_geomtrap,l51_geomtrap,l51_geomtrap]),
    [file(geomtrap,t32_geomtrap),interesting(0.37)]).

fof(t44_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ( r2_hidden(k1_domain_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C),k1_domain_1(u1_struct_0(A),u1_struct_0(A),D,E)),k5_geomtrap(A,F,G))
                              <=> r2_geomtrap(A,F,G,B,C,D,E) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_geomtrap,t33_zfmisc_1,d7_geomtrap]),
    [file(geomtrap,t44_geomtrap),interesting(0.35)]).

fof(l44_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,k1_numbers)
                         => ! [G] : 
                              ( m1_subset_1(G,k1_numbers)
                             => ! [H] : 
                                  ( m1_subset_1(H,k1_numbers)
                                 => ! [I] : 
                                      ( m1_subset_1(I,k1_numbers)
                                     => ( ( B = k4_rlvect_1(A,k3_rlvect_1(A,C,F),k3_rlvect_1(A,D,G))
                                          & E = k4_rlvect_1(A,k3_rlvect_1(A,C,H),k3_rlvect_1(A,D,I)) )
                                       => ( k4_rlvect_1(A,B,E) = k4_rlvect_1(A,k3_rlvect_1(A,C,k3_real_1(F,H)),k3_rlvect_1(A,D,k3_real_1(G,I)))
                                          & k6_rlvect_1(A,B,E) = k4_rlvect_1(A,k3_rlvect_1(A,C,k5_real_1(F,H)),k3_rlvect_1(A,D,k5_real_1(G,I))) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_rlvect_1,d6_rlvect_1,d9_rlvect_1,d6_rlvect_1,d9_rlvect_1,t45_rlvect_1,t39_rlvect_1,t39_rlvect_1,t38_rlvect_1,t38_rlvect_1,d6_rlvect_1,d6_rlvect_1,d9_rlvect_1,d6_rlvect_1,d9_rlvect_1]),
    [file(geomtrap,l44_geomtrap),interesting(0.33)]).

fof(t3_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ( r1_analmetr(A,B,C)
                               => ! [H] : 
                                    ( m1_subset_1(H,u1_struct_0(k2_diraf(k2_analoaf(A))))
                                   => ! [I] : 
                                        ( m1_subset_1(I,u1_struct_0(k2_diraf(k2_analoaf(A))))
                                       => ! [J] : 
                                            ( m1_subset_1(J,u1_struct_0(k2_diraf(k2_analoaf(A))))
                                           => ! [K] : 
                                                ( m1_subset_1(K,u1_struct_0(k2_diraf(k2_analoaf(A))))
                                               => ( ( H = D
                                                    & I = E
                                                    & J = F
                                                    & K = G )
                                                 => ( r2_analoaf(k2_diraf(k2_analoaf(A)),H,I,J,K)
                                                  <=> r1_geomtrap(A,D,E,F,G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t1_geomtrap,d2_diraf,t45_diraf,d4_diraf,t2_geomtrap,d1_geomtrap,d1_geomtrap,t2_geomtrap,d4_diraf,t45_diraf]),
    [file(geomtrap,t3_geomtrap),interesting(0.30)]).

fof(t38_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_analmetr(A,B,C)
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] : 
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ! [H] : 
                                    ( m1_subset_1(H,u1_struct_0(A))
                                   => ! [I] : 
                                        ( m1_subset_1(I,k1_numbers)
                                       => ( ( r2_geomtrap(A,B,C,D,E,F,G)
                                            & I = k4_real_1(k5_real_1(k4_geomtrap(A,B,C,k6_rlvect_1(A,D,E),k4_rlvect_1(A,D,E)),k4_real_1(2,k4_geomtrap(A,B,C,k6_rlvect_1(A,D,E),F))),k2_real_1(k4_geomtrap(A,B,C,k6_rlvect_1(A,D,E),k6_rlvect_1(A,D,E))))
                                            & H = k4_rlvect_1(A,F,k3_rlvect_1(A,k6_rlvect_1(A,D,E),I)) )
                                         => ( D = E
                                            | G = H ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t37_geomtrap,d9_rlvect_1,t78_rlsub_2,t18_analmetr,t21_analoaf,t32_geomtrap,t36_geomtrap,t36_geomtrap,t32_geomtrap,t32_geomtrap,t33_geomtrap,d7_xcmplx_0,t35_geomtrap,l22_geomtrap,l22_geomtrap,t32_geomtrap,t36_geomtrap,t36_geomtrap,t32_geomtrap,t32_geomtrap,t78_rlsub_2,t33_geomtrap,t33_geomtrap,d7_xcmplx_0,t33_geomtrap,t33_geomtrap,t35_geomtrap,l22_geomtrap,l22_geomtrap,l22_geomtrap,t35_geomtrap,d3_geomtrap,t27_geomtrap]),
    [file(geomtrap,t38_geomtrap),interesting(0.28)]).

fof(l51_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,k1_numbers)
                         => ( r1_analmetr(A,B,C)
                           => ( k2_geomtrap(A,B,C,k4_rlvect_1(A,D,E)) = k3_real_1(k2_geomtrap(A,B,C,D),k2_geomtrap(A,B,C,E))
                              & k3_geomtrap(A,B,C,k4_rlvect_1(A,D,E)) = k3_real_1(k3_geomtrap(A,B,C,D),k3_geomtrap(A,B,C,E))
                              & k2_geomtrap(A,B,C,k6_rlvect_1(A,D,E)) = k5_real_1(k2_geomtrap(A,B,C,D),k2_geomtrap(A,B,C,E))
                              & k3_geomtrap(A,B,C,k6_rlvect_1(A,D,E)) = k5_real_1(k3_geomtrap(A,B,C,D),k3_geomtrap(A,B,C,E))
                              & k2_geomtrap(A,B,C,k3_rlvect_1(A,D,F)) = k4_real_1(F,k2_geomtrap(A,B,C,D))
                              & k3_geomtrap(A,B,C,k3_rlvect_1(A,D,F)) = k4_real_1(F,k3_geomtrap(A,B,C,D)) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l49_geomtrap,d6_rlvect_1,d6_rlvect_1,d6_rlvect_1,d9_rlvect_1,d9_rlvect_1,l50_geomtrap,l44_geomtrap,l50_geomtrap,l45_geomtrap,l50_geomtrap]),
    [file(geomtrap,l51_geomtrap),interesting(0.20)]).

fof(d2_diraf,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => k2_diraf(A) = g1_analoaf(u1_struct_0(A),k1_diraf(u1_struct_0(A),u1_analoaf(A))) ) ),
    file(diraf,d2_diraf),
    [interesting(0.00)]).

fof(d14_geomtrap,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => ( v3_geomtrap(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] : 
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ! [H] : 
                                    ( m1_subset_1(H,u1_struct_0(A))
                                   => ! [I] : 
                                        ( m1_subset_1(I,u1_struct_0(A))
                                       => ! [J] : 
                                            ( m1_subset_1(J,u1_struct_0(A))
                                           => ! [K] : 
                                                ( m1_subset_1(K,u1_struct_0(A))
                                               => ( ( r2_analoaf(A,B,C,C,D)
                                                   => ( B = C
                                                      & C = D ) )
                                                  & ( ( r2_analoaf(A,B,C,F,G)
                                                      & r2_analoaf(A,B,C,H,I) )
                                                   => ( B = C
                                                      | r2_analoaf(A,F,G,H,I) ) )
                                                  & ( r2_analoaf(A,B,C,D,E)
                                                   => ( r2_analoaf(A,D,E,B,C)
                                                      & r2_analoaf(A,C,B,E,D) ) )
                                                  & ~ ! [L] : 
                                                        ( m1_subset_1(L,u1_struct_0(A))
                                                       => ( ~ r2_analoaf(A,B,C,D,L)
                                                          & ~ r2_analoaf(A,B,C,L,D) ) )
                                                  & ~ ( r2_analoaf(A,B,C,D,J)
                                                      & r2_analoaf(A,B,C,D,K)
                                                      & B != C
                                                      & J != K ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(geomtrap,d14_geomtrap),
    [interesting(0.00)]).

fof(d2_analoaf,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r2_analoaf(A,B,C,D,E)
                      <=> r2_hidden(k1_domain_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C),k1_domain_1(u1_struct_0(A),u1_struct_0(A),D,E)),u1_analoaf(A)) ) ) ) ) ) ) ),
    file(analoaf,d2_analoaf),
    [interesting(0.00)]).

fof(d1_diraf,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_relset_1(B,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
         => ! [C] : 
              ( m2_relset_1(C,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
             => ( C = k1_diraf(A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,A)
                   => ! [E] : 
                        ( m1_subset_1(E,A)
                       => ! [F] : 
                            ( m1_subset_1(F,A)
                           => ! [G] : 
                                ( m1_subset_1(G,A)
                               => ( r2_hidden(k1_domain_1(k2_zfmisc_1(A,A),k2_zfmisc_1(A,A),k1_domain_1(A,A,D,E),k1_domain_1(A,A,F,G)),C)
                                <=> ( r2_hidden(k1_domain_1(k2_zfmisc_1(A,A),k2_zfmisc_1(A,A),k1_domain_1(A,A,D,E),k1_domain_1(A,A,F,G)),B)
                                    | r2_hidden(k1_domain_1(k2_zfmisc_1(A,A),k2_zfmisc_1(A,A),k1_domain_1(A,A,D,E),k1_domain_1(A,A,G,F)),B) ) ) ) ) ) ) ) ) ) ) ),
    file(diraf,d1_diraf),
    [interesting(0.00)]).

fof(t51_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_geomtrap(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(k2_diraf(A)))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(k2_diraf(A)))
                             => ! [H] : 
                                  ( m1_subset_1(H,u1_struct_0(k2_diraf(A)))
                                 => ! [I] : 
                                      ( m1_subset_1(I,u1_struct_0(k2_diraf(A)))
                                     => ( ( B = F
                                          & C = G
                                          & D = H
                                          & E = I )
                                       => ( r2_analoaf(k2_diraf(A),F,G,H,I)
                                        <=> ( r2_analoaf(A,B,C,D,E)
                                            | r2_analoaf(A,B,C,E,D) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_diraf,d2_analoaf,d1_diraf,d2_analoaf,d2_analoaf,d1_diraf,d2_analoaf]),
    [file(geomtrap,t51_geomtrap),interesting(0.00)]).

