SET007 Axioms: SET007+430.ax
%------------------------------------------------------------------------------
% File : SET007+430 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Combining of 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 : circcomb [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 135 ( 2 unt; 0 def)
% Number of atoms : 1286 ( 125 equ)
% Maximal formula atoms : 38 ( 9 avg)
% Number of connectives : 1384 ( 233 ~; 5 |; 701 &)
% ( 19 <=>; 426 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 10 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 44 ( 42 usr; 1 prp; 0-4 aty)
% Number of functors : 58 ( 58 usr; 8 con; 0-8 aty)
% Number of variables : 473 ( 462 !; 11 ?)
% 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_circcomb,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( v1_relat_1(k2_funcop_1(A,B))
& v1_funct_1(k2_funcop_1(A,B))
& v1_funcop_1(k2_funcop_1(A,B)) ) ) ).
fof(fc2_circcomb,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A)
& v1_relat_1(B)
& v2_relat_1(B)
& v1_funct_1(B) )
=> ( v1_relat_1(k1_funct_4(A,B))
& v2_relat_1(k1_funct_4(A,B))
& v1_funct_1(k1_funct_4(A,B)) ) ) ).
fof(rc1_circcomb,axiom,
? [A] :
( v1_relat_1(A)
& v1_funct_1(A)
& v2_funct_1(A) ) ).
fof(fc3_circcomb,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ( ~ v3_struct_0(k3_circcomb(A,B))
& v1_msualg_1(k3_circcomb(A,B))
& ~ v2_msualg_1(k3_circcomb(A,B)) ) ) ).
fof(fc4_circcomb,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ( ~ v3_struct_0(k3_circcomb(B,A))
& v1_msualg_1(k3_circcomb(B,A))
& ~ v2_msualg_1(k3_circcomb(B,A)) ) ) ).
fof(fc5_circcomb,axiom,
! [A,B,C] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ( ~ v3_struct_0(k6_circcomb(A,B,C))
& v1_msualg_1(k6_circcomb(A,B,C))
& ~ v2_msualg_1(k6_circcomb(A,B,C)) ) ) ).
fof(fc6_circcomb,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ( ~ v3_struct_0(k7_circcomb(A,B))
& v1_msualg_1(k7_circcomb(A,B))
& ~ v2_msualg_1(k7_circcomb(A,B)) ) ) ).
fof(cc1_circcomb,axiom,
! [A] :
( l1_msualg_1(A)
=> ( ( ~ v3_struct_0(A)
& v3_circcomb(A) )
=> ( ~ v3_struct_0(A)
& v5_circcomb(A) ) ) ) ).
fof(cc2_circcomb,axiom,
! [A] :
( l1_msualg_1(A)
=> ( ( ~ v3_struct_0(A)
& v1_circcomb(A) )
=> ( ~ v3_struct_0(A)
& v2_msafree2(A) ) ) ) ).
fof(fc7_circcomb,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ( ~ v3_struct_0(k7_circcomb(A,B))
& v1_msualg_1(k7_circcomb(A,B))
& ~ v2_msualg_1(k7_circcomb(A,B))
& v2_msafree2(k7_circcomb(A,B))
& v1_circcomb(k7_circcomb(A,B))
& v2_circcomb(k7_circcomb(A,B)) ) ) ).
fof(rc2_circcomb,axiom,
? [A] :
( l1_msualg_1(A)
& ~ v3_struct_0(A)
& v1_msualg_1(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& v1_circcomb(A)
& v2_circcomb(A) ) ).
fof(fc8_circcomb,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v1_circcomb(A)
& l1_msualg_1(A)
& ~ v3_struct_0(B)
& v1_circcomb(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)) ) ) ).
fof(fc9_circcomb,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_circcomb(A)
& l1_msualg_1(A)
& ~ v3_struct_0(B)
& v2_circcomb(B)
& l1_msualg_1(B) )
=> ( ~ v3_struct_0(k3_circcomb(A,B))
& v1_msualg_1(k3_circcomb(A,B))
& v2_circcomb(k3_circcomb(A,B)) ) ) ).
