SET007 Axioms: SET007+768.ax


%------------------------------------------------------------------------------
% File     : SET007+768 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Full Subtracter 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    : fscirc_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   35 (   3 unit)
%            Number of atoms       :  357 ( 109 equality)
%            Maximal formula depth :   31 (  12 average)
%            Number of connectives :  369 (  47 ~  ;   1  |; 217  &)
%                                         (   4 <=>; 100 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   29 (   0 propositional; 1-3 arity)
%            Number of functors    :   61 (  14 constant; 0-4 arity)
%            Number of variables   :  152 (   0 singleton; 141 !;  11 ?)
%            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(fc1_fscirc_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(k3_fscirc_2(A,B,C))
        & v1_facirc_1(k3_fscirc_2(A,B,C)) ) ) )).

fof(d1_fscirc_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 = k1_fscirc_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),k8_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),k8_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,k8_fscirc_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)) = k6_fscirc_1(k1_funct_1(B,k1_nat_1(G,np__1)),k1_funct_1(C,k1_nat_1(G,np__1)),I) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d2_fscirc_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,k1_fscirc_2(A,B,C))
                    & v4_msafree2(D,k1_fscirc_2(A,B,C))
                    & v4_circcomb(D,k1_fscirc_2(A,B,C))
                    & v6_circcomb(D,k1_fscirc_2(A,B,C))
                    & l3_msualg_1(D,k1_fscirc_2(A,B,C)) )
                 => ( D = k2_fscirc_2(A,B,C)
                  <=> ? [E] :
                        ( m1_pboole(E,k5_numbers)
                        & ? [F] :
                            ( m1_pboole(F,k5_numbers)
                            & ? [G] :
                                ( m1_pboole(G,k5_numbers)
                                & k1_fscirc_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),k8_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),k8_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),k8_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,k8_fscirc_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,k8_fscirc_1(k1_funct_1(B,k1_nat_1(H,np__1)),k1_funct_1(C,k1_nat_1(H,np__1)),K),J,k9_fscirc_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)) = k6_fscirc_1(k1_funct_1(B,k1_nat_1(H,np__1)),k1_funct_1(C,k1_nat_1(H,np__1)),K) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d3_fscirc_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,k1_fscirc_2(A,B,C),k4_msafree2(k1_fscirc_2(A,B,C)))
                 => ( D = k3_fscirc_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),k8_margrel1))
                        & ! [F] :
                            ( m2_subset_1(F,k1_numbers,k5_numbers)
                           => k1_funct_1(E,k1_nat_1(F,np__1)) = k6_fscirc_1(k1_funct_1(B,k1_nat_1(F,np__1)),k1_funct_1(C,k1_nat_1(F,np__1)),k1_funct_1(E,F)) ) ) ) ) ) ) ) )).

fof(t1_fscirc_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),k8_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),k8_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),k8_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,k8_fscirc_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,k8_fscirc_1(k1_funct_1(A,k1_nat_1(F,np__1)),k1_funct_1(B,k1_nat_1(F,np__1)),I),H,k9_fscirc_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)) = k6_fscirc_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)
                           => ( k1_fscirc_2(F,A,B) = k1_funct_1(C,F)
                              & k2_fscirc_2(F,A,B) = k1_funct_1(D,F)
                              & k3_fscirc_2(F,A,B) = k1_funct_1(E,F) ) ) ) ) ) ) ) ) )).

fof(t2_fscirc_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) )
         => ( k1_fscirc_2(np__0,A,B) = k7_circcomb(k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k8_margrel1),k3_facirc_2)
            & k2_fscirc_2(np__0,A,B) = k9_circcomb(np__0,k10_circcomb,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k8_margrel1),k3_facirc_2)
            & k3_fscirc_2(np__0,A,B) = k4_tarski(k3_facirc_2,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k8_margrel1)) ) ) ) )).

