SET007 Axioms: SET007+718.ax
%------------------------------------------------------------------------------
% File : SET007+718 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Combining of Multi Cell 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 : circcmb2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 50 ( 0 unt; 0 def)
% Number of atoms : 1387 ( 366 equ)
% Maximal formula atoms : 82 ( 27 avg)
% Number of connectives : 1546 ( 209 ~; 2 |; 885 &)
% ( 1 <=>; 449 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 19 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 39 ( 38 usr; 0 prp; 1-4 aty)
% Number of functors : 171 ( 171 usr; 86 con; 0-4 aty)
% Number of variables : 476 ( 398 !; 78 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_circcmb2,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& v1_funct_1(B)
& v1_funct_2(B,k4_finseq_2(A,k10_circcomb),k10_circcomb)
& m1_relset_1(B,k4_finseq_2(A,k10_circcomb),k10_circcomb)
& m1_circcomb(C,A) )
=> ( v4_msualg_1(k9_circcomb(A,k10_circcomb,B,C),k7_circcomb(B,C))
& v5_msualg_1(k9_circcomb(A,k10_circcomb,B,C),k7_circcomb(B,C))
& v3_msafree2(k9_circcomb(A,k10_circcomb,B,C),k7_circcomb(B,C))
& v4_msafree2(k9_circcomb(A,k10_circcomb,B,C),k7_circcomb(B,C))
& v4_circcomb(k9_circcomb(A,k10_circcomb,B,C),k7_circcomb(B,C))
& v6_circcomb(k9_circcomb(A,k10_circcomb,B,C),k7_circcomb(B,C)) ) ) ).
fof(t1_circcmb2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_circcomb(C,B)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(B,A),A)
& m2_relset_1(D,k4_finseq_2(B,A),A) )
=> ! [E] :
( m1_subset_1(E,u1_msualg_1(k7_circcomb(D,C)))
=> ! [F] :
( m1_subset_1(F,k4_card_3(u4_msualg_1(k7_circcomb(D,C),k9_circcomb(B,A,D,C))))
=> k3_circuit1(k7_circcomb(D,C),k9_circcomb(B,A,D,C),F,E) = k5_relat_1(C,F) ) ) ) ) ) ) ).
fof(t2_circcmb2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_circcomb(C,B)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(B,A),A)
& m2_relset_1(D,k4_finseq_2(B,A),A) )
=> ! [E] :
( m1_subset_1(E,k4_card_3(u4_msualg_1(k7_circcomb(D,C),k9_circcomb(B,A,D,C))))
=> v1_circuit2(k6_circuit2(k7_circcomb(D,C),k9_circcomb(B,A,D,C),E),k7_circcomb(D,C),k9_circcomb(B,A,D,C)) ) ) ) ) ) ).
fof(t3_circcmb2,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)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k9_facirc_1(A,B,C,D) = C ) ) ) ) ) ).
fof(t4_circcmb2,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)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( v1_circuit2(k9_facirc_1(A,B,C,D),A,B)
& r1_xreal_0(D,E) )
=> k9_facirc_1(A,B,C,E) = k9_facirc_1(A,B,C,D) ) ) ) ) ) ) ).
fof(t5_circcmb2,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( r1_partfun1(A,B)
=> k2_relat_1(k1_funct_4(A,B)) = k2_xboole_0(k2_relat_1(A),k2_relat_1(B)) ) ) ) ).
fof(t6_circcmb2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ( r1_circcomb(A,B)
=> k2_msafree2(k3_circcomb(A,B)) = k2_xboole_0(k4_xboole_0(k2_msafree2(A),k3_msafree2(B)),k4_xboole_0(k2_msafree2(B),k3_msafree2(A))) ) ) ) ).
fof(t7_circcmb2,axiom,
! [A] :
( ~ v2_facirc_1(A)
=> ! [B] :
( v1_relat_1(B)
=> k4_xboole_0(A,B) = A ) ) ).
fof(t8_circcmb2,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B,C] :
( r1_tarski(C,B)
=> ( v2_facirc_1(k4_xboole_0(B,C))
| k4_xboole_0(A,B) = k4_xboole_0(A,C) ) ) ) ).
fof(t9_circcmb2,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> ( r1_tarski(B,C)
=> ( v2_facirc_1(k4_xboole_0(A,B))
| k4_xboole_0(A,C) = k4_xboole_0(A,B) ) ) ) ).
fof(d1_circcmb2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v5_msualg_1(C,A)
& l3_msualg_1(C,A) )
=> ( C = k1_circcmb2(A,B)
<=> C = B ) ) ) ) ).
fof(t10_circcmb2,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(k4_msafree2(A),k2_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(B,E)))
=> ! [H] :
( m1_subset_1(H,k4_card_3(u4_msualg_1(C,F)))
=> ( G = k7_relat_1(H,u1_struct_0(B))
=> k6_circuit2(B,E,G) = k7_relat_1(k6_circuit2(C,F,H),u1_struct_0(B)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t11_circcmb2,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(A,D)))
=> ! [H] :
( m1_subset_1(H,k4_card_3(u4_msualg_1(C,F)))
=> ( G = k7_relat_1(H,u1_struct_0(A))
=> k6_circuit2(A,D,G) = k7_relat_1(k6_circuit2(C,F,H),u1_struct_0(A)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t12_circcmb2,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_circcomb(A,B)
& r1_xboole_0(k4_msafree2(A),k2_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(A,D)))
=> ! [H] :
( m1_subset_1(H,k4_card_3(u4_msualg_1(B,E)))
=> ! [I] :
( m1_subset_1(I,k4_card_3(u4_msualg_1(C,F)))
=> ( ( G = k7_relat_1(I,u1_struct_0(A))
& H = k7_relat_1(I,u1_struct_0(B))
& v1_circuit2(G,A,D)
& v1_circuit2(H,B,E) )
=> v1_circuit2(I,C,F) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t13_circcmb2,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_circcomb(A,B)
& 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(A,D)))
=> ! [H] :
( m1_subset_1(H,k4_card_3(u4_msualg_1(B,E)))
=> ! [I] :
( m1_subset_1(I,k4_card_3(u4_msualg_1(C,F)))
=> ( ( G = k7_relat_1(I,u1_struct_0(A))
& H = k7_relat_1(I,u1_struct_0(B))
& v1_circuit2(G,A,D)
& v1_circuit2(H,B,E) )
=> v1_circuit2(I,C,F) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t14_circcmb2,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))
=> ! [I] :
( m2_subset_1(I,k1_numbers,k5_numbers)
=> k7_relat_1(k9_facirc_1(C,F,G,I),u1_struct_0(A)) = k9_facirc_1(A,D,H,I) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t15_circcmb2,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(B),k4_msafree2(A))
& 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(B,E)))
=> ( H = k7_relat_1(G,u1_struct_0(B))
=> ! [I] :
( m2_subset_1(I,k1_numbers,k5_numbers)
=> k7_relat_1(k9_facirc_1(C,F,G,I),u1_struct_0(B)) = k9_facirc_1(B,E,H,I) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t16_circcmb2,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_circuit2(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))
=> k7_relat_1(k6_circuit2(C,F,G),u1_struct_0(B)) = k6_circuit2(B,E,I) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t17_circcmb2,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) )
=> ( 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_circuit2(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_circuit2(I,B,E) )
=> v1_circuit2(G,C,F) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t18_circcmb2,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) )