fof(l102_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_geomtrap(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k2_diraf(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k2_diraf(A)))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k2_diraf(A)))
                 => ? [E] : 
                      ( m1_subset_1(E,u1_struct_0(k2_diraf(A)))
                      & r2_analoaf(k2_diraf(A),B,C,D,E) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t50_geomtrap,d14_geomtrap,t50_geomtrap,t51_geomtrap]),
    [file(geomtrap,l102_geomtrap),interesting(0.00)]).

fof(l103_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_geomtrap(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k2_diraf(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k2_diraf(A)))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k2_diraf(A)))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(k2_diraf(A)))
                     => ( r2_analoaf(k2_diraf(A),B,C,D,E)
                       => r2_analoaf(k2_diraf(A),D,E,B,C) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t50_geomtrap,d14_geomtrap,t51_geomtrap,d14_geomtrap,d14_geomtrap,t51_geomtrap,t51_geomtrap]),
    [file(geomtrap,l103_geomtrap),interesting(0.00)]).

fof(l104_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_geomtrap(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k2_diraf(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k2_diraf(A)))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k2_diraf(A)))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(k2_diraf(A)))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(k2_diraf(A)))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(k2_diraf(A)))
                             => ( ( r2_analoaf(k2_diraf(A),B,C,D,E)
                                  & r2_analoaf(k2_diraf(A),B,C,F,G) )
                               => ( B = C
                                  | r2_analoaf(k2_diraf(A),D,E,F,G) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t50_geomtrap,t51_geomtrap,d14_geomtrap,d14_geomtrap,t51_geomtrap]),
    [file(geomtrap,l104_geomtrap),interesting(0.00)]).

fof(l105_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_geomtrap(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k2_diraf(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k2_diraf(A)))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k2_diraf(A)))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(k2_diraf(A)))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(k2_diraf(A)))
                         => ~ ( r2_analoaf(k2_diraf(A),B,C,D,E)
                              & r2_analoaf(k2_diraf(A),B,C,D,F)
                              & B != C
                              & E != F ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t50_geomtrap,t51_geomtrap,d14_geomtrap,d14_geomtrap]),
    [file(geomtrap,l105_geomtrap),interesting(0.00)]).

fof(l97_geomtrap,theorem,(
    ? [A] : 
      ( ~ v3_struct_0(A)
      & v2_geomtrap(A)
      & l1_geomtrap(A) ) ),
    file(geomtrap,l97_geomtrap),
    [interesting(0.00)]).

fof(d13_geomtrap,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_geomtrap(A) )
     => ( v2_geomtrap(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] : 
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ! [H] : 
                                    ( m1_subset_1(H,u1_struct_0(A))
                                   => ! [I] : 
                                        ( m1_subset_1(I,u1_struct_0(A))
                                       => ! [J] : 
                                            ( m1_subset_1(J,u1_struct_0(A))
                                           => ! [K] : 
                                                ( m1_subset_1(K,u1_struct_0(A))
                                               => ( k9_geomtrap(A,B,C) = k9_geomtrap(A,C,B)
                                                  & k9_geomtrap(A,B,B) = B
                                                  & k9_geomtrap(A,k9_geomtrap(A,B,C),k9_geomtrap(A,D,E)) = k9_geomtrap(A,k9_geomtrap(A,B,D),k9_geomtrap(A,C,E))
                                                  & ? [L] : 
                                                      ( m1_subset_1(L,u1_struct_0(A))
                                                      & k9_geomtrap(A,L,B) = C )
                                                  & ( k9_geomtrap(A,B,C) = k9_geomtrap(A,B,D)
                                                   => C = D )
                                                  & ( r2_analoaf(A,B,C,D,E)
                                                   => r2_analoaf(A,B,C,k9_geomtrap(A,B,D),k9_geomtrap(A,C,E)) )
                                                  & ~ ( r2_analoaf(A,B,C,D,E)
                                                      & ~ r2_analoaf(A,B,C,k9_geomtrap(A,B,E),k9_geomtrap(A,C,D))
                                                      & ~ r2_analoaf(A,B,C,k9_geomtrap(A,C,D),k9_geomtrap(A,B,E)) )
                                                  & ( ( r2_analoaf(A,B,C,D,E)
                                                      & k9_geomtrap(A,B,F) = J
                                                      & k9_geomtrap(A,C,G) = J
                                                      & k9_geomtrap(A,D,H) = J
                                                      & k9_geomtrap(A,E,I) = J )
                                                   => r2_analoaf(A,F,G,H,I) )
                                                  & ( ( r2_analoaf(A,J,K,B,F)
                                                      & r2_analoaf(A,J,K,C,G)
                                                      & r2_analoaf(A,J,K,D,H)
                                                      & r2_analoaf(A,J,K,E,I)
                                                      & r2_analoaf(A,B,C,D,E) )
                                                   => ( J = K
                                                      | r2_analoaf(A,F,G,H,I) ) )
                                                  & ( r2_analoaf(A,B,C,C,D)
                                                   => ( B = C
                                                      & C = D ) )
                                                  & ( ( r2_analoaf(A,B,C,F,G)
                                                      & r2_analoaf(A,B,C,H,I) )
                                                   => ( B = C
                                                      | r2_analoaf(A,F,G,H,I) ) )
                                                  & ( r2_analoaf(A,B,C,D,E)
                                                   => ( r2_analoaf(A,D,E,B,C)
                                                      & r2_analoaf(A,C,B,E,D) ) )
                                                  & ~ ! [L] : 
                                                        ( m1_subset_1(L,u1_struct_0(A))
                                                       => ( ~ r2_analoaf(A,B,C,D,L)
                                                          & ~ r2_analoaf(A,B,C,L,D) ) )
                                                  & ~ ( r2_analoaf(A,B,C,D,J)
                                                      & r2_analoaf(A,B,C,D,K)
                                                      & B != C
                                                      & J != K ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(geomtrap,d13_geomtrap),
    [interesting(0.00)]).

fof(l98_geomtrap,theorem,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(k8_geomtrap(c1)))
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k8_geomtrap(c1)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k8_geomtrap(c1)))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k8_geomtrap(c1)))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(k8_geomtrap(c1)))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(k8_geomtrap(c1)))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(k8_geomtrap(c1)))
                             => ! [H] : 
                                  ( m1_subset_1(H,u1_struct_0(k8_geomtrap(c1)))
                                 => ! [I] : 
                                      ( m1_subset_1(I,u1_struct_0(k8_geomtrap(c1)))
                                     => ! [J] : 
                                          ( m1_subset_1(J,u1_struct_0(k8_geomtrap(c1)))
                                         => ( ( r2_analoaf(k8_geomtrap(c1),A,B,B,C)
                                             => ( A = B
                                                & B = C ) )
                                            & ( ( r2_analoaf(k8_geomtrap(c1),A,B,E,F)
                                                & r2_analoaf(k8_geomtrap(c1),A,B,G,H) )
                                             => ( A = B
                                                | r2_analoaf(k8_geomtrap(c1),E,F,G,H) ) )
                                            & ( r2_analoaf(k8_geomtrap(c1),A,B,C,D)
                                             => ( r2_analoaf(k8_geomtrap(c1),C,D,A,B)
                                                & r2_analoaf(k8_geomtrap(c1),B,A,D,C) ) )
                                            & ~ ! [K] : 
                                                  ( m1_subset_1(K,u1_struct_0(k8_geomtrap(c1)))
                                                 => ( ~ r2_analoaf(k8_geomtrap(c1),A,B,C,K)
                                                    & ~ r2_analoaf(k8_geomtrap(c1),A,B,K,C) ) )
                                            & ~ ( r2_analoaf(k8_geomtrap(c1),A,B,C,I)
                                                & r2_analoaf(k8_geomtrap(c1),A,B,C,J)
                                                & A != B
                                                & I != J ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_analoaf,d2_analoaf,d2_analoaf,d2_analoaf,d13_geomtrap,d13_geomtrap,d13_geomtrap,d13_geomtrap,d13_geomtrap]),
    [file(geomtrap,l98_geomtrap),interesting(0.00)]).

fof(d2_geomtrap,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( D = k1_geomtrap(A,B,C)
                  <=> k4_rlvect_1(A,D,D) = k4_rlvect_1(A,B,C) ) ) ) ) ) ),
    file(geomtrap,d2_geomtrap),
    [interesting(0.00)]).

fof(t48_rlvect_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & l2_rlvect_1(B) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(B))
                 => k3_rlvect_1(B,k6_rlvect_1(B,C,D),A) = k6_rlvect_1(B,k3_rlvect_1(B,C,A),k3_rlvect_1(B,D,A)) ) ) ) ) ),
    file(rlvect_1,t48_rlvect_1),
    [interesting(0.00)]).

fof(d9_rlvect_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_rlvect_1(A) )
     => ( v7_rlvect_1(A)
      <=> ( ! [B] : 
              ( m1_subset_1(B,k1_numbers)
             => ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => k3_rlvect_1(A,k2_rlvect_1(A,C,D),B) = k2_rlvect_1(A,k3_rlvect_1(A,C,B),k3_rlvect_1(A,D,B)) ) ) )
          & ! [B] : 
              ( m1_subset_1(B,k1_numbers)
             => ! [C] : 
                  ( m1_subset_1(C,k1_numbers)
                 => ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => k3_rlvect_1(A,D,k3_real_1(B,C)) = k2_rlvect_1(A,k3_rlvect_1(A,D,B),k3_rlvect_1(A,D,C)) ) ) )
          & ! [B] : 
              ( m1_subset_1(B,k1_numbers)
             => ! [C] : 
                  ( m1_subset_1(C,k1_numbers)
                 => ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => k3_rlvect_1(A,D,k4_real_1(B,C)) = k3_rlvect_1(A,k3_rlvect_1(A,D,C),B) ) ) )
          & ! [B] : 
              ( m1_subset_1(B,u1_struct_0(A))
             => k3_rlvect_1(A,B,1) = B ) ) ) ) ),
    file(rlvect_1,d9_rlvect_1),
    [interesting(0.00)]).

fof(d6_rlvect_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( v4_rlvect_1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k2_rlvect_1(A,k2_rlvect_1(A,B,C),D) = k2_rlvect_1(A,B,k2_rlvect_1(A,C,D)) ) ) ) ) ) ),
    file(rlvect_1,d6_rlvect_1),
    [interesting(0.00)]).

