SET007 Axioms: SET007+590.ax
%------------------------------------------------------------------------------
% File : SET007+590 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Full Subtracter Circuit. Part I
% 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_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 44 ( 13 unt; 0 def)
% Number of atoms : 211 ( 54 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 227 ( 60 ~; 0 |; 61 &)
% ( 0 <=>; 106 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 9 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 20 ( 19 usr; 0 prp; 1-3 aty)
% Number of functors : 43 ( 43 usr; 6 con; 0-4 aty)
% Number of variables : 174 ( 174 !; 0 ?)
% 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(d1_fscirc_1,axiom,
! [A,B,C] : k1_fscirc_1(A,B,C) = k13_facirc_1(A,B,C,k1_facirc_1) ).
fof(d2_fscirc_1,axiom,
! [A,B,C] : k2_fscirc_1(A,B,C) = k14_facirc_1(A,B,C,k1_facirc_1) ).
fof(d3_fscirc_1,axiom,
! [A,B,C] : k3_fscirc_1(A,B,C) = k3_circcomb(k3_circcomb(k7_circcomb(k3_twoscomp,k6_facirc_1(A,B)),k7_circcomb(k2_twoscomp,k6_facirc_1(B,C))),k7_circcomb(k3_twoscomp,k6_facirc_1(A,C))) ).
fof(d4_fscirc_1,axiom,
! [A,B,C] : k4_fscirc_1(A,B,C) = k3_circcomb(k3_fscirc_1(A,B,C),k7_circcomb(k4_facirc_1,k7_facirc_1(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(d5_fscirc_1,axiom,
! [A,B,C] : k5_fscirc_1(A,B,C) = k4_circcomb(k3_circcomb(k7_circcomb(k3_twoscomp,k6_facirc_1(A,B)),k7_circcomb(k2_twoscomp,k6_facirc_1(B,C))),k7_circcomb(k3_twoscomp,k6_facirc_1(A,C)),k4_circcomb(k7_circcomb(k3_twoscomp,k6_facirc_1(A,B)),k7_circcomb(k2_twoscomp,k6_facirc_1(B,C)),k10_facirc_1(A,B,k3_twoscomp),k10_facirc_1(B,C,k2_twoscomp)),k10_facirc_1(A,C,k3_twoscomp)) ).
fof(t1_fscirc_1,axiom,
! [A,B,C] : v1_relat_1(k4_msafree2(k4_fscirc_1(A,B,C))) ).
fof(t2_fscirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ! [B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(C)
=> ~ v2_facirc_1(k2_msafree2(k4_fscirc_1(A,B,C))) ) ) ) ).
fof(t3_fscirc_1,axiom,
! [A,B,C,D] :
( m1_subset_1(D,k4_card_3(u4_msualg_1(k3_fscirc_1(A,B,C),k5_fscirc_1(A,B,C))))
=> ! [E] :
( m1_subset_1(E,k10_circcomb)
=> ! [F] :
( m1_subset_1(F,k10_circcomb)
=> ( ( E = k1_funct_1(D,A)
& F = k1_funct_1(D,B) )
=> k1_funct_1(k6_circuit2(k3_fscirc_1(A,B,C),k5_fscirc_1(A,B,C),D),k4_tarski(k6_facirc_1(A,B),k3_twoscomp)) = k12_margrel1(k11_margrel1(E),F) ) ) ) ) ).
fof(t4_fscirc_1,axiom,
! [A,B,C,D] :
( m1_subset_1(D,k4_card_3(u4_msualg_1(k3_fscirc_1(A,B,C),k5_fscirc_1(A,B,C))))
=> ! [E] :
( m1_subset_1(E,k10_circcomb)
=> ! [F] :
( m1_subset_1(F,k10_circcomb)
=> ( ( E = k1_funct_1(D,B)
& F = k1_funct_1(D,C) )
=> k1_funct_1(k6_circuit2(k3_fscirc_1(A,B,C),k5_fscirc_1(A,B,C),D),k4_tarski(k6_facirc_1(B,C),k2_twoscomp)) = k12_margrel1(E,F) ) ) ) ) ).