fof(t3_fscirc_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),k8_margrel1))
             => ( k1_fscirc_2(np__1,A,B) = k3_circcomb(k7_circcomb(k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k8_margrel1),k3_facirc_2),k8_fscirc_1(k1_funct_1(A,np__1),k1_funct_1(B,np__1),C))
                & k2_fscirc_2(np__1,A,B) = k4_circcomb(k7_circcomb(k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k8_margrel1),k3_facirc_2),k8_fscirc_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),k8_margrel1),k3_facirc_2),k9_fscirc_1(k1_funct_1(A,np__1),k1_funct_1(B,np__1),C))
                & k3_fscirc_2(np__1,A,B) = k6_fscirc_1(k1_funct_1(A,np__1),k1_funct_1(B,np__1),C) ) ) ) ) )).

fof(t4_fscirc_2,axiom,(
    ! [A,B,C] :
      ( C = k4_tarski(k3_facirc_2,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k8_margrel1))
     => ( k1_fscirc_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),k8_margrel1),k3_facirc_2),k8_fscirc_1(A,B,C))
        & k2_fscirc_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),k8_margrel1),k3_facirc_2),k8_fscirc_1(A,B,C),k9_circcomb(np__0,k10_circcomb,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k8_margrel1),k3_facirc_2),k9_fscirc_1(A,B,C))
        & k3_fscirc_2(np__1,k5_facirc_1(A),k5_facirc_1(B)) = k6_fscirc_1(A,B,C) ) ) )).

fof(t5_fscirc_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) )
                             => ( k1_fscirc_2(A,k7_finseq_1(B,D),k7_finseq_1(C,F)) = k1_fscirc_2(A,k7_finseq_1(B,E),k7_finseq_1(C,G))
                                & k2_fscirc_2(A,k7_finseq_1(B,D),k7_finseq_1(C,F)) = k2_fscirc_2(A,k7_finseq_1(B,E),k7_finseq_1(C,G))
                                & k3_fscirc_2(A,k7_finseq_1(B,D),k7_finseq_1(C,F)) = k3_fscirc_2(A,k7_finseq_1(B,E),k7_finseq_1(C,G)) ) ) ) ) ) ) ) ) )).

fof(t6_fscirc_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_circcomb(B,A)
         => ! [C] :
              ( m1_circcomb(C,A)
             => ! [D,E] :
                  ( k1_fscirc_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(k1_fscirc_2(A,B,C),k8_fscirc_1(D,E,k3_fscirc_2(A,B,C)))
                  & k2_fscirc_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(k1_fscirc_2(A,B,C),k8_fscirc_1(D,E,k3_fscirc_2(A,B,C)),k2_fscirc_2(A,B,C),k9_fscirc_1(D,E,k3_fscirc_2(A,B,C)))
                  & k3_fscirc_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))) = k6_fscirc_1(D,E,k3_fscirc_2(A,B,C)) ) ) ) ) )).

fof(t7_fscirc_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) )
             => ( k1_fscirc_2(k1_nat_1(A,np__1),B,C) = k3_circcomb(k1_fscirc_2(A,B,C),k8_fscirc_1(k1_funct_1(B,k1_nat_1(A,np__1)),k1_funct_1(C,k1_nat_1(A,np__1)),k3_fscirc_2(A,B,C)))
                & k2_fscirc_2(k1_nat_1(A,np__1),B,C) = k4_circcomb(k1_fscirc_2(A,B,C),k8_fscirc_1(k1_funct_1(B,k1_nat_1(A,np__1)),k1_funct_1(C,k1_nat_1(A,np__1)),k3_fscirc_2(A,B,C)),k2_fscirc_2(A,B,C),k9_fscirc_1(k1_funct_1(B,k1_nat_1(A,np__1)),k1_funct_1(C,k1_nat_1(A,np__1)),k3_fscirc_2(A,B,C)))
                & k3_fscirc_2(k1_nat_1(A,np__1),B,C) = k6_fscirc_1(k1_funct_1(B,k1_nat_1(A,np__1)),k1_funct_1(C,k1_nat_1(A,np__1)),k3_fscirc_2(A,B,C)) ) ) ) ) )).

