SET007 Axioms: SET007+727.ax
%------------------------------------------------------------------------------
% File : SET007+727 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Automatic Generation of Mizar Documentation for Circuits
% 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 : circcmb3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 148 ( 8 unt; 0 def)
% Number of atoms : 1624 ( 178 equ)
% Maximal formula atoms : 40 ( 10 avg)
% Number of connectives : 1738 ( 262 ~; 25 |; 906 &)
% ( 20 <=>; 525 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 11 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 58 ( 56 usr; 1 prp; 0-4 aty)
% Number of functors : 155 ( 155 usr; 87 con; 0-5 aty)
% Number of variables : 621 ( 585 !; 36 ?)
% 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_circcmb3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ( ( v5_msualg_1(B,A)
& v4_msafree2(B,A)
& v3_circcmb3(B,A) )
=> ( v5_msualg_1(B,A)
& v4_msafree2(B,A)
& v2_circcmb3(B,A) ) ) ) ) ).
fof(fc1_circcmb3,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ( ~ v3_struct_0(k7_circcomb(B,A))
& v6_group_1(k7_circcomb(B,A))
& v1_msualg_1(k7_circcomb(B,A))
& ~ v2_msualg_1(k7_circcomb(B,A))
& v2_msafree2(k7_circcomb(B,A))
& v1_circcomb(k7_circcomb(B,A))
& v2_circcomb(k7_circcomb(B,A)) ) ) ).
fof(cc2_circcmb3,axiom,
! [A] :
( l1_msualg_1(A)
=> ( v4_circcmb3(A)
=> ( ~ v3_struct_0(A)
& v6_group_1(A)
& v1_msualg_1(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& v1_circcomb(A)
& v2_circcomb(A) ) ) ) ).
fof(cc3_circcmb3,axiom,
! [A] :
( l1_msualg_1(A)
=> ( ( ~ v3_struct_0(A)
& v4_circcmb3(A) )
=> ( ~ v3_struct_0(A)
& v5_circcomb(A) ) ) ) ).
fof(fc2_circcmb3,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& m1_subset_1(B,k5_numbers)
& m1_circcomb(C,B)
& v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(B,A),A)
& m1_relset_1(D,k4_finseq_2(B,A),A) )
=> ( ~ v3_struct_0(k7_circcomb(D,C))
& v6_group_1(k7_circcomb(D,C))
& v1_msualg_1(k7_circcomb(D,C))
& ~ v2_msualg_1(k7_circcomb(D,C))
& v2_msafree2(k7_circcomb(D,C))
& v1_circcomb(k7_circcomb(D,C))
& v2_circcomb(k7_circcomb(D,C))
& v5_circcomb(k7_circcomb(D,C))
& v4_circcmb3(k7_circcomb(D,C)) ) ) ).
fof(rc1_circcmb3,axiom,
? [A] :
( l1_msualg_1(A)
& ~ v3_struct_0(A)
& v6_group_1(A)
& v1_msualg_1(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& v1_circcomb(A)
& v2_circcomb(A)
& v5_circcomb(A)
& v4_circcmb3(A) ) ).
fof(cc4_circcmb3,axiom,
! [A] :
( ( v4_circcmb3(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ( ( v4_msafree2(B,A)
& v5_circcmb3(B,A) )
=> ( v4_msualg_1(B,A)
& v5_msualg_1(B,A)
& v4_msafree2(B,A) ) ) ) ) ).
fof(fc3_circcmb3,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& m1_subset_1(B,k5_numbers)
& m1_circcomb(C,B)
& v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(B,A),A)
& m1_relset_1(D,k4_finseq_2(B,A),A) )
=> ( v4_msualg_1(k9_circcomb(B,A,D,C),k7_circcomb(D,C))
& v5_msualg_1(k9_circcomb(B,A,D,C),k7_circcomb(D,C))
& v3_msafree2(k9_circcomb(B,A,D,C),k7_circcomb(D,C))
& v4_msafree2(k9_circcomb(B,A,D,C),k7_circcomb(D,C))
& v4_circcomb(k9_circcomb(B,A,D,C),k7_circcomb(D,C))
& v5_circcmb3(k9_circcomb(B,A,D,C),k7_circcomb(D,C)) ) ) ).
fof(rc2_circcmb3,axiom,
! [A] :
( ( v4_circcmb3(A)
& l1_msualg_1(A) )
=> ? [B] :
( l3_msualg_1(B,A)
& v4_msualg_1(B,A)
& v5_msualg_1(B,A)
& v4_msafree2(B,A)
& v5_circcmb3(B,A) ) ) ).
fof(fc4_circcmb3,axiom,
! [A] :
( ( v4_circcmb3(A)
& l1_msualg_1(A) )
=> ( ~ v1_xboole_0(k5_circcmb3(A))
& v1_facirc_1(k5_circcmb3(A)) ) ) ).
fof(cc5_circcmb3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ( ( v5_msualg_1(B,A)
& v4_msafree2(B,A)
& v5_circcmb3(B,A) )
=> ( v5_msualg_1(B,A)
& v4_msafree2(B,A)
& v2_circcmb3(B,A)
& v3_circcmb3(B,A) ) ) ) ) ).
fof(rc3_circcmb3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ? [B] :
( m1_circcmb3(B,A)
& ~ v3_struct_0(B)
& v6_group_1(B)
& v1_msualg_1(B)
& ~ v2_msualg_1(B)
& v2_msafree2(B)
& v1_circcomb(B)
& v2_circcomb(B)
& v5_circcomb(B)
& v4_circcmb3(B) ) ) ).
fof(cc6_circcmb3,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& m1_circcmb3(B,A) )
=> ! [C] :
( m2_circcmb3(C,A,B)
=> ( v5_msualg_1(C,B)
& v4_circcomb(C,B) ) ) ) ).
fof(rc4_circcmb3,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& v4_circcmb3(B)
& m1_circcmb3(B,A) )
=> ? [C] :
( m2_circcmb3(C,A,B)
& v4_msualg_1(C,B)
& v5_msualg_1(C,B)
& v4_msafree2(C,B)
& v4_circcomb(C,B)
& v2_circcmb3(C,B)
& v3_circcmb3(C,B)
& v5_circcmb3(C,B) ) ) ).
fof(rc5_circcmb3,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& m1_circcmb3(B,A) )
=> ? [C] :
( m2_circcmb3(C,A,B)
& v4_msualg_1(C,B)
& v5_msualg_1(C,B)
& v4_msafree2(C,B)
& v4_circcomb(C,B) ) ) ).
fof(fc5_circcmb3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v6_group_1(A)
& l1_msualg_1(A)
& ~ v3_struct_0(B)
& v6_group_1(B)
& l1_msualg_1(B) )
=> ( ~ v3_struct_0(k3_circcomb(A,B))
& v6_group_1(k3_circcomb(A,B))
& v1_msualg_1(k3_circcomb(A,B)) ) ) ).
fof(fc6_circcmb3,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& m1_circcmb3(B,A)
& m1_circcmb3(C,A) )
=> ( ~ v3_struct_0(k3_circcomb(B,C))
& v1_msualg_1(k3_circcomb(B,C))
& ~ v2_msualg_1(k3_circcomb(B,C))
& v2_msafree2(k3_circcomb(B,C))
& v1_circcomb(k3_circcomb(B,C))
& v2_circcomb(k3_circcomb(B,C))
& v5_circcomb(k3_circcomb(B,C)) ) ) ).
fof(cc7_circcmb3,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& v6_group_1(B)
& m1_circcmb3(B,A) )
=> ! [C] :
( m2_circcmb3(C,A,B)
=> ( v5_msualg_1(C,B)
& v4_circcomb(C,B)
& v3_circcmb3(C,B) ) ) ) ).
fof(fc7_circcmb3,axiom,
( ~ v1_xboole_0(k5_ordinal2)
& v1_ordinal1(k5_ordinal2)
& v2_ordinal1(k5_ordinal2)
& v3_ordinal1(k5_ordinal2)
& v1_membered(k5_ordinal2)
& v2_membered(k5_ordinal2)
& v3_membered(k5_ordinal2)
& v4_membered(k5_ordinal2)
& v5_membered(k5_ordinal2)
& ~ v2_facirc_1(k5_ordinal2) ) ).
fof(cc8_circcmb3,axiom,
! [A] :
( ~ v2_facirc_1(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ~ v2_facirc_1(B) ) ) ).
fof(cc9_circcmb3,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v7_seqm_3(A) )
=> ( v1_relat_1(A)
& v1_funct_1(A)
& v3_facirc_1(A) ) ) ).
fof(cc10_circcmb3,axiom,
! [A] :
( m1_finseq_1(A,k5_numbers)
=> v7_seqm_3(A) ) ).
fof(rc6_circcmb3,axiom,
? [A] :
( v1_relat_1(A)
& v1_funct_1(A)
& v2_funct_1(A)
& v1_finset_1(A)
& v1_finseq_1(A)
& v3_facirc_1(A)
& v7_seqm_3(A) ) ).
fof(rc7_circcmb3,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ? [B] :
( m1_circcomb(B,A)
& v1_relat_1(B)
& v1_funct_1(B)
& v2_funct_1(B)
& v1_finset_1(B)
& v1_finseq_1(B)
& v3_facirc_1(B)
& v7_seqm_3(B) ) ) ).
fof(fc8_circcmb3,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A)
& v3_facirc_1(A) )
=> ( ~ v3_struct_0(k7_circcomb(B,A))
& v6_group_1(k7_circcomb(B,A))
& v1_msualg_1(k7_circcomb(B,A))
& ~ v2_msualg_1(k7_circcomb(B,A))
& v2_msafree2(k7_circcomb(B,A))
& v1_circcomb(k7_circcomb(B,A))
& v2_circcomb(k7_circcomb(B,A))
& v6_circcmb3(k7_circcomb(B,A)) ) ) ).
fof(rc8_circcmb3,axiom,
? [A] :
( l1_msualg_1(A)
& ~ v3_struct_0(A)
& v6_group_1(A)
& v1_msualg_1(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& v1_circcomb(A)
& v2_circcomb(A)
& v5_circcomb(A)
& v4_circcmb3(A)
& v6_circcmb3(A) ) ).
fof(rc9_circcmb3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ? [B] :
( m1_circcmb3(B,A)
& ~ v3_struct_0(B)
& v6_group_1(B)
& v1_msualg_1(B)
& ~ v2_msualg_1(B)
& v2_msafree2(B)
& v1_circcomb(B)
& v2_circcomb(B)
& v5_circcomb(B)
& v4_circcmb3(B)
& v6_circcmb3(B) ) ) ).
fof(fc9_circcmb3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_circcmb3(A)
& l1_msualg_1(A) )
=> ~ v2_facirc_1(k2_msafree2(A)) ) ).
fof(fc10_circcmb3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_circcomb(A)
& v2_circcomb(A)
& l1_msualg_1(A) )
=> v1_relat_1(k3_msafree2(A)) ) ).
fof(fc11_circcmb3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v1_circcomb(A)
& v5_circcomb(A)
& l1_msualg_1(A) )
=> v1_relat_1(k3_msafree2(A)) ) ).
fof(fc12_circcmb3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v1_circcomb(A)
& v2_circcomb(A)
& v6_circcmb3(A)
& l1_msualg_1(A)
& ~ v3_struct_0(B)
& v1_circcomb(B)
& v2_circcomb(B)
& v6_circcmb3(B)
& l1_msualg_1(B) )
=> ( ~ v3_struct_0(k3_circcomb(A,B))
& v1_msualg_1(k3_circcomb(A,B))
& v2_msafree2(k3_circcomb(A,B))
& v1_circcomb(k3_circcomb(A,B))
& v2_circcomb(k3_circcomb(A,B))
& v6_circcmb3(k3_circcomb(A,B)) ) ) ).
fof(fc13_circcmb3,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& v6_circcmb3(B)
& m1_circcmb3(B,A)
& m1_subset_1(C,u1_struct_0(B))
& v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(np__1,A),A)
& m1_relset_1(D,k4_finseq_2(np__1,A),A) )
=> ( ~ v3_struct_0(k3_circcomb(B,k7_circcomb(D,k13_binarith(u1_struct_0(B),C))))
& v1_msualg_1(k3_circcomb(B,k7_circcomb(D,k13_binarith(u1_struct_0(B),C))))
& ~ v2_msualg_1(k3_circcomb(B,k7_circcomb(D,k13_binarith(u1_struct_0(B),C))))
& v2_msafree2(k3_circcomb(B,k7_circcomb(D,k13_binarith(u1_struct_0(B),C))))
& v1_circcomb(k3_circcomb(B,k7_circcomb(D,k13_binarith(u1_struct_0(B),C))))
& v2_circcomb(k3_circcomb(B,k7_circcomb(D,k13_binarith(u1_struct_0(B),C))))
& v6_circcmb3(k3_circcomb(B,k7_circcomb(D,k13_binarith(u1_struct_0(B),C)))) ) ) ).
fof(fc14_circcmb3,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& v6_circcmb3(B)
& m1_circcmb3(B,A)
& ~ v1_facirc_1(C)
& v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(np__1,A),A)
& m1_relset_1(D,k4_finseq_2(np__1,A),A) )
=> ( ~ v3_struct_0(k3_circcomb(B,k6_circcmb3(np__1,A,D,k5_facirc_1(C))))
& v1_msualg_1(k3_circcomb(B,k6_circcmb3(np__1,A,D,k5_facirc_1(C))))
& ~ v2_msualg_1(k3_circcomb(B,k6_circcmb3(np__1,A,D,k5_facirc_1(C))))
& v2_msafree2(k3_circcomb(B,k6_circcmb3(np__1,A,D,k5_facirc_1(C))))
& v1_circcomb(k3_circcomb(B,k6_circcmb3(np__1,A,D,k5_facirc_1(C))))
& v2_circcomb(k3_circcomb(B,k6_circcmb3(np__1,A,D,k5_facirc_1(C))))
& v5_circcomb(k3_circcomb(B,k6_circcmb3(np__1,A,D,k5_facirc_1(C))))
& v6_circcmb3(k3_circcomb(B,k6_circcmb3(np__1,A,D,k5_facirc_1(C)))) ) ) ).