fof(t5_fscirc_1,axiom,
! [A,B,C,D] :
( m1_subset_1(D,k4_card_3(u4_msualg_1(k3_fscirc_1(A,B,C),k5_fscirc_1(A,B,C))))
=> ! [E] :
( m1_subset_1(E,k10_circcomb)
=> ! [F] :
( m1_subset_1(F,k10_circcomb)
=> ( ( E = k1_funct_1(D,A)
& F = k1_funct_1(D,C) )
=> k1_funct_1(k6_circuit2(k3_fscirc_1(A,B,C),k5_fscirc_1(A,B,C),D),k4_tarski(k6_facirc_1(A,C),k3_twoscomp)) = k12_margrel1(k11_margrel1(E),F) ) ) ) ) ).
fof(d6_fscirc_1,axiom,
! [A,B,C] : k6_fscirc_1(A,B,C) = k4_tarski(k7_facirc_1(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)),k4_facirc_1) ).
fof(d7_fscirc_1,axiom,
! [A,B,C] : k7_fscirc_1(A,B,C) = k4_circcomb(k3_fscirc_1(A,B,C),k7_circcomb(k4_facirc_1,k7_facirc_1(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))),k5_fscirc_1(A,B,C),k11_facirc_1(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),k4_facirc_1)) ).
fof(t6_fscirc_1,axiom,
! [A,B,C] :
( r2_hidden(A,u1_struct_0(k4_fscirc_1(A,B,C)))
& r2_hidden(B,u1_struct_0(k4_fscirc_1(A,B,C)))
& r2_hidden(C,u1_struct_0(k4_fscirc_1(A,B,C))) ) ).
fof(t7_fscirc_1,axiom,
! [A,B,C] :
( r2_hidden(k4_tarski(k6_facirc_1(A,B),k3_twoscomp),k4_msafree2(k4_fscirc_1(A,B,C)))
& r2_hidden(k4_tarski(k6_facirc_1(B,C),k2_twoscomp),k4_msafree2(k4_fscirc_1(A,B,C)))
& r2_hidden(k4_tarski(k6_facirc_1(A,C),k3_twoscomp),k4_msafree2(k4_fscirc_1(A,B,C))) ) ).
fof(t8_fscirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ! [B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(C)
=> ( r2_hidden(A,k2_msafree2(k4_fscirc_1(A,B,C)))
& r2_hidden(B,k2_msafree2(k4_fscirc_1(A,B,C)))
& r2_hidden(C,k2_msafree2(k4_fscirc_1(A,B,C))) ) ) ) ) ).
fof(t9_fscirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ! [B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(C)
=> ( k2_msafree2(k4_fscirc_1(A,B,C)) = k1_enumset1(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(t10_fscirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ! [B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(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] :
( m1_subset_1(E,k10_circcomb)
=> ! [F] :
( m1_subset_1(F,k10_circcomb)
=> ( ( E = k1_funct_1(D,A)
& F = k1_funct_1(D,B) )
=> k1_funct_1(k6_circuit2(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C),D),k4_tarski(k6_facirc_1(A,B),k3_twoscomp)) = k12_margrel1(k11_margrel1(E),F) ) ) ) ) ) ) ) ).
fof(t11_fscirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ! [B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(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] :
( m1_subset_1(E,k10_circcomb)
=> ! [F] :
( m1_subset_1(F,k10_circcomb)
=> ( ( E = k1_funct_1(D,B)
& F = k1_funct_1(D,C) )
=> k1_funct_1(k6_circuit2(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C),D),k4_tarski(k6_facirc_1(B,C),k2_twoscomp)) = k12_margrel1(E,F) ) ) ) ) ) ) ) ).
fof(t12_fscirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ! [B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(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] :
( m1_subset_1(E,k10_circcomb)
=> ! [F] :
( m1_subset_1(F,k10_circcomb)
=> ( ( E = k1_funct_1(D,A)
& F = k1_funct_1(D,C) )
=> k1_funct_1(k6_circuit2(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C),D),k4_tarski(k6_facirc_1(A,C),k3_twoscomp)) = k12_margrel1(k11_margrel1(E),F) ) ) ) ) ) ) ) ).
fof(t13_fscirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ! [B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(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] :
( m1_subset_1(E,k10_circcomb)
=> ! [F] :
( m1_subset_1(F,k10_circcomb)
=> ! [G] :
( m1_subset_1(G,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(t14_fscirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ! [B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(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] :
( m1_subset_1(E,k10_circcomb)
=> ! [F] :
( m1_subset_1(F,k10_circcomb)
=> ( ( E = k1_funct_1(D,A)
& F = k1_funct_1(D,B) )
=> k1_funct_1(k9_facirc_1(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C),D,np__2),k4_tarski(k6_facirc_1(A,B),k3_twoscomp)) = k12_margrel1(k11_margrel1(E),F) ) ) ) ) ) ) ) ).
