SET007 Axioms: SET007+719.ax


%------------------------------------------------------------------------------
% File     : SET007+719 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Full Adder Circuit. Part II
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : facirc_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   58 (   7 unit)
%            Number of atoms       :  463 ( 127 equality)
%            Maximal formula depth :   31 (  10 average)
%            Number of connectives :  469 (  64 ~  ;   1  |; 278  &)
%                                         (   5 <=>; 121 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   48 (   1 propositional; 0-3 arity)
%            Number of functors    :   71 (  14 constant; 0-4 arity)
%            Number of variables   :  190 (   0 singleton; 173 !;  17 ?)
%            Maximal term depth    :    7 (   2 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(cc1_facirc_2,axiom,(
    ! [A] :
      ( l1_msualg_1(A)
     => ( v2_msualg_1(A)
       => ( v1_circcomb(A)
          & v2_circcomb(A)
          & v3_circcomb(A) ) ) ) )).

fof(rc1_facirc_2,axiom,(
    ? [A] :
      ( l1_msualg_1(A)
      & v1_msualg_1(A)
      & v2_msualg_1(A)
      & v1_circcomb(A)
      & v2_circcomb(A)
      & v3_circcomb(A) ) )).

fof(fc1_facirc_2,axiom,(
    ! [A] :
      ( ~ v3_struct_0(k1_facirc_2(A))
      & v1_msualg_1(k1_facirc_2(A))
      & v2_msualg_1(k1_facirc_2(A))
      & v2_msafree2(k1_facirc_2(A))
      & v1_circcomb(k1_facirc_2(A))
      & v2_circcomb(k1_facirc_2(A))
      & v3_circcomb(k1_facirc_2(A))
      & v5_circcomb(k1_facirc_2(A)) ) )).

fof(cc2_facirc_2,axiom,(
    ! [A] :
      ( v1_xboole_0(A)
     => ~ v1_facirc_1(A) ) )).

fof(fc2_facirc_2,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_ordinal1(k1_xboole_0)
    & v2_ordinal1(k1_xboole_0)
    & v3_ordinal1(k1_xboole_0)
    & v4_ordinal2(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0)
    & v1_xreal_0(k1_xboole_0)
    & ~ v2_xreal_0(k1_xboole_0)
    & ~ v3_xreal_0(k1_xboole_0)
    & v1_xcmplx_0(k1_xboole_0)
    & v1_margrel1(k1_xboole_0)
    & ~ v1_facirc_1(k1_xboole_0)
    & ~ v2_facirc_1(k1_xboole_0)
    & v3_facirc_1(k1_xboole_0) )).

fof(fc3_facirc_2,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_facirc_1(A) )
     => ~ v1_facirc_1(k1_funct_1(A,B)) ) )).

fof(fc4_facirc_2,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B)
        & v1_relat_1(C)
        & v1_funct_1(C)
        & v1_finseq_1(C) )
     => ( ~ v1_xboole_0(k6_facirc_2(A,B,C))
        & v1_facirc_1(k6_facirc_2(A,B,C)) ) ) )).

fof(t1_facirc_2,axiom,(
    ! [A,B,C] :
      ~ ( A != C
        & B != C
        & k4_xboole_0(k2_tarski(A,B),k1_tarski(C)) != k2_tarski(A,B) ) )).

fof(t2_facirc_2,axiom,(
    $true )).

fof(t3_facirc_2,axiom,(
    ! [A,B,C] :
      ( A != k4_tarski(k6_facirc_1(A,B),C)
      & B != k4_tarski(k6_facirc_1(A,B),C) ) )).

fof(d1_facirc_2,axiom,(
    ! [A,B] :
      ( ( v1_msualg_1(B)
        & v2_msualg_1(B)
        & l1_msualg_1(B) )
     => ( B = k1_facirc_2(A)
      <=> u1_struct_0(B) = k1_tarski(A) ) ) )).

fof(d2_facirc_2,axiom,(
    ! [A,B] :
      ( ( v4_msualg_1(B,k1_facirc_2(A))
        & v6_circcomb(B,k1_facirc_2(A))
        & l3_msualg_1(B,k1_facirc_2(A)) )
     => B = k2_facirc_2(A) ) )).

fof(t4_facirc_2,axiom,(
    ! [A,B] :
      ( l1_msualg_1(B)
     => r1_circcomb(k1_facirc_2(A),B) ) )).