fof(fc10_circcomb,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& ~ v1_xboole_0(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(k9_circcomb(A,B,C,D),k7_circcomb(C,D))
& v5_msualg_1(k9_circcomb(A,B,C,D),k7_circcomb(C,D))
& v4_circcomb(k9_circcomb(A,B,C,D),k7_circcomb(C,D)) ) ) ).
fof(fc11_circcomb,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& ~ v1_xboole_0(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) )
=> ( ~ v3_struct_0(k7_circcomb(C,D))
& v1_msualg_1(k7_circcomb(C,D))
& ~ v2_msualg_1(k7_circcomb(C,D))
& v2_msafree2(k7_circcomb(C,D))
& v1_circcomb(k7_circcomb(C,D))
& v2_circcomb(k7_circcomb(C,D))
& v5_circcomb(k7_circcomb(C,D)) ) ) ).
fof(fc12_circcomb,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& v1_funct_1(B)
& v1_funct_2(B,k4_finseq_2(A,k6_margrel1),k6_margrel1)
& m1_relset_1(B,k4_finseq_2(A,k6_margrel1),k6_margrel1)
& m1_circcomb(C,A) )
=> ( ~ v3_struct_0(k7_circcomb(B,C))
& v1_msualg_1(k7_circcomb(B,C))
& ~ v2_msualg_1(k7_circcomb(B,C))
& v2_msafree2(k7_circcomb(B,C))
& v1_circcomb(k7_circcomb(B,C))
& v2_circcomb(k7_circcomb(B,C))
& v3_circcomb(k7_circcomb(B,C))
& v5_circcomb(k7_circcomb(B,C)) ) ) ).
fof(rc3_circcomb,axiom,
? [A] :
( l1_msualg_1(A)
& ~ v3_struct_0(A)
& v3_circcomb(A)
& v5_circcomb(A) ) ).
fof(fc13_circcomb,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_circcomb(A)
& l1_msualg_1(A)
& ~ v3_struct_0(B)
& v3_circcomb(B)
& l1_msualg_1(B) )
=> ( ~ v3_struct_0(k3_circcomb(A,B))
& v1_msualg_1(k3_circcomb(A,B))
& v3_circcomb(k3_circcomb(A,B))
& v5_circcomb(k3_circcomb(A,B)) ) ) ).
fof(fc14_circcomb,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(k9_circcomb(A,B,C,D),k7_circcomb(C,D))
& v5_msualg_1(k9_circcomb(A,B,C,D),k7_circcomb(C,D))
& v3_msafree2(k9_circcomb(A,B,C,D),k7_circcomb(C,D))
& v4_msafree2(k9_circcomb(A,B,C,D),k7_circcomb(C,D))
& v4_circcomb(k9_circcomb(A,B,C,D),k7_circcomb(C,D)) ) ) ).
fof(cc3_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ( v6_circcomb(B,A)
=> ( v5_msualg_1(B,A)
& v3_msafree2(B,A)
& v4_msafree2(B,A) ) ) ) ) ).
fof(rc4_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ? [B] :
( l3_msualg_1(B,A)
& v4_msualg_1(B,A)
& v5_msualg_1(B,A)
& v3_msafree2(B,A)
& v4_msafree2(B,A)
& v6_circcomb(B,A) ) ) ).
fof(rc5_circcomb,axiom,
? [A] :
( l1_msualg_1(A)
& ~ v3_struct_0(A)
& v1_msualg_1(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& v1_circcomb(A)
& v2_circcomb(A)
& v3_circcomb(A)
& v5_circcomb(A) ) ).
fof(rc6_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_circcomb(A)
& l1_msualg_1(A) )
=> ? [B] :
( l3_msualg_1(B,A)
& v4_msualg_1(B,A)
& v5_msualg_1(B,A)
& v3_msafree2(B,A)
& v4_msafree2(B,A)
& v4_circcomb(B,A)
& v6_circcomb(B,A) ) ) ).