=> ( 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)))
=> ( v1_circuit2(G,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_circuit2(H,A,D) ) )
& ! [H] :
( m1_subset_1(H,k4_card_3(u4_msualg_1(B,E)))
=> ( H = k7_relat_1(G,u1_struct_0(B))
=> v1_circuit2(H,B,E) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t19_circcmb2,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(A,D)))
=> ! [H] :
( m1_subset_1(H,k4_card_3(u4_msualg_1(B,E)))
=> ! [I] :
( m1_subset_1(I,k4_card_3(u4_msualg_1(C,F)))
=> ( ( G = k7_relat_1(I,u1_struct_0(A))
& H = k7_relat_1(I,u1_struct_0(B))
& v1_circuit2(G,A,D) )
=> ! [J] :
( m2_subset_1(J,k1_numbers,k5_numbers)
=> k7_relat_1(k9_facirc_1(C,F,I,J),u1_struct_0(B)) = k9_facirc_1(B,E,H,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t20_circcmb2,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] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ! [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
=> ! [I] :
( m1_subset_1(I,k4_card_3(u4_msualg_1(C,F)))
=> ! [J] :
( m1_subset_1(J,k4_card_3(u4_msualg_1(A,D)))
=> ! [K] :
( m1_subset_1(K,k4_card_3(u4_msualg_1(B,E)))
=> ( ( J = k7_relat_1(I,u1_struct_0(A))
& v1_circuit2(k9_facirc_1(A,D,J,G),A,D)
& K = k7_relat_1(k9_facirc_1(C,F,I,G),u1_struct_0(B))
& v1_circuit2(k9_facirc_1(B,E,K,H),B,E) )
=> v1_circuit2(k9_facirc_1(C,F,I,k1_nat_1(G,H)),C,F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t21_circcmb2,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] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ! [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
=> ( ( ! [I] :
( m1_subset_1(I,k4_card_3(u4_msualg_1(A,D)))
=> v1_circuit2(k9_facirc_1(A,D,I,G),A,D) )
& ! [I] :
( m1_subset_1(I,k4_card_3(u4_msualg_1(B,E)))
=> v1_circuit2(k9_facirc_1(B,E,I,H),B,E) ) )
=> ! [I] :
( m1_subset_1(I,k4_card_3(u4_msualg_1(C,F)))
=> v1_circuit2(k9_facirc_1(C,F,I,k1_nat_1(G,H)),C,F) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t22_circcmb2,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))
& r1_xboole_0(k2_msafree2(B),k4_msafree2(A))
& 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))
=> ! [I] :
( m1_subset_1(I,k4_card_3(u4_msualg_1(B,E)))
=> ( I = k7_relat_1(G,u1_struct_0(B))
=> ! [J] :
( m2_subset_1(J,k1_numbers,k5_numbers)
=> k9_facirc_1(C,F,G,J) = k1_funct_4(k9_facirc_1(A,D,H,J),k9_facirc_1(B,E,I,J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t23_circcmb2,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))
& r1_xboole_0(k2_msafree2(B),k4_msafree2(A))
& 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] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ! [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
=> ! [I] :
( m1_subset_1(I,k4_card_3(u4_msualg_1(C,F)))
=> ! [J] :
( m1_subset_1(J,k4_card_3(u4_msualg_1(A,D)))
=> ( J = k7_relat_1(I,u1_struct_0(A))
=> ! [K] :
( m1_subset_1(K,k4_card_3(u4_msualg_1(B,E)))
=> ( ( K = k7_relat_1(I,u1_struct_0(B))
& v1_circuit2(k9_facirc_1(A,D,J,G),A,D)
& v1_circuit2(k9_facirc_1(B,E,K,H),B,E) )
=> v1_circuit2(k9_facirc_1(C,F,I,k1_limfunc1(G,H)),C,F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t24_circcmb2,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))
& r1_xboole_0(k2_msafree2(B),k4_msafree2(A))
& 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] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ! [H] :
( m1_subset_1(H,k4_card_3(u4_msualg_1(C,F)))
=> ! [I] :
( m1_subset_1(I,k4_card_3(u4_msualg_1(A,D)))
=> ( I = k7_relat_1(H,u1_struct_0(A))
=> ! [J] :
( m1_subset_1(J,k4_card_3(u4_msualg_1(B,E)))
=> ~ ( J = k7_relat_1(H,u1_struct_0(B))
& ~ ( v1_circuit2(k9_facirc_1(A,D,I,G),A,D)
& v1_circuit2(k9_facirc_1(B,E,J,G),B,E) )
& v1_circuit2(k9_facirc_1(C,F,H,G),C,F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t25_circcmb2,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))
& r1_xboole_0(k2_msafree2(B),k4_msafree2(A))
& 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] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ! [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
=> ( ( ! [I] :
( m1_subset_1(I,k4_card_3(u4_msualg_1(A,D)))
=> v1_circuit2(k9_facirc_1(A,D,I,G),A,D) )
& ! [I] :
( m1_subset_1(I,k4_card_3(u4_msualg_1(B,E)))
=> v1_circuit2(k9_facirc_1(B,E,I,H),B,E) ) )
=> ! [I] :
( m1_subset_1(I,k4_card_3(u4_msualg_1(C,F)))
=> v1_circuit2(k9_facirc_1(C,F,I,k1_limfunc1(G,H)),C,F) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(s1_circcmb2,axiom,
? [A] :
( m1_pboole(A,k5_numbers)
& ? [B] :
( m1_pboole(B,k5_numbers)
& k1_funct_1(A,np__0) = f1_s1_circcmb2
& k1_funct_1(B,np__0) = f2_s1_circcmb2
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ( ~ v3_struct_0(D)
& l1_msualg_1(D) )
=> ! [E] :
( ( D = k1_funct_1(A,C)
& E = k1_funct_1(B,C) )
=> ( k1_funct_1(A,k1_nat_1(C,np__1)) = f3_s1_circcmb2(D,E,C)
& k1_funct_1(B,k1_nat_1(C,np__1)) = f4_s1_circcmb2(E,C) ) ) ) ) ) ) ).
fof(s2_circcmb2,axiom,
( ( ? [A] :
( ~ v3_struct_0(A)
& l1_msualg_1(A)
& ? [B] :
( A = k1_funct_1(f3_s2_circcmb2,np__0)
& B = k1_funct_1(f4_s2_circcmb2,np__0)
& p1_s2_circcmb2(A,B,np__0) ) )
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( B = k1_funct_1(f3_s2_circcmb2,A)
& C = k1_funct_1(f4_s2_circcmb2,A) )
=> ( k1_funct_1(f3_s2_circcmb2,k1_nat_1(A,np__1)) = f1_s2_circcmb2(B,C,A)
& k1_funct_1(f4_s2_circcmb2,k1_nat_1(A,np__1)) = f2_s2_circcmb2(C,A) ) ) ) )
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( B = k1_funct_1(f3_s2_circcmb2,A)
& C = k1_funct_1(f4_s2_circcmb2,A)
& p1_s2_circcmb2(B,C,A) )
=> p1_s2_circcmb2(f1_s2_circcmb2(B,C,A),f2_s2_circcmb2(C,A),k1_nat_1(A,np__1)) ) ) ) )
=> ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ? [B] :
( ~ v3_struct_0(B)
& l1_msualg_1(B)
& B = k1_funct_1(f3_s2_circcmb2,A)
& p1_s2_circcmb2(B,k1_funct_1(f4_s2_circcmb2,A),A) ) ) ) ).
fof(s3_circcmb2,axiom,
( ( k1_funct_1(f4_s3_circcmb2,np__0) = f1_s3_circcmb2
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( B = k1_funct_1(f4_s3_circcmb2,A)
& C = k1_funct_1(f5_s3_circcmb2,A) )
=> ( k1_funct_1(f4_s3_circcmb2,k1_nat_1(A,np__1)) = f2_s3_circcmb2(B,C,A)
& k1_funct_1(f5_s3_circcmb2,k1_nat_1(A,np__1)) = f3_s3_circcmb2(C,A) ) ) ) ) )
=> ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( B = k1_funct_1(f5_s3_circcmb2,A)
=> k1_funct_1(f5_s3_circcmb2,k1_nat_1(A,np__1)) = f3_s3_circcmb2(B,A) ) ) ) ).