fof(t5_facirc_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & l1_msualg_1(B) )
     => ( r2_hidden(A,u1_struct_0(B))
       => k3_circcomb(k1_facirc_2(A),B) = g1_msualg_1(u1_struct_0(B),u1_msualg_1(B),u2_msualg_1(B),u3_msualg_1(B)) ) ) )).

fof(t6_facirc_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v1_msualg_1(B)
        & l1_msualg_1(B) )
     => ! [C] :
          ( ( v6_circcomb(C,B)
            & l3_msualg_1(C,B) )
         => ( r2_hidden(A,u1_struct_0(B))
           => k4_circcomb(k1_facirc_2(A),B,k2_facirc_2(A),C) = g3_msualg_1(B,u4_msualg_1(B,C),u5_msualg_1(B,C)) ) ) ) )).

fof(d3_facirc_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v1_msualg_1(D)
                    & ~ v2_msualg_1(D)
                    & v1_circcomb(D)
                    & v2_circcomb(D)
                    & v3_circcomb(D)
                    & l1_msualg_1(D) )
                 => ( D = k4_facirc_2(A,B,C)
                  <=> ? [E] :
                        ( m1_pboole(E,k5_numbers)
                        & ? [F] :
                            ( m1_pboole(F,k5_numbers)
                            & D = k1_funct_1(E,A)
                            & k1_funct_1(E,np__0) = k7_circcomb(k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1),k3_facirc_2)
                            & k1_funct_1(F,np__0) = k4_tarski(k3_facirc_2,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1))
                            & ! [G] :
                                ( m2_subset_1(G,k1_numbers,k5_numbers)
                               => ! [H] :
                                    ( ( ~ v3_struct_0(H)
                                      & l1_msualg_1(H) )
                                   => ! [I] :
                                        ( ( H = k1_funct_1(E,G)
                                          & I = k1_funct_1(F,G) )
                                       => ( k1_funct_1(E,k1_nat_1(G,np__1)) = k3_circcomb(H,k23_facirc_1(k1_funct_1(B,k1_nat_1(G,np__1)),k1_funct_1(C,k1_nat_1(G,np__1)),I))
                                          & k1_funct_1(F,k1_nat_1(G,np__1)) = k21_facirc_1(k1_funct_1(B,k1_nat_1(G,np__1)),k1_funct_1(C,k1_nat_1(G,np__1)),I) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d4_facirc_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ! [D] :
                  ( ( v4_msualg_1(D,k4_facirc_2(A,B,C))
                    & v4_msafree2(D,k4_facirc_2(A,B,C))
                    & v4_circcomb(D,k4_facirc_2(A,B,C))
                    & v6_circcomb(D,k4_facirc_2(A,B,C))
                    & l3_msualg_1(D,k4_facirc_2(A,B,C)) )
                 => ( D = k5_facirc_2(A,B,C)
                  <=> ? [E] :
                        ( m1_pboole(E,k5_numbers)
                        & ? [F] :
                            ( m1_pboole(F,k5_numbers)
                            & ? [G] :
                                ( m1_pboole(G,k5_numbers)
                                & k4_facirc_2(A,B,C) = k1_funct_1(E,A)
                                & D = k1_funct_1(F,A)
                                & k1_funct_1(E,np__0) = k7_circcomb(k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1),k3_facirc_2)
                                & k1_funct_1(F,np__0) = k9_circcomb(np__0,k10_circcomb,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1),k3_facirc_2)
                                & k1_funct_1(G,np__0) = k4_tarski(k3_facirc_2,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1))
                                & ! [H] :
                                    ( m2_subset_1(H,k1_numbers,k5_numbers)
                                   => ! [I] :
                                        ( ( ~ v3_struct_0(I)
                                          & l1_msualg_1(I) )
                                       => ! [J] :
                                            ( ( v5_msualg_1(J,I)
                                              & l3_msualg_1(J,I) )
                                           => ! [K] :
                                                ( ( I = k1_funct_1(E,H)
                                                  & J = k1_funct_1(F,H)
                                                  & K = k1_funct_1(G,H) )
                                               => ( k1_funct_1(E,k1_nat_1(H,np__1)) = k3_circcomb(I,k23_facirc_1(k1_funct_1(B,k1_nat_1(H,np__1)),k1_funct_1(C,k1_nat_1(H,np__1)),K))
                                                  & k1_funct_1(F,k1_nat_1(H,np__1)) = k4_circcomb(I,k23_facirc_1(k1_funct_1(B,k1_nat_1(H,np__1)),k1_funct_1(C,k1_nat_1(H,np__1)),K),J,k24_facirc_1(k1_funct_1(B,k1_nat_1(H,np__1)),k1_funct_1(C,k1_nat_1(H,np__1)),K))
                                                  & k1_funct_1(G,k1_nat_1(H,np__1)) = k21_facirc_1(k1_funct_1(B,k1_nat_1(H,np__1)),k1_funct_1(C,k1_nat_1(H,np__1)),K) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d5_facirc_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ! [D] :
                  ( m1_struct_0(D,k4_facirc_2(A,B,C),k4_msafree2(k4_facirc_2(A,B,C)))
                 => ( D = k6_facirc_2(A,B,C)
                  <=> ? [E] :
                        ( m1_pboole(E,k5_numbers)
                        & D = k1_funct_1(E,A)
                        & k1_funct_1(E,np__0) = k4_tarski(k3_facirc_2,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1))
                        & ! [F] :
                            ( m2_subset_1(F,k1_numbers,k5_numbers)
                           => ! [G] :
                                ( G = k1_funct_1(E,F)
                               => k1_funct_1(E,k1_nat_1(F,np__1)) = k21_facirc_1(k1_funct_1(B,k1_nat_1(F,np__1)),k1_funct_1(C,k1_nat_1(F,np__1)),G) ) ) ) ) ) ) ) ) )).

