SET007 Axioms: SET007+429.ax


%------------------------------------------------------------------------------
% File     : SET007+429 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Introduction to Circuits, 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    : circuit2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   39 (   0 unit)
%            Number of atoms       :  557 (  55 equality)
%            Maximal formula depth :   25 (  14 average)
%            Number of connectives :  598 (  80 ~  ;   6  |; 313  &)
%                                         (   6 <=>; 193 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   32 (   0 propositional; 1-4 arity)
%            Number of functors    :   54 (   4 constant; 0-5 arity)
%            Number of variables   :  193 (   0 singleton; 192 !;   1 ?)
%            Maximal term depth    :    6 (   1 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(t1_circuit2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m3_pboole(C,u1_struct_0(A),u4_msualg_1(A,k11_msafree(A,B)),u4_msualg_1(A,k11_msafree(A,B)))
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D)
                    & v1_funcop_1(D) )
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( ( v1_relat_1(F)
                            & v1_funct_1(F)
                            & v1_finseq_1(F)
                            & v6_trees_3(F) )
                         => ! [G] :
                              ( m1_subset_1(G,k1_funct_1(u4_msualg_1(A,k11_msafree(A,B)),E))
                             => ~ ( r2_hidden(E,k4_msafree2(A))
                                  & G = k4_trees_4(k4_tarski(k5_msafree2(A,E),u1_struct_0(A)),F)
                                  & r1_msualg_3(A,k11_msafree(A,B),k11_msafree(A,B),C)
                                  & D = k5_relat_1(k1_msualg_1(A,k5_msafree2(A,E)),C)
                                  & ! [H] :
                                      ( ( v1_relat_1(H)
                                        & v1_funct_1(H)
                                        & v1_finseq_1(H)
                                        & v6_trees_3(H) )
                                     => ~ ( H = k15_pralg_1(D,F)
                                          & k8_funct_2(k1_funct_1(u4_msualg_1(A,k11_msafree(A,B)),E),k1_funct_1(u4_msualg_1(A,k11_msafree(A,B)),E),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,k11_msafree(A,B)),u4_msualg_1(A,k11_msafree(A,B)),C,E),G) = k4_trees_4(k4_tarski(k5_msafree2(A,E),u1_struct_0(A)),H) ) ) ) ) ) ) ) ) ) ) )).

fof(d1_circuit2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & v4_msafree2(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m1_msafree2(C,A,B)
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),k13_msafree(A,u4_msualg_1(A,B)),u4_msualg_1(A,k6_msafree2(A,B)))
                 => ( D = k2_circuit2(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( ( r2_hidden(E,k2_msafree2(A))
                           => k1_msualg_3(u1_struct_0(A),k13_msafree(A,u4_msualg_1(A,B)),u4_msualg_1(A,k6_msafree2(A,B)),D,E) = k2_pre_circ(k12_msafree(A,u4_msualg_1(A,B),E),k1_trees_4(k4_tarski(k1_funct_1(C,E),E))) )
                          & ( r2_hidden(E,k1_msafree2(A))
                           => k1_msualg_3(u1_struct_0(A),k13_msafree(A,u4_msualg_1(A,B)),u4_msualg_1(A,k6_msafree2(A,B)),D,E) = k2_pre_circ(k12_msafree(A,u4_msualg_1(A,B),E),k1_trees_4(k4_tarski(k5_msafree2(A,E),u1_struct_0(A)))) )
                          & ( r2_hidden(E,k6_subset_1(u1_struct_0(A),k4_msafree2(A),k1_msafree2(A)))
                           => k1_msualg_3(u1_struct_0(A),k13_msafree(A,u4_msualg_1(A,B)),u4_msualg_1(A,k6_msafree2(A,B)),D,E) = k6_relat_1(k12_msafree(A,u4_msualg_1(A,B),E)) ) ) ) ) ) ) ) ) )).

fof(d2_circuit2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & v4_msafree2(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m1_msafree2(C,A,B)
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,k6_msafree2(A,B)),u4_msualg_1(A,k6_msafree2(A,B)))
                 => ( D = k3_circuit2(A,B,C)
                  <=> ( r1_msualg_3(A,k6_msafree2(A,B),k6_msafree2(A,B),D)
                      & r2_pboole(u1_struct_0(A),k2_circuit2(A,B,C),D) ) ) ) ) ) ) )).