fof(t41_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k6_rlvect_1(A,B,k2_rlvect_1(A,C,D)) = k6_rlvect_1(A,k6_rlvect_1(A,B,D),C) ) ) ) ) ),
    file(rlvect_1,t41_rlvect_1),
    [interesting(0.00)]).

fof(t28_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k6_rlvect_1(A,B,B) = k1_rlvect_1(A) ) ) ),
    file(rlvect_1,t28_rlvect_1),
    [interesting(0.00)]).

fof(t27_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k6_rlvect_1(A,k1_rlvect_1(A),B) = k5_rlvect_1(A,B) ) ) ),
    file(rlvect_1,t27_rlvect_1),
    [interesting(0.00)]).

fof(d1_analoaf,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r1_analoaf(A,B,C,D,E)
                      <=> ~ ( B != C
                            & D != E
                            & ! [F] : 
                                ( m1_subset_1(F,k1_numbers)
                               => ! [G] : 
                                    ( m1_subset_1(G,k1_numbers)
                                   => ~ ( ~ r1_xreal_0(F,0)
                                        & ~ r1_xreal_0(G,0)
                                        & k3_rlvect_1(A,k6_rlvect_1(A,C,B),F) = k3_rlvect_1(A,k6_rlvect_1(A,E,D),G) ) ) ) ) ) ) ) ) ) ) ),
    file(analoaf,d1_analoaf),
    [interesting(0.00)]).

fof(t10_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => r1_analoaf(A,B,C,k1_geomtrap(A,D,B),k1_geomtrap(A,D,C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_geomtrap,t48_rlvect_1,d9_rlvect_1,d9_rlvect_1,d9_rlvect_1,d9_rlvect_1,d9_rlvect_1,d9_rlvect_1,d6_rlvect_1,t41_rlvect_1,t28_rlvect_1,t27_rlvect_1,d9_rlvect_1,d1_analoaf]),
    [file(geomtrap,t10_geomtrap),interesting(0.00)]).

fof(d1_geomtrap,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r1_geomtrap(A,B,C,D,E)
                      <=> ( r1_analoaf(A,B,C,D,E)
                          | r1_analoaf(A,B,C,E,D) ) ) ) ) ) ) ) ),
    file(geomtrap,d1_geomtrap),
    [interesting(0.00)]).

fof(t11_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => r1_geomtrap(A,B,C,k1_geomtrap(A,D,B),k1_geomtrap(A,D,C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t10_geomtrap,d1_geomtrap]),
    [file(geomtrap,t11_geomtrap),interesting(0.00)]).

fof(t18_analoaf,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_analoaf(A,B,C,D,D)
                    & r1_analoaf(A,B,B,C,D) ) ) ) ) ) ),
    file(analoaf,t18_analoaf),
    [interesting(0.00)]).

fof(t9_analmetr,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_analmetr(A,B,C)
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( r2_analmetr(A,D,k1_rlvect_1(A),B,C)
                          & r2_analmetr(A,k1_rlvect_1(A),E,B,C) ) ) ) ) ) ) ) ),
    file(analmetr,t9_analmetr),
    [interesting(0.00)]).

fof(d3_analmetr,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ( r3_analmetr(A,B,C,D,E,F,G)
                              <=> r2_analmetr(A,k6_rlvect_1(A,C,B),k6_rlvect_1(A,E,D),F,G) ) ) ) ) ) ) ) ) ),
    file(analmetr,d3_analmetr),
    [interesting(0.00)]).

fof(l23_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( r1_analmetr(A,B,C)
                           => r3_analmetr(A,D,E,F,F,B,C) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t28_rlvect_1,t9_analmetr,d3_analmetr]),
    [file(geomtrap,l23_geomtrap),interesting(0.00)]).

fof(t8_analmetr,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r2_analmetr(A,B,C,D,E)
                       => r2_analmetr(A,C,B,D,E) ) ) ) ) ) ) ),
    file(analmetr,t8_analmetr),
    [interesting(0.00)]).

fof(t11_analmetr,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,k1_numbers)
                         => ! [G] : 
                              ( m1_subset_1(G,k1_numbers)
                             => ( r2_analmetr(A,B,C,D,E)
                               => ( r2_analmetr(A,k3_rlvect_1(A,B,F),C,D,E)
                                  & r2_analmetr(A,B,k3_rlvect_1(A,C,G),D,E) ) ) ) ) ) ) ) ) ) ),
    file(analmetr,t11_analmetr),
    [interesting(0.00)]).

fof(t29_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k5_rlvect_1(A,B) = k3_rlvect_1(A,B,k1_real_1(1)) ) ) ),
    file(rlvect_1,t29_rlvect_1),
    [interesting(0.00)]).

fof(t47_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k5_rlvect_1(A,k6_rlvect_1(A,B,C)) = k2_rlvect_1(A,C,k5_rlvect_1(A,B)) ) ) ) ),
    file(rlvect_1,t47_rlvect_1),
    [interesting(0.00)]).

fof(l22_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ( ( r1_analmetr(A,B,C)
                                  & r3_analmetr(A,D,E,F,G,B,C) )
                               => ( r3_analmetr(A,F,G,D,E,B,C)
                                  & r3_analmetr(A,D,E,G,F,B,C) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_analmetr,t8_analmetr,d3_analmetr,t11_analmetr,t29_rlvect_1,t47_rlvect_1,d3_analmetr]),
    [file(geomtrap,l22_geomtrap),interesting(0.00)]).

fof(d3_geomtrap,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ( r2_geomtrap(A,B,C,D,E,F,G)
                              <=> ( r1_analoaf(A,D,E,F,G)
                                  & r3_analmetr(A,D,E,k1_geomtrap(A,D,E),k1_geomtrap(A,F,G),B,C)
                                  & r3_analmetr(A,F,G,k1_geomtrap(A,D,E),k1_geomtrap(A,F,G),B,C) ) ) ) ) ) ) ) ) ) ),
    file(geomtrap,d3_geomtrap),
    [interesting(0.00)]).

fof(t17_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r1_analmetr(A,B,C)
                       => r2_geomtrap(A,B,C,D,D,E,E) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t18_analoaf,l23_geomtrap,l22_geomtrap,d3_geomtrap]),
    [file(geomtrap,t17_geomtrap),interesting(0.00)]).

fof(t17_analoaf,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => r1_analoaf(A,B,C,B,C) ) ) ) ),
    file(analoaf,t17_analoaf),
    [interesting(0.00)]).

fof(t18_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r1_analmetr(A,B,C)
                       => r2_geomtrap(A,B,C,D,E,D,E) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t17_analoaf,l23_geomtrap,d3_geomtrap]),
    [file(geomtrap,t18_geomtrap),interesting(0.00)]).

fof(t31_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => k4_geomtrap(A,B,C,D,E) = k4_geomtrap(A,B,C,E,D) ) ) ) ) ) ),
    file(geomtrap,t31_geomtrap),
    [interesting(0.00)]).

fof(d4_geomtrap,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_analmetr(A,B,C)
                   => ! [E] : 
                        ( m1_subset_1(E,k1_numbers)
                       => ( E = k2_geomtrap(A,B,C,D)
                        <=> ? [F] : 
                              ( m1_subset_1(F,k1_numbers)
                              & D = k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F)) ) ) ) ) ) ) ) ) ),
    file(geomtrap,d4_geomtrap),
    [interesting(0.00)]).

fof(d5_geomtrap,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_analmetr(A,B,C)
                   => ! [E] : 
                        ( m1_subset_1(E,k1_numbers)
                       => ( E = k3_geomtrap(A,B,C,D)
                        <=> ? [F] : 
                              ( m1_subset_1(F,k1_numbers)
                              & D = k4_rlvect_1(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,E)) ) ) ) ) ) ) ) ) ),
    file(geomtrap,d5_geomtrap),
    [interesting(0.00)]).

fof(t5_analmetr,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r1_analmetr(A,D,E)
                       => ( r2_analmetr(A,B,C,D,E)
                        <=> ! [F] : 
                              ( m1_subset_1(F,k1_numbers)
                             => ! [G] : 
                                  ( m1_subset_1(G,k1_numbers)
                                 => ! [H] : 
                                      ( m1_subset_1(H,k1_numbers)
                                     => ! [I] : 
                                          ( m1_subset_1(I,k1_numbers)
                                         => ( ( B = k4_rlvect_1(A,k3_rlvect_1(A,D,F),k3_rlvect_1(A,E,G))
                                              & C = k4_rlvect_1(A,k3_rlvect_1(A,D,H),k3_rlvect_1(A,E,I)) )
                                           => k3_real_1(k4_real_1(F,H),k4_real_1(G,I)) = 0 ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(analmetr,t5_analmetr),
    [interesting(0.00)]).

fof(d2_analmetr,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r2_analmetr(A,B,C,D,E)
                      <=> ? [F] : 
                            ( m1_subset_1(F,k1_numbers)
                            & ? [G] : 
                                ( m1_subset_1(G,k1_numbers)
                                & ? [H] : 
                                    ( m1_subset_1(H,k1_numbers)
                                    & ? [I] : 
                                        ( m1_subset_1(I,k1_numbers)
                                        & B = k4_rlvect_1(A,k3_rlvect_1(A,D,F),k3_rlvect_1(A,E,G))
                                        & C = k4_rlvect_1(A,k3_rlvect_1(A,D,H),k3_rlvect_1(A,E,I))
                                        & k3_real_1(k4_real_1(F,H),k4_real_1(G,I)) = 0 ) ) ) ) ) ) ) ) ) ) ),
    file(analmetr,d2_analmetr),
    [interesting(0.00)]).

fof(t34_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_analmetr(A,B,C)
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( r2_analmetr(A,D,E,B,C)
                        <=> k4_geomtrap(A,B,C,D,E) = 0 ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l49_geomtrap,t5_analmetr,d2_analmetr]),
    [file(geomtrap,t34_geomtrap),interesting(0.00)]).

fof(t15_analmetr,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( r1_analmetr(A,B,C)
                      & r2_analmetr(A,D,D,B,C) )
                   => D = k1_rlvect_1(A) ) ) ) ) ) ),
    file(analmetr,t15_analmetr),
    [interesting(0.00)]).

fof(t35_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k6_rlvect_1(A,B,C) = k1_rlvect_1(A)
               => B = C ) ) ) ) ),
    file(rlvect_1,t35_rlvect_1),
    [interesting(0.00)]).