fof(t7_facirc_2,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( m1_pboole(C,k5_numbers)
             => ! [D] :
                  ( m1_pboole(D,k5_numbers)
                 => ! [E] :
                      ( m1_pboole(E,k5_numbers)
                     => ( ( k1_funct_1(C,np__0) = k7_circcomb(k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1),k3_facirc_2)
                          & k1_funct_1(D,np__0) = k9_circcomb(np__0,k10_circcomb,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1),k3_facirc_2)
                          & k1_funct_1(E,np__0) = k4_tarski(k3_facirc_2,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1))
                          & ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ! [G] :
                                  ( ( ~ v3_struct_0(G)
                                    & l1_msualg_1(G) )
                                 => ! [H] :
                                      ( ( v5_msualg_1(H,G)
                                        & l3_msualg_1(H,G) )
                                     => ! [I] :
                                          ( ( G = k1_funct_1(C,F)
                                            & H = k1_funct_1(D,F)
                                            & I = k1_funct_1(E,F) )
                                         => ( k1_funct_1(C,k1_nat_1(F,np__1)) = k3_circcomb(G,k23_facirc_1(k1_funct_1(A,k1_nat_1(F,np__1)),k1_funct_1(B,k1_nat_1(F,np__1)),I))
                                            & k1_funct_1(D,k1_nat_1(F,np__1)) = k4_circcomb(G,k23_facirc_1(k1_funct_1(A,k1_nat_1(F,np__1)),k1_funct_1(B,k1_nat_1(F,np__1)),I),H,k24_facirc_1(k1_funct_1(A,k1_nat_1(F,np__1)),k1_funct_1(B,k1_nat_1(F,np__1)),I))
                                            & k1_funct_1(E,k1_nat_1(F,np__1)) = k21_facirc_1(k1_funct_1(A,k1_nat_1(F,np__1)),k1_funct_1(B,k1_nat_1(F,np__1)),I) ) ) ) ) ) )
                       => ! [F] :
                            ( m2_subset_1(F,k1_numbers,k5_numbers)
                           => ( k4_facirc_2(F,A,B) = k1_funct_1(C,F)
                              & k5_facirc_2(F,A,B) = k1_funct_1(D,F)
                              & k6_facirc_2(F,A,B) = k1_funct_1(E,F) ) ) ) ) ) ) ) ) )).

fof(t8_facirc_2,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( k4_facirc_2(np__0,A,B) = k7_circcomb(k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1),k3_facirc_2)
            & k5_facirc_2(np__0,A,B) = k9_circcomb(np__0,k10_circcomb,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1),k3_facirc_2)
            & k6_facirc_2(np__0,A,B) = k4_tarski(k3_facirc_2,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1)) ) ) ) )).

fof(t9_facirc_2,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( C = k4_tarski(k3_facirc_2,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1))
             => ( k4_facirc_2(np__1,A,B) = k3_circcomb(k7_circcomb(k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1),k3_facirc_2),k23_facirc_1(k1_funct_1(A,np__1),k1_funct_1(B,np__1),C))
                & k5_facirc_2(np__1,A,B) = k4_circcomb(k7_circcomb(k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1),k3_facirc_2),k23_facirc_1(k1_funct_1(A,np__1),k1_funct_1(B,np__1),C),k9_circcomb(np__0,k10_circcomb,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1),k3_facirc_2),k24_facirc_1(k1_funct_1(A,np__1),k1_funct_1(B,np__1),C))
                & k6_facirc_2(np__1,A,B) = k21_facirc_1(k1_funct_1(A,np__1),k1_funct_1(B,np__1),C) ) ) ) ) )).