fof(s4_circcmb2,axiom,
? [A] :
( ~ v3_struct_0(A)
& l1_msualg_1(A)
& ? [B] :
( m1_pboole(B,k5_numbers)
& ? [C] :
( m1_pboole(C,k5_numbers)
& A = k1_funct_1(B,f5_s4_circcmb2)
& k1_funct_1(B,np__0) = f1_s4_circcmb2
& k1_funct_1(C,np__0) = f2_s4_circcmb2
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( ( ~ v3_struct_0(E)
& l1_msualg_1(E) )
=> ! [F] :
( ( E = k1_funct_1(B,D)
& F = k1_funct_1(C,D) )
=> ( k1_funct_1(B,k1_nat_1(D,np__1)) = f3_s4_circcmb2(E,F,D)
& k1_funct_1(C,k1_nat_1(D,np__1)) = f4_s4_circcmb2(F,D) ) ) ) ) ) ) ) ).
fof(s5_circcmb2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ~ ( ? [C] :
( m1_pboole(C,k5_numbers)
& ? [D] :
( m1_pboole(D,k5_numbers)
& A = k1_funct_1(C,f5_s5_circcmb2)
& k1_funct_1(C,np__0) = f1_s5_circcmb2
& k1_funct_1(D,np__0) = f2_s5_circcmb2
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( ( ~ v3_struct_0(F)
& l1_msualg_1(F) )
=> ! [G] :
( ( F = k1_funct_1(C,E)
& G = k1_funct_1(D,E) )
=> ( k1_funct_1(C,k1_nat_1(E,np__1)) = f3_s5_circcmb2(F,G,E)
& k1_funct_1(D,k1_nat_1(E,np__1)) = f4_s5_circcmb2(G,E) ) ) ) ) ) )
& ? [C] :
( m1_pboole(C,k5_numbers)
& ? [D] :
( m1_pboole(D,k5_numbers)
& B = k1_funct_1(C,f5_s5_circcmb2)
& k1_funct_1(C,np__0) = f1_s5_circcmb2
& k1_funct_1(D,np__0) = f2_s5_circcmb2
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( ( ~ v3_struct_0(F)
& l1_msualg_1(F) )
=> ! [G] :
( ( F = k1_funct_1(C,E)
& G = k1_funct_1(D,E) )
=> ( k1_funct_1(C,k1_nat_1(E,np__1)) = f3_s5_circcmb2(F,G,E)
& k1_funct_1(D,k1_nat_1(E,np__1)) = f4_s5_circcmb2(G,E) ) ) ) ) ) )
& A != B ) ) ) ).
fof(s6_circcmb2,axiom,
( ? [A] :
( ~ v3_struct_0(A)
& l1_msualg_1(A)
& ? [B] :
( m1_pboole(B,k5_numbers)
& ? [C] :
( m1_pboole(C,k5_numbers)
& A = k1_funct_1(B,f5_s6_circcmb2)
& k1_funct_1(B,np__0) = f1_s6_circcmb2
& k1_funct_1(C,np__0) = f2_s6_circcmb2
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( ( ~ v3_struct_0(E)
& l1_msualg_1(E) )
=> ! [F] :
( ( E = k1_funct_1(B,D)
& F = k1_funct_1(C,D) )
=> ( k1_funct_1(B,k1_nat_1(D,np__1)) = f3_s6_circcmb2(E,F,D)
& k1_funct_1(C,k1_nat_1(D,np__1)) = f4_s6_circcmb2(F,D) ) ) ) ) ) ) )
& ! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ~ ( ? [C] :
( m1_pboole(C,k5_numbers)
& ? [D] :
( m1_pboole(D,k5_numbers)
& A = k1_funct_1(C,f5_s6_circcmb2)
& k1_funct_1(C,np__0) = f1_s6_circcmb2
& k1_funct_1(D,np__0) = f2_s6_circcmb2
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( ( ~ v3_struct_0(F)
& l1_msualg_1(F) )
=> ! [G] :
( ( F = k1_funct_1(C,E)
& G = k1_funct_1(D,E) )
=> ( k1_funct_1(C,k1_nat_1(E,np__1)) = f3_s6_circcmb2(F,G,E)
& k1_funct_1(D,k1_nat_1(E,np__1)) = f4_s6_circcmb2(G,E) ) ) ) ) ) )
& ? [C] :
( m1_pboole(C,k5_numbers)
& ? [D] :
( m1_pboole(D,k5_numbers)
& B = k1_funct_1(C,f5_s6_circcmb2)
& k1_funct_1(C,np__0) = f1_s6_circcmb2
& k1_funct_1(D,np__0) = f2_s6_circcmb2
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( ( ~ v3_struct_0(F)
& l1_msualg_1(F) )
=> ! [G] :
( ( F = k1_funct_1(C,E)
& G = k1_funct_1(D,E) )
=> ( k1_funct_1(C,k1_nat_1(E,np__1)) = f3_s6_circcmb2(F,G,E)
& k1_funct_1(D,k1_nat_1(E,np__1)) = f4_s6_circcmb2(G,E) ) ) ) ) ) )
& A != B ) ) ) ) ).
fof(s7_circcmb2,axiom,
( ( v1_circcomb(f1_s7_circcmb2)
& v2_circcomb(f1_s7_circcmb2)
& v3_circcomb(f1_s7_circcmb2)
& ~ v2_msualg_1(f1_s7_circcmb2)
& ~ v3_struct_0(f1_s7_circcmb2)
& v1_msualg_1(f1_s7_circcmb2)
& ! [A] :
( ( ~ v3_struct_0(A)
& v1_msualg_1(A)
& ~ v2_msualg_1(A)
& v1_circcomb(A)
& v2_circcomb(A)
& v3_circcomb(A)
& l1_msualg_1(A) )
=> ! [B,C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( v1_circcomb(f2_s7_circcmb2(A,B,C))
& v2_circcomb(f2_s7_circcmb2(A,B,C))
& v3_circcomb(f2_s7_circcmb2(A,B,C))
& ~ v2_msualg_1(f2_s7_circcmb2(A,B,C))
& ~ v3_struct_0(f2_s7_circcmb2(A,B,C))
& v1_msualg_1(f2_s7_circcmb2(A,B,C)) ) ) ) )
=> ? [A] :
( ~ v3_struct_0(A)
& v1_msualg_1(A)
& ~ v2_msualg_1(A)
& v1_circcomb(A)
& v2_circcomb(A)
& v3_circcomb(A)
& l1_msualg_1(A)
& ? [B] :
( m1_pboole(B,k5_numbers)
& ? [C] :
( m1_pboole(C,k5_numbers)
& A = k1_funct_1(B,f5_s7_circcmb2)
& k1_funct_1(B,np__0) = f1_s7_circcmb2
& k1_funct_1(C,np__0) = f3_s7_circcmb2
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( ( ~ v3_struct_0(E)
& l1_msualg_1(E) )
=> ! [F] :
( ( E = k1_funct_1(B,D)
& F = k1_funct_1(C,D) )
=> ( k1_funct_1(B,k1_nat_1(D,np__1)) = f2_s7_circcmb2(E,F,D)
& k1_funct_1(C,k1_nat_1(D,np__1)) = f4_s7_circcmb2(F,D) ) ) ) ) ) ) ) ) ).