fof(t2_circuit2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & v4_msafree2(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m1_msafree2(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),D))
                     => ! [F] :
                          ( ( r2_hidden(D,k6_subset_1(u1_struct_0(A),k4_msafree2(A),k1_msafree2(A)))
                            & E = k1_trees_4(k4_tarski(F,D)) )
                         => k8_funct_2(k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),D),k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),D),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,k6_msafree2(A,B)),u4_msualg_1(A,k6_msafree2(A,B)),k3_circuit2(A,B,C),D),E) = E ) ) ) ) ) ) )).

fof(t3_circuit2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & v4_msafree2(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m1_msafree2(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,k1_funct_1(u4_msualg_1(A,B),D))
                     => ( r2_hidden(D,k2_msafree2(A))
                       => k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,k6_msafree2(A,B)),u4_msualg_1(A,k6_msafree2(A,B)),k3_circuit2(A,B,C),D),k1_trees_4(k4_tarski(E,D))) = k1_trees_4(k4_tarski(k1_funct_1(C,D),D)) ) ) ) ) ) ) )).

fof(t4_circuit2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & v4_msafree2(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m1_msafree2(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),D))
                     => ! [F] :
                          ( ( v1_relat_1(F)
                            & v1_funct_1(F)
                            & v1_finseq_1(F)
                            & v6_trees_3(F) )
                         => ! [G] :
                              ( ( v1_relat_1(G)
                                & v1_funct_1(G)
                                & v1_finseq_1(G)
                                & v6_trees_3(G) )
                             => ( ( r2_hidden(D,k4_msafree2(A))
                                  & E = k4_trees_4(k4_tarski(k5_msafree2(A,D),u1_struct_0(A)),F)
                                  & k4_finseq_1(F) = k4_finseq_1(G)
                                  & ! [H] :
                                      ( m2_subset_1(H,k1_numbers,k5_numbers)
                                     => ( r2_hidden(H,k4_finseq_1(F))
                                       => k1_funct_1(G,H) = k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,k6_msafree2(A,B)),u4_msualg_1(A,k6_msafree2(A,B)),k3_circuit2(A,B,C),k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,k5_msafree2(A,D)),H)),k1_funct_1(F,H)) ) ) )
                               => k8_funct_2(k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),D),k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),D),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,k6_msafree2(A,B)),u4_msualg_1(A,k6_msafree2(A,B)),k3_circuit2(A,B,C),D),E) = k4_trees_4(k4_tarski(k5_msafree2(A,D),u1_struct_0(A)),G) ) ) ) ) ) ) ) ) )).

fof(t5_circuit2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & v4_msafree2(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m1_msafree2(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),D))
                     => ( r2_hidden(D,k1_msafree2(A))
                       => k8_funct_2(k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),D),k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),D),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,k6_msafree2(A,B)),u4_msualg_1(A,k6_msafree2(A,B)),k3_circuit2(A,B,C),D),E) = k1_trees_4(k4_tarski(k5_msafree2(A,D),u1_struct_0(A))) ) ) ) ) ) ) )).

fof(t6_circuit2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & v4_msafree2(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m1_msafree2(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),D))
                     => ! [F] :
                          ( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),D))
                         => ! [G] :
                              ( ( v1_relat_1(G)
                                & v1_funct_1(G)
                                & v3_trees_2(G) )
                             => ! [H] :
                                  ( ( v1_relat_1(H)
                                    & v1_funct_1(H)
                                    & v3_trees_2(H) )
                                 => ( ( G = E
                                      & H = F
                                      & F = k8_funct_2(k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),D),k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),D),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,k6_msafree2(A,B)),u4_msualg_1(A,k6_msafree2(A,B)),k3_circuit2(A,B,C),D),E) )
                                   => k1_relat_1(G) = k1_relat_1(H) ) ) ) ) ) ) ) ) ) )).

fof(t7_circuit2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & v4_msafree2(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m1_msafree2(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),D))
                     => ! [F] :
                          ( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),D))
                         => ( F = k8_funct_2(k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),D),k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),D),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,k6_msafree2(A,B)),u4_msualg_1(A,k6_msafree2(A,B)),k3_circuit2(A,B,C),D),E)
                           => k4_card_1(E) = k4_card_1(F) ) ) ) ) ) ) ) )).