fof(t15_fscirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ! [B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(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] :
( m1_subset_1(E,k10_circcomb)
=> ! [F] :
( m1_subset_1(F,k10_circcomb)
=> ( ( E = k1_funct_1(D,B)
& F = k1_funct_1(D,C) )
=> k1_funct_1(k9_facirc_1(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C),D,np__2),k4_tarski(k6_facirc_1(B,C),k2_twoscomp)) = k12_margrel1(E,F) ) ) ) ) ) ) ) ).
fof(t16_fscirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ! [B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(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] :
( m1_subset_1(E,k10_circcomb)
=> ! [F] :
( m1_subset_1(F,k10_circcomb)
=> ( ( E = k1_funct_1(D,A)
& F = k1_funct_1(D,C) )
=> k1_funct_1(k9_facirc_1(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C),D,np__2),k4_tarski(k6_facirc_1(A,C),k3_twoscomp)) = k12_margrel1(k11_margrel1(E),F) ) ) ) ) ) ) ) ).
fof(t17_fscirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ! [B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(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] :
( m1_subset_1(E,k10_circcomb)
=> ! [F] :
( m1_subset_1(F,k10_circcomb)
=> ! [G] :
( m1_subset_1(G,k10_circcomb)
=> ( ( E = k1_funct_1(D,A)
& F = k1_funct_1(D,B)
& G = k1_funct_1(D,C) )
=> k15_facirc_1(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C),k9_facirc_1(k4_fscirc_1(A,B,C),k7_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(t18_fscirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ! [B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(C)
=> ! [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(d8_fscirc_1,axiom,
! [A,B,C] : k8_fscirc_1(A,B,C) = k3_circcomb(k12_facirc_1(A,B,C,k1_facirc_1),k4_fscirc_1(A,B,C)) ).
fof(t19_fscirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ! [B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(C)
=> k2_msafree2(k8_fscirc_1(A,B,C)) = k1_enumset1(A,B,C) ) ) ) ).
fof(t20_fscirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ! [B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(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(t21_fscirc_1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(D)
& l1_msualg_1(D) )
=> ( D = k8_fscirc_1(A,B,C)
=> ( r2_hidden(A,u1_struct_0(D))
& r2_hidden(B,u1_struct_0(D))
& r2_hidden(C,u1_struct_0(D)) ) ) ) ).
fof(d9_fscirc_1,axiom,
! [A,B,C] : k9_fscirc_1(A,B,C) = k4_circcomb(k12_facirc_1(A,B,C,k1_facirc_1),k4_fscirc_1(A,B,C),k2_fscirc_1(A,B,C),k7_fscirc_1(A,B,C)) ).
fof(t22_fscirc_1,axiom,
! [A,B,C] : v1_relat_1(k4_msafree2(k8_fscirc_1(A,B,C))) ).
fof(t23_fscirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ! [B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(C)
=> ~ v2_facirc_1(k2_msafree2(k8_fscirc_1(A,B,C))) ) ) ) ).
fof(t24_fscirc_1,axiom,
! [A,B,C] :
( r2_hidden(k1_fscirc_1(A,B,C),k4_msafree2(k8_fscirc_1(A,B,C)))
& r2_hidden(k6_fscirc_1(A,B,C),k4_msafree2(k8_fscirc_1(A,B,C))) ) ).
fof(t25_fscirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ! [B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(C)
=> ! [D] :
( m1_subset_1(D,k4_card_3(u4_msualg_1(k8_fscirc_1(A,B,C),k9_fscirc_1(A,B,C))))
=> ! [E] :
( m1_subset_1(E,k10_circcomb)
=> ! [F] :
( m1_subset_1(F,k10_circcomb)
=> ! [G] :
( m1_subset_1(G,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(t26_fscirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ! [B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(C)
=> ! [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(dt_k1_fscirc_1,axiom,
! [A,B,C] : m1_struct_0(k1_fscirc_1(A,B,C),k12_facirc_1(A,B,C,k1_facirc_1),k4_msafree2(k12_facirc_1(A,B,C,k1_facirc_1))) ).