fof(s8_circcmb2,axiom,
( ( v1_circcomb(f1_s8_circcmb2)
& v2_circcomb(f1_s8_circcmb2)
& v3_circcomb(f1_s8_circcmb2)
& ~ v2_msualg_1(f1_s8_circcmb2)
& ~ v3_struct_0(f1_s8_circcmb2)
& v1_msualg_1(f1_s8_circcmb2) )
=> ? [A] :
( ~ v3_struct_0(A)
& v1_msualg_1(A)
& ~ v2_msualg_1(A)
& v1_circcomb(A)
& v2_circcomb(A)
& v3_circcomb(A)
& l1_msualg_1(A)
& ? [B] :
( m1_pboole(B,k5_numbers)
& ? [C] :
( m1_pboole(C,k5_numbers)
& A = k1_funct_1(B,f5_s8_circcmb2)
& k1_funct_1(B,np__0) = f1_s8_circcmb2
& k1_funct_1(C,np__0) = f3_s8_circcmb2
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( ( ~ v3_struct_0(E)
& l1_msualg_1(E) )
=> ! [F] :
( ( E = k1_funct_1(B,D)
& F = k1_funct_1(C,D) )
=> ( k1_funct_1(B,k1_nat_1(D,np__1)) = k3_circcomb(E,f2_s8_circcmb2(F,D))
& k1_funct_1(C,k1_nat_1(D,np__1)) = f4_s8_circcmb2(F,D) ) ) ) ) ) ) ) ) ).
fof(s9_circcmb2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_msualg_1(A)
& ~ v2_msualg_1(A)
& v1_circcomb(A)
& v2_circcomb(A)
& v3_circcomb(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_msualg_1(B)
& ~ v2_msualg_1(B)
& v1_circcomb(B)
& v2_circcomb(B)
& v3_circcomb(B)
& l1_msualg_1(B) )
=> ~ ( ? [C] :
( m1_pboole(C,k5_numbers)
& ? [D] :
( m1_pboole(D,k5_numbers)
& A = k1_funct_1(C,f5_s9_circcmb2)
& k1_funct_1(C,np__0) = f1_s9_circcmb2
& k1_funct_1(D,np__0) = f2_s9_circcmb2
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( ( ~ v3_struct_0(F)
& l1_msualg_1(F) )
=> ! [G] :
( ( F = k1_funct_1(C,E)
& G = k1_funct_1(D,E) )
=> ( k1_funct_1(C,k1_nat_1(E,np__1)) = f3_s9_circcmb2(F,G,E)
& k1_funct_1(D,k1_nat_1(E,np__1)) = f4_s9_circcmb2(G,E) ) ) ) ) ) )
& ? [C] :
( m1_pboole(C,k5_numbers)
& ? [D] :
( m1_pboole(D,k5_numbers)
& B = k1_funct_1(C,f5_s9_circcmb2)
& k1_funct_1(C,np__0) = f1_s9_circcmb2
& k1_funct_1(D,np__0) = f2_s9_circcmb2
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( ( ~ v3_struct_0(F)
& l1_msualg_1(F) )
=> ! [G] :
( ( F = k1_funct_1(C,E)
& G = k1_funct_1(D,E) )
=> ( k1_funct_1(C,k1_nat_1(E,np__1)) = f3_s9_circcmb2(F,G,E)
& k1_funct_1(D,k1_nat_1(E,np__1)) = f4_s9_circcmb2(G,E) ) ) ) ) ) )
& A != B ) ) ) ).
fof(s10_circcmb2,axiom,
( ( v1_relat_1(k4_msafree2(f1_s10_circcmb2))
& ~ v2_facirc_1(k2_msafree2(f1_s10_circcmb2))
& f2_s10_circcmb2(np__0) = f1_s10_circcmb2
& r2_hidden(k1_funct_1(f3_s10_circcmb2,np__0),k4_msafree2(f1_s10_circcmb2))
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] : v1_relat_1(k4_msafree2(f4_s10_circcmb2(B,A))) )
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
~ ( B = k1_funct_1(f3_s10_circcmb2,A)
& v2_facirc_1(k4_xboole_0(k2_msafree2(f4_s10_circcmb2(B,A)),k1_tarski(B))) ) )
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( B = f2_s10_circcmb2(A)
& C = k1_funct_1(f3_s10_circcmb2,A) )
=> ( f2_s10_circcmb2(k1_nat_1(A,np__1)) = k3_circcomb(B,f4_s10_circcmb2(C,A))
& k1_funct_1(f3_s10_circcmb2,k1_nat_1(A,np__1)) = f5_s10_circcmb2(C,A)
& r2_hidden(C,k2_msafree2(f4_s10_circcmb2(C,A)))
& r2_hidden(f5_s10_circcmb2(C,A),k4_msafree2(f4_s10_circcmb2(C,A))) ) ) ) ) )
=> ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ? [B] :
( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& v1_circcomb(B)
& v2_circcomb(B)
& v3_circcomb(B)
& l1_msualg_1(B)
& ? [C] :
( ~ v3_struct_0(C)
& ~ v2_msualg_1(C)
& v1_circcomb(C)
& v2_circcomb(C)
& v3_circcomb(C)
& l1_msualg_1(C)
& B = f2_s10_circcmb2(A)
& C = f2_s10_circcmb2(k1_nat_1(A,np__1))
& k2_msafree2(C) = k2_xboole_0(k2_msafree2(B),k4_xboole_0(k2_msafree2(f4_s10_circcmb2(k1_funct_1(f3_s10_circcmb2,A),A)),k1_tarski(k1_funct_1(f3_s10_circcmb2,A))))
& v1_relat_1(k4_msafree2(B))
& ~ v2_facirc_1(k2_msafree2(B)) ) ) ) ) ).
fof(s11_circcmb2,axiom,
( ( v1_relat_1(k4_msafree2(f1_s11_circcmb2(np__0)))
& ~ v2_facirc_1(k2_msafree2(f1_s11_circcmb2(np__0)))
& r2_hidden(k1_funct_1(f2_s11_circcmb2,np__0),k4_msafree2(f1_s11_circcmb2(np__0)))
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] : v1_relat_1(k4_msafree2(f3_s11_circcmb2(B,A))) )
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
~ ( B = k1_funct_1(f2_s11_circcmb2,A)
& v2_facirc_1(k4_xboole_0(k2_msafree2(f3_s11_circcmb2(B,A)),k1_tarski(B))) ) )
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( B = f1_s11_circcmb2(A)
& C = k1_funct_1(f2_s11_circcmb2,A) )
=> ( f1_s11_circcmb2(k1_nat_1(A,np__1)) = k3_circcomb(B,f3_s11_circcmb2(C,A))
& k1_funct_1(f2_s11_circcmb2,k1_nat_1(A,np__1)) = f4_s11_circcmb2(C,A)
& r2_hidden(C,k2_msafree2(f3_s11_circcmb2(C,A)))
& r2_hidden(f4_s11_circcmb2(C,A),k4_msafree2(f3_s11_circcmb2(C,A))) ) ) ) ) )
=> ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( k2_msafree2(f1_s11_circcmb2(k1_nat_1(A,np__1))) = k2_xboole_0(k2_msafree2(f1_s11_circcmb2(A)),k4_xboole_0(k2_msafree2(f3_s11_circcmb2(k1_funct_1(f2_s11_circcmb2,A),A)),k1_tarski(k1_funct_1(f2_s11_circcmb2,A))))
& v1_relat_1(k4_msafree2(f1_s11_circcmb2(A)))
& ~ v2_facirc_1(k2_msafree2(f1_s11_circcmb2(A))) ) ) ) ).
fof(s12_circcmb2,axiom,
? [A] :
( m1_pboole(A,k5_numbers)
& ? [B] :
( m1_pboole(B,k5_numbers)
& ? [C] :
( m1_pboole(C,k5_numbers)
& k1_funct_1(A,np__0) = f1_s12_circcmb2
& k1_funct_1(B,np__0) = f2_s12_circcmb2
& k1_funct_1(C,np__0) = f3_s12_circcmb2
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( ( ~ v3_struct_0(E)
& l1_msualg_1(E) )
=> ! [F] :
( ( v5_msualg_1(F,E)
& l3_msualg_1(F,E) )
=> ! [G] :
( ( E = k1_funct_1(A,D)
& F = k1_funct_1(B,D)
& G = k1_funct_1(C,D) )
=> ( k1_funct_1(A,k1_nat_1(D,np__1)) = f4_s12_circcmb2(E,G,D)
& k1_funct_1(B,k1_nat_1(D,np__1)) = f5_s12_circcmb2(E,F,G,D)
& k1_funct_1(C,k1_nat_1(D,np__1)) = f6_s12_circcmb2(G,D) ) ) ) ) ) ) ) ) ).