fof(d3_circuit2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & v4_msafree2(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_msafree2(D,A,B)
                 => ! [E] :
                      ( m1_subset_1(E,k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),C))
                     => ( E = k4_circuit2(A,B,C,D)
                      <=> ? [F] :
                            ( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),C))
                            & k4_card_1(F) = k4_circuit1(A,B,C)
                            & E = k8_funct_2(k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),C),k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),C),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,k6_msafree2(A,B)),u4_msualg_1(A,k6_msafree2(A,B)),k3_circuit2(A,B,D),C),F) ) ) ) ) ) ) ) )).

fof(t8_circuit2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & v4_msafree2(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_msafree2(D,A,B)
                 => k4_circuit2(A,B,C,D) = k8_funct_2(k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),C),k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),C),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,k6_msafree2(A,B)),u4_msualg_1(A,k6_msafree2(A,B)),k3_circuit2(A,B,D),C),k4_circuit2(A,B,C,D)) ) ) ) ) )).

fof(t9_circuit2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & v4_msafree2(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_msafree2(D,A,B)
                 => ! [E] :
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E)
                        & v1_finseq_1(E)
                        & v6_trees_3(E) )
                     => ( ( r2_hidden(C,k4_msafree2(A))
                          & k4_finseq_1(E) = k4_finseq_1(k1_msualg_1(A,k5_msafree2(A,C)))
                          & ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ( r2_hidden(F,k4_finseq_1(E))
                               => k1_funct_1(E,F) = k4_circuit2(A,B,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,k5_msafree2(A,C)),F),D) ) ) )
                       => k4_circuit2(A,B,C,D) = k4_trees_4(k4_tarski(k5_msafree2(A,C),u1_struct_0(A)),E) ) ) ) ) ) ) )).

fof(d4_circuit2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & v4_msafree2(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_msafree2(D,A,B)
                 => k5_circuit2(A,B,C,D) = k8_funct_2(k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),C),k1_funct_1(u4_msualg_1(A,B),C),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,k6_msafree2(A,B)),u4_msualg_1(A,B),k7_msafree2(A,B),C),k4_circuit2(A,B,C,D)) ) ) ) ) )).

fof(t10_circuit2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & v4_msafree2(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_msafree2(D,A,B)
                 => ( r2_hidden(C,k2_msafree2(A))
                   => k5_circuit2(A,B,C,D) = k1_funct_1(D,C) ) ) ) ) ) )).

fof(t11_circuit2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & v4_msafree2(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_msafree2(D,A,B)
                 => ( r2_hidden(C,k1_msafree2(A))
                   => k5_circuit2(A,B,C,D) = k1_funct_1(k1_circuit1(A,B),C) ) ) ) ) ) )).

fof(d5_circuit2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & v4_msafree2(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u4_msualg_1(A,B)))
             => ! [D] :
                  ( m1_subset_1(D,k4_card_3(u4_msualg_1(A,B)))
                 => ( D = k6_circuit2(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( ( r2_hidden(E,k2_msafree2(A))
                           => k1_funct_1(D,E) = k1_funct_1(C,E) )
                          & ( r2_hidden(E,k4_msafree2(A))
                           => k1_funct_1(D,E) = k8_funct_2(k3_msualg_1(A,k5_msafree2(A,E),B),k4_msualg_1(A,k5_msafree2(A,E),B),k5_msualg_1(A,k5_msafree2(A,E),B),k3_circuit1(A,B,C,k5_msafree2(A,E))) ) ) ) ) ) ) ) ) )).

fof(t12_circuit2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & v4_msafree2(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u4_msualg_1(A,B)))
             => ! [D] :
                  ( m1_msafree2(D,A,B)
                 => ( r1_tarski(D,C)
                   => r1_tarski(D,k6_circuit2(A,B,C)) ) ) ) ) ) )).

fof(d6_circuit2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & v4_msafree2(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u4_msualg_1(A,B)))
             => ( v1_circuit2(C,A,B)
              <=> C = k6_circuit2(A,B,C) ) ) ) ) )).

fof(d7_circuit2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & v4_msafree2(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u4_msualg_1(A,B)))
             => ! [D] :
                  ( m1_msafree2(D,A,B)
                 => k7_circuit2(A,B,C,D) = k6_circuit2(A,B,k1_circuit2(A,B,C,D)) ) ) ) ) )).