fof(t37_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_analmetr(A,B,C)
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ~ ( D != E
                            & k4_geomtrap(A,B,C,k6_rlvect_1(A,D,E),k6_rlvect_1(A,D,E)) = 0 ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t34_geomtrap,t15_analmetr,t35_rlvect_1]),
    [file(geomtrap,t37_geomtrap),interesting(0.00)]).

fof(t78_rlsub_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( B = k2_rlvect_1(A,C,D)
                  <=> C = k6_rlvect_1(A,B,D) ) ) ) ) ) ),
    file(rlsub_2,t78_rlsub_2),
    [interesting(0.00)]).

fof(t18_analmetr,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ~ ( ( r1_analoaf(A,B,C,D,E)
                              | r1_analoaf(A,B,C,E,D) )
                            & ! [F] : 
                                ( m1_subset_1(F,k1_numbers)
                               => ! [G] : 
                                    ( m1_subset_1(G,k1_numbers)
                                   => ~ ( k3_rlvect_1(A,k6_rlvect_1(A,C,B),F) = k3_rlvect_1(A,k6_rlvect_1(A,E,D),G)
                                        & ~ ( F = 0
                                            & G = 0 ) ) ) ) )
                        & ~ ( ? [F] : 
                                ( m1_subset_1(F,k1_numbers)
                                & ? [G] : 
                                    ( m1_subset_1(G,k1_numbers)
                                    & k3_rlvect_1(A,k6_rlvect_1(A,C,B),F) = k3_rlvect_1(A,k6_rlvect_1(A,E,D),G)
                                    & ~ ( F = 0
                                        & G = 0 ) ) )
                            & ~ r1_analoaf(A,B,C,D,E)
                            & ~ r1_analoaf(A,B,C,E,D) ) ) ) ) ) ) ) ),
    file(analmetr,t18_analmetr),
    [interesting(0.00)]).

fof(t21_analoaf,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r1_analoaf(A,B,C,D,E)
                       => ( r1_analoaf(A,C,B,E,D)
                          & r1_analoaf(A,D,E,B,C) ) ) ) ) ) ) ) ),
    file(analoaf,t21_analoaf),
    [interesting(0.00)]).

fof(t45_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k5_rlvect_1(A,k2_rlvect_1(A,B,C)) = k2_rlvect_1(A,k5_rlvect_1(A,C),k5_rlvect_1(A,B)) ) ) ) ),
    file(rlvect_1,t45_rlvect_1),
    [interesting(0.00)]).

fof(t39_rlvect_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & l2_rlvect_1(B) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(B))
             => k3_rlvect_1(B,k5_rlvect_1(B,C),A) = k5_rlvect_1(B,k3_rlvect_1(B,C,A)) ) ) ) ),
    file(rlvect_1,t39_rlvect_1),
    [interesting(0.00)]).

fof(t38_rlvect_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & l2_rlvect_1(B) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(B))
             => k3_rlvect_1(B,k5_rlvect_1(B,C),A) = k3_rlvect_1(B,C,k1_real_1(A)) ) ) ) ),
    file(rlvect_1,t38_rlvect_1),
    [interesting(0.00)]).

fof(d1_analmetr,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_analmetr(A,B,C)
              <=> ( ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ? [E] : 
                          ( m1_subset_1(E,k1_numbers)
                          & ? [F] : 
                              ( m1_subset_1(F,k1_numbers)
                              & D = k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F)) ) ) )
                  & ! [D] : 
                      ( m1_subset_1(D,k1_numbers)
                     => ! [E] : 
                          ( m1_subset_1(E,k1_numbers)
                         => ( k4_rlvect_1(A,k3_rlvect_1(A,B,D),k3_rlvect_1(A,C,E)) = k1_rlvect_1(A)
                           => ( D = 0
                              & E = 0 ) ) ) ) ) ) ) ) ) ),
    file(analmetr,d1_analmetr),
    [interesting(0.00)]).

fof(l46_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,k1_numbers)
                 => ! [E] : 
                      ( m1_subset_1(E,k1_numbers)
                     => ! [F] : 
                          ( m1_subset_1(F,k1_numbers)
                         => ! [G] : 
                              ( m1_subset_1(G,k1_numbers)
                             => ( ( r1_analmetr(A,B,C)
                                  & k4_rlvect_1(A,k3_rlvect_1(A,B,D),k3_rlvect_1(A,C,E)) = k4_rlvect_1(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,G)) )
                               => ( D = F
                                  & E = G ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t28_rlvect_1,l44_geomtrap,d1_analmetr]),
    [file(geomtrap,l46_geomtrap),interesting(0.00)]).

fof(l45_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,k1_numbers)
                     => ! [F] : 
                          ( m1_subset_1(F,k1_numbers)
                         => ! [G] : 
                              ( m1_subset_1(G,k1_numbers)
                             => ( B = k4_rlvect_1(A,k3_rlvect_1(A,C,E),k3_rlvect_1(A,D,F))
                               => k3_rlvect_1(A,B,G) = k4_rlvect_1(A,k3_rlvect_1(A,C,k4_real_1(G,E)),k3_rlvect_1(A,D,k4_real_1(G,F))) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d9_rlvect_1,d9_rlvect_1,d9_rlvect_1]),
    [file(geomtrap,l45_geomtrap),interesting(0.00)]).

fof(d7_xcmplx_0,definition,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => ( ( A != 0
             => ( B = k5_xcmplx_0(A)
              <=> k3_xcmplx_0(A,B) = 1 ) )
            & ( A = 0
             => ( B = k5_xcmplx_0(A)
              <=> B = 0 ) ) ) ) ) ),
    file(xcmplx_0,d7_xcmplx_0),
    [interesting(0.00)]).

fof(t20_analoaf,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ( ( r1_analoaf(A,B,C,D,E)
                                  & r1_analoaf(A,B,C,F,G) )
                               => ( B = C
                                  | r1_analoaf(A,D,E,F,G) ) ) ) ) ) ) ) ) ) ),
    file(analoaf,t20_analoaf),
    [interesting(0.00)]).

fof(t14_analmetr,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( r1_analmetr(A,B,C)
                              & r2_analmetr(A,D,E,B,C)
                              & r2_analmetr(A,D,F,B,C) )
                           => ( r2_analmetr(A,D,k4_rlvect_1(A,E,F),B,C)
                              & r2_analmetr(A,D,k6_rlvect_1(A,E,F),B,C) ) ) ) ) ) ) ) ) ),
    file(analmetr,t14_analmetr),
    [interesting(0.00)]).

fof(t43_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k6_rlvect_1(A,B,k6_rlvect_1(A,C,D)) = k4_rlvect_1(A,k6_rlvect_1(A,B,C),D) ) ) ) ) ),
    file(rlvect_1,t43_rlvect_1),
    [interesting(0.00)]).

fof(t26_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k6_rlvect_1(A,B,k1_rlvect_1(A)) = B ) ) ),
    file(rlvect_1,t26_rlvect_1),
    [interesting(0.00)]).

fof(l24_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ! [H] : 
                                  ( m1_subset_1(H,u1_struct_0(A))
                                 => ( ( r1_analmetr(A,B,C)
                                      & r3_analmetr(A,D,E,F,G,B,C)
                                      & r3_analmetr(A,D,E,F,H,B,C) )
                                   => r3_analmetr(A,D,E,G,H,B,C) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_analmetr,t14_analmetr,t41_rlvect_1,t43_rlvect_1,t28_rlvect_1,t26_rlvect_1,d3_analmetr]),
    [file(geomtrap,l24_geomtrap),interesting(0.00)]).

fof(t44_analmetr,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_analmetr(A,B,C)
               => ( ~ v3_struct_0(k2_analmetr(A,B,C))
                  & v2_analmetr(k2_analmetr(A,B,C))
                  & l1_analmetr(k2_analmetr(A,B,C)) ) ) ) ) ) ),
    file(analmetr,t44_analmetr),
    [interesting(0.00)]).

fof(t28_analmetr,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( u1_struct_0(k2_analmetr(A,B,C)) = u1_struct_0(A)
                & u1_analoaf(k2_analmetr(A,B,C)) = k1_diraf(u1_struct_0(A),k1_analoaf(A))
                & u1_analmetr(k2_analmetr(A,B,C)) = k1_analmetr(A,B,C) ) ) ) ) ),
    file(analmetr,t28_analmetr),
    [interesting(0.00)]).

fof(t31_analmetr,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ! [H] : 
                                  ( m1_subset_1(H,u1_struct_0(k2_analmetr(A,F,G)))
                                 => ! [I] : 
                                      ( m1_subset_1(I,u1_struct_0(k2_analmetr(A,F,G)))
                                     => ! [J] : 
                                          ( m1_subset_1(J,u1_struct_0(k2_analmetr(A,F,G)))
                                         => ! [K] : 
                                              ( m1_subset_1(K,u1_struct_0(k2_analmetr(A,F,G)))
                                             => ( ( H = B
                                                  & I = C
                                                  & J = D
                                                  & K = E )
                                               => ( r5_analmetr(k2_analmetr(A,F,G),H,J,I,K)
                                                <=> r3_analmetr(A,B,D,C,E,F,G) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(analmetr,t31_analmetr),
    [interesting(0.00)]).

fof(t32_analmetr,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ! [H] : 
                                  ( m1_subset_1(H,u1_struct_0(k2_analmetr(A,B,C)))
                                 => ! [I] : 
                                      ( m1_subset_1(I,u1_struct_0(k2_analmetr(A,B,C)))
                                     => ! [J] : 
                                          ( m1_subset_1(J,u1_struct_0(k2_analmetr(A,B,C)))
                                         => ! [K] : 
                                              ( m1_subset_1(K,u1_struct_0(k2_analmetr(A,B,C)))
                                             => ( ( H = D
                                                  & I = E
                                                  & J = F
                                                  & K = G )
                                               => ( r4_analmetr(k2_analmetr(A,B,C),H,I,J,K)
                                                <=> ? [L] : 
                                                      ( m1_subset_1(L,k1_numbers)
                                                      & ? [M] : 
                                                          ( m1_subset_1(M,k1_numbers)
                                                          & k3_rlvect_1(A,k6_rlvect_1(A,E,D),L) = k3_rlvect_1(A,k6_rlvect_1(A,G,F),M)
                                                          & ~ ( L = 0
                                                              & M = 0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(analmetr,t32_analmetr),
    [interesting(0.00)]).