fof(s13_circcmb2,axiom,
( ( ? [A] :
( ~ v3_struct_0(A)
& l1_msualg_1(A)
& ? [B] :
( v5_msualg_1(B,A)
& l3_msualg_1(B,A)
& ? [C] :
( A = k1_funct_1(f4_s13_circcmb2,np__0)
& B = k1_funct_1(f5_s13_circcmb2,np__0)
& C = k1_funct_1(f6_s13_circcmb2,np__0)
& p1_s13_circcmb2(A,B,C,np__0) ) ) )
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v5_msualg_1(C,B)
& l3_msualg_1(C,B) )
=> ! [D] :
( ( B = k1_funct_1(f4_s13_circcmb2,A)
& C = k1_funct_1(f5_s13_circcmb2,A)
& D = k1_funct_1(f6_s13_circcmb2,A) )
=> ( k1_funct_1(f4_s13_circcmb2,k1_nat_1(A,np__1)) = f1_s13_circcmb2(B,D,A)
& k1_funct_1(f5_s13_circcmb2,k1_nat_1(A,np__1)) = f2_s13_circcmb2(B,C,D,A)
& k1_funct_1(f6_s13_circcmb2,k1_nat_1(A,np__1)) = f3_s13_circcmb2(D,A) ) ) ) ) )
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v5_msualg_1(C,B)
& l3_msualg_1(C,B) )
=> ! [D] :
( ( B = k1_funct_1(f4_s13_circcmb2,A)
& C = k1_funct_1(f5_s13_circcmb2,A)
& D = k1_funct_1(f6_s13_circcmb2,A)
& p1_s13_circcmb2(B,C,D,A) )
=> p1_s13_circcmb2(f1_s13_circcmb2(B,D,A),f2_s13_circcmb2(B,C,D,A),f3_s13_circcmb2(D,A),k1_nat_1(A,np__1)) ) ) ) )
& ! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C,D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( v5_msualg_1(f2_s13_circcmb2(A,B,C,D),f1_s13_circcmb2(A,C,D))
& l3_msualg_1(f2_s13_circcmb2(A,B,C,D),f1_s13_circcmb2(A,C,D)) ) ) ) ) )
=> ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ? [B] :
( ~ v3_struct_0(B)
& l1_msualg_1(B)
& ? [C] :
( v5_msualg_1(C,B)
& l3_msualg_1(C,B)
& B = k1_funct_1(f4_s13_circcmb2,A)
& C = k1_funct_1(f5_s13_circcmb2,A)
& p1_s13_circcmb2(B,C,k1_funct_1(f6_s13_circcmb2,A),A) ) ) ) ) ).
fof(s14_circcmb2,axiom,
( ( ? [A] :
( ~ v3_struct_0(A)
& l1_msualg_1(A)
& ? [B] :
( v5_msualg_1(B,A)
& l3_msualg_1(B,A)
& A = k1_funct_1(f4_s14_circcmb2,np__0)
& B = k1_funct_1(f6_s14_circcmb2,np__0) ) )
& k1_funct_1(f4_s14_circcmb2,np__0) = k1_funct_1(f5_s14_circcmb2,np__0)
& k1_funct_1(f6_s14_circcmb2,np__0) = k1_funct_1(f7_s14_circcmb2,np__0)
& k1_funct_1(f8_s14_circcmb2,np__0) = k1_funct_1(f9_s14_circcmb2,np__0)
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v5_msualg_1(C,B)
& l3_msualg_1(C,B) )
=> ! [D] :
( ( B = k1_funct_1(f4_s14_circcmb2,A)
& C = k1_funct_1(f6_s14_circcmb2,A)
& D = k1_funct_1(f8_s14_circcmb2,A) )
=> ( k1_funct_1(f4_s14_circcmb2,k1_nat_1(A,np__1)) = f1_s14_circcmb2(B,D,A)
& k1_funct_1(f6_s14_circcmb2,k1_nat_1(A,np__1)) = f2_s14_circcmb2(B,C,D,A)
& k1_funct_1(f8_s14_circcmb2,k1_nat_1(A,np__1)) = f3_s14_circcmb2(D,A) ) ) ) ) )
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v5_msualg_1(C,B)
& l3_msualg_1(C,B) )
=> ! [D] :
( ( B = k1_funct_1(f5_s14_circcmb2,A)
& C = k1_funct_1(f7_s14_circcmb2,A)
& D = k1_funct_1(f9_s14_circcmb2,A) )
=> ( k1_funct_1(f5_s14_circcmb2,k1_nat_1(A,np__1)) = f1_s14_circcmb2(B,D,A)
& k1_funct_1(f7_s14_circcmb2,k1_nat_1(A,np__1)) = f2_s14_circcmb2(B,C,D,A)
& k1_funct_1(f9_s14_circcmb2,k1_nat_1(A,np__1)) = f3_s14_circcmb2(D,A) ) ) ) ) )
& ! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C,D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( v5_msualg_1(f2_s14_circcmb2(A,B,C,D),f1_s14_circcmb2(A,C,D))
& l3_msualg_1(f2_s14_circcmb2(A,B,C,D),f1_s14_circcmb2(A,C,D)) ) ) ) ) )
=> ( r6_pboole(k5_numbers,f4_s14_circcmb2,f5_s14_circcmb2)
& r6_pboole(k5_numbers,f6_s14_circcmb2,f7_s14_circcmb2)
& r6_pboole(k5_numbers,f8_s14_circcmb2,f9_s14_circcmb2) ) ) ).
fof(s15_circcmb2,axiom,
( ( k1_funct_1(f6_s15_circcmb2,np__0) = f1_s15_circcmb2
& k1_funct_1(f7_s15_circcmb2,np__0) = f2_s15_circcmb2
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v5_msualg_1(C,B)
& l3_msualg_1(C,B) )
=> ! [D] :
( ( B = k1_funct_1(f6_s15_circcmb2,A)
& C = k1_funct_1(f7_s15_circcmb2,A)
& D = k1_funct_1(f8_s15_circcmb2,A) )
=> ( k1_funct_1(f6_s15_circcmb2,k1_nat_1(A,np__1)) = f3_s15_circcmb2(B,D,A)
& k1_funct_1(f7_s15_circcmb2,k1_nat_1(A,np__1)) = f4_s15_circcmb2(B,C,D,A)
& k1_funct_1(f8_s15_circcmb2,k1_nat_1(A,np__1)) = f5_s15_circcmb2(D,A) ) ) ) ) )
& ! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C,D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( v5_msualg_1(f4_s15_circcmb2(A,B,C,D),f3_s15_circcmb2(A,C,D))
& l3_msualg_1(f4_s15_circcmb2(A,B,C,D),f3_s15_circcmb2(A,C,D)) ) ) ) ) )
=> ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( B = k1_funct_1(f6_s15_circcmb2,A)
& C = k1_funct_1(f8_s15_circcmb2,A) )
=> ( k1_funct_1(f6_s15_circcmb2,k1_nat_1(A,np__1)) = f3_s15_circcmb2(B,C,A)
& k1_funct_1(f8_s15_circcmb2,k1_nat_1(A,np__1)) = f5_s15_circcmb2(C,A) ) ) ) ) ) ).