fof(d8_circuit2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & v4_msafree2(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m3_pboole(C,k2_msafree2(A),k2_pre_circ(k2_msafree2(A),k5_numbers),k3_pre_circ(u1_struct_0(A),u4_msualg_1(A,B),k2_msafree2(A)))
             => ! [D] :
                  ( m1_subset_1(D,k4_card_3(u4_msualg_1(A,B)))
                 => k8_circuit2(A,B,C,D) = k1_funct_4(k1_circuit2(A,B,D,k2_circuit1(A,B,C,np__0)),k1_circuit1(A,B)) ) ) ) ) )).

fof(d9_circuit2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & v4_msafree2(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m3_pboole(C,k2_msafree2(A),k2_pre_circ(k2_msafree2(A),k5_numbers),k3_pre_circ(u1_struct_0(A),u4_msualg_1(A,B),k2_msafree2(A)))
             => ! [D] :
                  ( m1_subset_1(D,k4_card_3(u4_msualg_1(A,B)))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k5_numbers,k4_card_3(u4_msualg_1(A,B)))
                        & m2_relset_1(E,k5_numbers,k4_card_3(u4_msualg_1(A,B))) )
                     => ( E = k9_circuit2(A,B,C,D)
                      <=> ( k8_funct_2(k5_numbers,k4_card_3(u4_msualg_1(A,B)),E,np__0) = k8_circuit2(A,B,C,D)
                          & ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => k8_funct_2(k5_numbers,k4_card_3(u4_msualg_1(A,B)),E,k1_nat_1(F,np__1)) = k7_circuit2(A,B,k8_funct_2(k5_numbers,k4_card_3(u4_msualg_1(A,B)),E,F),k2_circuit1(A,B,C,k1_nat_1(F,np__1))) ) ) ) ) ) ) ) ) )).

fof(t13_circuit2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & v4_msafree2(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u4_msualg_1(A,B)))
             => ! [D] :
                  ( m1_msafree2(D,A,B)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( r1_xreal_0(k6_circuit1(A,B,F),E)
                             => k1_funct_1(C,F) = k5_circuit2(A,B,F,D) ) )
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( r1_xreal_0(k6_circuit1(A,B,F),k1_nat_1(E,np__1))
                             => k1_funct_1(k6_circuit2(A,B,C),F) = k5_circuit2(A,B,F,D) ) ) ) ) ) ) ) ) )).

fof(t14_circuit2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_group_1(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & v4_msafree2(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m3_pboole(C,k2_msafree2(A),k2_pre_circ(k2_msafree2(A),k5_numbers),k3_pre_circ(u1_struct_0(A),u4_msualg_1(A,B),k2_msafree2(A)))
             => ( v5_seqm_3(k10_funct_6(C))
               => ( v1_xboole_0(k2_msafree2(A))
                  | ! [D] :
                      ( m1_subset_1(D,k4_card_3(u4_msualg_1(A,B)))
                     => ! [E] :
                          ( m1_msafree2(E,A,B)
                         => ( E = k1_funct_1(k10_funct_6(C),np__0)
                           => ! [F] :
                                ( m2_subset_1(F,k1_numbers,k5_numbers)
                               => r1_tarski(E,k8_funct_2(k5_numbers,k4_card_3(u4_msualg_1(A,B)),k9_circuit2(A,B,C,D),F)) ) ) ) ) ) ) ) ) ) )).

fof(t15_circuit2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_group_1(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & v4_msafree2(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m3_pboole(C,k2_msafree2(A),k2_pre_circ(k2_msafree2(A),k5_numbers),k3_pre_circ(u1_struct_0(A),u4_msualg_1(A,B),k2_msafree2(A)))
             => ! [D] :
                  ( m1_subset_1(D,k4_card_3(u4_msualg_1(A,B)))
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( ( v5_seqm_3(k10_funct_6(C))
                          & v1_circuit2(k8_funct_2(k5_numbers,k4_card_3(u4_msualg_1(A,B)),k9_circuit2(A,B,C,D),E),A,B) )
                       => ( v1_xboole_0(k2_msafree2(A))
                          | ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ( r1_xreal_0(E,F)
                               => k8_funct_2(k5_numbers,k4_card_3(u4_msualg_1(A,B)),k9_circuit2(A,B,C,D),E) = k8_funct_2(k5_numbers,k4_card_3(u4_msualg_1(A,B)),k9_circuit2(A,B,C,D),F) ) ) ) ) ) ) ) ) ) )).