fof(t4_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ! [H] : 
                                  ( m1_subset_1(H,u1_struct_0(k2_analmetr(A,B,C)))
                                 => ! [I] : 
                                      ( m1_subset_1(I,u1_struct_0(k2_analmetr(A,B,C)))
                                     => ! [J] : 
                                          ( m1_subset_1(J,u1_struct_0(k2_analmetr(A,B,C)))
                                         => ! [K] : 
                                              ( m1_subset_1(K,u1_struct_0(k2_analmetr(A,B,C)))
                                             => ( ( H = D
                                                  & I = E
                                                  & J = F
                                                  & K = G )
                                               => ( r4_analmetr(k2_analmetr(A,B,C),H,I,J,K)
                                                <=> r1_geomtrap(A,D,E,F,G) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_geomtrap,t18_analmetr,t32_analmetr,t32_analmetr,t18_analmetr,d1_geomtrap]),
    [file(geomtrap,t4_geomtrap),interesting(0.00)]).

fof(t84_analmetr,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ~ ( B != C
                                  & ~ ( ~ ( r4_analmetr(A,B,C,D,E)
                                          & r5_analmetr(A,B,C,F,G) )
                                      & ~ ( r4_analmetr(A,B,C,F,G)
                                          & r5_analmetr(A,B,C,D,E) )
                                      & ~ ( r4_analmetr(A,B,C,D,E)
                                          & r5_analmetr(A,F,G,B,C) )
                                      & ~ ( r4_analmetr(A,B,C,F,G)
                                          & r5_analmetr(A,D,E,B,C) )
                                      & ~ ( r4_analmetr(A,D,E,B,C)
                                          & r5_analmetr(A,F,G,B,C) )
                                      & ~ ( r4_analmetr(A,F,G,B,C)
                                          & r5_analmetr(A,D,E,B,C) )
                                      & ~ ( r4_analmetr(A,D,E,B,C)
                                          & r5_analmetr(A,B,C,F,G) )
                                      & ~ ( r4_analmetr(A,F,G,B,C)
                                          & r5_analmetr(A,B,C,D,E) ) )
                                  & ~ r5_analmetr(A,D,E,F,G) ) ) ) ) ) ) ) ) ),
    file(analmetr,t84_analmetr),
    [interesting(0.00)]).

fof(l27_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ! [H] : 
                                  ( m1_subset_1(H,u1_struct_0(A))
                                 => ! [I] : 
                                      ( m1_subset_1(I,u1_struct_0(A))
                                     => ( r1_analmetr(A,B,C)
                                       => ( ( ~ r1_geomtrap(A,D,E,F,G)
                                            & ~ r1_geomtrap(A,F,G,D,E) )
                                          | ( ~ r3_analmetr(A,H,I,F,G,B,C)
                                            & ~ r3_analmetr(A,F,G,H,I,B,C) )
                                          | F = G
                                          | ( r3_analmetr(A,D,E,H,I,B,C)
                                            & r3_analmetr(A,H,I,D,E,B,C) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t44_analmetr,t28_analmetr,t31_analmetr,t4_geomtrap,t84_analmetr,t31_analmetr]),
    [file(geomtrap,l27_geomtrap),interesting(0.00)]).

fof(t21_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ! [H] : 
                                  ( m1_subset_1(H,u1_struct_0(A))
                                 => ! [I] : 
                                      ( m1_subset_1(I,u1_struct_0(A))
                                     => ( ( r1_analmetr(A,B,C)
                                          & r2_geomtrap(A,B,C,D,E,F,G)
                                          & r2_geomtrap(A,B,C,D,E,H,I) )
                                       => ( D = E
                                          | r2_geomtrap(A,B,C,F,G,H,I) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_geomtrap,d3_geomtrap,d1_geomtrap,t20_analoaf,l24_geomtrap,l27_geomtrap,d3_geomtrap]),
    [file(geomtrap,t21_geomtrap),interesting(0.00)]).

fof(t21_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( k2_rlvect_1(A,B,D) = k2_rlvect_1(A,B,E)
                          | k2_rlvect_1(A,D,B) = k2_rlvect_1(A,E,B) )
                       => D = E ) ) ) ) ) ) ),
    file(rlvect_1,t21_rlvect_1),
    [interesting(0.00)]).

fof(t9_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( k1_geomtrap(A,B,C) = k1_geomtrap(A,B,D)
                   => C = D ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_geomtrap,d2_geomtrap,t21_rlvect_1]),
    [file(geomtrap,t9_geomtrap),interesting(0.00)]).

fof(t49_rlvect_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( m1_subset_1(B,k1_numbers)
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_rlvect_1(C)
                & l2_rlvect_1(C) )
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(C))
                 => k3_rlvect_1(C,D,k5_real_1(A,B)) = k6_rlvect_1(C,k3_rlvect_1(C,D,A),k3_rlvect_1(C,D,B)) ) ) ) ) ),
    file(rlvect_1,t49_rlvect_1),
    [interesting(0.00)]).

fof(t12_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k3_rlvect_1(A,k6_rlvect_1(A,k1_geomtrap(A,B,C),B),2) = k6_rlvect_1(A,C,B)
                & k3_rlvect_1(A,k6_rlvect_1(A,C,k1_geomtrap(A,B,C)),2) = k6_rlvect_1(A,C,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t48_rlvect_1,d9_rlvect_1,d9_rlvect_1,d9_rlvect_1,d2_geomtrap,d6_rlvect_1,d9_rlvect_1,t49_rlvect_1,t29_rlvect_1,t48_rlvect_1,d9_rlvect_1,d9_rlvect_1,d9_rlvect_1,d2_geomtrap,t41_rlvect_1,d9_rlvect_1,t49_rlvect_1,d9_rlvect_1]),
    [file(geomtrap,t12_geomtrap),interesting(0.00)]).

fof(t22_analoaf,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_analoaf(A,B,C,C,D)
                   => r1_analoaf(A,B,C,B,D) ) ) ) ) ) ),
    file(analoaf,t22_analoaf),
    [interesting(0.00)]).

fof(l17_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_analoaf(A,B,C,C,D)
                   => ( r1_analoaf(A,D,C,C,B)
                      & r1_analoaf(A,B,C,B,D)
                      & r1_analoaf(A,C,D,B,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t21_analoaf,t21_analoaf,t22_analoaf,t22_analoaf,t21_analoaf]),
    [file(geomtrap,l17_geomtrap),interesting(0.00)]).

fof(t15_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_analoaf(A,B,C,C,D)
                   => r1_analoaf(A,k1_geomtrap(A,B,C),C,C,k1_geomtrap(A,C,D)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t13_geomtrap,l17_geomtrap,t21_analoaf,t20_analoaf,t20_analoaf,t18_analoaf]),
    [file(geomtrap,t15_geomtrap),interesting(0.00)]).

fof(t14_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_analoaf(A,B,C,B,k1_geomtrap(A,B,C))
                & r1_analoaf(A,B,C,k1_geomtrap(A,B,C),C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d9_rlvect_1,t12_geomtrap,d1_analoaf,d9_rlvect_1,t12_geomtrap,d1_analoaf]),
    [file(geomtrap,t14_geomtrap),interesting(0.00)]).

fof(l25_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r1_analmetr(A,B,C)
                          & r3_analmetr(A,D,E,D,E,B,C) )
                       => D = E ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_analmetr,t15_analmetr,t35_rlvect_1]),
    [file(geomtrap,l25_geomtrap),interesting(0.00)]).

fof(t19_analoaf,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_analoaf(A,B,C,C,B)
               => B = C ) ) ) ) ),
    file(analoaf,t19_analoaf),
    [interesting(0.00)]).

fof(t19_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r2_geomtrap(A,D,E,B,C,C,B)
                       => B = C ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_geomtrap,t19_analoaf]),
    [file(geomtrap,t19_geomtrap),interesting(0.00)]).

fof(t22_analmetr,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => u1_struct_0(k2_diraf(k2_analoaf(A))) = u1_struct_0(A) ) ),
    file(analmetr,t22_analmetr),
    [interesting(0.00)]).

fof(t38_analoaf,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ( ? [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
            & ? [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
                & ! [D] : 
                    ( m1_subset_1(D,k1_numbers)
                   => ! [E] : 
                        ( m1_subset_1(E,k1_numbers)
                       => ( k4_rlvect_1(A,k3_rlvect_1(A,B,D),k3_rlvect_1(A,C,E)) = k1_rlvect_1(A)
                         => ( D = 0
                            & E = 0 ) ) ) ) ) )
       => ( ~ v3_struct_0(k2_analoaf(A))
          & ~ v3_realset2(k2_analoaf(A))
          & v2_analoaf(k2_analoaf(A))
          & l1_analoaf(k2_analoaf(A)) ) ) ) ),
    file(analoaf,t38_analoaf),
    [interesting(0.00)]).

fof(t48_diraf,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ( ~ v3_struct_0(k2_diraf(A))
        & ~ v3_realset2(k2_diraf(A))
        & v1_diraf(k2_diraf(A))
        & l1_analoaf(k2_diraf(A)) ) ) ),
    file(diraf,t48_diraf),
    [interesting(0.00)]).

fof(t45_diraf,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_analoaf(B) )
         => ( B = k2_diraf(A)
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] : 
                                ( m1_subset_1(G,u1_struct_0(B))
                               => ! [H] : 
                                    ( m1_subset_1(H,u1_struct_0(B))
                                   => ! [I] : 
                                        ( m1_subset_1(I,u1_struct_0(B))
                                       => ! [J] : 
                                            ( m1_subset_1(J,u1_struct_0(B))
                                           => ( ( C = G
                                                & D = H
                                                & E = I
                                                & F = J )
                                             => ( r2_analoaf(B,G,H,I,J)
                                              <=> r2_diraf(A,C,D,E,F) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(diraf,t45_diraf),
    [interesting(0.00)]).

fof(d4_diraf,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r2_diraf(A,B,C,D,E)
                      <=> ( r2_analoaf(A,B,C,D,E)
                          | r2_analoaf(A,B,C,E,D) ) ) ) ) ) ) ) ),
    file(diraf,d4_diraf),
    [interesting(0.00)]).

fof(d4_analoaf,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => k2_analoaf(A) = g1_analoaf(u1_struct_0(A),k1_analoaf(A)) ) ),
    file(analoaf,d4_analoaf),
    [interesting(0.00)]).

fof(t33_analoaf,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r2_hidden(k1_domain_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C),k1_domain_1(u1_struct_0(A),u1_struct_0(A),D,E)),k1_analoaf(A))
                      <=> r1_analoaf(A,B,C,D,E) ) ) ) ) ) ) ),
    file(analoaf,t33_analoaf),
    [interesting(0.00)]).