fof(s16_circcmb2,axiom,
( ! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C,D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( v5_msualg_1(f5_s16_circcmb2(A,B,C,D),f4_s16_circcmb2(A,C,D))
& l3_msualg_1(f5_s16_circcmb2(A,B,C,D),f4_s16_circcmb2(A,C,D)) ) ) ) )
=> ? [A] :
( ~ v3_struct_0(A)
& l1_msualg_1(A)
& ? [B] :
( v5_msualg_1(B,A)
& l3_msualg_1(B,A)
& ? [C] :
( m1_pboole(C,k5_numbers)
& ? [D] :
( m1_pboole(D,k5_numbers)
& ? [E] :
( m1_pboole(E,k5_numbers)
& A = k1_funct_1(C,f7_s16_circcmb2)
& B = k1_funct_1(D,f7_s16_circcmb2)
& k1_funct_1(C,np__0) = f1_s16_circcmb2
& k1_funct_1(D,np__0) = f2_s16_circcmb2
& k1_funct_1(E,np__0) = f3_s16_circcmb2
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( ( ~ v3_struct_0(G)
& l1_msualg_1(G) )
=> ! [H] :
( ( v5_msualg_1(H,G)
& l3_msualg_1(H,G) )
=> ! [I] :
( ( G = k1_funct_1(C,F)
& H = k1_funct_1(D,F)
& I = k1_funct_1(E,F) )
=> ( k1_funct_1(C,k1_nat_1(F,np__1)) = f4_s16_circcmb2(G,I,F)
& k1_funct_1(D,k1_nat_1(F,np__1)) = f5_s16_circcmb2(G,H,I,F)
& k1_funct_1(E,k1_nat_1(F,np__1)) = f6_s16_circcmb2(I,F) ) ) ) ) ) ) ) ) ) ) ) ).
fof(s17_circcmb2,axiom,
( ( ? [A] :
( m1_pboole(A,k5_numbers)
& ? [B] :
( m1_pboole(B,k5_numbers)
& f2_s17_circcmb2 = k1_funct_1(A,f8_s17_circcmb2)
& k1_funct_1(A,np__0) = f1_s17_circcmb2
& k1_funct_1(B,np__0) = f4_s17_circcmb2
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ( ~ v3_struct_0(D)
& l1_msualg_1(D) )
=> ! [E] :
( ( D = k1_funct_1(A,C)
& E = k1_funct_1(B,C) )
=> ( k1_funct_1(A,k1_nat_1(C,np__1)) = f5_s17_circcmb2(D,E,C)
& k1_funct_1(B,k1_nat_1(C,np__1)) = f7_s17_circcmb2(E,C) ) ) ) ) ) )
& ! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C,D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( v5_msualg_1(f6_s17_circcmb2(A,B,C,D),f5_s17_circcmb2(A,C,D))
& l3_msualg_1(f6_s17_circcmb2(A,B,C,D),f5_s17_circcmb2(A,C,D)) ) ) ) ) )
=> ? [A] :
( v5_msualg_1(A,f2_s17_circcmb2)
& l3_msualg_1(A,f2_s17_circcmb2)
& ? [B] :
( m1_pboole(B,k5_numbers)
& ? [C] :
( m1_pboole(C,k5_numbers)
& ? [D] :
( m1_pboole(D,k5_numbers)
& f2_s17_circcmb2 = k1_funct_1(B,f8_s17_circcmb2)
& A = k1_funct_1(C,f8_s17_circcmb2)
& k1_funct_1(B,np__0) = f1_s17_circcmb2
& k1_funct_1(C,np__0) = f3_s17_circcmb2
& k1_funct_1(D,np__0) = f4_s17_circcmb2
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( ( ~ v3_struct_0(F)
& l1_msualg_1(F) )
=> ! [G] :
( ( v5_msualg_1(G,F)
& l3_msualg_1(G,F) )
=> ! [H] :
( ( F = k1_funct_1(B,E)
& G = k1_funct_1(C,E)
& H = k1_funct_1(D,E) )
=> ( k1_funct_1(B,k1_nat_1(E,np__1)) = f5_s17_circcmb2(F,H,E)
& k1_funct_1(C,k1_nat_1(E,np__1)) = f6_s17_circcmb2(F,G,H,E)
& k1_funct_1(D,k1_nat_1(E,np__1)) = f7_s17_circcmb2(H,E) ) ) ) ) ) ) ) ) ) ) ).
fof(s18_circcmb2,axiom,
( ! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C,D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( v5_msualg_1(f6_s18_circcmb2(A,B,C,D),f5_s18_circcmb2(A,C,D))
& l3_msualg_1(f6_s18_circcmb2(A,B,C,D),f5_s18_circcmb2(A,C,D)) ) ) ) )
=> ! [A] :
( ( v5_msualg_1(A,f2_s18_circcmb2)
& l3_msualg_1(A,f2_s18_circcmb2) )
=> ! [B] :
( ( v5_msualg_1(B,f2_s18_circcmb2)
& l3_msualg_1(B,f2_s18_circcmb2) )
=> ~ ( ? [C] :
( m1_pboole(C,k5_numbers)
& ? [D] :
( m1_pboole(D,k5_numbers)
& ? [E] :
( m1_pboole(E,k5_numbers)
& f2_s18_circcmb2 = k1_funct_1(C,f8_s18_circcmb2)
& A = k1_funct_1(D,f8_s18_circcmb2)
& k1_funct_1(C,np__0) = f1_s18_circcmb2
& k1_funct_1(D,np__0) = f3_s18_circcmb2
& k1_funct_1(E,np__0) = f4_s18_circcmb2
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( ( ~ v3_struct_0(G)
& l1_msualg_1(G) )
=> ! [H] :
( ( v5_msualg_1(H,G)
& l3_msualg_1(H,G) )
=> ! [I] :
( ( G = k1_funct_1(C,F)
& H = k1_funct_1(D,F)
& I = k1_funct_1(E,F) )
=> ( k1_funct_1(C,k1_nat_1(F,np__1)) = f5_s18_circcmb2(G,I,F)
& k1_funct_1(D,k1_nat_1(F,np__1)) = f6_s18_circcmb2(G,H,I,F)
& k1_funct_1(E,k1_nat_1(F,np__1)) = f7_s18_circcmb2(I,F) ) ) ) ) ) ) ) )
& ? [C] :
( m1_pboole(C,k5_numbers)
& ? [D] :
( m1_pboole(D,k5_numbers)
& ? [E] :
( m1_pboole(E,k5_numbers)
& f2_s18_circcmb2 = k1_funct_1(C,f8_s18_circcmb2)
& B = k1_funct_1(D,f8_s18_circcmb2)
& k1_funct_1(C,np__0) = f1_s18_circcmb2
& k1_funct_1(D,np__0) = f3_s18_circcmb2
& k1_funct_1(E,np__0) = f4_s18_circcmb2
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( ( ~ v3_struct_0(G)
& l1_msualg_1(G) )
=> ! [H] :
( ( v5_msualg_1(H,G)
& l3_msualg_1(H,G) )
=> ! [I] :
( ( G = k1_funct_1(C,F)
& H = k1_funct_1(D,F)
& I = k1_funct_1(E,F) )
=> ( k1_funct_1(C,k1_nat_1(F,np__1)) = f5_s18_circcmb2(G,I,F)
& k1_funct_1(D,k1_nat_1(F,np__1)) = f6_s18_circcmb2(G,H,I,F)
& k1_funct_1(E,k1_nat_1(F,np__1)) = f7_s18_circcmb2(I,F) ) ) ) ) ) ) ) )
& A != B ) ) ) ) ).