fof(t8_fscirc_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(k1_fscirc_2(A,C,D)),k4_msafree2(k1_fscirc_2(B,C,D))) ) ) ) ) ) )).

fof(t9_fscirc_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(k1_fscirc_2(k1_nat_1(A,np__1),B,C)) = k2_xboole_0(k4_msafree2(k1_fscirc_2(A,B,C)),k4_msafree2(k8_fscirc_1(k1_funct_1(B,k1_nat_1(A,np__1)),k1_funct_1(C,k1_nat_1(A,np__1)),k3_fscirc_2(A,B,C)))) ) ) ) )).

fof(d4_fscirc_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,k1_fscirc_2(B,C,D),k4_msafree2(k1_fscirc_2(B,C,D)))
                       => ( E = k4_fscirc_2(A,B,C,D)
                        <=> ? [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                              & A = k1_nat_1(F,np__1)
                              & E = k1_fscirc_1(k1_funct_1(C,A),k1_funct_1(D,A),k3_fscirc_2(F,C,D)) ) ) ) ) ) ) ) ) )).

fof(t10_fscirc_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) )
                   => k4_fscirc_2(k1_nat_1(B,np__1),A,C,D) = k1_fscirc_1(k1_funct_1(C,k1_nat_1(B,np__1)),k1_funct_1(D,k1_nat_1(B,np__1)),k3_fscirc_2(B,C,D)) ) ) ) ) ) )).

fof(t11_fscirc_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(k1_fscirc_2(A,B,C))) ) ) ) )).

fof(t12_fscirc_2,axiom,(
    ! [A,B,C] : k4_msafree2(k3_fscirc_1(A,B,C)) = k1_enumset1(k4_tarski(k6_facirc_1(A,B),k3_twoscomp),k4_tarski(k6_facirc_1(B,C),k2_twoscomp),k4_tarski(k6_facirc_1(A,C),k3_twoscomp)) )).

fof(t13_fscirc_2,axiom,(
    ! [A,B,C] :
      ~ ( A != k4_tarski(k6_facirc_1(B,C),k2_twoscomp)
        & B != k4_tarski(k6_facirc_1(A,C),k3_twoscomp)
        & C != k4_tarski(k6_facirc_1(A,B),k3_twoscomp)
        & k2_msafree2(k3_fscirc_1(A,B,C)) != k1_enumset1(A,B,C) ) )).

fof(t14_fscirc_2,axiom,(
    ! [A,B,C] : k4_msafree2(k4_fscirc_1(A,B,C)) = k2_xboole_0(k1_enumset1(k4_tarski(k6_facirc_1(A,B),k3_twoscomp),k4_tarski(k6_facirc_1(B,C),k2_twoscomp),k4_tarski(k6_facirc_1(A,C),k3_twoscomp)),k1_struct_0(k4_fscirc_1(A,B,C),k6_fscirc_1(A,B,C))) )).

fof(t15_fscirc_2,axiom,(
    ! [A,B,C] :
      ~ ( A != k4_tarski(k6_facirc_1(B,C),k2_twoscomp)
        & B != k4_tarski(k6_facirc_1(A,C),k3_twoscomp)
        & C != k4_tarski(k6_facirc_1(A,B),k3_twoscomp)
        & k2_msafree2(k4_fscirc_1(A,B,C)) != k1_enumset1(A,B,C) ) )).

fof(t16_fscirc_2,axiom,(
    ! [A,B,C] :
      ~ ( A != k4_tarski(k6_facirc_1(B,C),k2_twoscomp)
        & B != k4_tarski(k6_facirc_1(A,C),k3_twoscomp)
        & C != k4_tarski(k6_facirc_1(A,B),k3_twoscomp)
        & C != k4_tarski(k6_facirc_1(A,B),k1_facirc_1)
        & k2_msafree2(k8_fscirc_1(A,B,C)) != k1_enumset1(A,B,C) ) )).