fof(fc15_circcmb3,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& v6_circcmb3(B)
& m1_circcmb3(B,A)
& m1_subset_1(C,u1_struct_0(B))
& ~ v1_facirc_1(D)
& v1_funct_1(E)
& v1_funct_2(E,k4_finseq_2(np__2,A),A)
& m1_relset_1(E,k4_finseq_2(np__2,A),A) )
=> ( ~ v3_struct_0(k3_circcomb(B,k6_circcmb3(np__2,A,E,k6_facirc_1(C,D))))
& v1_msualg_1(k3_circcomb(B,k6_circcmb3(np__2,A,E,k6_facirc_1(C,D))))
& ~ v2_msualg_1(k3_circcomb(B,k6_circcmb3(np__2,A,E,k6_facirc_1(C,D))))
& v2_msafree2(k3_circcomb(B,k6_circcmb3(np__2,A,E,k6_facirc_1(C,D))))
& v1_circcomb(k3_circcomb(B,k6_circcmb3(np__2,A,E,k6_facirc_1(C,D))))
& v2_circcomb(k3_circcomb(B,k6_circcmb3(np__2,A,E,k6_facirc_1(C,D))))
& v5_circcomb(k3_circcomb(B,k6_circcmb3(np__2,A,E,k6_facirc_1(C,D))))
& v6_circcmb3(k3_circcomb(B,k6_circcmb3(np__2,A,E,k6_facirc_1(C,D)))) ) ) ).
fof(fc16_circcmb3,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& v6_circcmb3(B)
& m1_circcmb3(B,A)
& m1_subset_1(C,u1_struct_0(B))
& ~ v1_facirc_1(D)
& v1_funct_1(E)
& v1_funct_2(E,k4_finseq_2(np__2,A),A)
& m1_relset_1(E,k4_finseq_2(np__2,A),A) )
=> ( ~ v3_struct_0(k3_circcomb(B,k6_circcmb3(np__2,A,E,k6_facirc_1(D,C))))
& v1_msualg_1(k3_circcomb(B,k6_circcmb3(np__2,A,E,k6_facirc_1(D,C))))
& ~ v2_msualg_1(k3_circcomb(B,k6_circcmb3(np__2,A,E,k6_facirc_1(D,C))))
& v2_msafree2(k3_circcomb(B,k6_circcmb3(np__2,A,E,k6_facirc_1(D,C))))
& v1_circcomb(k3_circcomb(B,k6_circcmb3(np__2,A,E,k6_facirc_1(D,C))))
& v2_circcomb(k3_circcomb(B,k6_circcmb3(np__2,A,E,k6_facirc_1(D,C))))
& v5_circcomb(k3_circcomb(B,k6_circcmb3(np__2,A,E,k6_facirc_1(D,C))))
& v6_circcmb3(k3_circcomb(B,k6_circcmb3(np__2,A,E,k6_facirc_1(D,C)))) ) ) ).
fof(fc17_circcmb3,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& v6_circcmb3(B)
& m1_circcmb3(B,A)
& m1_subset_1(C,u1_struct_0(B))
& m1_subset_1(D,u1_struct_0(B))
& v1_funct_1(E)
& v1_funct_2(E,k4_finseq_2(np__2,A),A)
& m1_relset_1(E,k4_finseq_2(np__2,A),A) )
=> ( ~ v3_struct_0(k3_circcomb(B,k6_circcmb3(np__2,A,E,k6_facirc_1(C,D))))
& v1_msualg_1(k3_circcomb(B,k6_circcmb3(np__2,A,E,k6_facirc_1(C,D))))
& ~ v2_msualg_1(k3_circcomb(B,k6_circcmb3(np__2,A,E,k6_facirc_1(C,D))))
& v2_msafree2(k3_circcomb(B,k6_circcmb3(np__2,A,E,k6_facirc_1(C,D))))
& v1_circcomb(k3_circcomb(B,k6_circcmb3(np__2,A,E,k6_facirc_1(C,D))))
& v2_circcomb(k3_circcomb(B,k6_circcmb3(np__2,A,E,k6_facirc_1(C,D))))
& v5_circcomb(k3_circcomb(B,k6_circcmb3(np__2,A,E,k6_facirc_1(C,D))))
& v6_circcmb3(k3_circcomb(B,k6_circcmb3(np__2,A,E,k6_facirc_1(C,D)))) ) ) ).
fof(fc18_circcmb3,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& v6_circcmb3(B)
& m1_circcmb3(B,A)
& m1_subset_1(C,u1_struct_0(B))
& m1_subset_1(D,u1_struct_0(B))
& ~ v1_facirc_1(E)
& v1_funct_1(F)
& v1_funct_2(F,k4_finseq_2(np__3,A),A)
& m1_relset_1(F,k4_finseq_2(np__3,A),A) )
=> ( ~ v3_struct_0(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(C,D,E))))
& v1_msualg_1(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(C,D,E))))
& ~ v2_msualg_1(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(C,D,E))))
& v2_msafree2(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(C,D,E))))
& v1_circcomb(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(C,D,E))))
& v2_circcomb(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(C,D,E))))
& v5_circcomb(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(C,D,E))))
& v6_circcmb3(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(C,D,E)))) ) ) ).
fof(fc19_circcmb3,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& v6_circcmb3(B)
& m1_circcmb3(B,A)
& m1_subset_1(C,u1_struct_0(B))
& m1_subset_1(D,u1_struct_0(B))
& ~ v1_facirc_1(E)
& v1_funct_1(F)
& v1_funct_2(F,k4_finseq_2(np__3,A),A)
& m1_relset_1(F,k4_finseq_2(np__3,A),A) )
=> ( ~ v3_struct_0(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(C,E,D))))
& v1_msualg_1(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(C,E,D))))
& ~ v2_msualg_1(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(C,E,D))))
& v2_msafree2(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(C,E,D))))
& v1_circcomb(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(C,E,D))))
& v2_circcomb(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(C,E,D))))
& v5_circcomb(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(C,E,D))))
& v6_circcmb3(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(C,E,D)))) ) ) ).
fof(fc20_circcmb3,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& v6_circcmb3(B)
& m1_circcmb3(B,A)
& m1_subset_1(C,u1_struct_0(B))
& m1_subset_1(D,u1_struct_0(B))
& ~ v1_facirc_1(E)
& v1_funct_1(F)
& v1_funct_2(F,k4_finseq_2(np__3,A),A)
& m1_relset_1(F,k4_finseq_2(np__3,A),A) )
=> ( ~ v3_struct_0(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(E,C,D))))
& v1_msualg_1(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(E,C,D))))
& ~ v2_msualg_1(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(E,C,D))))
& v2_msafree2(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(E,C,D))))
& v1_circcomb(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(E,C,D))))
& v2_circcomb(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(E,C,D))))
& v5_circcomb(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(E,C,D))))
& v6_circcmb3(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(E,C,D)))) ) ) ).
fof(fc21_circcmb3,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& v6_circcmb3(B)
& m1_circcmb3(B,A)
& m1_subset_1(C,u1_struct_0(B))
& ~ v1_facirc_1(D)
& ~ v1_facirc_1(E)
& v1_funct_1(F)
& v1_funct_2(F,k4_finseq_2(np__3,A),A)
& m1_relset_1(F,k4_finseq_2(np__3,A),A) )
=> ( ~ v3_struct_0(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(C,D,E))))
& v1_msualg_1(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(C,D,E))))
& ~ v2_msualg_1(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(C,D,E))))
& v2_msafree2(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(C,D,E))))
& v1_circcomb(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(C,D,E))))
& v2_circcomb(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(C,D,E))))
& v5_circcomb(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(C,D,E))))
& v6_circcmb3(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(C,D,E)))) ) ) ).
fof(fc22_circcmb3,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& v6_circcmb3(B)
& m1_circcmb3(B,A)
& m1_subset_1(C,u1_struct_0(B))
& ~ v1_facirc_1(D)
& ~ v1_facirc_1(E)
& v1_funct_1(F)
& v1_funct_2(F,k4_finseq_2(np__3,A),A)
& m1_relset_1(F,k4_finseq_2(np__3,A),A) )
=> ( ~ v3_struct_0(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(D,C,E))))
& v1_msualg_1(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(D,C,E))))
& ~ v2_msualg_1(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(D,C,E))))
& v2_msafree2(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(D,C,E))))
& v1_circcomb(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(D,C,E))))
& v2_circcomb(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(D,C,E))))
& v5_circcomb(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(D,C,E))))
& v6_circcmb3(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(D,C,E)))) ) ) ).
fof(fc23_circcmb3,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& v6_circcmb3(B)
& m1_circcmb3(B,A)
& m1_subset_1(C,u1_struct_0(B))
& ~ v1_facirc_1(D)
& ~ v1_facirc_1(E)
& v1_funct_1(F)
& v1_funct_2(F,k4_finseq_2(np__3,A),A)
& m1_relset_1(F,k4_finseq_2(np__3,A),A) )
=> ( ~ v3_struct_0(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(D,E,C))))
& v1_msualg_1(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(D,E,C))))
& ~ v2_msualg_1(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(D,E,C))))
& v2_msafree2(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(D,E,C))))
& v1_circcomb(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(D,E,C))))
& v2_circcomb(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(D,E,C))))
& v5_circcomb(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(D,E,C))))
& v6_circcmb3(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(D,E,C)))) ) ) ).
fof(fc24_circcmb3,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& v6_circcmb3(B)
& m1_circcmb3(B,A)
& m1_subset_1(C,u1_struct_0(B))
& m1_subset_1(D,u1_struct_0(B))
& m1_subset_1(E,u1_struct_0(B))
& v1_funct_1(F)
& v1_funct_2(F,k4_finseq_2(np__3,A),A)
& m1_relset_1(F,k4_finseq_2(np__3,A),A) )
=> ( ~ v3_struct_0(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(C,D,E))))
& v1_msualg_1(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(C,D,E))))
& ~ v2_msualg_1(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(C,D,E))))
& v2_msafree2(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(C,D,E))))
& v1_circcomb(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(C,D,E))))
& v2_circcomb(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(C,D,E))))
& v5_circcomb(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(C,D,E))))
& v6_circcmb3(k3_circcomb(B,k6_circcmb3(np__3,A,F,k7_facirc_1(C,D,E)))) ) ) ).
fof(t1_circcmb3,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] :
( r2_hidden(D,k2_msafree2(A))
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k1_funct_1(k9_facirc_1(A,B,C,E),D) = k1_funct_1(C,D) ) ) ) ) ) ).
fof(d1_circcmb3,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_circcmb3(C,A,B)
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& v1_circuit2(k9_facirc_1(A,B,C,D),A,B) ) ) ) ) ) ).
fof(d2_circcmb3,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) )
=> ( v2_circcmb3(B,A)
<=> ! [C] :
( m1_subset_1(C,k4_card_3(u4_msualg_1(A,B)))
=> v1_circcmb3(C,A,B) ) ) ) ) ).
fof(d3_circcmb3,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) )
=> ( v3_circcmb3(B,A)
<=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& ! [D] :
( m1_subset_1(D,k4_card_3(u4_msualg_1(A,B)))
=> v1_circuit2(k9_facirc_1(A,B,D,C),A,B) ) ) ) ) ) ).
fof(d4_circcmb3,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_circcmb3(C,A,B)
=> ! [D] :
( m1_subset_1(D,k4_card_3(u4_msualg_1(A,B)))
=> ( D = k1_circcmb3(A,B,C)
<=> ( v1_circuit2(D,A,B)
& ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& D = k9_facirc_1(A,B,C,E) ) ) ) ) ) ) ) ) ).
fof(d5_circcmb3,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_circcmb3(C,A,B)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( D = k2_circcmb3(A,B,C)
<=> ( v1_circuit2(k9_facirc_1(A,B,C,D),A,B)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(D,E)
& v1_circuit2(k9_facirc_1(A,B,C,E),A,B) ) ) ) ) ) ) ) ) ) ).
fof(t2_circcmb3,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_circcmb3(C,A,B)
=> k1_circcmb3(A,B,C) = k9_facirc_1(A,B,C,k2_circcmb3(A,B,C)) ) ) ) ) ).
fof(t3_circcmb3,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] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( v1_circuit2(k9_facirc_1(A,B,C,D),A,B)
=> r1_xreal_0(k2_circcmb3(A,B,C),D) ) ) ) ) ) ).
fof(t4_circcmb3,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] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( v1_circuit2(k9_facirc_1(A,B,C,D),A,B)
=> k1_circcmb3(A,B,C) = k9_facirc_1(A,B,C,D) ) ) ) ) ) ).
fof(t5_circcmb3,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] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( v1_circcmb3(C,A,B)
& r1_xreal_0(k2_circcmb3(A,B,C),D) )
=> k1_circcmb3(A,B,C) = k9_facirc_1(A,B,C,D) ) ) ) ) ) ).
fof(t6_circcmb3,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_circcmb3(C,A,B)
=> ! [D] :
( r2_hidden(D,k2_msafree2(A))
=> k1_funct_1(k1_circcmb3(A,B,C),D) = k1_funct_1(C,D) ) ) ) ) ) ).
fof(t7_circcmb3,axiom,
$true ).