fof(t2_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(k2_analoaf(A)))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(k2_analoaf(A)))
                             => ! [H] : 
                                  ( m1_subset_1(H,u1_struct_0(k2_analoaf(A)))
                                 => ! [I] : 
                                      ( m1_subset_1(I,u1_struct_0(k2_analoaf(A)))
                                     => ( ( F = B
                                          & G = C
                                          & H = D
                                          & I = E )
                                       => ( r2_analoaf(k2_analoaf(A),F,G,H,I)
                                        <=> r1_analoaf(A,B,C,D,E) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_analoaf,d2_analoaf,t33_analoaf,t33_analoaf,d2_analoaf]),
    [file(geomtrap,t2_geomtrap),interesting(0.00)]).

fof(d1_aff_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_aff_1(A,B,C,D)
                  <=> r2_analoaf(A,B,C,B,D) ) ) ) ) ) ),
    file(aff_1,d1_aff_1),
    [interesting(0.00)]).

fof(t17_aff_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( r1_aff_1(A,B,C,D)
                              & r1_aff_1(A,B,C,E)
                              & r1_aff_1(A,B,C,F) )
                           => ( B = C
                              | r1_aff_1(A,D,E,F) ) ) ) ) ) ) ) ) ),
    file(aff_1,t17_aff_1),
    [interesting(0.00)]).

fof(t19_aff_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r1_aff_1(A,B,C,D)
                          & r1_aff_1(A,B,C,E) )
                       => r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) ),
    file(aff_1,t19_aff_1),
    [interesting(0.00)]).

fof(l37_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ! [H] : 
                                  ( m1_subset_1(H,u1_struct_0(A))
                                 => ! [I] : 
                                      ( m1_subset_1(I,u1_struct_0(A))
                                     => ( ( r1_analmetr(A,B,C)
                                          & r1_geomtrap(A,D,E,D,F)
                                          & r1_geomtrap(A,D,E,D,G)
                                          & r1_geomtrap(A,D,E,D,H)
                                          & r1_geomtrap(A,D,E,D,I) )
                                       => ( D = E
                                          | r1_geomtrap(A,F,G,H,I) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t22_analmetr,t1_geomtrap,t48_diraf,t3_geomtrap,d1_aff_1,t17_aff_1,t19_aff_1,t3_geomtrap]),
    [file(geomtrap,l37_geomtrap),interesting(0.00)]).

fof(t45_geomtrap,theorem,(
    $true ),
    file(geomtrap,t45_geomtrap),
    [interesting(0.00)]).

fof(t46_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k7_geomtrap(A,B,C)))
                <=> m1_subset_1(D,u1_struct_0(A)) ) ) ) ) ),
    file(geomtrap,t46_geomtrap),
    [interesting(0.00)]).

fof(d7_geomtrap,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m2_relset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
                 => ( D = k5_geomtrap(A,B,C)
                  <=> ! [E,F] : 
                        ( r2_hidden(k4_tarski(E,F),D)
                      <=> ? [G] : 
                            ( m1_subset_1(G,u1_struct_0(A))
                            & ? [H] : 
                                ( m1_subset_1(H,u1_struct_0(A))
                                & ? [I] : 
                                    ( m1_subset_1(I,u1_struct_0(A))
                                    & ? [J] : 
                                        ( m1_subset_1(J,u1_struct_0(A))
                                        & E = k1_domain_1(u1_struct_0(A),u1_struct_0(A),G,H)
                                        & F = k1_domain_1(u1_struct_0(A),u1_struct_0(A),I,J)
                                        & r2_geomtrap(A,B,C,G,H,I,J) ) ) ) ) ) ) ) ) ) ) ),
    file(geomtrap,d7_geomtrap),
    [interesting(0.00)]).

fof(t33_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( k4_tarski(A,B) = k4_tarski(C,D)
     => ( A = C
        & B = D ) ) ),
    file(zfmisc_1,t33_zfmisc_1),
    [interesting(0.00)]).

fof(t47_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ! [H] : 
                                  ( m1_subset_1(H,u1_struct_0(k7_geomtrap(A,B,C)))
                                 => ! [I] : 
                                      ( m1_subset_1(I,u1_struct_0(k7_geomtrap(A,B,C)))
                                     => ! [J] : 
                                          ( m1_subset_1(J,u1_struct_0(k7_geomtrap(A,B,C)))
                                         => ! [K] : 
                                              ( m1_subset_1(K,u1_struct_0(k7_geomtrap(A,B,C)))
                                             => ( ( r1_analmetr(A,B,C)
                                                  & D = H
                                                  & E = I
                                                  & F = J
                                                  & G = K )
                                               => ( r2_analoaf(k7_geomtrap(A,B,C),H,I,J,K)
                                                <=> r2_geomtrap(A,B,C,D,E,F,G) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_analoaf,t44_geomtrap,t44_geomtrap,d2_analoaf]),
    [file(geomtrap,t47_geomtrap),interesting(0.00)]).

fof(l82_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k7_geomtrap(A,B,C)))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(k7_geomtrap(A,B,C)))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(k7_geomtrap(A,B,C)))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(k7_geomtrap(A,B,C)))
                             => ! [H] : 
                                  ( m1_subset_1(H,u1_struct_0(k7_geomtrap(A,B,C)))
                                 => ! [I] : 
                                      ( m1_subset_1(I,u1_struct_0(k7_geomtrap(A,B,C)))
                                     => ( ( r1_analmetr(A,B,C)
                                          & r2_analoaf(k7_geomtrap(A,B,C),D,E,F,G)
                                          & r2_analoaf(k7_geomtrap(A,B,C),D,E,H,I) )
                                       => ( D = E
                                          | r2_analoaf(k7_geomtrap(A,B,C),F,G,H,I) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t47_geomtrap,t21_geomtrap,t47_geomtrap]),
    [file(geomtrap,l82_geomtrap),interesting(0.00)]).

fof(t23_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ( ( r1_analmetr(A,B,C)
                                  & r2_geomtrap(A,B,C,D,E,F,G) )
                               => r2_geomtrap(A,B,C,F,G,D,E) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_geomtrap,l22_geomtrap,t21_analoaf,d3_geomtrap]),
    [file(geomtrap,t23_geomtrap),interesting(0.00)]).

fof(t24_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ( ( r1_analmetr(A,B,C)
                                  & r2_geomtrap(A,B,C,D,E,F,G) )
                               => r2_geomtrap(A,B,C,E,D,G,F) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_geomtrap,l22_geomtrap,l22_geomtrap,l22_geomtrap,t21_analoaf,d3_geomtrap]),
    [file(geomtrap,t24_geomtrap),interesting(0.00)]).

fof(l83_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k7_geomtrap(A,B,C)))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(k7_geomtrap(A,B,C)))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(k7_geomtrap(A,B,C)))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(k7_geomtrap(A,B,C)))
                             => ( ( r1_analmetr(A,B,C)
                                  & r2_analoaf(k7_geomtrap(A,B,C),D,E,F,G) )
                               => ( r2_analoaf(k7_geomtrap(A,B,C),F,G,D,E)
                                  & r2_analoaf(k7_geomtrap(A,B,C),E,D,G,F) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t47_geomtrap,t23_geomtrap,t24_geomtrap,t47_geomtrap]),
    [file(geomtrap,l83_geomtrap),interesting(0.00)]).

fof(t17_analmetr,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ~ ( r1_analmetr(A,B,C)
                          & D != k1_rlvect_1(A)
                          & ! [F] : 
                              ( m1_subset_1(F,k1_numbers)
                             => ~ r2_analmetr(A,k6_rlvect_1(A,E,k3_rlvect_1(A,D,F)),D,B,C) ) ) ) ) ) ) ) ),
    file(analmetr,t17_analmetr),
    [interesting(0.00)]).

fof(t10_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( k2_rlvect_1(A,B,k1_rlvect_1(A)) = B
            & k2_rlvect_1(A,k1_rlvect_1(A),B) = B ) ) ) ),
    file(rlvect_1,t10_rlvect_1),
    [interesting(0.00)]).

fof(t23_rlvect_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & l2_rlvect_1(B) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(B))
             => ( ( A = 0
                  | C = k1_rlvect_1(B) )
               => k3_rlvect_1(B,C,A) = k1_rlvect_1(B) ) ) ) ) ),
    file(rlvect_1,t23_rlvect_1),
    [interesting(0.00)]).

fof(l84_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k7_geomtrap(A,B,C)))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(k7_geomtrap(A,B,C)))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(k7_geomtrap(A,B,C)))
                         => ~ ( r1_analmetr(A,B,C)
                              & ! [G] : 
                                  ( m1_subset_1(G,u1_struct_0(k7_geomtrap(A,B,C)))
                                 => ( ~ r2_analoaf(k7_geomtrap(A,B,C),D,E,F,G)
                                    & ~ r2_analoaf(k7_geomtrap(A,B,C),D,E,G,F) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t22_geomtrap,t47_geomtrap]),
    [file(geomtrap,l84_geomtrap),interesting(0.00)]).

fof(l85_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k7_geomtrap(A,B,C)))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(k7_geomtrap(A,B,C)))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(k7_geomtrap(A,B,C)))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(k7_geomtrap(A,B,C)))
                             => ! [H] : 
                                  ( m1_subset_1(H,u1_struct_0(k7_geomtrap(A,B,C)))
                                 => ~ ( r1_analmetr(A,B,C)
                                      & r2_analoaf(k7_geomtrap(A,B,C),D,E,F,G)
                                      & r2_analoaf(k7_geomtrap(A,B,C),D,E,F,H)
                                      & D != E
                                      & G != H ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t47_geomtrap,t26_geomtrap]),
    [file(geomtrap,l85_geomtrap),interesting(0.00)]).

fof(d8_geomtrap,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
            & m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) )
         => ( B = k6_geomtrap(A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),B,C,D) = k1_geomtrap(A,C,D) ) ) ) ) ) ),
    file(geomtrap,d8_geomtrap),
    [interesting(0.00)]).

fof(t48_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(k7_geomtrap(A,B,C)))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(k7_geomtrap(A,B,C)))
                             => ( ( r1_analmetr(A,B,C)
                                  & D = F
                                  & E = G )
                               => k1_geomtrap(A,D,E) = k9_geomtrap(k7_geomtrap(A,B,C),F,G) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_geomtrap]),
    [file(geomtrap,t48_geomtrap),interesting(0.00)]).