fof(t17_fscirc_2,axiom,(
    ! [A,B,C] : k4_msafree2(k8_fscirc_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_twoscomp),k4_tarski(k6_facirc_1(B,C),k2_twoscomp),k4_tarski(k6_facirc_1(A,C),k3_twoscomp))),k1_struct_0(k4_fscirc_1(A,B,C),k6_fscirc_1(A,B,C))) )).

fof(t18_fscirc_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(k3_fscirc_2(C,A,B)) = k3_facirc_2
                  & k2_mcart_1(k3_fscirc_2(C,A,B)) = k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k8_margrel1)
                  & k1_funct_5(k2_mcart_1(k3_fscirc_2(C,A,B))) = k4_finseq_2(np__0,k10_circcomb) )
                | ( k1_card_1(k1_mcart_1(k3_fscirc_2(C,A,B))) = np__3
                  & k2_mcart_1(k3_fscirc_2(C,A,B)) = k4_facirc_1
                  & k1_funct_5(k2_mcart_1(k3_fscirc_2(C,A,B))) = k4_finseq_2(np__3,k10_circcomb) ) ) ) ) ) )).

fof(t19_fscirc_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] :
                  ( k3_fscirc_2(A,B,C) != k4_tarski(D,k2_twoscomp)
                  & k3_fscirc_2(A,B,C) != k4_tarski(D,k3_twoscomp)
                  & k3_fscirc_2(A,B,C) != k4_tarski(D,k1_facirc_1) ) ) ) ) )).

fof(t20_fscirc_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(k1_fscirc_2(k1_nat_1(C,np__1),A,B)) = k2_xboole_0(k2_msafree2(k1_fscirc_2(C,A,B)),k4_xboole_0(k2_msafree2(k8_fscirc_1(k1_funct_1(A,k1_nat_1(C,np__1)),k1_funct_1(B,k1_nat_1(C,np__1)),k3_fscirc_2(C,A,B))),k1_struct_0(k1_fscirc_2(C,A,B),k3_fscirc_2(C,A,B))))
                & v1_relat_1(k4_msafree2(k1_fscirc_2(C,A,B)))
                & ~ v2_facirc_1(k2_msafree2(k1_fscirc_2(C,A,B))) ) ) ) ) )).

fof(t21_fscirc_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(k1_fscirc_2(A,B,C)) = k2_xboole_0(k2_relat_1(B),k2_relat_1(C)) ) ) ) )).

fof(t22_fscirc_2,axiom,(
    ! [A,B,C,D] :
      ( m1_subset_1(D,k4_card_3(u4_msualg_1(k4_fscirc_1(A,B,C),k7_fscirc_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_twoscomp))
                      & F = k1_funct_1(D,k4_tarski(k6_facirc_1(B,C),k2_twoscomp))
                      & G = k1_funct_1(D,k4_tarski(k6_facirc_1(A,C),k3_twoscomp)) )
                   => k15_facirc_1(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C),k6_circuit2(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C),D),k6_fscirc_1(A,B,C)) = k3_binarith(k3_binarith(E,F),G) ) ) ) ) ) )).

fof(t23_fscirc_2,axiom,(
    ! [A,B,C] :
      ~ ( A != k4_tarski(k6_facirc_1(B,C),k2_twoscomp)
        & B != k4_tarski(k6_facirc_1(A,C),k3_twoscomp)
        & C != k4_tarski(k6_facirc_1(A,B),k3_twoscomp)
        & C != k4_tarski(k6_facirc_1(A,B),k1_facirc_1)
        & ~ ! [D] :
              ( m1_subset_1(D,k4_card_3(u4_msualg_1(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C))))
             => v1_circuit2(k9_facirc_1(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C),D,np__2),k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C)) ) ) )).