fof(s19_circcmb2,axiom,
( ( ! [A] :
( ( ~ v3_struct_0(A)
& v1_msualg_1(A)
& ~ v2_msualg_1(A)
& v1_circcomb(A)
& v2_circcomb(A)
& v3_circcomb(A)
& l1_msualg_1(A) )
=> ! [B,C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( v1_circcomb(f4_s19_circcmb2(A,B,C))
& v2_circcomb(f4_s19_circcmb2(A,B,C))
& v3_circcomb(f4_s19_circcmb2(A,B,C))
& ~ v2_msualg_1(f4_s19_circcmb2(A,B,C))
& v1_msualg_1(f4_s19_circcmb2(A,B,C)) ) ) )
& ? [A] :
( m1_pboole(A,k5_numbers)
& ? [B] :
( m1_pboole(B,k5_numbers)
& f2_s19_circcmb2 = k1_funct_1(A,f8_s19_circcmb2)
& k1_funct_1(A,np__0) = f1_s19_circcmb2
& k1_funct_1(B,np__0) = f6_s19_circcmb2
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ( ~ v3_struct_0(D)
& l1_msualg_1(D) )
=> ! [E] :
( ( D = k1_funct_1(A,C)
& E = k1_funct_1(B,C) )
=> ( k1_funct_1(A,k1_nat_1(C,np__1)) = f4_s19_circcmb2(D,E,C)
& k1_funct_1(B,k1_nat_1(C,np__1)) = f7_s19_circcmb2(E,C) ) ) ) ) ) )
& ! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C,D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( v5_msualg_1(f5_s19_circcmb2(A,B,C,D),f4_s19_circcmb2(A,C,D))
& l3_msualg_1(f5_s19_circcmb2(A,B,C,D),f4_s19_circcmb2(A,C,D)) ) ) ) )
& ! [A] :
( ( ~ v3_struct_0(A)
& v1_msualg_1(A)
& ~ v2_msualg_1(A)
& v1_circcomb(A)
& v2_circcomb(A)
& v3_circcomb(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_msualg_1(B)
& ~ v2_msualg_1(B)
& v1_circcomb(B)
& v2_circcomb(B)
& v3_circcomb(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v4_msualg_1(C,A)
& v4_msafree2(C,A)
& v4_circcomb(C,A)
& v6_circcomb(C,A)
& l3_msualg_1(C,A) )
=> ! [D,E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( B = f4_s19_circcmb2(A,D,E)
=> ( v4_msualg_1(f5_s19_circcmb2(A,C,D,E),B)
& v4_msafree2(f5_s19_circcmb2(A,C,D,E),B)
& v4_circcomb(f5_s19_circcmb2(A,C,D,E),B)
& v6_circcomb(f5_s19_circcmb2(A,C,D,E),B)
& l3_msualg_1(f5_s19_circcmb2(A,C,D,E),B) ) ) ) ) ) ) )
=> ? [A] :
( v4_msualg_1(A,f2_s19_circcmb2)
& v4_msafree2(A,f2_s19_circcmb2)
& v4_circcomb(A,f2_s19_circcmb2)
& v6_circcomb(A,f2_s19_circcmb2)
& l3_msualg_1(A,f2_s19_circcmb2)
& ? [B] :
( m1_pboole(B,k5_numbers)
& ? [C] :
( m1_pboole(C,k5_numbers)
& ? [D] :
( m1_pboole(D,k5_numbers)
& f2_s19_circcmb2 = k1_funct_1(B,f8_s19_circcmb2)
& A = k1_funct_1(C,f8_s19_circcmb2)
& k1_funct_1(B,np__0) = f1_s19_circcmb2
& k1_funct_1(C,np__0) = f3_s19_circcmb2
& k1_funct_1(D,np__0) = f6_s19_circcmb2
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( ( ~ v3_struct_0(F)
& l1_msualg_1(F) )
=> ! [G] :
( ( v5_msualg_1(G,F)
& l3_msualg_1(G,F) )
=> ! [H] :
( ( F = k1_funct_1(B,E)
& G = k1_funct_1(C,E)
& H = k1_funct_1(D,E) )
=> ( k1_funct_1(B,k1_nat_1(E,np__1)) = f4_s19_circcmb2(F,H,E)
& k1_funct_1(C,k1_nat_1(E,np__1)) = f5_s19_circcmb2(F,G,H,E)
& k1_funct_1(D,k1_nat_1(E,np__1)) = f7_s19_circcmb2(H,E) ) ) ) ) ) ) ) ) ) ) ).
fof(s20_circcmb2,axiom,
( ( ? [A] :
( m1_pboole(A,k5_numbers)
& ? [B] :
( m1_pboole(B,k5_numbers)
& f2_s20_circcmb2 = k1_funct_1(A,f8_s20_circcmb2)
& k1_funct_1(A,np__0) = f1_s20_circcmb2
& k1_funct_1(B,np__0) = f6_s20_circcmb2
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ( ~ v3_struct_0(D)
& l1_msualg_1(D) )
=> ! [E] :
( ( D = k1_funct_1(A,C)
& E = k1_funct_1(B,C) )
=> ( k1_funct_1(A,k1_nat_1(C,np__1)) = k3_circcomb(D,f4_s20_circcmb2(E,C))
& k1_funct_1(B,k1_nat_1(C,np__1)) = f7_s20_circcmb2(E,C) ) ) ) ) ) )
& ! [A,B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( v4_msualg_1(f5_s20_circcmb2(A,B),f4_s20_circcmb2(A,B))
& v4_msafree2(f5_s20_circcmb2(A,B),f4_s20_circcmb2(A,B))
& v4_circcomb(f5_s20_circcmb2(A,B),f4_s20_circcmb2(A,B))
& v6_circcomb(f5_s20_circcmb2(A,B),f4_s20_circcmb2(A,B))
& l3_msualg_1(f5_s20_circcmb2(A,B),f4_s20_circcmb2(A,B)) ) ) )
=> ? [A] :
( v4_msualg_1(A,f2_s20_circcmb2)
& v4_msafree2(A,f2_s20_circcmb2)
& v4_circcomb(A,f2_s20_circcmb2)
& v6_circcomb(A,f2_s20_circcmb2)
& l3_msualg_1(A,f2_s20_circcmb2)
& ? [B] :
( m1_pboole(B,k5_numbers)
& ? [C] :
( m1_pboole(C,k5_numbers)
& ? [D] :
( m1_pboole(D,k5_numbers)
& f2_s20_circcmb2 = k1_funct_1(B,f8_s20_circcmb2)
& A = k1_funct_1(C,f8_s20_circcmb2)
& k1_funct_1(B,np__0) = f1_s20_circcmb2
& k1_funct_1(C,np__0) = f3_s20_circcmb2
& k1_funct_1(D,np__0) = f6_s20_circcmb2
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( ( ~ v3_struct_0(F)
& l1_msualg_1(F) )
=> ! [G] :
( ( v5_msualg_1(G,F)
& l3_msualg_1(G,F) )
=> ! [H,I] :
( ( v5_msualg_1(I,f4_s20_circcmb2(H,E))
& l3_msualg_1(I,f4_s20_circcmb2(H,E)) )
=> ( ( F = k1_funct_1(B,E)
& G = k1_funct_1(C,E)
& H = k1_funct_1(D,E)
& I = f5_s20_circcmb2(H,E) )
=> ( k1_funct_1(B,k1_nat_1(E,np__1)) = k3_circcomb(F,f4_s20_circcmb2(H,E))
& k1_funct_1(C,k1_nat_1(E,np__1)) = k4_circcomb(F,f4_s20_circcmb2(H,E),G,I)
& k1_funct_1(D,k1_nat_1(E,np__1)) = f7_s20_circcmb2(H,E) ) ) ) ) ) ) ) ) ) ) ) ).