fof(t8_circcmb3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& v2_msafree2(B)
& l1_msualg_1(B) )
=> ( ( r1_xboole_0(k2_msafree2(A),k4_msafree2(B))
& r1_xboole_0(k2_msafree2(B),k4_msafree2(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& ~ v2_msualg_1(C)
& v2_msafree2(C)
& l1_msualg_1(C) )
=> ( C = k3_circcomb(A,B)
=> ! [D] :
( ( v5_msualg_1(D,A)
& v4_msafree2(D,A)
& l3_msualg_1(D,A) )
=> ! [E] :
( ( v5_msualg_1(E,B)
& v4_msafree2(E,B)
& l3_msualg_1(E,B) )
=> ( r2_circcomb(A,B,D,E)
=> ! [F] :
( ( v5_msualg_1(F,C)
& v4_msafree2(F,C)
& l3_msualg_1(F,C) )
=> ( F = k4_circcomb(A,B,D,E)
=> ! [G] :
( m1_subset_1(G,k4_card_3(u4_msualg_1(C,F)))
=> ! [H] :
( m1_subset_1(H,k4_card_3(u4_msualg_1(A,D)))
=> ! [I] :
( m1_subset_1(I,k4_card_3(u4_msualg_1(B,E)))
=> ( ( H = k7_relat_1(G,u1_struct_0(A))
& I = k7_relat_1(G,u1_struct_0(B))
& v1_circcmb3(H,A,D)
& v1_circcmb3(I,B,E) )
=> v1_circcmb3(G,C,F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t9_circcmb3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& v2_msafree2(B)
& l1_msualg_1(B) )
=> ( ( r1_xboole_0(k2_msafree2(A),k4_msafree2(B))
& r1_xboole_0(k2_msafree2(B),k4_msafree2(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& ~ v2_msualg_1(C)
& v2_msafree2(C)
& l1_msualg_1(C) )
=> ( C = k3_circcomb(A,B)
=> ! [D] :
( ( v5_msualg_1(D,A)
& v4_msafree2(D,A)
& l3_msualg_1(D,A) )
=> ! [E] :
( ( v5_msualg_1(E,B)
& v4_msafree2(E,B)
& l3_msualg_1(E,B) )
=> ( r2_circcomb(A,B,D,E)
=> ! [F] :
( ( v5_msualg_1(F,C)
& v4_msafree2(F,C)
& l3_msualg_1(F,C) )
=> ( F = k4_circcomb(A,B,D,E)
=> ! [G] :
( m1_subset_1(G,k4_card_3(u4_msualg_1(C,F)))
=> ! [H] :
( m1_subset_1(H,k4_card_3(u4_msualg_1(A,D)))
=> ( ( H = k7_relat_1(G,u1_struct_0(A))
& v1_circcmb3(H,A,D) )
=> ! [I] :
( m1_subset_1(I,k4_card_3(u4_msualg_1(B,E)))
=> ( ( I = k7_relat_1(G,u1_struct_0(B))
& v1_circcmb3(I,B,E) )
=> k2_circcmb3(C,F,G) = k1_limfunc1(k2_circcmb3(A,D,H),k2_circcmb3(B,E,I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t10_circcmb3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& v2_msafree2(B)
& l1_msualg_1(B) )
=> ( r1_xboole_0(k2_msafree2(A),k4_msafree2(B))
=> ! [C] :
( ( ~ v3_struct_0(C)
& ~ v2_msualg_1(C)
& v2_msafree2(C)
& l1_msualg_1(C) )
=> ( C = k3_circcomb(A,B)
=> ! [D] :
( ( v5_msualg_1(D,A)
& v4_msafree2(D,A)
& l3_msualg_1(D,A) )
=> ! [E] :
( ( v5_msualg_1(E,B)
& v4_msafree2(E,B)
& l3_msualg_1(E,B) )
=> ( r2_circcomb(A,B,D,E)
=> ! [F] :
( ( v5_msualg_1(F,C)
& v4_msafree2(F,C)
& l3_msualg_1(F,C) )
=> ( F = k4_circcomb(A,B,D,E)
=> ! [G] :
( m1_subset_1(G,k4_card_3(u4_msualg_1(C,F)))
=> ! [H] :
( m1_subset_1(H,k4_card_3(u4_msualg_1(A,D)))
=> ( ( H = k7_relat_1(G,u1_struct_0(A))
& v1_circcmb3(H,A,D) )
=> ! [I] :
( m1_subset_1(I,k4_card_3(u4_msualg_1(B,E)))
=> ( ( I = k7_relat_1(k9_facirc_1(C,F,G,k2_circcmb3(A,D,H)),u1_struct_0(B))
& v1_circcmb3(I,B,E) )
=> v1_circcmb3(G,C,F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t11_circcmb3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& v2_msafree2(B)
& l1_msualg_1(B) )
=> ( r1_xboole_0(k2_msafree2(A),k4_msafree2(B))
=> ! [C] :
( ( ~ v3_struct_0(C)
& ~ v2_msualg_1(C)
& v2_msafree2(C)
& l1_msualg_1(C) )
=> ( C = k3_circcomb(A,B)
=> ! [D] :
( ( v5_msualg_1(D,A)
& v4_msafree2(D,A)
& l3_msualg_1(D,A) )
=> ! [E] :
( ( v5_msualg_1(E,B)
& v4_msafree2(E,B)
& l3_msualg_1(E,B) )
=> ( r2_circcomb(A,B,D,E)
=> ! [F] :
( ( v5_msualg_1(F,C)
& v4_msafree2(F,C)
& l3_msualg_1(F,C) )
=> ( F = k4_circcomb(A,B,D,E)
=> ! [G] :
( m1_subset_1(G,k4_card_3(u4_msualg_1(C,F)))
=> ! [H] :
( m1_subset_1(H,k4_card_3(u4_msualg_1(A,D)))
=> ( ( H = k7_relat_1(G,u1_struct_0(A))
& v1_circcmb3(H,A,D) )
=> ! [I] :
( m1_subset_1(I,k4_card_3(u4_msualg_1(B,E)))
=> ( ( I = k7_relat_1(k9_facirc_1(C,F,G,k2_circcmb3(A,D,H)),u1_struct_0(B))
& v1_circcmb3(I,B,E) )
=> k2_circcmb3(C,F,G) = k1_nat_1(k2_circcmb3(A,D,H),k2_circcmb3(B,E,I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t12_circcmb3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& v2_msafree2(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& ~ v2_msualg_1(C)
& v2_msafree2(C)
& l1_msualg_1(C) )
=> ( ( r1_xboole_0(k2_msafree2(A),k4_msafree2(B))
& C = k3_circcomb(A,B) )
=> ! [D] :
( ( v5_msualg_1(D,A)
& v4_msafree2(D,A)
& l3_msualg_1(D,A) )
=> ! [E] :
( ( v5_msualg_1(E,B)
& v4_msafree2(E,B)
& l3_msualg_1(E,B) )
=> ! [F] :
( ( v5_msualg_1(F,C)
& v4_msafree2(F,C)
& l3_msualg_1(F,C) )
=> ( ( r2_circcomb(A,B,D,E)
& F = k4_circcomb(A,B,D,E) )
=> ! [G] :
( m1_subset_1(G,k4_card_3(u4_msualg_1(C,F)))
=> ! [H] :
( m1_subset_1(H,k4_card_3(u4_msualg_1(A,D)))
=> ( ( H = k7_relat_1(G,u1_struct_0(A))
& v1_circcmb3(H,A,D) )
=> ! [I] :
( m1_subset_1(I,k4_card_3(u4_msualg_1(B,E)))
=> ( ( I = k7_relat_1(k9_facirc_1(C,F,G,k2_circcmb3(A,D,H)),u1_struct_0(B))
& v1_circcmb3(I,B,E) )
=> k7_relat_1(k1_circcmb3(C,F,G),u1_struct_0(A)) = k1_circcmb3(A,D,H) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t13_circcmb3,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m1_circcomb(D,C)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k4_finseq_2(C,B),B)
& m2_relset_1(E,k4_finseq_2(C,B),B) )
=> ! [F] :
( m1_subset_1(F,k4_card_3(u4_msualg_1(k7_circcomb(E,D),k9_circcomb(C,B,E,D))))
=> m2_finseq_2(k5_relat_1(D,F),B,k4_finseq_2(C,B)) ) ) ) ) ) ).
fof(t14_circcmb3,axiom,
! [A,B,C,D] : k2_relat_1(k1_scmpds_1(A,B,C,D)) = k2_enumset1(A,B,C,D) ).
fof(t15_circcmb3,axiom,
! [A,B,C,D,E] : k2_relat_1(k2_scmpds_1(A,B,C,D,E)) = k3_enumset1(A,B,C,D,E) ).
fof(d6_circcmb3,axiom,
! [A] :
( l1_msualg_1(A)
=> ( v4_circcmb3(A)
<=> ? [B] :
( ~ v1_xboole_0(B)
& v1_finset_1(B)
& ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& ? [D] :
( m1_circcomb(D,C)
& ? [E] :
( v1_funct_1(E)
& v1_funct_2(E,k4_finseq_2(C,B),B)
& m2_relset_1(E,k4_finseq_2(C,B),B)
& A = k7_circcomb(E,D) ) ) ) ) ) ) ).
fof(d7_circcmb3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ( v5_circcmb3(B,A)
<=> ? [C] :
( ~ v1_xboole_0(C)
& v1_finset_1(C)
& ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& ? [E] :
( m1_circcomb(E,D)
& ? [F] :
( v1_funct_1(F)
& v1_funct_2(F,k4_finseq_2(D,C),C)
& m2_relset_1(F,k4_finseq_2(D,C),C)
& A = k7_circcomb(F,E)
& B = k9_circcomb(D,C,F,E) ) ) ) ) ) ) ) ).
fof(d8_circcmb3,axiom,
! [A] :
( ( v4_circcmb3(A)
& l1_msualg_1(A) )
=> k5_circcmb3(A) = k3_tarski(u1_msualg_1(A)) ) ).
fof(t16_circcmb3,axiom,
! [A] :
( ( v4_circcmb3(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ! [C] :
( A = k7_circcomb(C,B)
=> k5_circcmb3(A) = k4_tarski(B,C) ) ) ) ).
fof(t17_circcmb3,axiom,
! [A] :
( ( v4_circcmb3(A)
& l1_msualg_1(A) )
=> k4_msafree2(A) = k1_struct_0(A,k5_circcmb3(A)) ) ).
fof(t18_circcmb3,axiom,
! [A] :
( ( v4_circcmb3(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v4_msafree2(B,A)
& v5_circcmb3(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ( ~ v1_xboole_0(D)
& v1_finset_1(D) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k4_finseq_2(C,D),D)
& m2_relset_1(E,k4_finseq_2(C,D),D) )
=> ! [F] :
( m1_circcomb(F,C)
=> ( B = k9_circcomb(C,D,E,F)
=> A = k7_circcomb(E,F) ) ) ) ) ) ) ) ).
fof(t19_circcmb3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k4_finseq_2(A,B),B)
& m2_relset_1(C,k4_finseq_2(A,B),B) )
=> ! [D] :
( m1_circcomb(D,A)
=> ! [E] :
( m1_subset_1(E,k4_card_3(u4_msualg_1(k7_circcomb(C,D),k9_circcomb(A,B,C,D))))
=> k1_funct_1(k6_circuit2(k7_circcomb(C,D),k9_circcomb(A,B,C,D),E),k5_circcmb3(k7_circcomb(C,D))) = k1_funct_1(C,k5_relat_1(D,E)) ) ) ) ) ) ).
fof(t20_circcmb3,axiom,
! [A] :
( ( v4_circcmb3(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v4_msafree2(B,A)
& v5_circcmb3(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u4_msualg_1(A,B)))
=> v1_circuit2(k6_circuit2(A,B,C),A,B) ) ) ) ).
fof(t21_circcmb3,axiom,
! [A] :
( ( v4_circcmb3(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v4_msafree2(B,A)
& v5_circcmb3(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u4_msualg_1(A,B)))
=> k1_circcmb3(A,B,C) = k6_circuit2(A,B,C) ) ) ) ).
fof(t22_circcmb3,axiom,
! [A] :
( ( v4_circcmb3(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v4_msafree2(B,A)
& v5_circcmb3(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u4_msualg_1(A,B)))
=> r1_xreal_0(k2_circcmb3(A,B,C),np__1) ) ) ) ).
fof(t23_circcmb3,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v5_seqm_3(A) )
=> A = k2_pre_circ(k1_relat_1(A),k1_yellow_6(A)) ) ).
fof(t24_circcmb3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( k4_finseq_2(C,A) = k4_finseq_2(D,B)
=> ( C = np__0
| ( A = B
& C = D ) ) ) ) ) ) ) ).
fof(t25_circcmb3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> m1_subset_1(C,u1_struct_0(k3_circcomb(A,B))) ) ) ) ).
fof(t26_circcmb3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> m1_subset_1(C,u1_struct_0(k3_circcomb(A,B))) ) ) ) ).
fof(d9_circcmb3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& v1_circcomb(B)
& v2_circcomb(B)
& v5_circcomb(B)
& l1_msualg_1(B) )
=> ( m1_circcmb3(B,A)
<=> ? [C] :
( v4_msafree2(C,B)
& l3_msualg_1(C,B)
& v5_seqm_3(u4_msualg_1(B,C))
& k1_yellow_6(u4_msualg_1(B,C)) = A
& v4_circcomb(C,B) ) ) ) ) ).
fof(t27_circcmb3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k4_finseq_2(A,B),B)
& m2_relset_1(C,k4_finseq_2(A,B),B) )
=> ! [D] :
( m1_circcomb(D,A)
=> m1_circcmb3(k7_circcomb(C,D),B) ) ) ) ) ).