fof(fc15_circcomb,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v1_circcomb(A)
& v3_circcomb(A)
& l1_msualg_1(A)
& ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& v1_circcomb(B)
& v3_circcomb(B)
& l1_msualg_1(B)
& v4_msafree2(C,A)
& v4_circcomb(C,A)
& v6_circcomb(C,A)
& l3_msualg_1(C,A)
& v4_msafree2(D,B)
& v4_circcomb(D,B)
& v6_circcomb(D,B)
& l3_msualg_1(D,B) )
=> ( v4_msualg_1(k4_circcomb(A,B,C,D),k3_circcomb(A,B))
& v5_msualg_1(k4_circcomb(A,B,C,D),k3_circcomb(A,B))
& v3_msafree2(k4_circcomb(A,B,C,D),k3_circcomb(A,B))
& v4_msafree2(k4_circcomb(A,B,C,D),k3_circcomb(A,B))
& v4_circcomb(k4_circcomb(A,B,C,D),k3_circcomb(A,B))
& v6_circcomb(k4_circcomb(A,B,C,D),k3_circcomb(A,B)) ) ) ).
fof(rc7_circcomb,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) )
=> ? [E] :
( l3_msualg_1(E,k7_circcomb(C,D))
& v4_msualg_1(E,k7_circcomb(C,D))
& v5_msualg_1(E,k7_circcomb(C,D))
& v3_msafree2(E,k7_circcomb(C,D))
& v4_msafree2(E,k7_circcomb(C,D))
& v4_circcomb(E,k7_circcomb(C,D)) ) ) ).
fof(fc16_circcomb,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(k9_circcomb(A,B,C,D),k7_circcomb(C,D))
& v5_msualg_1(k9_circcomb(A,B,C,D),k7_circcomb(C,D))
& v3_msafree2(k9_circcomb(A,B,C,D),k7_circcomb(C,D))
& v4_msafree2(k9_circcomb(A,B,C,D),k7_circcomb(C,D))
& v4_circcomb(k9_circcomb(A,B,C,D),k7_circcomb(C,D)) ) ) ).
fof(t1_circcomb,axiom,
$true ).
fof(t2_circcomb,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( ( r1_tarski(k2_relat_1(C),k1_relat_1(A))
& r1_tarski(k2_relat_1(C),k1_relat_1(B))
& r1_partfun1(A,B) )
=> k5_relat_1(C,A) = k5_relat_1(C,B) ) ) ) ) ).
fof(t3_circcomb,axiom,
! [A,B,C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,B)
=> ( r1_tarski(C,D)
=> r1_tarski(k6_pboole(A,C),k6_pboole(B,D)) ) ) ) ).
fof(t4_circcomb,axiom,
! [A,B,C,D] :
( r1_partfun1(k2_pre_circ(A,C),k2_pre_circ(B,D))
<=> ( C = D
| r1_xboole_0(A,B) ) ) ).
fof(t5_circcomb,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( ( r1_partfun1(A,B)
& r1_partfun1(B,C)
& r1_partfun1(C,A) )
=> r1_partfun1(k1_funct_4(A,B),C) ) ) ) ) ).
fof(t6_circcomb,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m2_finseq_1(C,A)
=> k1_funct_1(k6_pboole(A,k2_pre_circ(A,B)),C) = k4_finseq_2(k3_finseq_1(C),B) ) ) ).
fof(d1_circcomb,axiom,
! [A] :
( l1_msualg_1(A)
=> ! [B] :
( l1_msualg_1(B)
=> ( r1_circcomb(A,B)
<=> ( r1_partfun1(u2_msualg_1(A),u2_msualg_1(B))
& r1_partfun1(u3_msualg_1(A),u3_msualg_1(B)) ) ) ) ) ).