fof(l86_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k7_geomtrap(A,B,C)))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(k7_geomtrap(A,B,C)))
                     => ( r1_analmetr(A,B,C)
                       => k9_geomtrap(k7_geomtrap(A,B,C),D,E) = k9_geomtrap(k7_geomtrap(A,B,C),E,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t48_geomtrap,t48_geomtrap]),
    [file(geomtrap,l86_geomtrap),interesting(0.00)]).

fof(l87_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k7_geomtrap(A,B,C)))
                 => ( r1_analmetr(A,B,C)
                   => k9_geomtrap(k7_geomtrap(A,B,C),D,D) = D ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t48_geomtrap]),
    [file(geomtrap,l87_geomtrap),interesting(0.00)]).

fof(t50_rlvect_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & l2_rlvect_1(B) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ( k3_rlvect_1(B,C,A) = k3_rlvect_1(B,D,A)
                   => ( A = 0
                      | C = D ) ) ) ) ) ) ),
    file(rlvect_1,t50_rlvect_1),
    [interesting(0.00)]).

fof(t8_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => k1_geomtrap(A,k1_geomtrap(A,B,C),k1_geomtrap(A,D,E)) = k1_geomtrap(A,k1_geomtrap(A,B,D),k1_geomtrap(A,C,E)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_geomtrap,d2_geomtrap,d6_rlvect_1,d6_rlvect_1,d6_rlvect_1,d2_geomtrap,d2_geomtrap,d6_rlvect_1,d6_rlvect_1,d6_rlvect_1,d2_geomtrap,d2_geomtrap,d6_rlvect_1,d6_rlvect_1,d6_rlvect_1,d2_geomtrap,d2_geomtrap,d9_rlvect_1,d9_rlvect_1,d9_rlvect_1,d9_rlvect_1,t50_rlvect_1]),
    [file(geomtrap,t8_geomtrap),interesting(0.00)]).

fof(l88_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k7_geomtrap(A,B,C)))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(k7_geomtrap(A,B,C)))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(k7_geomtrap(A,B,C)))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(k7_geomtrap(A,B,C)))
                             => ( r1_analmetr(A,B,C)
                               => k9_geomtrap(k7_geomtrap(A,B,C),k9_geomtrap(k7_geomtrap(A,B,C),D,E),k9_geomtrap(k7_geomtrap(A,B,C),F,G)) = k9_geomtrap(k7_geomtrap(A,B,C),k9_geomtrap(k7_geomtrap(A,B,C),D,F),k9_geomtrap(k7_geomtrap(A,B,C),E,G)) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t48_geomtrap,t48_geomtrap,t8_geomtrap,t48_geomtrap]),
    [file(geomtrap,l88_geomtrap),interesting(0.00)]).

fof(t16_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( k2_rlvect_1(A,B,k5_rlvect_1(A,B)) = k1_rlvect_1(A)
            & k2_rlvect_1(A,k5_rlvect_1(A,B),B) = k1_rlvect_1(A) ) ) ) ),
    file(rlvect_1,t16_rlvect_1),
    [interesting(0.00)]).

fof(t7_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ? [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                  & k1_geomtrap(A,B,D) = C ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_rlvect_1,t16_rlvect_1,t10_rlvect_1,d2_geomtrap]),
    [file(geomtrap,t7_geomtrap),interesting(0.00)]).

fof(l89_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k7_geomtrap(A,B,C)))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(k7_geomtrap(A,B,C)))
                     => ~ ( r1_analmetr(A,B,C)
                          & ! [F] : 
                              ( m1_subset_1(F,u1_struct_0(k7_geomtrap(A,B,C)))
                             => k9_geomtrap(k7_geomtrap(A,B,C),F,D) != E ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t7_geomtrap,t48_geomtrap]),
    [file(geomtrap,l89_geomtrap),interesting(0.00)]).

fof(l90_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k7_geomtrap(A,B,C)))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(k7_geomtrap(A,B,C)))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(k7_geomtrap(A,B,C)))
                         => ( ( r1_analmetr(A,B,C)
                              & k9_geomtrap(k7_geomtrap(A,B,C),D,E) = k9_geomtrap(k7_geomtrap(A,B,C),D,F) )
                           => E = F ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t48_geomtrap,t9_geomtrap]),
    [file(geomtrap,l90_geomtrap),interesting(0.00)]).

fof(t36_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(0,A)
              & ~ r1_xreal_0(B,0)
              & r1_xreal_0(k2_xcmplx_0(A,B),0) ) ) ) ),
    file(xreal_1,t36_xreal_1),
    [interesting(0.00)]).

fof(t131_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,0)
              & ~ r1_xreal_0(B,0)
              & r1_xreal_0(k3_xcmplx_0(A,B),0) ) ) ) ),
    file(xreal_1,t131_xreal_1),
    [interesting(0.00)]).

fof(t16_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r1_analoaf(A,B,C,D,E)
                       => r1_analoaf(A,B,C,k1_geomtrap(A,B,D),k1_geomtrap(A,C,E)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_analoaf,t36_xreal_1,t131_xreal_1,d9_rlvect_1,t48_rlvect_1,d9_rlvect_1,d9_rlvect_1,d9_rlvect_1,d2_geomtrap,d6_rlvect_1,d9_rlvect_1,d9_rlvect_1,d9_rlvect_1,d2_geomtrap,t41_rlvect_1,d6_rlvect_1,d6_rlvect_1,d9_rlvect_1,d9_rlvect_1,d1_analoaf,t10_geomtrap,t18_analoaf]),
    [file(geomtrap,t16_geomtrap),interesting(0.00)]).

fof(l26_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( r1_analmetr(A,B,C)
                           => ( r3_analmetr(A,D,E,F,F,B,C)
                              & r3_analmetr(A,F,F,D,E,B,C) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t28_rlvect_1,t9_analmetr,d3_analmetr,l22_geomtrap]),
    [file(geomtrap,l26_geomtrap),interesting(0.00)]).

fof(l91_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k7_geomtrap(A,B,C)))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(k7_geomtrap(A,B,C)))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(k7_geomtrap(A,B,C)))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(k7_geomtrap(A,B,C)))
                             => ( ( r1_analmetr(A,B,C)
                                  & r2_analoaf(k7_geomtrap(A,B,C),D,E,F,G) )
                               => r2_analoaf(k7_geomtrap(A,B,C),D,E,k9_geomtrap(k7_geomtrap(A,B,C),D,F),k9_geomtrap(k7_geomtrap(A,B,C),E,G)) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t48_geomtrap,t47_geomtrap,t28_geomtrap,t47_geomtrap]),
    [file(geomtrap,l91_geomtrap),interesting(0.00)]).

fof(t81_vectsp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k5_rlvect_1(A,k6_rlvect_1(A,B,C)) = k6_rlvect_1(A,C,B) ) ) ) ),
    file(vectsp_1,t81_vectsp_1),
    [interesting(0.00)]).

fof(l92_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k7_geomtrap(A,B,C)))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(k7_geomtrap(A,B,C)))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(k7_geomtrap(A,B,C)))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(k7_geomtrap(A,B,C)))
                             => ~ ( r1_analmetr(A,B,C)
                                  & r2_analoaf(k7_geomtrap(A,B,C),D,E,F,G)
                                  & ~ r2_analoaf(k7_geomtrap(A,B,C),D,E,k9_geomtrap(k7_geomtrap(A,B,C),D,G),k9_geomtrap(k7_geomtrap(A,B,C),E,F))
                                  & ~ r2_analoaf(k7_geomtrap(A,B,C),D,E,k9_geomtrap(k7_geomtrap(A,B,C),E,F),k9_geomtrap(k7_geomtrap(A,B,C),D,G)) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t48_geomtrap,t47_geomtrap,t29_geomtrap,t47_geomtrap]),
    [file(geomtrap,l92_geomtrap),interesting(0.00)]).

fof(t19_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k2_rlvect_1(A,B,C) = k1_rlvect_1(A)
               => B = k5_rlvect_1(A,C) ) ) ) ) ),
    file(rlvect_1,t19_rlvect_1),
    [interesting(0.00)]).

fof(l21_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( k1_geomtrap(A,B,C) = k1_geomtrap(A,D,E)
                       => k6_rlvect_1(A,D,B) = k5_rlvect_1(A,k6_rlvect_1(A,E,C)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_geomtrap,d6_rlvect_1,t78_rlsub_2,d6_rlvect_1,t28_rlvect_1,t19_rlvect_1]),
    [file(geomtrap,l21_geomtrap),interesting(0.00)]).

fof(t30_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k5_rlvect_1(A,k5_rlvect_1(A,B)) = B ) ) ),
    file(rlvect_1,t30_rlvect_1),
    [interesting(0.00)]).

fof(t10_analmetr,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,k1_numbers)
                         => ! [G] : 
                              ( m1_subset_1(G,k1_numbers)
                             => ( r2_analmetr(A,B,C,D,E)
                               => r2_analmetr(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,G),D,E) ) ) ) ) ) ) ) ) ),
    file(analmetr,t10_analmetr),
    [interesting(0.00)]).

fof(t30_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ! [H] : 
                                  ( m1_subset_1(H,u1_struct_0(A))
                                 => ! [I] : 
                                      ( m1_subset_1(I,u1_struct_0(A))
                                     => ! [J] : 
                                          ( m1_subset_1(J,u1_struct_0(A))
                                         => ! [K] : 
                                              ( m1_subset_1(K,u1_struct_0(A))
                                             => ! [L] : 
                                                  ( m1_subset_1(L,u1_struct_0(A))
                                                 => ( ( r1_analmetr(A,B,C)
                                                      & D = k1_geomtrap(A,E,I)
                                                      & D = k1_geomtrap(A,F,J)
                                                      & D = k1_geomtrap(A,G,K)
                                                      & D = k1_geomtrap(A,H,L)
                                                      & r2_geomtrap(A,B,C,E,F,G,H) )
                                                   => r2_geomtrap(A,B,C,I,J,K,L) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_geomtrap,l21_geomtrap,t9_geomtrap,l26_geomtrap,t18_analoaf,t9_geomtrap,l26_geomtrap,t18_analoaf,d1_analoaf,t30_rlvect_1,t39_rlvect_1,t39_rlvect_1,t30_rlvect_1,d1_analoaf,t8_geomtrap,t8_geomtrap,l21_geomtrap,t29_rlvect_1,l21_geomtrap,t29_rlvect_1,d3_analmetr,t10_analmetr,d3_analmetr,d3_geomtrap]),
    [file(geomtrap,t30_geomtrap),interesting(0.00)]).