fof(d10_circcmb3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( m1_circcmb3(B,A)
=> ! [C] :
( ( v4_msafree2(C,B)
& l3_msualg_1(C,B) )
=> ( m2_circcmb3(C,A,B)
<=> ( v4_circcomb(C,B)
& v5_seqm_3(u4_msualg_1(B,C))
& k1_yellow_6(u4_msualg_1(B,C)) = A ) ) ) ) ) ).
fof(t28_circcmb3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k4_finseq_2(A,B),B)
& m2_relset_1(C,k4_finseq_2(A,B),B) )
=> ! [D] :
( m1_circcomb(D,A)
=> m2_circcmb3(k9_circcomb(A,B,C,D),B,k6_circcmb3(A,B,C,D)) ) ) ) ) ).
fof(t29_circcmb3,axiom,
$true ).
fof(t30_circcmb3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( m1_circcmb3(B,A)
=> ! [C] :
( m1_circcmb3(C,A)
=> ! [D] :
( m2_circcmb3(D,A,B)
=> ! [E] :
( m2_circcmb3(E,A,C)
=> r2_circcomb(B,C,D,E) ) ) ) ) ) ).
fof(t31_circcmb3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( m1_circcmb3(B,A)
=> ! [C] :
( m1_circcmb3(C,A)
=> ! [D] :
( m2_circcmb3(D,A,B)
=> ! [E] :
( m2_circcmb3(E,A,C)
=> ( v4_msafree2(k4_circcomb(B,C,D,E),k3_circcomb(B,C))
& l3_msualg_1(k4_circcomb(B,C,D,E),k3_circcomb(B,C)) ) ) ) ) ) ) ).
fof(t32_circcmb3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( m1_circcmb3(B,A)
=> ! [C] :
( m1_circcmb3(C,A)
=> ! [D] :
( m2_circcmb3(D,A,B)
=> ! [E] :
( m2_circcmb3(E,A,C)
=> v4_circcomb(k4_circcomb(B,C,D,E),k3_circcomb(B,C)) ) ) ) ) ) ).
fof(t33_circcmb3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( m1_circcmb3(B,A)
=> ! [C] :
( m1_circcmb3(C,A)
=> ! [D] :
( m2_circcmb3(D,A,B)
=> ! [E] :
( m2_circcmb3(E,A,C)
=> ( v5_seqm_3(u4_msualg_1(k3_circcomb(B,C),k4_circcomb(B,C,D,E)))
& k1_yellow_6(u4_msualg_1(k3_circcomb(B,C),k4_circcomb(B,C,D,E))) = A ) ) ) ) ) ) ).
fof(t34_circcmb3,axiom,
! [A,B] :
( r2_hidden(k6_classes1(A),k6_classes1(k4_tarski(A,B)))
& r2_hidden(k6_classes1(B),k6_classes1(k4_tarski(A,B))) ) ).
fof(t35_circcmb3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_group_1(A)
& ~ v2_msualg_1(A)
& v1_circcomb(A)
& v2_circcomb(A)
& v5_circcomb(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v4_msafree2(B,A)
& l3_msualg_1(B,A) )
=> ( v4_circcomb(B,A)
=> v3_circcmb3(B,A) ) ) ) ).
fof(t36_circcmb3,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( r2_hidden(B,k1_relat_1(A))
=> k5_relat_1(k5_facirc_1(B),A) = k5_facirc_1(k1_funct_1(A,B)) ) ) ).
fof(t37_circcmb3,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C,D,E] :
( ( r2_hidden(B,k1_relat_1(A))
& r2_hidden(C,k1_relat_1(A))
& r2_hidden(D,k1_relat_1(A))
& r2_hidden(E,k1_relat_1(A)) )
=> k5_relat_1(k3_circcmb3(B,C,D,E),A) = k3_circcmb3(k1_funct_1(A,B),k1_funct_1(A,C),k1_funct_1(A,D),k1_funct_1(A,E)) ) ) ).
fof(t38_circcmb3,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C,D,E,F] :
( ( r2_hidden(B,k1_relat_1(A))
& r2_hidden(C,k1_relat_1(A))
& r2_hidden(D,k1_relat_1(A))
& r2_hidden(E,k1_relat_1(A))
& r2_hidden(F,k1_relat_1(A)) )
=> k5_relat_1(k4_circcmb3(B,C,D,E,F),A) = k4_circcmb3(k1_funct_1(A,B),k1_funct_1(A,C),k1_funct_1(A,D),k1_funct_1(A,E),k1_funct_1(A,F)) ) ) ).
fof(t39_circcmb3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k4_finseq_2(A,B),B)
& m2_relset_1(C,k4_finseq_2(A,B),B) )
=> ! [D] :
( m1_circcomb(D,A)
=> ! [E] :
( m1_circcmb3(E,B)
=> ( r1_tarski(k2_relat_1(D),u1_struct_0(E))
=> ( r2_hidden(k5_circcmb3(k6_circcmb3(A,B,C,D)),k2_msafree2(E))
| k2_msafree2(k8_circcmb3(B,E,k6_circcmb3(A,B,C,D))) = k2_msafree2(E) ) ) ) ) ) ) ) ).
fof(t40_circcmb3,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(C)
& v1_finset_1(C) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k4_finseq_2(D,C),C)
& m2_relset_1(E,k4_finseq_2(D,C),C) )
=> ! [F] :
( m1_circcomb(F,D)
=> ! [G] :
( m1_circcmb3(G,C)
=> ( ( k2_relat_1(F) = k2_xboole_0(A,B)
& r1_tarski(A,u1_struct_0(G))
& r1_xboole_0(B,k4_msafree2(G)) )
=> ( r2_hidden(k5_circcmb3(k6_circcmb3(D,C,E,F)),k2_msafree2(G))
| k2_msafree2(k8_circcmb3(C,G,k6_circcmb3(D,C,E,F))) = k2_xboole_0(k2_msafree2(G),B) ) ) ) ) ) ) ) ).
fof(t41_circcmb3,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k4_finseq_2(np__1,B),B)
& m2_relset_1(C,k4_finseq_2(np__1,B),B) )
=> ! [D] :
( m1_circcmb3(D,B)
=> ( r2_hidden(A,u1_struct_0(D))
=> ( r2_hidden(k5_circcmb3(k6_circcmb3(np__1,B,C,k5_facirc_1(A))),k2_msafree2(D))
| k2_msafree2(k8_circcmb3(B,D,k6_circcmb3(np__1,B,C,k5_facirc_1(A)))) = k2_msafree2(D) ) ) ) ) ) ).
fof(t42_circcmb3,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(C)
& v1_finset_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(np__2,C),C)
& m2_relset_1(D,k4_finseq_2(np__2,C),C) )
=> ! [E] :
( m1_circcmb3(E,C)
=> ( r2_hidden(A,u1_struct_0(E))
=> ( r2_hidden(B,k4_msafree2(E))
| r2_hidden(k5_circcmb3(k6_circcmb3(np__2,C,D,k6_facirc_1(A,B))),k2_msafree2(E))
| k2_msafree2(k8_circcmb3(C,E,k6_circcmb3(np__2,C,D,k6_facirc_1(A,B)))) = k2_xboole_0(k2_msafree2(E),k1_tarski(B)) ) ) ) ) ) ).
fof(t43_circcmb3,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(C)
& v1_finset_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(np__2,C),C)
& m2_relset_1(D,k4_finseq_2(np__2,C),C) )
=> ! [E] :
( m1_circcmb3(E,C)
=> ( r2_hidden(B,u1_struct_0(E))
=> ( r2_hidden(A,k4_msafree2(E))
| r2_hidden(k5_circcmb3(k6_circcmb3(np__2,C,D,k6_facirc_1(A,B))),k2_msafree2(E))
| k2_msafree2(k8_circcmb3(C,E,k6_circcmb3(np__2,C,D,k6_facirc_1(A,B)))) = k2_xboole_0(k2_msafree2(E),k1_tarski(A)) ) ) ) ) ) ).
fof(t44_circcmb3,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(C)
& v1_finset_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(np__2,C),C)
& m2_relset_1(D,k4_finseq_2(np__2,C),C) )
=> ! [E] :
( m1_circcmb3(E,C)
=> ( ( r2_hidden(A,u1_struct_0(E))
& r2_hidden(B,u1_struct_0(E)) )
=> ( r2_hidden(k5_circcmb3(k6_circcmb3(np__2,C,D,k6_facirc_1(A,B))),k2_msafree2(E))
| k2_msafree2(k8_circcmb3(C,E,k6_circcmb3(np__2,C,D,k6_facirc_1(A,B)))) = k2_msafree2(E) ) ) ) ) ) ).
fof(t45_circcmb3,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(D)
& v1_finset_1(D) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k4_finseq_2(np__3,D),D)
& m2_relset_1(E,k4_finseq_2(np__3,D),D) )
=> ! [F] :
( m1_circcmb3(F,D)
=> ( r2_hidden(A,u1_struct_0(F))
=> ( r2_hidden(B,k4_msafree2(F))
| r2_hidden(C,k4_msafree2(F))
| r2_hidden(k5_circcmb3(k6_circcmb3(np__3,D,E,k7_facirc_1(A,B,C))),k2_msafree2(F))
| k2_msafree2(k8_circcmb3(D,F,k6_circcmb3(np__3,D,E,k7_facirc_1(A,B,C)))) = k2_xboole_0(k2_msafree2(F),k2_tarski(B,C)) ) ) ) ) ) ).
fof(t46_circcmb3,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(D)
& v1_finset_1(D) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k4_finseq_2(np__3,D),D)
& m2_relset_1(E,k4_finseq_2(np__3,D),D) )
=> ! [F] :
( m1_circcmb3(F,D)
=> ( r2_hidden(B,u1_struct_0(F))
=> ( r2_hidden(A,k4_msafree2(F))
| r2_hidden(C,k4_msafree2(F))
| r2_hidden(k5_circcmb3(k6_circcmb3(np__3,D,E,k7_facirc_1(A,B,C))),k2_msafree2(F))
| k2_msafree2(k8_circcmb3(D,F,k6_circcmb3(np__3,D,E,k7_facirc_1(A,B,C)))) = k2_xboole_0(k2_msafree2(F),k2_tarski(A,C)) ) ) ) ) ) ).
fof(t47_circcmb3,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(D)
& v1_finset_1(D) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k4_finseq_2(np__3,D),D)
& m2_relset_1(E,k4_finseq_2(np__3,D),D) )
=> ! [F] :
( m1_circcmb3(F,D)
=> ( r2_hidden(C,u1_struct_0(F))
=> ( r2_hidden(A,k4_msafree2(F))
| r2_hidden(B,k4_msafree2(F))
| r2_hidden(k5_circcmb3(k6_circcmb3(np__3,D,E,k7_facirc_1(A,B,C))),k2_msafree2(F))
| k2_msafree2(k8_circcmb3(D,F,k6_circcmb3(np__3,D,E,k7_facirc_1(A,B,C)))) = k2_xboole_0(k2_msafree2(F),k2_tarski(A,B)) ) ) ) ) ) ).
fof(t48_circcmb3,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(D)
& v1_finset_1(D) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k4_finseq_2(np__3,D),D)
& m2_relset_1(E,k4_finseq_2(np__3,D),D) )
=> ! [F] :
( m1_circcmb3(F,D)
=> ( ( r2_hidden(A,u1_struct_0(F))
& r2_hidden(B,u1_struct_0(F)) )
=> ( r2_hidden(C,k4_msafree2(F))
| r2_hidden(k5_circcmb3(k6_circcmb3(np__3,D,E,k7_facirc_1(A,B,C))),k2_msafree2(F))
| k2_msafree2(k8_circcmb3(D,F,k6_circcmb3(np__3,D,E,k7_facirc_1(A,B,C)))) = k2_xboole_0(k2_msafree2(F),k1_tarski(C)) ) ) ) ) ) ).
fof(t49_circcmb3,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(D)
& v1_finset_1(D) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k4_finseq_2(np__3,D),D)
& m2_relset_1(E,k4_finseq_2(np__3,D),D) )
=> ! [F] :
( m1_circcmb3(F,D)
=> ( ( r2_hidden(A,u1_struct_0(F))
& r2_hidden(C,u1_struct_0(F)) )
=> ( r2_hidden(B,k4_msafree2(F))
| r2_hidden(k5_circcmb3(k6_circcmb3(np__3,D,E,k7_facirc_1(A,B,C))),k2_msafree2(F))
| k2_msafree2(k8_circcmb3(D,F,k6_circcmb3(np__3,D,E,k7_facirc_1(A,B,C)))) = k2_xboole_0(k2_msafree2(F),k1_tarski(B)) ) ) ) ) ) ).
fof(t50_circcmb3,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(D)
& v1_finset_1(D) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k4_finseq_2(np__3,D),D)
& m2_relset_1(E,k4_finseq_2(np__3,D),D) )
=> ! [F] :
( m1_circcmb3(F,D)
=> ( ( r2_hidden(B,u1_struct_0(F))
& r2_hidden(C,u1_struct_0(F)) )
=> ( r2_hidden(A,k4_msafree2(F))
| r2_hidden(k5_circcmb3(k6_circcmb3(np__3,D,E,k7_facirc_1(A,B,C))),k2_msafree2(F))
| k2_msafree2(k8_circcmb3(D,F,k6_circcmb3(np__3,D,E,k7_facirc_1(A,B,C)))) = k2_xboole_0(k2_msafree2(F),k1_tarski(A)) ) ) ) ) ) ).