fof(s21_circcmb2,axiom,
( ! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C,D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( v5_msualg_1(f6_s21_circcmb2(A,B,C,D),f5_s21_circcmb2(A,C,D))
& l3_msualg_1(f6_s21_circcmb2(A,B,C,D),f5_s21_circcmb2(A,C,D)) ) ) ) )
=> ! [A] :
( ( v4_msualg_1(A,f2_s21_circcmb2)
& v4_msafree2(A,f2_s21_circcmb2)
& v4_circcomb(A,f2_s21_circcmb2)
& v6_circcomb(A,f2_s21_circcmb2)
& l3_msualg_1(A,f2_s21_circcmb2) )
=> ! [B] :
( ( v4_msualg_1(B,f2_s21_circcmb2)
& v4_msafree2(B,f2_s21_circcmb2)
& v4_circcomb(B,f2_s21_circcmb2)
& v6_circcomb(B,f2_s21_circcmb2)
& l3_msualg_1(B,f2_s21_circcmb2) )
=> ~ ( ? [C] :
( m1_pboole(C,k5_numbers)
& ? [D] :
( m1_pboole(D,k5_numbers)
& ? [E] :
( m1_pboole(E,k5_numbers)
& f2_s21_circcmb2 = k1_funct_1(C,f8_s21_circcmb2)
& A = k1_funct_1(D,f8_s21_circcmb2)
& k1_funct_1(C,np__0) = f1_s21_circcmb2
& k1_funct_1(D,np__0) = f3_s21_circcmb2
& k1_funct_1(E,np__0) = f4_s21_circcmb2
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( ( ~ v3_struct_0(G)
& l1_msualg_1(G) )
=> ! [H] :
( ( v5_msualg_1(H,G)
& l3_msualg_1(H,G) )
=> ! [I] :
( ( G = k1_funct_1(C,F)
& H = k1_funct_1(D,F)
& I = k1_funct_1(E,F) )
=> ( k1_funct_1(C,k1_nat_1(F,np__1)) = f5_s21_circcmb2(G,I,F)
& k1_funct_1(D,k1_nat_1(F,np__1)) = f6_s21_circcmb2(G,H,I,F)
& k1_funct_1(E,k1_nat_1(F,np__1)) = f7_s21_circcmb2(I,F) ) ) ) ) ) ) ) )
& ? [C] :
( m1_pboole(C,k5_numbers)
& ? [D] :
( m1_pboole(D,k5_numbers)
& ? [E] :
( m1_pboole(E,k5_numbers)
& f2_s21_circcmb2 = k1_funct_1(C,f8_s21_circcmb2)
& B = k1_funct_1(D,f8_s21_circcmb2)
& k1_funct_1(C,np__0) = f1_s21_circcmb2
& k1_funct_1(D,np__0) = f3_s21_circcmb2
& k1_funct_1(E,np__0) = f4_s21_circcmb2
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( ( ~ v3_struct_0(G)
& l1_msualg_1(G) )
=> ! [H] :
( ( v5_msualg_1(H,G)
& l3_msualg_1(H,G) )
=> ! [I] :
( ( G = k1_funct_1(C,F)
& H = k1_funct_1(D,F)
& I = k1_funct_1(E,F) )
=> ( k1_funct_1(C,k1_nat_1(F,np__1)) = f5_s21_circcmb2(G,I,F)
& k1_funct_1(D,k1_nat_1(F,np__1)) = f6_s21_circcmb2(G,H,I,F)
& k1_funct_1(E,k1_nat_1(F,np__1)) = f7_s21_circcmb2(I,F) ) ) ) ) ) ) ) )
& A != B ) ) ) ) ).
fof(s22_circcmb2,axiom,
( ( ! [A,B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( v4_msualg_1(f6_s22_circcmb2(A,B),f5_s22_circcmb2(A,B))
& v4_msafree2(f6_s22_circcmb2(A,B),f5_s22_circcmb2(A,B))
& v4_circcomb(f6_s22_circcmb2(A,B),f5_s22_circcmb2(A,B))
& v6_circcomb(f6_s22_circcmb2(A,B),f5_s22_circcmb2(A,B))
& l3_msualg_1(f6_s22_circcmb2(A,B),f5_s22_circcmb2(A,B)) ) )
& ! [A] :
( m1_subset_1(A,k4_card_3(u4_msualg_1(f1_s22_circcmb2,f3_s22_circcmb2)))
=> v1_circuit2(k9_facirc_1(f1_s22_circcmb2,f3_s22_circcmb2,A,f10_s22_circcmb2(np__0)),f1_s22_circcmb2,f3_s22_circcmb2) )
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B,C] :
( ( v5_msualg_1(C,f5_s22_circcmb2(B,A))
& v4_msafree2(C,f5_s22_circcmb2(B,A))
& l3_msualg_1(C,f5_s22_circcmb2(B,A)) )
=> ( ( B = k1_funct_1(f7_s22_circcmb2,A)
& C = f6_s22_circcmb2(B,A) )
=> ! [D] :
( m1_subset_1(D,k4_card_3(u4_msualg_1(f5_s22_circcmb2(B,A),C)))
=> v1_circuit2(k9_facirc_1(f5_s22_circcmb2(B,A),C,D,f10_s22_circcmb2(np__1)),f5_s22_circcmb2(B,A),C) ) ) ) )
& ? [A] :
( m1_pboole(A,k5_numbers)
& ? [B] :
( m1_pboole(B,k5_numbers)
& f2_s22_circcmb2 = k1_funct_1(A,f10_s22_circcmb2(np__2))
& f4_s22_circcmb2 = k1_funct_1(B,f10_s22_circcmb2(np__2))
& k1_funct_1(A,np__0) = f1_s22_circcmb2
& k1_funct_1(B,np__0) = f3_s22_circcmb2
& k1_funct_1(f7_s22_circcmb2,np__0) = f8_s22_circcmb2
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ( ~ v3_struct_0(D)
& l1_msualg_1(D) )
=> ! [E] :
( ( v5_msualg_1(E,D)
& l3_msualg_1(E,D) )
=> ! [F,G] :
( ( v5_msualg_1(G,f5_s22_circcmb2(F,C))
& l3_msualg_1(G,f5_s22_circcmb2(F,C)) )
=> ( ( D = k1_funct_1(A,C)
& E = k1_funct_1(B,C)
& F = k1_funct_1(f7_s22_circcmb2,C)
& G = f6_s22_circcmb2(F,C) )
=> ( k1_funct_1(A,k1_nat_1(C,np__1)) = k3_circcomb(D,f5_s22_circcmb2(F,C))
& k1_funct_1(B,k1_nat_1(C,np__1)) = k4_circcomb(D,f5_s22_circcmb2(F,C),E,G)
& k1_funct_1(f7_s22_circcmb2,k1_nat_1(C,np__1)) = f9_s22_circcmb2(F,C) ) ) ) ) ) ) ) )
& v1_relat_1(k4_msafree2(f1_s22_circcmb2))
& ~ v2_facirc_1(k2_msafree2(f1_s22_circcmb2))
& k1_funct_1(f7_s22_circcmb2,np__0) = f8_s22_circcmb2
& r2_hidden(f8_s22_circcmb2,k4_msafree2(f1_s22_circcmb2))
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] : v1_relat_1(k4_msafree2(f5_s22_circcmb2(B,A))) )
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
~ ( B = k1_funct_1(f7_s22_circcmb2,A)
& v2_facirc_1(k4_xboole_0(k2_msafree2(f5_s22_circcmb2(B,A)),k1_tarski(B))) ) )
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( B = k1_funct_1(f7_s22_circcmb2,A)
=> ( k1_funct_1(f7_s22_circcmb2,k1_nat_1(A,np__1)) = f9_s22_circcmb2(B,A)
& r2_hidden(B,k2_msafree2(f5_s22_circcmb2(B,A)))
& r2_hidden(f9_s22_circcmb2(B,A),k4_msafree2(f5_s22_circcmb2(B,A))) ) ) ) )
=> ! [A] :
( m1_subset_1(A,k4_card_3(u4_msualg_1(f2_s22_circcmb2,f4_s22_circcmb2)))
=> v1_circuit2(k9_facirc_1(f2_s22_circcmb2,f4_s22_circcmb2,A,k1_nat_1(f10_s22_circcmb2(np__0),k2_nat_1(f10_s22_circcmb2(np__2),f10_s22_circcmb2(np__1)))),f2_s22_circcmb2,f4_s22_circcmb2) ) ) ).
fof(dt_k1_circcmb2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ( v5_msualg_1(k1_circcmb2(A,B),A)
& l3_msualg_1(k1_circcmb2(A,B),A) ) ) ).
%------------------------------------------------------------------------------