fof(t16_analoaf,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ~ ( r1_analoaf(A,B,C,D,E)
                          & B != C
                          & D != E
                          & ! [F] : 
                              ( m1_subset_1(F,k1_numbers)
                             => ! [G] : 
                                  ( m1_subset_1(G,k1_numbers)
                                 => ~ ( k3_rlvect_1(A,k6_rlvect_1(A,C,B),F) = k3_rlvect_1(A,k6_rlvect_1(A,E,D),G)
                                      & ~ r1_xreal_0(F,0)
                                      & ~ r1_xreal_0(G,0) ) ) ) ) ) ) ) ) ) ),
    file(analoaf,t16_analoaf),
    [interesting(0.00)]).

fof(l54_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,k1_numbers)
                     => ! [F] : 
                          ( m1_subset_1(F,k1_numbers)
                         => k6_rlvect_1(A,k4_rlvect_1(A,B,k3_rlvect_1(A,C,E)),k4_rlvect_1(A,D,k3_rlvect_1(A,C,F))) = k4_rlvect_1(A,k6_rlvect_1(A,B,D),k3_rlvect_1(A,C,k5_real_1(E,F))) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t41_rlvect_1,d6_rlvect_1,d6_rlvect_1,t49_rlvect_1]),
    [file(geomtrap,l54_geomtrap),interesting(0.00)]).

fof(t40_xcmplx_1,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => ! [C] : 
              ( v1_xcmplx_0(C)
             => k3_xcmplx_0(A,k6_xcmplx_0(B,C)) = k6_xcmplx_0(k3_xcmplx_0(A,B),k3_xcmplx_0(A,C)) ) ) ) ),
    file(xcmplx_1,t40_xcmplx_1),
    [interesting(0.00)]).

fof(l64_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_analmetr(A,B,C)
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] : 
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ! [H] : 
                                    ( m1_subset_1(H,u1_struct_0(A))
                                   => ! [I] : 
                                        ( m1_subset_1(I,u1_struct_0(A))
                                       => ! [J] : 
                                            ( m1_subset_1(J,k1_numbers)
                                           => ! [K] : 
                                                ( m1_subset_1(K,k1_numbers)
                                               => ( ( J = k4_real_1(k5_real_1(k4_geomtrap(A,B,C,k6_rlvect_1(A,D,E),k4_rlvect_1(A,D,E)),k4_real_1(2,k4_geomtrap(A,B,C,k6_rlvect_1(A,D,E),F))),k2_real_1(k4_geomtrap(A,B,C,k6_rlvect_1(A,D,E),k6_rlvect_1(A,D,E))))
                                                    & K = k4_real_1(k5_real_1(k4_geomtrap(A,B,C,k6_rlvect_1(A,D,E),k4_rlvect_1(A,D,E)),k4_real_1(2,k4_geomtrap(A,B,C,k6_rlvect_1(A,D,E),G))),k2_real_1(k4_geomtrap(A,B,C,k6_rlvect_1(A,D,E),k6_rlvect_1(A,D,E))))
                                                    & H = k4_rlvect_1(A,F,k3_rlvect_1(A,k6_rlvect_1(A,D,E),J))
                                                    & I = k4_rlvect_1(A,G,k3_rlvect_1(A,k6_rlvect_1(A,D,E),K)) )
                                                 => ( D = E
                                                    | ( k6_rlvect_1(A,I,H) = k4_rlvect_1(A,k6_rlvect_1(A,G,F),k3_rlvect_1(A,k6_rlvect_1(A,D,E),k5_real_1(K,J)))
                                                      & k5_real_1(K,J) = k4_real_1(k4_real_1(k1_real_1(2),k4_geomtrap(A,B,C,k6_rlvect_1(A,D,E),k6_rlvect_1(A,G,F))),k2_real_1(k4_geomtrap(A,B,C,k6_rlvect_1(A,D,E),k6_rlvect_1(A,D,E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t33_geomtrap,t33_geomtrap,t32_geomtrap,t47_rlvect_1,t48_rlvect_1,t39_rlvect_1,t38_rlvect_1,t33_geomtrap,l54_geomtrap,t40_xcmplx_1]),
    [file(geomtrap,l64_geomtrap),interesting(0.00)]).

fof(t4_xcmplx_1,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => ! [C] : 
              ( v1_xcmplx_0(C)
             => k3_xcmplx_0(A,k3_xcmplx_0(B,C)) = k3_xcmplx_0(k3_xcmplx_0(A,B),C) ) ) ) ),
    file(xcmplx_1,t4_xcmplx_1),
    [interesting(0.00)]).

fof(d10_rlvect_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( ( v4_rlvect_1(A)
              & v5_rlvect_1(A)
              & v6_rlvect_1(A) )
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ( C = k5_rlvect_1(A,B)
                <=> k2_rlvect_1(A,B,C) = k1_rlvect_1(A) ) ) ) ) ) ),
    file(rlvect_1,d10_rlvect_1),
    [interesting(0.00)]).

fof(l53_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k4_rlvect_1(A,k5_rlvect_1(A,B),k5_rlvect_1(A,C)) = k5_rlvect_1(A,k4_rlvect_1(A,B,C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_rlvect_1,d6_rlvect_1,t16_rlvect_1,t10_rlvect_1,t16_rlvect_1,d10_rlvect_1]),
    [file(geomtrap,l53_geomtrap),interesting(0.00)]).

fof(t42_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_analmetr(A,B,C)
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] : 
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ! [H] : 
                                    ( m1_subset_1(H,u1_struct_0(A))
                                   => ! [I] : 
                                        ( m1_subset_1(I,u1_struct_0(A))
                                       => ! [J] : 
                                            ( m1_subset_1(J,u1_struct_0(A))
                                           => ! [K] : 
                                                ( m1_subset_1(K,u1_struct_0(A))
                                               => ! [L] : 
                                                    ( m1_subset_1(L,u1_struct_0(A))
                                                   => ! [M] : 
                                                        ( m1_subset_1(M,u1_struct_0(A))
                                                       => ( ( r2_geomtrap(A,B,C,D,E,F,J)
                                                            & r2_geomtrap(A,B,C,D,E,G,K)
                                                            & r2_geomtrap(A,B,C,D,E,H,L)
                                                            & r2_geomtrap(A,B,C,D,E,I,M)
                                                            & r3_analmetr(A,F,G,H,I,B,C) )
                                                         => ( D = E
                                                            | r3_analmetr(A,J,K,L,M,B,C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t38_geomtrap,t38_geomtrap,t37_geomtrap,l64_geomtrap,l64_geomtrap,t32_geomtrap,t32_geomtrap,t35_geomtrap,t32_geomtrap,t33_geomtrap,t33_geomtrap,l64_geomtrap,d7_xcmplx_0,l64_geomtrap,t33_geomtrap,l64_geomtrap,t33_geomtrap,l64_geomtrap,t35_geomtrap]),
    [file(geomtrap,t42_geomtrap),interesting(0.00)]).

fof(t43_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ! [H] : 
                                  ( m1_subset_1(H,u1_struct_0(A))
                                 => ! [I] : 
                                      ( m1_subset_1(I,u1_struct_0(A))
                                     => ! [J] : 
                                          ( m1_subset_1(J,u1_struct_0(A))
                                         => ! [K] : 
                                              ( m1_subset_1(K,u1_struct_0(A))
                                             => ! [L] : 
                                                  ( m1_subset_1(L,u1_struct_0(A))
                                                 => ! [M] : 
                                                      ( m1_subset_1(M,u1_struct_0(A))
                                                     => ( ( r1_analmetr(A,B,C)
                                                          & r2_geomtrap(A,B,C,D,E,F,J)
                                                          & r2_geomtrap(A,B,C,D,E,G,K)
                                                          & r2_geomtrap(A,B,C,D,E,H,L)
                                                          & r2_geomtrap(A,B,C,D,E,I,M)
                                                          & r2_geomtrap(A,B,C,F,G,H,I) )
                                                       => ( D = E
                                                          | r2_geomtrap(A,B,C,J,K,L,M) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_geomtrap,t39_geomtrap,t41_geomtrap,d3_geomtrap,t42_geomtrap,d3_geomtrap,t42_geomtrap,d3_geomtrap]),
    [file(geomtrap,t43_geomtrap),interesting(0.00)]).

fof(l94_geomtrap,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k7_geomtrap(A,B,C)))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(k7_geomtrap(A,B,C)))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(k7_geomtrap(A,B,C)))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(k7_geomtrap(A,B,C)))
                             => ! [H] : 
                                  ( m1_subset_1(H,u1_struct_0(k7_geomtrap(A,B,C)))
                                 => ! [I] : 
                                      ( m1_subset_1(I,u1_struct_0(k7_geomtrap(A,B,C)))
                                     => ! [J] : 
                                          ( m1_subset_1(J,u1_struct_0(k7_geomtrap(A,B,C)))
                                         => ! [K] : 
                                              ( m1_subset_1(K,u1_struct_0(k7_geomtrap(A,B,C)))
                                             => ! [L] : 
                                                  ( m1_subset_1(L,u1_struct_0(k7_geomtrap(A,B,C)))
                                                 => ! [M] : 
                                                      ( m1_subset_1(M,u1_struct_0(k7_geomtrap(A,B,C)))
                                                     => ( ( r1_analmetr(A,B,C)
                                                          & r2_analoaf(k7_geomtrap(A,B,C),D,E,F,G)
                                                          & r2_analoaf(k7_geomtrap(A,B,C),D,E,H,I)
                                                          & r2_analoaf(k7_geomtrap(A,B,C),D,E,J,K)
                                                          & r2_analoaf(k7_geomtrap(A,B,C),D,E,L,M)
                                                          & r2_analoaf(k7_geomtrap(A,B,C),F,H,J,L) )
                                                       => ( D = E
                                                          | r2_analoaf(k7_geomtrap(A,B,C),G,I,K,M) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t47_geomtrap,t43_geomtrap,t47_geomtrap]),
    [file(geomtrap,l94_geomtrap),interesting(0.00)]).

fof(t5_geomtrap,theorem,(
    $true ),
    file(geomtrap,t5_geomtrap),
    [interesting(0.00)]).

fof(t6_geomtrap,theorem,(
    $true ),
    file(geomtrap,t6_geomtrap),
    [interesting(0.00)]).