fof(t16_circuit2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_group_1(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & v4_msafree2(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m3_pboole(C,k2_msafree2(A),k2_pre_circ(k2_msafree2(A),k5_numbers),k3_pre_circ(u1_struct_0(A),u4_msualg_1(A,B),k2_msafree2(A)))
             => ( v5_seqm_3(k10_funct_6(C))
               => ( v1_xboole_0(k2_msafree2(A))
                  | ! [D] :
                      ( m1_subset_1(D,k4_card_3(u4_msualg_1(A,B)))
                     => ! [E] :
                          ( m1_msafree2(E,A,B)
                         => ( E = k1_funct_1(k10_funct_6(C),np__0)
                           => ! [F] :
                                ( m2_subset_1(F,k1_numbers,k5_numbers)
                               => ! [G] :
                                    ( m1_subset_1(G,u1_struct_0(A))
                                   => ( r1_xreal_0(k6_circuit1(A,B,G),F)
                                     => k1_funct_1(k8_funct_2(k5_numbers,k4_card_3(u4_msualg_1(A,B)),k9_circuit2(A,B,C,D),F),G) = k5_circuit2(A,B,G,E) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t17_circuit2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_group_1(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & v4_msafree2(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m3_pboole(C,k2_msafree2(A),k2_pre_circ(k2_msafree2(A),k5_numbers),k3_pre_circ(u1_struct_0(A),u4_msualg_1(A,B),k2_msafree2(A)))
             => ! [D] :
                  ( m1_msafree2(D,A,B)
                 => ( ( v5_seqm_3(k10_funct_6(C))
                      & D = k1_funct_1(k10_funct_6(C),np__0) )
                   => ( v1_xboole_0(k2_msafree2(A))
                      | ! [E] :
                          ( m1_subset_1(E,k4_card_3(u4_msualg_1(A,B)))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ! [G] :
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ( G = k7_circuit1(A,B)
                                   => k1_funct_1(k8_funct_2(k5_numbers,k4_card_3(u4_msualg_1(A,B)),k9_circuit2(A,B,C,E),G),F) = k5_circuit2(A,B,F,D) ) ) ) ) ) ) ) ) ) ) )).

fof(t18_circuit2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_group_1(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & v4_msafree2(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m3_pboole(C,k2_msafree2(A),k2_pre_circ(k2_msafree2(A),k5_numbers),k3_pre_circ(u1_struct_0(A),u4_msualg_1(A,B),k2_msafree2(A)))
             => ( v5_seqm_3(k10_funct_6(C))
               => ( v1_xboole_0(k2_msafree2(A))
                  | ! [D] :
                      ( m1_subset_1(D,k4_card_3(u4_msualg_1(A,B)))
                     => ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( E = k7_circuit1(A,B)
                           => v1_circuit2(k8_funct_2(k5_numbers,k4_card_3(u4_msualg_1(A,B)),k9_circuit2(A,B,C,D),E),A,B) ) ) ) ) ) ) ) ) )).

fof(t19_circuit2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_group_1(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & v4_msafree2(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m3_pboole(C,k2_msafree2(A),k2_pre_circ(k2_msafree2(A),k5_numbers),k3_pre_circ(u1_struct_0(A),u4_msualg_1(A,B),k2_msafree2(A)))
             => ( v5_seqm_3(k10_funct_6(C))
               => ( v1_xboole_0(k2_msafree2(A))
                  | ! [D] :
                      ( m1_subset_1(D,k4_card_3(u4_msualg_1(A,B)))
                     => ! [E] :
                          ( m1_subset_1(E,k4_card_3(u4_msualg_1(A,B)))
                         => k1_funct_1(k9_circuit2(A,B,C,D),k7_circuit1(A,B)) = k1_funct_1(k9_circuit2(A,B,C,E),k7_circuit1(A,B)) ) ) ) ) ) ) ) )).