fof(t10_facirc_2,axiom,(
    ! [A,B,C] :
      ( C = k4_tarski(k3_facirc_2,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1))
     => ( k4_facirc_2(np__1,k5_facirc_1(A),k5_facirc_1(B)) = k3_circcomb(k7_circcomb(k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1),k3_facirc_2),k23_facirc_1(A,B,C))
        & k5_facirc_2(np__1,k5_facirc_1(A),k5_facirc_1(B)) = k4_circcomb(k7_circcomb(k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1),k3_facirc_2),k23_facirc_1(A,B,C),k9_circcomb(np__0,k10_circcomb,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1),k3_facirc_2),k24_facirc_1(A,B,C))
        & k6_facirc_2(np__1,k5_facirc_1(A),k5_facirc_1(B)) = k21_facirc_1(A,B,C) ) ) )).

fof(t11_facirc_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_circcomb(B,A)
         => ! [C] :
              ( m1_circcomb(C,A)
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D) )
                 => ! [E] :
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E)
                        & v1_finseq_1(E) )
                     => ! [F] :
                          ( ( v1_relat_1(F)
                            & v1_funct_1(F)
                            & v1_finseq_1(F) )
                         => ! [G] :
                              ( ( v1_relat_1(G)
                                & v1_funct_1(G)
                                & v1_finseq_1(G) )
                             => ( k4_facirc_2(A,k7_finseq_1(B,D),k7_finseq_1(C,F)) = k4_facirc_2(A,k7_finseq_1(B,E),k7_finseq_1(C,G))
                                & k5_facirc_2(A,k7_finseq_1(B,D),k7_finseq_1(C,F)) = k5_facirc_2(A,k7_finseq_1(B,E),k7_finseq_1(C,G))
                                & k6_facirc_2(A,k7_finseq_1(B,D),k7_finseq_1(C,F)) = k6_facirc_2(A,k7_finseq_1(B,E),k7_finseq_1(C,G)) ) ) ) ) ) ) ) ) )).

fof(t12_facirc_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_circcomb(B,A)
         => ! [C] :
              ( m1_circcomb(C,A)
             => ! [D,E] :
                  ( k4_facirc_2(k1_nat_1(A,np__1),k8_facirc_1(A,np__1,B,k5_facirc_1(D)),k8_facirc_1(A,np__1,C,k5_facirc_1(E))) = k3_circcomb(k4_facirc_2(A,B,C),k23_facirc_1(D,E,k6_facirc_2(A,B,C)))
                  & k5_facirc_2(k1_nat_1(A,np__1),k8_facirc_1(A,np__1,B,k5_facirc_1(D)),k8_facirc_1(A,np__1,C,k5_facirc_1(E))) = k4_circcomb(k4_facirc_2(A,B,C),k23_facirc_1(D,E,k6_facirc_2(A,B,C)),k5_facirc_2(A,B,C),k24_facirc_1(D,E,k6_facirc_2(A,B,C)))
                  & k6_facirc_2(k1_nat_1(A,np__1),k8_facirc_1(A,np__1,B,k5_facirc_1(D)),k8_facirc_1(A,np__1,C,k5_facirc_1(E))) = k21_facirc_1(D,E,k6_facirc_2(A,B,C)) ) ) ) ) )).

fof(t13_facirc_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( k4_facirc_2(k1_nat_1(A,np__1),B,C) = k3_circcomb(k4_facirc_2(A,B,C),k23_facirc_1(k1_funct_1(B,k1_nat_1(A,np__1)),k1_funct_1(C,k1_nat_1(A,np__1)),k6_facirc_2(A,B,C)))
                & k5_facirc_2(k1_nat_1(A,np__1),B,C) = k4_circcomb(k4_facirc_2(A,B,C),k23_facirc_1(k1_funct_1(B,k1_nat_1(A,np__1)),k1_funct_1(C,k1_nat_1(A,np__1)),k6_facirc_2(A,B,C)),k5_facirc_2(A,B,C),k24_facirc_1(k1_funct_1(B,k1_nat_1(A,np__1)),k1_funct_1(C,k1_nat_1(A,np__1)),k6_facirc_2(A,B,C)))
                & k6_facirc_2(k1_nat_1(A,np__1),B,C) = k21_facirc_1(k1_funct_1(B,k1_nat_1(A,np__1)),k1_funct_1(C,k1_nat_1(A,np__1)),k6_facirc_2(A,B,C)) ) ) ) ) )).