fof(d2_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v1_msualg_1(C)
& l1_msualg_1(C) )
=> ( C = k3_circcomb(A,B)
<=> ( u1_struct_0(C) = k2_xboole_0(u1_struct_0(A),u1_struct_0(B))
& u1_msualg_1(C) = k2_xboole_0(u1_msualg_1(A),u1_msualg_1(B))
& u2_msualg_1(C) = k1_funct_4(u2_msualg_1(A),u2_msualg_1(B))
& u3_msualg_1(C) = k1_funct_4(u3_msualg_1(A),u3_msualg_1(B)) ) ) ) ) ) ).
fof(t7_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_msualg_1(C) )
=> ( ( r1_circcomb(A,B)
& r1_circcomb(B,C)
& r1_circcomb(C,A) )
=> r1_circcomb(k3_circcomb(A,B),C) ) ) ) ) ).
fof(t8_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> k3_circcomb(A,A) = g1_msualg_1(u1_struct_0(A),u1_msualg_1(A),u2_msualg_1(A),u3_msualg_1(A)) ) ).
fof(t9_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ( r1_circcomb(A,B)
=> k3_circcomb(A,B) = k3_circcomb(B,A) ) ) ) ).
fof(t10_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_msualg_1(C) )
=> k3_circcomb(k3_circcomb(A,B),C) = k3_circcomb(A,k3_circcomb(B,C)) ) ) ) ).
fof(t11_circcomb,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v2_funct_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_msafree2(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_msafree2(C)
& l1_msualg_1(C) )
=> ( ( r1_tarski(u3_msualg_1(B),A)
& r1_tarski(u3_msualg_1(C),A) )
=> v2_msafree2(k3_circcomb(B,C)) ) ) ) ) ).
fof(t12_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_msafree2(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_msafree2(B)
& l1_msualg_1(B) )
=> ( r1_xboole_0(k3_msafree2(A),k3_msafree2(B))
=> v2_msafree2(k3_circcomb(A,B)) ) ) ) ).
fof(t13_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ~ ( ~ ( v2_msualg_1(A)
& v2_msualg_1(B) )
& v2_msualg_1(k3_circcomb(A,B)) ) ) ) ).
fof(t14_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_group_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_group_1(B)
& l1_msualg_1(B) )
=> v6_group_1(k3_circcomb(A,B)) ) ) ).
fof(t15_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ( r1_circcomb(A,B)
=> ( k3_msafree2(k3_circcomb(A,B)) = k2_xboole_0(k3_msafree2(A),k3_msafree2(B))
& r1_tarski(k2_msafree2(k3_circcomb(A,B)),k2_xboole_0(k2_msafree2(A),k2_msafree2(B))) ) ) ) ) ).
fof(t16_circcomb,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))
=> ( r2_hidden(C,k2_msafree2(k3_circcomb(A,B)))
=> r2_hidden(C,k2_msafree2(B)) ) ) ) ) ).
fof(t17_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ( r1_circcomb(A,B)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,k2_msafree2(k3_circcomb(A,B)))
=> r2_hidden(C,k2_msafree2(A)) ) ) ) ) ) ).
fof(t18_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(B))
=> ! [D] :
( m1_subset_1(D,u1_msualg_1(k3_circcomb(A,B)))
=> ( C = D
=> ( k1_msualg_1(k3_circcomb(A,B),D) = k1_msualg_1(B,C)
& k2_msualg_1(k3_circcomb(A,B),D) = k2_msualg_1(B,C) ) ) ) ) ) ) ).
fof(t19_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(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] :
( m1_subset_1(D,u1_struct_0(B))
=> ( r2_hidden(D,k4_msafree2(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ( D = E
=> ( r2_hidden(E,k4_msafree2(C))
& k5_msafree2(C,E) = k5_msafree2(B,D) ) ) ) ) ) ) ) ) ) ).