fof(dt_k1_circuit2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & v4_msafree2(B,A)
        & l3_msualg_1(B,A)
        & m1_subset_1(C,k4_card_3(u4_msualg_1(A,B)))
        & m1_msafree2(D,A,B) )
     => m1_subset_1(k1_circuit2(A,B,C,D),k4_card_3(u4_msualg_1(A,B))) ) )).

fof(idempotence_k1_circuit2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & v4_msafree2(B,A)
        & l3_msualg_1(B,A)
        & m1_subset_1(C,k4_card_3(u4_msualg_1(A,B)))
        & m1_msafree2(D,A,B) )
     => k1_circuit2(A,B,C,C) = C ) )).

fof(redefinition_k1_circuit2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & v4_msafree2(B,A)
        & l3_msualg_1(B,A)
        & m1_subset_1(C,k4_card_3(u4_msualg_1(A,B)))
        & m1_msafree2(D,A,B) )
     => k1_circuit2(A,B,C,D) = k1_funct_4(C,D) ) )).

fof(dt_k2_circuit2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & v4_msafree2(B,A)
        & l3_msualg_1(B,A)
        & m1_msafree2(C,A,B) )
     => m3_pboole(k2_circuit2(A,B,C),u1_struct_0(A),k13_msafree(A,u4_msualg_1(A,B)),u4_msualg_1(A,k6_msafree2(A,B))) ) )).

fof(dt_k3_circuit2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & v4_msafree2(B,A)
        & l3_msualg_1(B,A)
        & m1_msafree2(C,A,B) )
     => m3_pboole(k3_circuit2(A,B,C),u1_struct_0(A),u4_msualg_1(A,k6_msafree2(A,B)),u4_msualg_1(A,k6_msafree2(A,B))) ) )).

fof(dt_k4_circuit2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & v4_msafree2(B,A)
        & l3_msualg_1(B,A)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_msafree2(D,A,B) )
     => m1_subset_1(k4_circuit2(A,B,C,D),k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),C)) ) )).

fof(dt_k5_circuit2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & v4_msafree2(B,A)
        & l3_msualg_1(B,A)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_msafree2(D,A,B) )
     => m1_subset_1(k5_circuit2(A,B,C,D),k1_funct_1(u4_msualg_1(A,B),C)) ) )).

fof(dt_k6_circuit2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & v4_msafree2(B,A)
        & l3_msualg_1(B,A)
        & m1_subset_1(C,k4_card_3(u4_msualg_1(A,B))) )
     => m1_subset_1(k6_circuit2(A,B,C),k4_card_3(u4_msualg_1(A,B))) ) )).

fof(dt_k7_circuit2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & v4_msafree2(B,A)
        & l3_msualg_1(B,A)
        & m1_subset_1(C,k4_card_3(u4_msualg_1(A,B)))
        & m1_msafree2(D,A,B) )
     => m1_subset_1(k7_circuit2(A,B,C,D),k4_card_3(u4_msualg_1(A,B))) ) )).

fof(dt_k8_circuit2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & v4_msafree2(B,A)
        & l3_msualg_1(B,A)
        & m3_pboole(C,k2_msafree2(A),k2_pre_circ(k2_msafree2(A),k5_numbers),k3_pre_circ(u1_struct_0(A),u4_msualg_1(A,B),k2_msafree2(A)))
        & m1_subset_1(D,k4_card_3(u4_msualg_1(A,B))) )
     => m1_subset_1(k8_circuit2(A,B,C,D),k4_card_3(u4_msualg_1(A,B))) ) )).

fof(dt_k9_circuit2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & v5_msafree2(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & v4_msafree2(B,A)
        & l3_msualg_1(B,A)
        & m3_pboole(C,k2_msafree2(A),k2_pre_circ(k2_msafree2(A),k5_numbers),k3_pre_circ(u1_struct_0(A),u4_msualg_1(A,B),k2_msafree2(A)))
        & m1_subset_1(D,k4_card_3(u4_msualg_1(A,B))) )
     => ( v1_funct_1(k9_circuit2(A,B,C,D))
        & v1_funct_2(k9_circuit2(A,B,C,D),k5_numbers,k4_card_3(u4_msualg_1(A,B)))
        & m2_relset_1(k9_circuit2(A,B,C,D),k5_numbers,k4_card_3(u4_msualg_1(A,B))) ) ) )).
%------------------------------------------------------------------------------