fof(t14_facirc_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_xreal_0(A,B)
           => ! [C] :
                ( ( v1_relat_1(C)
                  & v1_funct_1(C)
                  & v1_finseq_1(C) )
               => ! [D] :
                    ( ( v1_relat_1(D)
                      & v1_funct_1(D)
                      & v1_finseq_1(D) )
                   => r1_tarski(k4_msafree2(k4_facirc_2(A,C,D)),k4_msafree2(k4_facirc_2(B,C,D))) ) ) ) ) ) )).

fof(t15_facirc_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => k4_msafree2(k4_facirc_2(k1_nat_1(A,np__1),B,C)) = k2_xboole_0(k4_msafree2(k4_facirc_2(A,B,C)),k4_msafree2(k23_facirc_1(k1_funct_1(B,k1_nat_1(A,np__1)),k1_funct_1(C,k1_nat_1(A,np__1)),k6_facirc_2(A,B,C)))) ) ) ) )).

fof(d6_facirc_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ( r1_xreal_0(np__1,A)
              & r1_xreal_0(A,B) )
           => ! [C] :
                ( ( v1_relat_1(C)
                  & v1_funct_1(C)
                  & v1_finseq_1(C) )
               => ! [D] :
                    ( ( v1_relat_1(D)
                      & v1_funct_1(D)
                      & v1_finseq_1(D) )
                   => ! [E] :
                        ( m1_struct_0(E,k4_facirc_2(B,C,D),k4_msafree2(k4_facirc_2(B,C,D)))
                       => ( E = k7_facirc_2(A,B,C,D)
                        <=> ? [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                              & A = k1_nat_1(F,np__1)
                              & E = k16_facirc_1(k1_funct_1(C,A),k1_funct_1(D,A),k6_facirc_2(F,C,D)) ) ) ) ) ) ) ) ) )).

fof(t16_facirc_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ~ r1_xreal_0(A,B)
           => ! [C] :
                ( ( v1_relat_1(C)
                  & v1_funct_1(C)
                  & v1_finseq_1(C) )
               => ! [D] :
                    ( ( v1_relat_1(D)
                      & v1_funct_1(D)
                      & v1_finseq_1(D) )
                   => k7_facirc_2(k1_nat_1(B,np__1),A,C,D) = k16_facirc_1(k1_funct_1(C,k1_nat_1(B,np__1)),k1_funct_1(D,k1_nat_1(B,np__1)),k6_facirc_2(B,C,D)) ) ) ) ) ) )).

fof(t17_facirc_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => v1_relat_1(k4_msafree2(k4_facirc_2(A,B,C))) ) ) ) )).

fof(t18_facirc_2,axiom,(
    ! [A,B,C] : k4_msafree2(k18_facirc_1(A,B,C)) = k1_enumset1(k4_tarski(k6_facirc_1(A,B),k3_facirc_1),k4_tarski(k6_facirc_1(B,C),k3_facirc_1),k4_tarski(k6_facirc_1(C,A),k3_facirc_1)) )).

fof(t19_facirc_2,axiom,(
    ! [A,B,C] :
      ~ ( A != k4_tarski(k6_facirc_1(B,C),k3_facirc_1)
        & B != k4_tarski(k6_facirc_1(C,A),k3_facirc_1)
        & C != k4_tarski(k6_facirc_1(A,B),k3_facirc_1)
        & k2_msafree2(k18_facirc_1(A,B,C)) != k1_enumset1(A,B,C) ) )).

fof(t20_facirc_2,axiom,(
    ! [A,B,C] : k4_msafree2(k19_facirc_1(A,B,C)) = k2_xboole_0(k1_enumset1(k4_tarski(k6_facirc_1(A,B),k3_facirc_1),k4_tarski(k6_facirc_1(B,C),k3_facirc_1),k4_tarski(k6_facirc_1(C,A),k3_facirc_1)),k1_struct_0(k19_facirc_1(A,B,C),k21_facirc_1(A,B,C))) )).