fof(t51_circcmb3,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(D)
& v1_finset_1(D) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k4_finseq_2(np__3,D),D)
& m2_relset_1(E,k4_finseq_2(np__3,D),D) )
=> ! [F] :
( m1_circcmb3(F,D)
=> ( ( r2_hidden(A,u1_struct_0(F))
& r2_hidden(B,u1_struct_0(F))
& r2_hidden(C,u1_struct_0(F)) )
=> ( r2_hidden(k5_circcmb3(k6_circcmb3(np__3,D,E,k7_facirc_1(A,B,C))),k2_msafree2(F))
| k2_msafree2(k8_circcmb3(D,F,k6_circcmb3(np__3,D,E,k7_facirc_1(A,B,C)))) = k2_msafree2(F) ) ) ) ) ) ).
fof(t52_circcmb3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( ( v6_group_1(B)
& m1_circcmb3(B,A) )
=> ! [C] :
( m2_circcmb3(C,A,B)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k4_finseq_2(D,A),A)
& m2_relset_1(E,k4_finseq_2(D,A),A) )
=> ! [F] :
( m1_circcomb(F,D)
=> ( ~ r2_hidden(k5_circcmb3(k6_circcmb3(D,A,E,F)),k2_msafree2(B))
=> ! [G] :
( m1_subset_1(G,k4_card_3(u4_msualg_1(k8_circcmb3(A,B,k6_circcmb3(D,A,E,F)),k9_circcmb3(A,B,k6_circcmb3(D,A,E,F),C,k7_circcmb3(D,A,E,F)))))
=> ! [H] :
( m1_subset_1(H,k4_card_3(u4_msualg_1(B,C)))
=> ( H = k7_relat_1(G,u1_struct_0(B))
=> r1_xreal_0(k2_circcmb3(k8_circcmb3(A,B,k6_circcmb3(D,A,E,F)),k9_circcmb3(A,B,k6_circcmb3(D,A,E,F),C,k7_circcmb3(D,A,E,F)),G),k1_nat_1(np__1,k2_circcmb3(B,C,H))) ) ) ) ) ) ) ) ) ) ) ).
fof(d11_circcmb3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ( v6_circcmb3(A)
<=> ~ v2_facirc_1(k2_msafree2(A)) ) ) ).
fof(t53_circcmb3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_circcmb3(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v1_facirc_1(B)
=> r2_hidden(B,k3_msafree2(A)) ) ) ) ).
fof(t54_circcmb3,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ! [B] :
( v1_relat_1(B)
=> ~ r2_hidden(A,B) ) ) ).
fof(t55_circcmb3,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k4_finseq_2(np__1,B),B)
& m2_relset_1(C,k4_finseq_2(np__1,B),B) )
=> ! [D] :
( ( v6_circcmb3(D)
& m1_circcmb3(D,B) )
=> ( ~ ( ~ r2_hidden(A,u1_struct_0(D))
& v1_facirc_1(A) )
=> v6_circcmb3(k8_circcmb3(B,D,k6_circcmb3(np__1,B,C,k5_facirc_1(A)))) ) ) ) ) ).
fof(t56_circcmb3,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(C)
& v1_finset_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(np__2,C),C)
& m2_relset_1(D,k4_finseq_2(np__2,C),C) )
=> ! [E] :
( ( v6_circcmb3(E)
& m1_circcmb3(E,C) )
=> ~ ( ~ ( ~ r2_hidden(A,u1_struct_0(E))
& v1_facirc_1(A) )
& ~ ( ~ r2_hidden(B,u1_struct_0(E))
& v1_facirc_1(B) )
& ~ v6_circcmb3(k8_circcmb3(C,E,k6_circcmb3(np__2,C,D,k6_facirc_1(A,B)))) ) ) ) ) ).
fof(t57_circcmb3,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(D)
& v1_finset_1(D) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k4_finseq_2(np__3,D),D)
& m2_relset_1(E,k4_finseq_2(np__3,D),D) )
=> ! [F] :
( ( v6_circcmb3(F)
& m1_circcmb3(F,D) )
=> ~ ( ~ ( ~ r2_hidden(A,u1_struct_0(F))
& v1_facirc_1(A) )
& ~ ( ~ r2_hidden(B,u1_struct_0(F))
& v1_facirc_1(B) )
& ~ ( ~ r2_hidden(C,u1_struct_0(F))
& v1_facirc_1(C) )
& ~ v6_circcmb3(k8_circcmb3(D,F,k6_circcmb3(np__3,D,E,k7_facirc_1(A,B,C)))) ) ) ) ) ).
fof(s1_circcmb3,axiom,
? [A] :
( v4_circcmb3(A)
& l1_msualg_1(A)
& ? [B] :
( v4_msafree2(B,A)
& v5_circcmb3(B,A)
& l3_msualg_1(B,A)
& k2_msafree2(A) = k1_tarski(f1_s1_circcmb3)
& ! [C] :
( m1_subset_1(C,k4_card_3(u4_msualg_1(A,B)))
=> k1_funct_1(k1_circcmb3(A,B,C),k5_circcmb3(A)) = f3_s1_circcmb3(k1_funct_1(C,f1_s1_circcmb3)) ) ) ) ).
fof(s2_circcmb3,axiom,
? [A] :
( v4_circcmb3(A)
& l1_msualg_1(A)
& ? [B] :
( v4_msafree2(B,A)
& v5_circcmb3(B,A)
& l3_msualg_1(B,A)
& k2_msafree2(A) = k2_tarski(f1_s2_circcmb3,f2_s2_circcmb3)
& ! [C] :
( m1_subset_1(C,k4_card_3(u4_msualg_1(A,B)))
=> k1_funct_1(k1_circcmb3(A,B,C),k5_circcmb3(A)) = f4_s2_circcmb3(k1_funct_1(C,f1_s2_circcmb3),k1_funct_1(C,f2_s2_circcmb3)) ) ) ) ).
fof(s3_circcmb3,axiom,
? [A] :
( v4_circcmb3(A)
& l1_msualg_1(A)
& ? [B] :
( v4_msafree2(B,A)
& v5_circcmb3(B,A)
& l3_msualg_1(B,A)
& k2_msafree2(A) = k1_enumset1(f1_s3_circcmb3,f2_s3_circcmb3,f3_s3_circcmb3)
& ! [C] :
( m1_subset_1(C,k4_card_3(u4_msualg_1(A,B)))
=> k1_funct_1(k1_circcmb3(A,B,C),k5_circcmb3(A)) = f5_s3_circcmb3(k1_funct_1(C,f1_s3_circcmb3),k1_funct_1(C,f2_s3_circcmb3),k1_funct_1(C,f3_s3_circcmb3)) ) ) ) ).
fof(s4_circcmb3,axiom,
? [A] :
( v4_circcmb3(A)
& l1_msualg_1(A)
& ? [B] :
( v4_msafree2(B,A)
& v5_circcmb3(B,A)
& l3_msualg_1(B,A)
& k2_msafree2(A) = k2_enumset1(f1_s4_circcmb3,f2_s4_circcmb3,f3_s4_circcmb3,f4_s4_circcmb3)
& ! [C] :
( m1_subset_1(C,k4_card_3(u4_msualg_1(A,B)))
=> k1_funct_1(k1_circcmb3(A,B,C),k5_circcmb3(A)) = f6_s4_circcmb3(k1_funct_1(C,f1_s4_circcmb3),k1_funct_1(C,f2_s4_circcmb3),k1_funct_1(C,f3_s4_circcmb3),k1_funct_1(C,f4_s4_circcmb3)) ) ) ) ).
fof(s5_circcmb3,axiom,
? [A] :
( v4_circcmb3(A)
& l1_msualg_1(A)
& ? [B] :
( v4_msafree2(B,A)
& v5_circcmb3(B,A)
& l3_msualg_1(B,A)
& k2_msafree2(A) = k3_enumset1(f1_s5_circcmb3,f2_s5_circcmb3,f3_s5_circcmb3,f4_s5_circcmb3,f5_s5_circcmb3)
& ! [C] :
( m1_subset_1(C,k4_card_3(u4_msualg_1(A,B)))
=> k1_funct_1(k1_circcmb3(A,B,C),k5_circcmb3(A)) = f7_s5_circcmb3(k1_funct_1(C,f1_s5_circcmb3),k1_funct_1(C,f2_s5_circcmb3),k1_funct_1(C,f3_s5_circcmb3),k1_funct_1(C,f4_s5_circcmb3),k1_funct_1(C,f5_s5_circcmb3)) ) ) ) ).
fof(s6_circcmb3,axiom,
( ? [A] :
( v1_funct_1(A)
& v1_funct_2(A,k4_finseq_2(np__1,f1_s6_circcmb3),f1_s6_circcmb3)
& m2_relset_1(A,k4_finseq_2(np__1,f1_s6_circcmb3),f1_s6_circcmb3)
& ! [B] :
( m1_subset_1(B,f1_s6_circcmb3)
=> k8_funct_2(k4_finseq_2(np__1,f1_s6_circcmb3),f1_s6_circcmb3,A,k13_binarith(f1_s6_circcmb3,B)) = f2_s6_circcmb3(B) ) )
& ! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k4_finseq_2(np__1,f1_s6_circcmb3),f1_s6_circcmb3)
& m2_relset_1(A,k4_finseq_2(np__1,f1_s6_circcmb3),f1_s6_circcmb3) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k4_finseq_2(np__1,f1_s6_circcmb3),f1_s6_circcmb3)
& m2_relset_1(B,k4_finseq_2(np__1,f1_s6_circcmb3),f1_s6_circcmb3) )
=> ( ( ! [C] :
( m1_subset_1(C,f1_s6_circcmb3)
=> k8_funct_2(k4_finseq_2(np__1,f1_s6_circcmb3),f1_s6_circcmb3,A,k13_binarith(f1_s6_circcmb3,C)) = f2_s6_circcmb3(C) )
& ! [C] :
( m1_subset_1(C,f1_s6_circcmb3)
=> k8_funct_2(k4_finseq_2(np__1,f1_s6_circcmb3),f1_s6_circcmb3,B,k13_binarith(f1_s6_circcmb3,C)) = f2_s6_circcmb3(C) ) )
=> A = B ) ) ) ) ).
fof(s7_circcmb3,axiom,
( ? [A] :
( v1_funct_1(A)
& v1_funct_2(A,k4_finseq_2(np__2,f1_s7_circcmb3),f1_s7_circcmb3)
& m2_relset_1(A,k4_finseq_2(np__2,f1_s7_circcmb3),f1_s7_circcmb3)
& ! [B] :
( m1_subset_1(B,f1_s7_circcmb3)
=> ! [C] :
( m1_subset_1(C,f1_s7_circcmb3)
=> k1_funct_1(A,k6_facirc_1(B,C)) = f2_s7_circcmb3(B,C) ) ) )
& ! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k4_finseq_2(np__2,f1_s7_circcmb3),f1_s7_circcmb3)
& m2_relset_1(A,k4_finseq_2(np__2,f1_s7_circcmb3),f1_s7_circcmb3) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k4_finseq_2(np__2,f1_s7_circcmb3),f1_s7_circcmb3)
& m2_relset_1(B,k4_finseq_2(np__2,f1_s7_circcmb3),f1_s7_circcmb3) )
=> ( ( ! [C] :
( m1_subset_1(C,f1_s7_circcmb3)
=> ! [D] :
( m1_subset_1(D,f1_s7_circcmb3)
=> k1_funct_1(A,k6_facirc_1(C,D)) = f2_s7_circcmb3(C,D) ) )
& ! [C] :
( m1_subset_1(C,f1_s7_circcmb3)
=> ! [D] :
( m1_subset_1(D,f1_s7_circcmb3)
=> k1_funct_1(B,k6_facirc_1(C,D)) = f2_s7_circcmb3(C,D) ) ) )
=> A = B ) ) ) ) ).
fof(s8_circcmb3,axiom,
( ? [A] :
( v1_funct_1(A)
& v1_funct_2(A,k4_finseq_2(np__3,f1_s8_circcmb3),f1_s8_circcmb3)
& m2_relset_1(A,k4_finseq_2(np__3,f1_s8_circcmb3),f1_s8_circcmb3)
& ! [B] :
( m1_subset_1(B,f1_s8_circcmb3)
=> ! [C] :
( m1_subset_1(C,f1_s8_circcmb3)
=> ! [D] :
( m1_subset_1(D,f1_s8_circcmb3)
=> k1_funct_1(A,k7_facirc_1(B,C,D)) = f2_s8_circcmb3(B,C,D) ) ) ) )
& ! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k4_finseq_2(np__3,f1_s8_circcmb3),f1_s8_circcmb3)
& m2_relset_1(A,k4_finseq_2(np__3,f1_s8_circcmb3),f1_s8_circcmb3) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k4_finseq_2(np__3,f1_s8_circcmb3),f1_s8_circcmb3)
& m2_relset_1(B,k4_finseq_2(np__3,f1_s8_circcmb3),f1_s8_circcmb3) )
=> ( ( ! [C] :
( m1_subset_1(C,f1_s8_circcmb3)
=> ! [D] :
( m1_subset_1(D,f1_s8_circcmb3)
=> ! [E] :
( m1_subset_1(E,f1_s8_circcmb3)
=> k1_funct_1(A,k7_facirc_1(C,D,E)) = f2_s8_circcmb3(C,D,E) ) ) )
& ! [C] :
( m1_subset_1(C,f1_s8_circcmb3)
=> ! [D] :
( m1_subset_1(D,f1_s8_circcmb3)
=> ! [E] :
( m1_subset_1(E,f1_s8_circcmb3)
=> k1_funct_1(B,k7_facirc_1(C,D,E)) = f2_s8_circcmb3(C,D,E) ) ) ) )
=> A = B ) ) ) ) ).