fof(t20_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ( r1_circcomb(A,B)
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ! [D] :
( m1_subset_1(D,u1_msualg_1(k3_circcomb(A,B)))
=> ( C = D
=> ( k1_msualg_1(k3_circcomb(A,B),D) = k1_msualg_1(A,C)
& k2_msualg_1(k3_circcomb(A,B),D) = k2_msualg_1(A,C) ) ) ) ) ) ) ) ).
fof(t21_circcomb,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)
& l1_msualg_1(C) )
=> ( ( r1_circcomb(A,C)
& B = k3_circcomb(A,C) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(D,k4_msafree2(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( D = E
=> ( r2_hidden(E,k4_msafree2(B))
& k5_msafree2(B,E) = k5_msafree2(A,D) ) ) ) ) ) ) ) ) ) ).
fof(d3_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( l3_msualg_1(C,A)
=> ! [D] :
( l3_msualg_1(D,B)
=> ( r2_circcomb(A,B,C,D)
<=> ( r1_circcomb(A,B)
& r1_partfun1(u4_msualg_1(A,C),u4_msualg_1(B,D))
& r1_partfun1(u5_msualg_1(A,C),u5_msualg_1(B,D)) ) ) ) ) ) ) ).
fof(d4_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v5_msualg_1(C,A)
& l3_msualg_1(C,A) )
=> ! [D] :
( ( v5_msualg_1(D,B)
& l3_msualg_1(D,B) )
=> ( r1_partfun1(u4_msualg_1(A,C),u4_msualg_1(B,D))
=> ! [E] :
( ( v4_msualg_1(E,k3_circcomb(A,B))
& v5_msualg_1(E,k3_circcomb(A,B))
& l3_msualg_1(E,k3_circcomb(A,B)) )
=> ( E = k4_circcomb(A,B,C,D)
<=> ( u4_msualg_1(k3_circcomb(A,B),E) = k1_circcomb(u1_struct_0(A),u1_struct_0(B),u4_msualg_1(A,C),u4_msualg_1(B,D))
& u5_msualg_1(k3_circcomb(A,B),E) = k1_circcomb(u1_msualg_1(A),u1_msualg_1(B),u5_msualg_1(A,C),u5_msualg_1(B,D)) ) ) ) ) ) ) ) ) ).
fof(t22_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> r2_circcomb(A,A,B,B) ) ) ).
fof(t23_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) )
=> ! [C] :
( l3_msualg_1(C,A)
=> ! [D] :
( l3_msualg_1(D,B)
=> ( r2_circcomb(A,B,C,D)
=> r2_circcomb(B,A,D,C) ) ) ) ) ) ).
fof(t24_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_msualg_1(C) )
=> ! [D] :
( ( v5_msualg_1(D,A)
& l3_msualg_1(D,A) )
=> ! [E] :
( ( v5_msualg_1(E,B)
& l3_msualg_1(E,B) )
=> ! [F] :
( l3_msualg_1(F,C)
=> ( ( r2_circcomb(A,B,D,E)
& r2_circcomb(B,C,E,F)
& r2_circcomb(C,A,F,D) )
=> r2_circcomb(k3_circcomb(A,B),C,k4_circcomb(A,B,D,E),F) ) ) ) ) ) ) ) ).
fof(t25_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> k4_circcomb(A,A,B,B) = g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)) ) ) ).
fof(t26_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v5_msualg_1(C,A)
& l3_msualg_1(C,A) )
=> ! [D] :
( ( v5_msualg_1(D,B)
& l3_msualg_1(D,B) )
=> ( r2_circcomb(A,B,C,D)
=> k4_circcomb(A,B,C,D) = k4_circcomb(B,A,D,C) ) ) ) ) ) ).