fof(t21_facirc_2,axiom,(
    ! [A,B,C] :
      ~ ( A != k4_tarski(k6_facirc_1(B,C),k3_facirc_1)
        & B != k4_tarski(k6_facirc_1(C,A),k3_facirc_1)
        & C != k4_tarski(k6_facirc_1(A,B),k3_facirc_1)
        & k2_msafree2(k19_facirc_1(A,B,C)) != k1_enumset1(A,B,C) ) )).

fof(t22_facirc_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_msualg_1(B) )
         => ( ( r1_circcomb(A,B)
              & k2_msafree2(A) = k2_msafree2(B) )
           => k2_msafree2(k3_circcomb(A,B)) = k2_msafree2(A) ) ) ) )).

fof(t23_facirc_2,axiom,(
    ! [A,B,C] :
      ~ ( A != k4_tarski(k6_facirc_1(B,C),k3_facirc_1)
        & B != k4_tarski(k6_facirc_1(C,A),k3_facirc_1)
        & C != k4_tarski(k6_facirc_1(A,B),k3_facirc_1)
        & C != k4_tarski(k6_facirc_1(A,B),k1_facirc_1)
        & k2_msafree2(k23_facirc_1(A,B,C)) != k1_enumset1(A,B,C) ) )).

fof(t24_facirc_2,axiom,(
    ! [A,B,C] : k4_msafree2(k23_facirc_1(A,B,C)) = k2_xboole_0(k2_xboole_0(k2_tarski(k4_tarski(k6_facirc_1(A,B),k1_facirc_1),k13_facirc_1(A,B,C,k1_facirc_1)),k1_enumset1(k4_tarski(k6_facirc_1(A,B),k3_facirc_1),k4_tarski(k6_facirc_1(B,C),k3_facirc_1),k4_tarski(k6_facirc_1(C,A),k3_facirc_1))),k1_struct_0(k19_facirc_1(A,B,C),k21_facirc_1(A,B,C))) )).

fof(t25_facirc_2,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( k1_mcart_1(k6_facirc_2(C,A,B)) = k3_facirc_2
                  & k2_mcart_1(k6_facirc_2(C,A,B)) = k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1)
                  & k1_funct_5(k2_mcart_1(k6_facirc_2(C,A,B))) = k4_finseq_2(np__0,k10_circcomb) )
                | ( k1_card_1(k1_mcart_1(k6_facirc_2(C,A,B))) = np__3
                  & k2_mcart_1(k6_facirc_2(C,A,B)) = k4_facirc_1
                  & k1_funct_5(k2_mcart_1(k6_facirc_2(C,A,B))) = k4_finseq_2(np__3,k10_circcomb) ) ) ) ) ) )).

fof(t26_facirc_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ! [D] :
                  ( k6_facirc_2(A,B,C) != k4_tarski(D,k3_facirc_1)
                  & k6_facirc_2(A,B,C) != k4_tarski(D,k1_facirc_1) ) ) ) ) )).

fof(t27_facirc_2,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v3_facirc_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B)
            & v3_facirc_1(B) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( k2_msafree2(k4_facirc_2(k1_nat_1(C,np__1),A,B)) = k2_xboole_0(k2_msafree2(k4_facirc_2(C,A,B)),k4_xboole_0(k2_msafree2(k23_facirc_1(k1_funct_1(A,k1_nat_1(C,np__1)),k1_funct_1(B,k1_nat_1(C,np__1)),k6_facirc_2(C,A,B))),k1_struct_0(k4_facirc_2(C,A,B),k6_facirc_2(C,A,B))))
                & v1_relat_1(k4_msafree2(k4_facirc_2(C,A,B)))
                & ~ v2_facirc_1(k2_msafree2(k4_facirc_2(C,A,B))) ) ) ) ) )).

fof(t28_facirc_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v3_facirc_1(B)
            & m1_circcomb(B,A) )
         => ! [C] :
              ( ( v3_facirc_1(C)
                & m1_circcomb(C,A) )
             => k2_msafree2(k4_facirc_2(A,B,C)) = k2_xboole_0(k2_relat_1(B),k2_relat_1(C)) ) ) ) )).