fof(s9_circcmb3,axiom,
( ! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k4_finseq_2(np__1,f2_s9_circcmb3),f2_s9_circcmb3)
& m2_relset_1(A,k4_finseq_2(np__1,f2_s9_circcmb3),f2_s9_circcmb3) )
=> ( A = f4_s9_circcmb3
<=> ! [B] :
( m1_subset_1(B,f2_s9_circcmb3)
=> k8_funct_2(k4_finseq_2(np__1,f2_s9_circcmb3),f2_s9_circcmb3,A,k13_binarith(f2_s9_circcmb3,B)) = f3_s9_circcmb3(B) ) ) )
=> ! [A] :
( m1_subset_1(A,k4_card_3(u4_msualg_1(k7_circcomb(f4_s9_circcmb3,k5_facirc_1(f1_s9_circcmb3)),k7_circcmb3(np__1,f2_s9_circcmb3,f4_s9_circcmb3,k5_facirc_1(f1_s9_circcmb3)))))
=> ! [B] :
( m1_subset_1(B,f2_s9_circcmb3)
=> ( B = k1_funct_1(A,f1_s9_circcmb3)
=> k1_funct_1(k1_circcmb3(k7_circcomb(f4_s9_circcmb3,k5_facirc_1(f1_s9_circcmb3)),k7_circcmb3(np__1,f2_s9_circcmb3,f4_s9_circcmb3,k5_facirc_1(f1_s9_circcmb3)),A),k5_circcmb3(k6_circcmb3(np__1,f2_s9_circcmb3,f4_s9_circcmb3,k5_facirc_1(f1_s9_circcmb3)))) = f3_s9_circcmb3(B) ) ) ) ) ).
fof(s10_circcmb3,axiom,
( ! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k4_finseq_2(np__2,f3_s10_circcmb3),f3_s10_circcmb3)
& m2_relset_1(A,k4_finseq_2(np__2,f3_s10_circcmb3),f3_s10_circcmb3) )
=> ( A = f5_s10_circcmb3
<=> ! [B] :
( m1_subset_1(B,f3_s10_circcmb3)
=> ! [C] :
( m1_subset_1(C,f3_s10_circcmb3)
=> k1_funct_1(A,k6_facirc_1(B,C)) = f4_s10_circcmb3(B,C) ) ) ) )
=> ! [A] :
( m1_subset_1(A,k4_card_3(u4_msualg_1(k7_circcomb(f5_s10_circcmb3,k6_facirc_1(f1_s10_circcmb3,f2_s10_circcmb3)),k7_circcmb3(np__2,f3_s10_circcmb3,f5_s10_circcmb3,k6_facirc_1(f1_s10_circcmb3,f2_s10_circcmb3)))))
=> ! [B] :
( m1_subset_1(B,f3_s10_circcmb3)
=> ! [C] :
( m1_subset_1(C,f3_s10_circcmb3)
=> ( ( B = k1_funct_1(A,f1_s10_circcmb3)
& C = k1_funct_1(A,f2_s10_circcmb3) )
=> k1_funct_1(k1_circcmb3(k7_circcomb(f5_s10_circcmb3,k6_facirc_1(f1_s10_circcmb3,f2_s10_circcmb3)),k7_circcmb3(np__2,f3_s10_circcmb3,f5_s10_circcmb3,k6_facirc_1(f1_s10_circcmb3,f2_s10_circcmb3)),A),k5_circcmb3(k6_circcmb3(np__2,f3_s10_circcmb3,f5_s10_circcmb3,k6_facirc_1(f1_s10_circcmb3,f2_s10_circcmb3)))) = f4_s10_circcmb3(B,C) ) ) ) ) ) ).
fof(s11_circcmb3,axiom,
( ! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k4_finseq_2(np__3,f4_s11_circcmb3),f4_s11_circcmb3)
& m2_relset_1(A,k4_finseq_2(np__3,f4_s11_circcmb3),f4_s11_circcmb3) )
=> ( A = f6_s11_circcmb3
<=> ! [B] :
( m1_subset_1(B,f4_s11_circcmb3)
=> ! [C] :
( m1_subset_1(C,f4_s11_circcmb3)
=> ! [D] :
( m1_subset_1(D,f4_s11_circcmb3)
=> k1_funct_1(A,k7_facirc_1(B,C,D)) = f5_s11_circcmb3(B,C,D) ) ) ) ) )
=> ! [A] :
( m1_subset_1(A,k4_card_3(u4_msualg_1(k7_circcomb(f6_s11_circcmb3,k7_facirc_1(f1_s11_circcmb3,f2_s11_circcmb3,f3_s11_circcmb3)),k7_circcmb3(np__3,f4_s11_circcmb3,f6_s11_circcmb3,k7_facirc_1(f1_s11_circcmb3,f2_s11_circcmb3,f3_s11_circcmb3)))))
=> ! [B] :
( m1_subset_1(B,f4_s11_circcmb3)
=> ! [C] :
( m1_subset_1(C,f4_s11_circcmb3)
=> ! [D] :
( m1_subset_1(D,f4_s11_circcmb3)
=> ( ( B = k1_funct_1(A,f1_s11_circcmb3)
& C = k1_funct_1(A,f2_s11_circcmb3)
& D = k1_funct_1(A,f3_s11_circcmb3) )
=> k1_funct_1(k1_circcmb3(k7_circcomb(f6_s11_circcmb3,k7_facirc_1(f1_s11_circcmb3,f2_s11_circcmb3,f3_s11_circcmb3)),k7_circcmb3(np__3,f4_s11_circcmb3,f6_s11_circcmb3,k7_facirc_1(f1_s11_circcmb3,f2_s11_circcmb3,f3_s11_circcmb3)),A),k5_circcmb3(k6_circcmb3(np__3,f4_s11_circcmb3,f6_s11_circcmb3,k7_facirc_1(f1_s11_circcmb3,f2_s11_circcmb3,f3_s11_circcmb3)))) = f5_s11_circcmb3(B,C,D) ) ) ) ) ) ) ).
fof(s12_circcmb3,axiom,
( ! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k4_finseq_2(np__4,f5_s12_circcmb3),f5_s12_circcmb3)
& m2_relset_1(A,k4_finseq_2(np__4,f5_s12_circcmb3),f5_s12_circcmb3) )
=> ( A = f7_s12_circcmb3
<=> ! [B] :
( m1_subset_1(B,f5_s12_circcmb3)
=> ! [C] :
( m1_subset_1(C,f5_s12_circcmb3)
=> ! [D] :
( m1_subset_1(D,f5_s12_circcmb3)
=> ! [E] :
( m1_subset_1(E,f5_s12_circcmb3)
=> k1_funct_1(A,k3_circcmb3(B,C,D,E)) = f6_s12_circcmb3(B,C,D,E) ) ) ) ) ) )
=> ! [A] :
( m1_subset_1(A,k4_card_3(u4_msualg_1(k7_circcomb(f7_s12_circcmb3,k3_circcmb3(f1_s12_circcmb3,f2_s12_circcmb3,f3_s12_circcmb3,f4_s12_circcmb3)),k7_circcmb3(np__4,f5_s12_circcmb3,f7_s12_circcmb3,k3_circcmb3(f1_s12_circcmb3,f2_s12_circcmb3,f3_s12_circcmb3,f4_s12_circcmb3)))))
=> ! [B] :
( m1_subset_1(B,f5_s12_circcmb3)
=> ! [C] :
( m1_subset_1(C,f5_s12_circcmb3)
=> ! [D] :
( m1_subset_1(D,f5_s12_circcmb3)
=> ! [E] :
( m1_subset_1(E,f5_s12_circcmb3)
=> ( ( B = k1_funct_1(A,f1_s12_circcmb3)
& C = k1_funct_1(A,f2_s12_circcmb3)
& D = k1_funct_1(A,f3_s12_circcmb3)
& E = k1_funct_1(A,f4_s12_circcmb3) )
=> k1_funct_1(k1_circcmb3(k7_circcomb(f7_s12_circcmb3,k3_circcmb3(f1_s12_circcmb3,f2_s12_circcmb3,f3_s12_circcmb3,f4_s12_circcmb3)),k7_circcmb3(np__4,f5_s12_circcmb3,f7_s12_circcmb3,k3_circcmb3(f1_s12_circcmb3,f2_s12_circcmb3,f3_s12_circcmb3,f4_s12_circcmb3)),A),k5_circcmb3(k6_circcmb3(np__4,f5_s12_circcmb3,f7_s12_circcmb3,k3_circcmb3(f1_s12_circcmb3,f2_s12_circcmb3,f3_s12_circcmb3,f4_s12_circcmb3)))) = f6_s12_circcmb3(B,C,D,E) ) ) ) ) ) ) ) ).
fof(s13_circcmb3,axiom,
( ! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k4_finseq_2(np__5,f6_s13_circcmb3),f6_s13_circcmb3)
& m2_relset_1(A,k4_finseq_2(np__5,f6_s13_circcmb3),f6_s13_circcmb3) )
=> ( A = f8_s13_circcmb3
<=> ! [B] :
( m1_subset_1(B,f6_s13_circcmb3)
=> ! [C] :
( m1_subset_1(C,f6_s13_circcmb3)
=> ! [D] :
( m1_subset_1(D,f6_s13_circcmb3)
=> ! [E] :
( m1_subset_1(E,f6_s13_circcmb3)
=> ! [F] :
( m1_subset_1(F,f6_s13_circcmb3)
=> k1_funct_1(A,k4_circcmb3(B,C,D,E,F)) = f7_s13_circcmb3(B,C,D,E,F) ) ) ) ) ) ) )
=> ! [A] :
( m1_subset_1(A,k4_card_3(u4_msualg_1(k7_circcomb(f8_s13_circcmb3,k4_circcmb3(f1_s13_circcmb3,f2_s13_circcmb3,f3_s13_circcmb3,f4_s13_circcmb3,f5_s13_circcmb3)),k7_circcmb3(np__5,f6_s13_circcmb3,f8_s13_circcmb3,k4_circcmb3(f1_s13_circcmb3,f2_s13_circcmb3,f3_s13_circcmb3,f4_s13_circcmb3,f5_s13_circcmb3)))))
=> ! [B] :
( m1_subset_1(B,f6_s13_circcmb3)
=> ! [C] :
( m1_subset_1(C,f6_s13_circcmb3)
=> ! [D] :
( m1_subset_1(D,f6_s13_circcmb3)
=> ! [E] :
( m1_subset_1(E,f6_s13_circcmb3)
=> ! [F] :
( m1_subset_1(F,f6_s13_circcmb3)
=> ( ( B = k1_funct_1(A,f1_s13_circcmb3)
& C = k1_funct_1(A,f2_s13_circcmb3)
& D = k1_funct_1(A,f3_s13_circcmb3)
& E = k1_funct_1(A,f4_s13_circcmb3)
& F = k1_funct_1(A,f5_s13_circcmb3) )
=> k1_funct_1(k1_circcmb3(k7_circcomb(f8_s13_circcmb3,k4_circcmb3(f1_s13_circcmb3,f2_s13_circcmb3,f3_s13_circcmb3,f4_s13_circcmb3,f5_s13_circcmb3)),k7_circcmb3(np__5,f6_s13_circcmb3,f8_s13_circcmb3,k4_circcmb3(f1_s13_circcmb3,f2_s13_circcmb3,f3_s13_circcmb3,f4_s13_circcmb3,f5_s13_circcmb3)),A),k5_circcmb3(k6_circcmb3(np__5,f6_s13_circcmb3,f8_s13_circcmb3,k4_circcmb3(f1_s13_circcmb3,f2_s13_circcmb3,f3_s13_circcmb3,f4_s13_circcmb3,f5_s13_circcmb3)))) = f7_s13_circcmb3(B,C,D,E,F) ) ) ) ) ) ) ) ) ).
fof(s14_circcmb3,axiom,
( ( ! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k4_finseq_2(np__1,f2_s14_circcmb3),f2_s14_circcmb3)
& m2_relset_1(A,k4_finseq_2(np__1,f2_s14_circcmb3),f2_s14_circcmb3) )
=> ( A = f6_s14_circcmb3
<=> ! [B] :
( m1_subset_1(B,f2_s14_circcmb3)
=> k8_funct_2(k4_finseq_2(np__1,f2_s14_circcmb3),f2_s14_circcmb3,A,k13_binarith(f2_s14_circcmb3,B)) = f3_s14_circcmb3(B) ) ) )
& ~ r2_hidden(k5_circcmb3(k6_circcmb3(np__1,f2_s14_circcmb3,f6_s14_circcmb3,k5_facirc_1(f1_s14_circcmb3))),k2_msafree2(f4_s14_circcmb3)) )
=> ! [A] :
( m1_subset_1(A,k4_card_3(u4_msualg_1(k8_circcmb3(f2_s14_circcmb3,f4_s14_circcmb3,k6_circcmb3(np__1,f2_s14_circcmb3,f6_s14_circcmb3,k5_facirc_1(f1_s14_circcmb3))),k9_circcmb3(f2_s14_circcmb3,f4_s14_circcmb3,k6_circcmb3(np__1,f2_s14_circcmb3,f6_s14_circcmb3,k5_facirc_1(f1_s14_circcmb3)),f5_s14_circcmb3,k7_circcmb3(np__1,f2_s14_circcmb3,f6_s14_circcmb3,k5_facirc_1(f1_s14_circcmb3))))))
=> ! [B] :
( m1_subset_1(B,k4_card_3(u4_msualg_1(f4_s14_circcmb3,f5_s14_circcmb3)))
=> ( B = k7_relat_1(A,u1_struct_0(f4_s14_circcmb3))
=> ! [C] :
( m1_subset_1(C,f2_s14_circcmb3)
=> ~ ( ( r2_hidden(f1_s14_circcmb3,k4_msafree2(f4_s14_circcmb3))
=> C = k1_funct_1(k1_circcmb3(f4_s14_circcmb3,f5_s14_circcmb3,B),f1_s14_circcmb3) )
& ( ~ r2_hidden(f1_s14_circcmb3,k4_msafree2(f4_s14_circcmb3))
=> C = k1_funct_1(A,f1_s14_circcmb3) )
& k1_funct_1(k1_circcmb3(k8_circcmb3(f2_s14_circcmb3,f4_s14_circcmb3,k6_circcmb3(np__1,f2_s14_circcmb3,f6_s14_circcmb3,k5_facirc_1(f1_s14_circcmb3))),k9_circcmb3(f2_s14_circcmb3,f4_s14_circcmb3,k6_circcmb3(np__1,f2_s14_circcmb3,f6_s14_circcmb3,k5_facirc_1(f1_s14_circcmb3)),f5_s14_circcmb3,k7_circcmb3(np__1,f2_s14_circcmb3,f6_s14_circcmb3,k5_facirc_1(f1_s14_circcmb3))),A),k5_circcmb3(k6_circcmb3(np__1,f2_s14_circcmb3,f6_s14_circcmb3,k5_facirc_1(f1_s14_circcmb3)))) != f3_s14_circcmb3(C) ) ) ) ) ) ) ).