fof(t24_fscirc_2,axiom,(
    ! [A,B,C] :
      ~ ( A != k4_tarski(k6_facirc_1(B,C),k2_twoscomp)
        & B != k4_tarski(k6_facirc_1(A,C),k3_twoscomp)
        & C != k4_tarski(k6_facirc_1(A,B),k3_twoscomp)
        & C != k4_tarski(k6_facirc_1(A,B),k1_facirc_1)
        & ? [D] :
            ( m1_subset_1(D,k4_card_3(u4_msualg_1(k8_fscirc_1(A,B,C),k9_fscirc_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(k8_fscirc_1(A,B,C),k9_fscirc_1(A,B,C),D,np__2),k1_fscirc_1(A,B,C)) = k4_binarith(k4_binarith(E,F),G)
                            & k1_funct_1(k9_facirc_1(k8_fscirc_1(A,B,C),k9_fscirc_1(A,B,C),D,np__2),k6_fscirc_1(A,B,C)) = k3_binarith(k3_binarith(k12_margrel1(k11_margrel1(E),F),k12_margrel1(F,G)),k12_margrel1(k11_margrel1(E),G)) ) ) ) ) ) ) )).

fof(t25_fscirc_2,axiom,(
    ! [A,B,C] :
      ~ ( A != k4_tarski(k6_facirc_1(B,C),k2_twoscomp)
        & B != k4_tarski(k6_facirc_1(A,C),k3_twoscomp)
        & C != k4_tarski(k6_facirc_1(A,B),k3_twoscomp)
        & C != k4_tarski(k6_facirc_1(A,B),k1_facirc_1)
        & ~ ! [D] :
              ( m1_subset_1(D,k4_card_3(u4_msualg_1(k8_fscirc_1(A,B,C),k9_fscirc_1(A,B,C))))
             => v1_circuit2(k9_facirc_1(k8_fscirc_1(A,B,C),k9_fscirc_1(A,B,C),D,np__2),k8_fscirc_1(A,B,C),k9_fscirc_1(A,B,C)) ) ) )).

fof(t26_fscirc_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(k1_fscirc_2(A,B,C),k2_fscirc_2(A,B,C))))
                 => v1_circuit2(k9_facirc_1(k1_fscirc_2(A,B,C),k2_fscirc_2(A,B,C),D,k1_nat_1(np__1,k2_nat_1(np__2,A))),k1_fscirc_2(A,B,C),k2_fscirc_2(A,B,C)) ) ) ) ) )).

fof(dt_k1_fscirc_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(k1_fscirc_2(A,B,C))
        & v1_msualg_1(k1_fscirc_2(A,B,C))
        & ~ v2_msualg_1(k1_fscirc_2(A,B,C))
        & v1_circcomb(k1_fscirc_2(A,B,C))
        & v2_circcomb(k1_fscirc_2(A,B,C))
        & v3_circcomb(k1_fscirc_2(A,B,C))
        & l1_msualg_1(k1_fscirc_2(A,B,C)) ) ) )).

fof(dt_k2_fscirc_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(k2_fscirc_2(A,B,C),k1_fscirc_2(A,B,C))
        & v4_msafree2(k2_fscirc_2(A,B,C),k1_fscirc_2(A,B,C))
        & v4_circcomb(k2_fscirc_2(A,B,C),k1_fscirc_2(A,B,C))
        & v6_circcomb(k2_fscirc_2(A,B,C),k1_fscirc_2(A,B,C))
        & l3_msualg_1(k2_fscirc_2(A,B,C),k1_fscirc_2(A,B,C)) ) ) )).

fof(dt_k3_fscirc_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(k3_fscirc_2(A,B,C),k1_fscirc_2(A,B,C),k4_msafree2(k1_fscirc_2(A,B,C))) ) )).

fof(dt_k4_fscirc_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(k4_fscirc_2(A,B,C,D),k1_fscirc_2(B,C,D),k4_msafree2(k1_fscirc_2(B,C,D))) ) )).
%------------------------------------------------------------------------------