fof(t29_facirc_2,axiom,(
    ! [A,B,C,D] :
      ( m1_subset_1(D,k4_card_3(u4_msualg_1(k19_facirc_1(A,B,C),k22_facirc_1(A,B,C))))
     => ! [E] :
          ( m2_subset_1(E,k5_numbers,k10_circcomb)
         => ! [F] :
              ( m2_subset_1(F,k5_numbers,k10_circcomb)
             => ! [G] :
                  ( m2_subset_1(G,k5_numbers,k10_circcomb)
                 => ( ( E = k1_funct_1(D,k4_tarski(k6_facirc_1(A,B),k3_facirc_1))
                      & F = k1_funct_1(D,k4_tarski(k6_facirc_1(B,C),k3_facirc_1))
                      & G = k1_funct_1(D,k4_tarski(k6_facirc_1(C,A),k3_facirc_1)) )
                   => k15_facirc_1(k19_facirc_1(A,B,C),k22_facirc_1(A,B,C),k6_circuit2(k19_facirc_1(A,B,C),k22_facirc_1(A,B,C),D),k21_facirc_1(A,B,C)) = k3_binarith(k3_binarith(E,F),G) ) ) ) ) ) )).

fof(t30_facirc_2,axiom,(
    ! [A,B,C] :
      ~ ( A != k4_tarski(k6_facirc_1(B,C),k3_facirc_1)
        & B != k4_tarski(k6_facirc_1(C,A),k3_facirc_1)
        & C != k4_tarski(k6_facirc_1(A,B),k3_facirc_1)
        & C != k4_tarski(k6_facirc_1(A,B),k1_facirc_1)
        & ~ ! [D] :
              ( m1_subset_1(D,k4_card_3(u4_msualg_1(k19_facirc_1(A,B,C),k22_facirc_1(A,B,C))))
             => v1_circuit2(k9_facirc_1(k19_facirc_1(A,B,C),k22_facirc_1(A,B,C),D,np__2),k19_facirc_1(A,B,C),k22_facirc_1(A,B,C)) ) ) )).

fof(t31_facirc_2,axiom,(
    ! [A,B,C] :
      ~ ( A != k4_tarski(k6_facirc_1(B,C),k3_facirc_1)
        & B != k4_tarski(k6_facirc_1(C,A),k3_facirc_1)
        & C != k4_tarski(k6_facirc_1(A,B),k3_facirc_1)
        & C != k4_tarski(k6_facirc_1(A,B),k1_facirc_1)
        & ? [D] :
            ( m1_subset_1(D,k4_card_3(u4_msualg_1(k23_facirc_1(A,B,C),k24_facirc_1(A,B,C))))
            & ? [E] :
                ( m2_subset_1(E,k5_numbers,k10_circcomb)
                & ? [F] :
                    ( m2_subset_1(F,k5_numbers,k10_circcomb)
                    & ? [G] :
                        ( m2_subset_1(G,k5_numbers,k10_circcomb)
                        & E = k1_funct_1(D,A)
                        & F = k1_funct_1(D,B)
                        & G = k1_funct_1(D,C)
                        & ~ ( k1_funct_1(k9_facirc_1(k23_facirc_1(A,B,C),k24_facirc_1(A,B,C),D,np__2),k16_facirc_1(A,B,C)) = k4_binarith(k4_binarith(E,F),G)
                            & k1_funct_1(k9_facirc_1(k23_facirc_1(A,B,C),k24_facirc_1(A,B,C),D,np__2),k21_facirc_1(A,B,C)) = k3_binarith(k3_binarith(k12_margrel1(E,F),k12_margrel1(F,G)),k12_margrel1(G,E)) ) ) ) ) ) ) )).

fof(t32_facirc_2,axiom,(
    ! [A,B,C] :
      ~ ( A != k4_tarski(k6_facirc_1(B,C),k3_facirc_1)
        & B != k4_tarski(k6_facirc_1(C,A),k3_facirc_1)
        & C != k4_tarski(k6_facirc_1(A,B),k3_facirc_1)
        & C != k4_tarski(k6_facirc_1(A,B),k1_facirc_1)
        & ~ ! [D] :
              ( m1_subset_1(D,k4_card_3(u4_msualg_1(k23_facirc_1(A,B,C),k24_facirc_1(A,B,C))))
             => v1_circuit2(k9_facirc_1(k23_facirc_1(A,B,C),k24_facirc_1(A,B,C),D,np__2),k23_facirc_1(A,B,C),k24_facirc_1(A,B,C)) ) ) )).

fof(t33_facirc_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v3_facirc_1(B)
            & m1_circcomb(B,A) )
         => ! [C] :
              ( ( v3_facirc_1(C)
                & m1_circcomb(C,A) )
             => ! [D] :
                  ( m1_subset_1(D,k4_card_3(u4_msualg_1(k4_facirc_2(A,B,C),k5_facirc_2(A,B,C))))
                 => v1_circuit2(k9_facirc_1(k4_facirc_2(A,B,C),k5_facirc_2(A,B,C),D,k1_nat_1(np__1,k2_nat_1(np__2,A))),k4_facirc_2(A,B,C),k5_facirc_2(A,B,C)) ) ) ) ) )).