fof(s15_circcmb3,axiom,
( ( ! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k4_finseq_2(np__2,f3_s15_circcmb3),f3_s15_circcmb3)
& m2_relset_1(A,k4_finseq_2(np__2,f3_s15_circcmb3),f3_s15_circcmb3) )
=> ( A = f7_s15_circcmb3
<=> ! [B] :
( m1_subset_1(B,f3_s15_circcmb3)
=> ! [C] :
( m1_subset_1(C,f3_s15_circcmb3)
=> k1_funct_1(A,k6_facirc_1(B,C)) = f4_s15_circcmb3(B,C) ) ) ) )
& ~ r2_hidden(k5_circcmb3(k6_circcmb3(np__2,f3_s15_circcmb3,f7_s15_circcmb3,k6_facirc_1(f1_s15_circcmb3,f2_s15_circcmb3))),k2_msafree2(f5_s15_circcmb3)) )
=> ! [A] :
( m1_subset_1(A,k4_card_3(u4_msualg_1(k8_circcmb3(f3_s15_circcmb3,f5_s15_circcmb3,k6_circcmb3(np__2,f3_s15_circcmb3,f7_s15_circcmb3,k6_facirc_1(f1_s15_circcmb3,f2_s15_circcmb3))),k9_circcmb3(f3_s15_circcmb3,f5_s15_circcmb3,k6_circcmb3(np__2,f3_s15_circcmb3,f7_s15_circcmb3,k6_facirc_1(f1_s15_circcmb3,f2_s15_circcmb3)),f6_s15_circcmb3,k7_circcmb3(np__2,f3_s15_circcmb3,f7_s15_circcmb3,k6_facirc_1(f1_s15_circcmb3,f2_s15_circcmb3))))))
=> ! [B] :
( m1_subset_1(B,k4_card_3(u4_msualg_1(f5_s15_circcmb3,f6_s15_circcmb3)))
=> ( B = k7_relat_1(A,u1_struct_0(f5_s15_circcmb3))
=> ! [C] :
( m1_subset_1(C,f3_s15_circcmb3)
=> ! [D] :
( m1_subset_1(D,f3_s15_circcmb3)
=> ~ ( ( r2_hidden(f1_s15_circcmb3,k4_msafree2(f5_s15_circcmb3))
=> C = k1_funct_1(k1_circcmb3(f5_s15_circcmb3,f6_s15_circcmb3,B),f1_s15_circcmb3) )
& ( ~ r2_hidden(f1_s15_circcmb3,k4_msafree2(f5_s15_circcmb3))
=> C = k1_funct_1(A,f1_s15_circcmb3) )
& ( r2_hidden(f2_s15_circcmb3,k4_msafree2(f5_s15_circcmb3))
=> D = k1_funct_1(k1_circcmb3(f5_s15_circcmb3,f6_s15_circcmb3,B),f2_s15_circcmb3) )
& ( ~ r2_hidden(f2_s15_circcmb3,k4_msafree2(f5_s15_circcmb3))
=> D = k1_funct_1(A,f2_s15_circcmb3) )
& k1_funct_1(k1_circcmb3(k8_circcmb3(f3_s15_circcmb3,f5_s15_circcmb3,k6_circcmb3(np__2,f3_s15_circcmb3,f7_s15_circcmb3,k6_facirc_1(f1_s15_circcmb3,f2_s15_circcmb3))),k9_circcmb3(f3_s15_circcmb3,f5_s15_circcmb3,k6_circcmb3(np__2,f3_s15_circcmb3,f7_s15_circcmb3,k6_facirc_1(f1_s15_circcmb3,f2_s15_circcmb3)),f6_s15_circcmb3,k7_circcmb3(np__2,f3_s15_circcmb3,f7_s15_circcmb3,k6_facirc_1(f1_s15_circcmb3,f2_s15_circcmb3))),A),k5_circcmb3(k6_circcmb3(np__2,f3_s15_circcmb3,f7_s15_circcmb3,k6_facirc_1(f1_s15_circcmb3,f2_s15_circcmb3)))) != f4_s15_circcmb3(C,D) ) ) ) ) ) ) ) ).
fof(s16_circcmb3,axiom,
( ( ! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k4_finseq_2(np__3,f4_s16_circcmb3),f4_s16_circcmb3)
& m2_relset_1(A,k4_finseq_2(np__3,f4_s16_circcmb3),f4_s16_circcmb3) )
=> ( A = f8_s16_circcmb3
<=> ! [B] :
( m1_subset_1(B,f4_s16_circcmb3)
=> ! [C] :
( m1_subset_1(C,f4_s16_circcmb3)
=> ! [D] :
( m1_subset_1(D,f4_s16_circcmb3)
=> k1_funct_1(A,k7_facirc_1(B,C,D)) = f5_s16_circcmb3(B,C,D) ) ) ) ) )
& ~ r2_hidden(k5_circcmb3(k6_circcmb3(np__3,f4_s16_circcmb3,f8_s16_circcmb3,k7_facirc_1(f1_s16_circcmb3,f2_s16_circcmb3,f3_s16_circcmb3))),k2_msafree2(f6_s16_circcmb3)) )
=> ! [A] :
( m1_subset_1(A,k4_card_3(u4_msualg_1(k8_circcmb3(f4_s16_circcmb3,f6_s16_circcmb3,k6_circcmb3(np__3,f4_s16_circcmb3,f8_s16_circcmb3,k7_facirc_1(f1_s16_circcmb3,f2_s16_circcmb3,f3_s16_circcmb3))),k9_circcmb3(f4_s16_circcmb3,f6_s16_circcmb3,k6_circcmb3(np__3,f4_s16_circcmb3,f8_s16_circcmb3,k7_facirc_1(f1_s16_circcmb3,f2_s16_circcmb3,f3_s16_circcmb3)),f7_s16_circcmb3,k7_circcmb3(np__3,f4_s16_circcmb3,f8_s16_circcmb3,k7_facirc_1(f1_s16_circcmb3,f2_s16_circcmb3,f3_s16_circcmb3))))))
=> ! [B] :
( m1_subset_1(B,k4_card_3(u4_msualg_1(f6_s16_circcmb3,f7_s16_circcmb3)))
=> ( B = k7_relat_1(A,u1_struct_0(f6_s16_circcmb3))
=> ! [C] :
( m1_subset_1(C,f4_s16_circcmb3)
=> ! [D] :
( m1_subset_1(D,f4_s16_circcmb3)
=> ! [E] :
( m1_subset_1(E,f4_s16_circcmb3)
=> ~ ( ( r2_hidden(f1_s16_circcmb3,k4_msafree2(f6_s16_circcmb3))
=> C = k1_funct_1(k1_circcmb3(f6_s16_circcmb3,f7_s16_circcmb3,B),f1_s16_circcmb3) )
& ( ~ r2_hidden(f1_s16_circcmb3,k4_msafree2(f6_s16_circcmb3))
=> C = k1_funct_1(A,f1_s16_circcmb3) )
& ( r2_hidden(f2_s16_circcmb3,k4_msafree2(f6_s16_circcmb3))
=> D = k1_funct_1(k1_circcmb3(f6_s16_circcmb3,f7_s16_circcmb3,B),f2_s16_circcmb3) )
& ( ~ r2_hidden(f2_s16_circcmb3,k4_msafree2(f6_s16_circcmb3))
=> D = k1_funct_1(A,f2_s16_circcmb3) )
& ( r2_hidden(f3_s16_circcmb3,k4_msafree2(f6_s16_circcmb3))
=> E = k1_funct_1(k1_circcmb3(f6_s16_circcmb3,f7_s16_circcmb3,B),f3_s16_circcmb3) )
& ( ~ r2_hidden(f3_s16_circcmb3,k4_msafree2(f6_s16_circcmb3))
=> E = k1_funct_1(A,f3_s16_circcmb3) )
& k1_funct_1(k1_circcmb3(k8_circcmb3(f4_s16_circcmb3,f6_s16_circcmb3,k6_circcmb3(np__3,f4_s16_circcmb3,f8_s16_circcmb3,k7_facirc_1(f1_s16_circcmb3,f2_s16_circcmb3,f3_s16_circcmb3))),k9_circcmb3(f4_s16_circcmb3,f6_s16_circcmb3,k6_circcmb3(np__3,f4_s16_circcmb3,f8_s16_circcmb3,k7_facirc_1(f1_s16_circcmb3,f2_s16_circcmb3,f3_s16_circcmb3)),f7_s16_circcmb3,k7_circcmb3(np__3,f4_s16_circcmb3,f8_s16_circcmb3,k7_facirc_1(f1_s16_circcmb3,f2_s16_circcmb3,f3_s16_circcmb3))),A),k5_circcmb3(k6_circcmb3(np__3,f4_s16_circcmb3,f8_s16_circcmb3,k7_facirc_1(f1_s16_circcmb3,f2_s16_circcmb3,f3_s16_circcmb3)))) != f5_s16_circcmb3(C,D,E) ) ) ) ) ) ) ) ) ).
fof(s17_circcmb3,axiom,
( ( ! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k4_finseq_2(np__4,f5_s17_circcmb3),f5_s17_circcmb3)
& m2_relset_1(A,k4_finseq_2(np__4,f5_s17_circcmb3),f5_s17_circcmb3) )
=> ( A = f9_s17_circcmb3
<=> ! [B] :
( m1_subset_1(B,f5_s17_circcmb3)
=> ! [C] :
( m1_subset_1(C,f5_s17_circcmb3)
=> ! [D] :
( m1_subset_1(D,f5_s17_circcmb3)
=> ! [E] :
( m1_subset_1(E,f5_s17_circcmb3)
=> k1_funct_1(A,k3_circcmb3(B,C,D,E)) = f6_s17_circcmb3(B,C,D,E) ) ) ) ) ) )
& ~ r2_hidden(k5_circcmb3(k6_circcmb3(np__4,f5_s17_circcmb3,f9_s17_circcmb3,k3_circcmb3(f1_s17_circcmb3,f2_s17_circcmb3,f3_s17_circcmb3,f4_s17_circcmb3))),k2_msafree2(f7_s17_circcmb3)) )
=> ! [A] :
( m1_subset_1(A,k4_card_3(u4_msualg_1(k8_circcmb3(f5_s17_circcmb3,f7_s17_circcmb3,k6_circcmb3(np__4,f5_s17_circcmb3,f9_s17_circcmb3,k3_circcmb3(f1_s17_circcmb3,f2_s17_circcmb3,f3_s17_circcmb3,f4_s17_circcmb3))),k9_circcmb3(f5_s17_circcmb3,f7_s17_circcmb3,k6_circcmb3(np__4,f5_s17_circcmb3,f9_s17_circcmb3,k3_circcmb3(f1_s17_circcmb3,f2_s17_circcmb3,f3_s17_circcmb3,f4_s17_circcmb3)),f8_s17_circcmb3,k7_circcmb3(np__4,f5_s17_circcmb3,f9_s17_circcmb3,k3_circcmb3(f1_s17_circcmb3,f2_s17_circcmb3,f3_s17_circcmb3,f4_s17_circcmb3))))))
=> ! [B] :
( m1_subset_1(B,k4_card_3(u4_msualg_1(f7_s17_circcmb3,f8_s17_circcmb3)))
=> ( B = k7_relat_1(A,u1_struct_0(f7_s17_circcmb3))
=> ! [C] :
( m1_subset_1(C,f5_s17_circcmb3)
=> ! [D] :
( m1_subset_1(D,f5_s17_circcmb3)
=> ! [E] :
( m1_subset_1(E,f5_s17_circcmb3)
=> ! [F] :
( m1_subset_1(F,f5_s17_circcmb3)
=> ~ ( ( r2_hidden(f1_s17_circcmb3,k4_msafree2(f7_s17_circcmb3))
=> C = k1_funct_1(k1_circcmb3(f7_s17_circcmb3,f8_s17_circcmb3,B),f1_s17_circcmb3) )
& ( ~ r2_hidden(f1_s17_circcmb3,k4_msafree2(f7_s17_circcmb3))
=> C = k1_funct_1(A,f1_s17_circcmb3) )
& ( r2_hidden(f2_s17_circcmb3,k4_msafree2(f7_s17_circcmb3))
=> D = k1_funct_1(k1_circcmb3(f7_s17_circcmb3,f8_s17_circcmb3,B),f2_s17_circcmb3) )
& ( ~ r2_hidden(f2_s17_circcmb3,k4_msafree2(f7_s17_circcmb3))
=> D = k1_funct_1(A,f2_s17_circcmb3) )
& ( r2_hidden(f3_s17_circcmb3,k4_msafree2(f7_s17_circcmb3))
=> E = k1_funct_1(k1_circcmb3(f7_s17_circcmb3,f8_s17_circcmb3,B),f3_s17_circcmb3) )
& ( ~ r2_hidden(f3_s17_circcmb3,k4_msafree2(f7_s17_circcmb3))
=> E = k1_funct_1(A,f3_s17_circcmb3) )
& ( r2_hidden(f4_s17_circcmb3,k4_msafree2(f7_s17_circcmb3))
=> F = k1_funct_1(k1_circcmb3(f7_s17_circcmb3,f8_s17_circcmb3,B),f4_s17_circcmb3) )
& ( ~ r2_hidden(f4_s17_circcmb3,k4_msafree2(f7_s17_circcmb3))
=> F = k1_funct_1(A,f4_s17_circcmb3) )
& k1_funct_1(k1_circcmb3(k8_circcmb3(f5_s17_circcmb3,f7_s17_circcmb3,k6_circcmb3(np__4,f5_s17_circcmb3,f9_s17_circcmb3,k3_circcmb3(f1_s17_circcmb3,f2_s17_circcmb3,f3_s17_circcmb3,f4_s17_circcmb3))),k9_circcmb3(f5_s17_circcmb3,f7_s17_circcmb3,k6_circcmb3(np__4,f5_s17_circcmb3,f9_s17_circcmb3,k3_circcmb3(f1_s17_circcmb3,f2_s17_circcmb3,f3_s17_circcmb3,f4_s17_circcmb3)),f8_s17_circcmb3,k7_circcmb3(np__4,f5_s17_circcmb3,f9_s17_circcmb3,k3_circcmb3(f1_s17_circcmb3,f2_s17_circcmb3,f3_s17_circcmb3,f4_s17_circcmb3))),A),k5_circcmb3(k6_circcmb3(np__4,f5_s17_circcmb3,f9_s17_circcmb3,k3_circcmb3(f1_s17_circcmb3,f2_s17_circcmb3,f3_s17_circcmb3,f4_s17_circcmb3)))) != f6_s17_circcmb3(C,D,E,F) ) ) ) ) ) ) ) ) ) ).