fof(dt_k2_fscirc_1,axiom,
! [A,B,C] :
( v4_msualg_1(k2_fscirc_1(A,B,C),k12_facirc_1(A,B,C,k1_facirc_1))
& v4_msafree2(k2_fscirc_1(A,B,C),k12_facirc_1(A,B,C,k1_facirc_1))
& v4_circcomb(k2_fscirc_1(A,B,C),k12_facirc_1(A,B,C,k1_facirc_1))
& v6_circcomb(k2_fscirc_1(A,B,C),k12_facirc_1(A,B,C,k1_facirc_1))
& l3_msualg_1(k2_fscirc_1(A,B,C),k12_facirc_1(A,B,C,k1_facirc_1)) ) ).
fof(dt_k3_fscirc_1,axiom,
! [A,B,C] :
( ~ v3_struct_0(k3_fscirc_1(A,B,C))
& v1_msualg_1(k3_fscirc_1(A,B,C))
& ~ v2_msualg_1(k3_fscirc_1(A,B,C))
& v1_circcomb(k3_fscirc_1(A,B,C))
& v2_circcomb(k3_fscirc_1(A,B,C))
& v3_circcomb(k3_fscirc_1(A,B,C))
& l1_msualg_1(k3_fscirc_1(A,B,C)) ) ).
fof(dt_k4_fscirc_1,axiom,
! [A,B,C] :
( ~ v3_struct_0(k4_fscirc_1(A,B,C))
& v1_msualg_1(k4_fscirc_1(A,B,C))
& ~ v2_msualg_1(k4_fscirc_1(A,B,C))
& v1_circcomb(k4_fscirc_1(A,B,C))
& v2_circcomb(k4_fscirc_1(A,B,C))
& v3_circcomb(k4_fscirc_1(A,B,C))
& l1_msualg_1(k4_fscirc_1(A,B,C)) ) ).
fof(dt_k5_fscirc_1,axiom,
! [A,B,C] :
( v4_msualg_1(k5_fscirc_1(A,B,C),k3_fscirc_1(A,B,C))
& v4_msafree2(k5_fscirc_1(A,B,C),k3_fscirc_1(A,B,C))
& v4_circcomb(k5_fscirc_1(A,B,C),k3_fscirc_1(A,B,C))
& v6_circcomb(k5_fscirc_1(A,B,C),k3_fscirc_1(A,B,C))
& l3_msualg_1(k5_fscirc_1(A,B,C),k3_fscirc_1(A,B,C)) ) ).
fof(dt_k6_fscirc_1,axiom,
! [A,B,C] : m1_struct_0(k6_fscirc_1(A,B,C),k4_fscirc_1(A,B,C),k4_msafree2(k4_fscirc_1(A,B,C))) ).
fof(dt_k7_fscirc_1,axiom,
! [A,B,C] :
( v4_msualg_1(k7_fscirc_1(A,B,C),k4_fscirc_1(A,B,C))
& v4_msafree2(k7_fscirc_1(A,B,C),k4_fscirc_1(A,B,C))
& v4_circcomb(k7_fscirc_1(A,B,C),k4_fscirc_1(A,B,C))
& v6_circcomb(k7_fscirc_1(A,B,C),k4_fscirc_1(A,B,C))
& l3_msualg_1(k7_fscirc_1(A,B,C),k4_fscirc_1(A,B,C)) ) ).
fof(dt_k8_fscirc_1,axiom,
! [A,B,C] :
( ~ v3_struct_0(k8_fscirc_1(A,B,C))
& v1_msualg_1(k8_fscirc_1(A,B,C))
& ~ v2_msualg_1(k8_fscirc_1(A,B,C))
& v1_circcomb(k8_fscirc_1(A,B,C))
& v2_circcomb(k8_fscirc_1(A,B,C))
& v3_circcomb(k8_fscirc_1(A,B,C))
& l1_msualg_1(k8_fscirc_1(A,B,C)) ) ).
fof(dt_k9_fscirc_1,axiom,
! [A,B,C] :
( v4_msualg_1(k9_fscirc_1(A,B,C),k8_fscirc_1(A,B,C))
& v4_msafree2(k9_fscirc_1(A,B,C),k8_fscirc_1(A,B,C))
& v4_circcomb(k9_fscirc_1(A,B,C),k8_fscirc_1(A,B,C))
& v6_circcomb(k9_fscirc_1(A,B,C),k8_fscirc_1(A,B,C))
& l3_msualg_1(k9_fscirc_1(A,B,C),k8_fscirc_1(A,B,C)) ) ).
%------------------------------------------------------------------------------