fof(t34_facirc_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_circcomb(B,k1_nat_1(A,np__1))
         => ? [C] :
              ( m1_circcomb(C,A)
              & ? [D] : B = k8_facirc_1(A,np__1,C,k5_facirc_1(D)) ) ) ) )).

fof(t35_facirc_2,axiom,(
    $true )).

fof(t36_facirc_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v3_facirc_1(B)
            & m1_circcomb(B,k1_nat_1(A,np__1)) )
         => ? [C] :
              ( v3_facirc_1(C)
              & m1_circcomb(C,A)
              & ? [D] :
                  ( ~ v1_facirc_1(D)
                  & B = k8_facirc_1(A,np__1,C,k5_facirc_1(D)) ) ) ) ) )).

fof(t37_facirc_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ? [B] :
          ( v1_funct_1(B)
          & v1_funct_2(B,k5_numbers,k5_numbers)
          & m2_relset_1(B,k5_numbers,k5_numbers)
          & k8_funct_2(k5_numbers,k5_numbers,B,np__0) = np__1
          & k8_funct_2(k5_numbers,k5_numbers,B,np__1) = np__2
          & k8_funct_2(k5_numbers,k5_numbers,B,np__2) = A ) ) )).

fof(dt_k1_facirc_2,axiom,(
    ! [A] :
      ( v1_msualg_1(k1_facirc_2(A))
      & v2_msualg_1(k1_facirc_2(A))
      & l1_msualg_1(k1_facirc_2(A)) ) )).

fof(dt_k2_facirc_2,axiom,(
    ! [A] :
      ( v4_msualg_1(k2_facirc_2(A),k1_facirc_2(A))
      & v6_circcomb(k2_facirc_2(A),k1_facirc_2(A))
      & l3_msualg_1(k2_facirc_2(A),k1_facirc_2(A)) ) )).

fof(dt_k3_facirc_2,axiom,(
    m1_circcomb(k3_facirc_2,np__0) )).

fof(redefinition_k3_facirc_2,axiom,(
    k3_facirc_2 = k1_xboole_0 )).

fof(dt_k4_facirc_2,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B)
        & v1_relat_1(C)
        & v1_funct_1(C)
        & v1_finseq_1(C) )
     => ( ~ v3_struct_0(k4_facirc_2(A,B,C))
        & v1_msualg_1(k4_facirc_2(A,B,C))
        & ~ v2_msualg_1(k4_facirc_2(A,B,C))
        & v1_circcomb(k4_facirc_2(A,B,C))
        & v2_circcomb(k4_facirc_2(A,B,C))
        & v3_circcomb(k4_facirc_2(A,B,C))
        & l1_msualg_1(k4_facirc_2(A,B,C)) ) ) )).

fof(dt_k5_facirc_2,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B)
        & v1_relat_1(C)
        & v1_funct_1(C)
        & v1_finseq_1(C) )
     => ( v4_msualg_1(k5_facirc_2(A,B,C),k4_facirc_2(A,B,C))
        & v4_msafree2(k5_facirc_2(A,B,C),k4_facirc_2(A,B,C))
        & v4_circcomb(k5_facirc_2(A,B,C),k4_facirc_2(A,B,C))
        & v6_circcomb(k5_facirc_2(A,B,C),k4_facirc_2(A,B,C))
        & l3_msualg_1(k5_facirc_2(A,B,C),k4_facirc_2(A,B,C)) ) ) )).

fof(dt_k6_facirc_2,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B)
        & v1_relat_1(C)
        & v1_funct_1(C)
        & v1_finseq_1(C) )
     => m1_struct_0(k6_facirc_2(A,B,C),k4_facirc_2(A,B,C),k4_msafree2(k4_facirc_2(A,B,C))) ) )).

fof(dt_k7_facirc_2,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers)
        & v1_relat_1(C)
        & v1_funct_1(C)
        & v1_finseq_1(C)
        & v1_relat_1(D)
        & v1_funct_1(D)
        & v1_finseq_1(D) )
     => m1_struct_0(k7_facirc_2(A,B,C,D),k4_facirc_2(B,C,D),k4_msafree2(k4_facirc_2(B,C,D))) ) )).
%------------------------------------------------------------------------------