fof(s18_circcmb3,axiom,
( ( ! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k4_finseq_2(np__5,f6_s18_circcmb3),f6_s18_circcmb3)
& m2_relset_1(A,k4_finseq_2(np__5,f6_s18_circcmb3),f6_s18_circcmb3) )
=> ( A = f10_s18_circcmb3
<=> ! [B] :
( m1_subset_1(B,f6_s18_circcmb3)
=> ! [C] :
( m1_subset_1(C,f6_s18_circcmb3)
=> ! [D] :
( m1_subset_1(D,f6_s18_circcmb3)
=> ! [E] :
( m1_subset_1(E,f6_s18_circcmb3)
=> ! [F] :
( m1_subset_1(F,f6_s18_circcmb3)
=> k1_funct_1(A,k4_circcmb3(B,C,D,E,F)) = f7_s18_circcmb3(B,C,D,E,F) ) ) ) ) ) ) )
& ~ r2_hidden(k5_circcmb3(k6_circcmb3(np__5,f6_s18_circcmb3,f10_s18_circcmb3,k4_circcmb3(f1_s18_circcmb3,f2_s18_circcmb3,f3_s18_circcmb3,f4_s18_circcmb3,f5_s18_circcmb3))),k2_msafree2(f8_s18_circcmb3)) )
=> ! [A] :
( m1_subset_1(A,k4_card_3(u4_msualg_1(k8_circcmb3(f6_s18_circcmb3,f8_s18_circcmb3,k6_circcmb3(np__5,f6_s18_circcmb3,f10_s18_circcmb3,k4_circcmb3(f1_s18_circcmb3,f2_s18_circcmb3,f3_s18_circcmb3,f4_s18_circcmb3,f5_s18_circcmb3))),k9_circcmb3(f6_s18_circcmb3,f8_s18_circcmb3,k6_circcmb3(np__5,f6_s18_circcmb3,f10_s18_circcmb3,k4_circcmb3(f1_s18_circcmb3,f2_s18_circcmb3,f3_s18_circcmb3,f4_s18_circcmb3,f5_s18_circcmb3)),f9_s18_circcmb3,k7_circcmb3(np__5,f6_s18_circcmb3,f10_s18_circcmb3,k4_circcmb3(f1_s18_circcmb3,f2_s18_circcmb3,f3_s18_circcmb3,f4_s18_circcmb3,f5_s18_circcmb3))))))
=> ! [B] :
( m1_subset_1(B,k4_card_3(u4_msualg_1(f8_s18_circcmb3,f9_s18_circcmb3)))
=> ( B = k7_relat_1(A,u1_struct_0(f8_s18_circcmb3))
=> ! [C] :
( m1_subset_1(C,f6_s18_circcmb3)
=> ! [D] :
( m1_subset_1(D,f6_s18_circcmb3)
=> ! [E] :
( m1_subset_1(E,f6_s18_circcmb3)
=> ! [F] :
( m1_subset_1(F,f6_s18_circcmb3)
=> ! [G] :
( m1_subset_1(G,f6_s18_circcmb3)
=> ~ ( ( r2_hidden(f1_s18_circcmb3,k4_msafree2(f8_s18_circcmb3))
=> C = k1_funct_1(k1_circcmb3(f8_s18_circcmb3,f9_s18_circcmb3,B),f1_s18_circcmb3) )
& ( ~ r2_hidden(f1_s18_circcmb3,k4_msafree2(f8_s18_circcmb3))
=> C = k1_funct_1(A,f1_s18_circcmb3) )
& ( r2_hidden(f2_s18_circcmb3,k4_msafree2(f8_s18_circcmb3))
=> D = k1_funct_1(k1_circcmb3(f8_s18_circcmb3,f9_s18_circcmb3,B),f2_s18_circcmb3) )
& ( ~ r2_hidden(f2_s18_circcmb3,k4_msafree2(f8_s18_circcmb3))
=> D = k1_funct_1(A,f2_s18_circcmb3) )
& ( r2_hidden(f3_s18_circcmb3,k4_msafree2(f8_s18_circcmb3))
=> E = k1_funct_1(k1_circcmb3(f8_s18_circcmb3,f9_s18_circcmb3,B),f3_s18_circcmb3) )
& ( ~ r2_hidden(f3_s18_circcmb3,k4_msafree2(f8_s18_circcmb3))
=> E = k1_funct_1(A,f3_s18_circcmb3) )
& ( r2_hidden(f4_s18_circcmb3,k4_msafree2(f8_s18_circcmb3))
=> F = k1_funct_1(k1_circcmb3(f8_s18_circcmb3,f9_s18_circcmb3,B),f4_s18_circcmb3) )
& ( ~ r2_hidden(f4_s18_circcmb3,k4_msafree2(f8_s18_circcmb3))
=> F = k1_funct_1(A,f4_s18_circcmb3) )
& ( r2_hidden(f5_s18_circcmb3,k4_msafree2(f8_s18_circcmb3))
=> G = k1_funct_1(k1_circcmb3(f8_s18_circcmb3,f9_s18_circcmb3,B),f5_s18_circcmb3) )
& ( ~ r2_hidden(f5_s18_circcmb3,k4_msafree2(f8_s18_circcmb3))
=> G = k1_funct_1(A,f5_s18_circcmb3) )
& k1_funct_1(k1_circcmb3(k8_circcmb3(f6_s18_circcmb3,f8_s18_circcmb3,k6_circcmb3(np__5,f6_s18_circcmb3,f10_s18_circcmb3,k4_circcmb3(f1_s18_circcmb3,f2_s18_circcmb3,f3_s18_circcmb3,f4_s18_circcmb3,f5_s18_circcmb3))),k9_circcmb3(f6_s18_circcmb3,f8_s18_circcmb3,k6_circcmb3(np__5,f6_s18_circcmb3,f10_s18_circcmb3,k4_circcmb3(f1_s18_circcmb3,f2_s18_circcmb3,f3_s18_circcmb3,f4_s18_circcmb3,f5_s18_circcmb3)),f9_s18_circcmb3,k7_circcmb3(np__5,f6_s18_circcmb3,f10_s18_circcmb3,k4_circcmb3(f1_s18_circcmb3,f2_s18_circcmb3,f3_s18_circcmb3,f4_s18_circcmb3,f5_s18_circcmb3))),A),k5_circcmb3(k6_circcmb3(np__5,f6_s18_circcmb3,f10_s18_circcmb3,k4_circcmb3(f1_s18_circcmb3,f2_s18_circcmb3,f3_s18_circcmb3,f4_s18_circcmb3,f5_s18_circcmb3)))) != f7_s18_circcmb3(C,D,E,F,G) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_m1_circcmb3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( m1_circcmb3(B,A)
=> ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& v1_circcomb(B)
& v2_circcomb(B)
& v5_circcomb(B)
& l1_msualg_1(B) ) ) ) ).
fof(existence_m1_circcmb3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ? [B] : m1_circcmb3(B,A) ) ).
fof(dt_m2_circcmb3,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& m1_circcmb3(B,A) )
=> ! [C] :
( m2_circcmb3(C,A,B)
=> ( v4_msafree2(C,B)
& l3_msualg_1(C,B) ) ) ) ).
fof(existence_m2_circcmb3,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& m1_circcmb3(B,A) )
=> ? [C] : m2_circcmb3(C,A,B) ) ).
fof(dt_k1_circcmb3,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(k1_circcmb3(A,B,C),k4_card_3(u4_msualg_1(A,B))) ) ).
fof(dt_k2_circcmb3,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))) )
=> m2_subset_1(k2_circcmb3(A,B,C),k1_numbers,k5_numbers) ) ).
fof(dt_k3_circcmb3,axiom,
! [A,B,C,D] : m1_circcomb(k3_circcmb3(A,B,C,D),np__4) ).
fof(redefinition_k3_circcmb3,axiom,
! [A,B,C,D] : k3_circcmb3(A,B,C,D) = k1_scmpds_1(A,B,C,D) ).
fof(dt_k4_circcmb3,axiom,
! [A,B,C,D,E] : m1_circcomb(k4_circcmb3(A,B,C,D,E),np__5) ).
fof(redefinition_k4_circcmb3,axiom,
! [A,B,C,D,E] : k4_circcmb3(A,B,C,D,E) = k2_scmpds_1(A,B,C,D,E) ).
fof(dt_k5_circcmb3,axiom,
! [A] :
( ( v4_circcmb3(A)
& l1_msualg_1(A) )
=> m1_subset_1(k5_circcmb3(A),u1_struct_0(A)) ) ).
fof(dt_k6_circcmb3,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& ~ v1_xboole_0(B)
& v1_finset_1(B)
& v1_funct_1(C)
& v1_funct_2(C,k4_finseq_2(A,B),B)
& m1_relset_1(C,k4_finseq_2(A,B),B)
& m1_circcomb(D,A) )
=> ( v1_msualg_1(k6_circcmb3(A,B,C,D))
& m1_circcmb3(k6_circcmb3(A,B,C,D),B) ) ) ).
fof(redefinition_k6_circcmb3,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& ~ v1_xboole_0(B)
& v1_finset_1(B)
& v1_funct_1(C)
& v1_funct_2(C,k4_finseq_2(A,B),B)
& m1_relset_1(C,k4_finseq_2(A,B),B)
& m1_circcomb(D,A) )
=> k6_circcmb3(A,B,C,D) = k7_circcomb(C,D) ) ).
fof(dt_k7_circcmb3,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& ~ v1_xboole_0(B)
& v1_finset_1(B)
& v1_funct_1(C)
& v1_funct_2(C,k4_finseq_2(A,B),B)
& m1_relset_1(C,k4_finseq_2(A,B),B)
& m1_circcomb(D,A) )
=> ( v4_msualg_1(k7_circcmb3(A,B,C,D),k6_circcmb3(A,B,C,D))
& m2_circcmb3(k7_circcmb3(A,B,C,D),B,k6_circcmb3(A,B,C,D)) ) ) ).
fof(redefinition_k7_circcmb3,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& ~ v1_xboole_0(B)
& v1_finset_1(B)
& v1_funct_1(C)
& v1_funct_2(C,k4_finseq_2(A,B),B)
& m1_relset_1(C,k4_finseq_2(A,B),B)
& m1_circcomb(D,A) )
=> k7_circcmb3(A,B,C,D) = k9_circcomb(A,B,C,D) ) ).
fof(dt_k8_circcmb3,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& m1_circcmb3(B,A)
& m1_circcmb3(C,A) )
=> ( v1_msualg_1(k8_circcmb3(A,B,C))
& m1_circcmb3(k8_circcmb3(A,B,C),A) ) ) ).
fof(redefinition_k8_circcmb3,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& m1_circcmb3(B,A)
& m1_circcmb3(C,A) )
=> k8_circcmb3(A,B,C) = k3_circcomb(B,C) ) ).
fof(dt_k9_circcmb3,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& m1_circcmb3(B,A)
& m1_circcmb3(C,A)
& m2_circcmb3(D,A,B)
& m2_circcmb3(E,A,C) )
=> ( v4_msualg_1(k9_circcmb3(A,B,C,D,E),k8_circcmb3(A,B,C))
& m2_circcmb3(k9_circcmb3(A,B,C,D,E),A,k8_circcmb3(A,B,C)) ) ) ).
fof(redefinition_k9_circcmb3,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& m1_circcmb3(B,A)
& m1_circcmb3(C,A)
& m2_circcmb3(D,A,B)
& m2_circcmb3(E,A,C) )
=> k9_circcmb3(A,B,C,D,E) = k4_circcomb(B,C,D,E) ) ).
%------------------------------------------------------------------------------