fof(t27_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_msualg_1(C) )
=> ! [D] :
( ( v5_msualg_1(D,A)
& l3_msualg_1(D,A) )
=> ! [E] :
( ( v5_msualg_1(E,B)
& l3_msualg_1(E,B) )
=> ! [F] :
( ( v5_msualg_1(F,C)
& l3_msualg_1(F,C) )
=> ( ( r1_partfun1(u4_msualg_1(A,D),u4_msualg_1(B,E))
& r1_partfun1(u4_msualg_1(B,E),u4_msualg_1(C,F))
& r1_partfun1(u4_msualg_1(C,F),u4_msualg_1(A,D)) )
=> k4_circcomb(k3_circcomb(A,B),C,k4_circcomb(A,B,D,E),F) = k4_circcomb(A,k3_circcomb(B,C),D,k4_circcomb(B,C,E,F)) ) ) ) ) ) ) ) ).
fof(t28_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v5_msualg_1(C,A)
& v4_msafree2(C,A)
& l3_msualg_1(C,A) )
=> ! [D] :
( ( v5_msualg_1(D,B)
& v4_msafree2(D,B)
& l3_msualg_1(D,B) )
=> ( r1_partfun1(u4_msualg_1(A,C),u4_msualg_1(B,D))
=> v4_msafree2(k4_circcomb(A,B,C,D),k3_circcomb(A,B)) ) ) ) ) ) ).
fof(t29_circcomb,axiom,
! [A] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v2_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(A))
=> ! [D] :
( m1_subset_1(D,k4_card_3(B))
=> r2_hidden(k1_funct_4(C,D),k4_card_3(k1_funct_4(A,B))) ) ) ) ) ).
fof(t30_circcomb,axiom,
! [A] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v2_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(k1_funct_4(A,B)))
=> r2_hidden(k7_relat_1(C,k1_relat_1(B)),k4_card_3(B)) ) ) ) ).
fof(t31_circcomb,axiom,
! [A] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v2_relat_1(B)
& v1_funct_1(B) )
=> ( r1_partfun1(A,B)
=> ! [C] :
( m1_subset_1(C,k4_card_3(k1_funct_4(A,B)))
=> r2_hidden(k7_relat_1(C,k1_relat_1(A)),k4_card_3(A)) ) ) ) ) ).
fof(t32_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v5_msualg_1(C,A)
& l3_msualg_1(C,A) )
=> ! [D] :
( m1_subset_1(D,k4_card_3(u4_msualg_1(A,C)))
=> ! [E] :
( ( v5_msualg_1(E,B)
& l3_msualg_1(E,B) )
=> ! [F] :
( m1_subset_1(F,k4_card_3(u4_msualg_1(B,E)))
=> ( r1_partfun1(u4_msualg_1(A,C),u4_msualg_1(B,E))
=> r2_hidden(k1_funct_4(D,F),k4_card_3(u4_msualg_1(k3_circcomb(A,B),k4_circcomb(A,B,C,E)))) ) ) ) ) ) ) ) ).
fof(t33_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v5_msualg_1(C,A)
& l3_msualg_1(C,A) )
=> ! [D] :
( ( v5_msualg_1(D,B)
& l3_msualg_1(D,B) )
=> ( r1_partfun1(u4_msualg_1(A,C),u4_msualg_1(B,D))
=> ! [E] :
( m1_subset_1(E,k4_card_3(u4_msualg_1(k3_circcomb(A,B),k4_circcomb(A,B,C,D))))
=> ( r2_hidden(k7_relat_1(E,u1_struct_0(A)),k4_card_3(u4_msualg_1(A,C)))
& r2_hidden(k7_relat_1(E,u1_struct_0(B)),k4_card_3(u4_msualg_1(B,D))) ) ) ) ) ) ) ) ).
fof(t34_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v5_msualg_1(C,A)
& l3_msualg_1(C,A) )
=> ! [D] :
( ( v5_msualg_1(D,B)
& l3_msualg_1(D,B) )
=> ( r1_partfun1(u4_msualg_1(A,C),u4_msualg_1(B,D))
=> ! [E] :
( m1_subset_1(E,u1_msualg_1(k3_circcomb(A,B)))
=> ! [F] :
( m1_subset_1(F,u1_msualg_1(B))
=> ( E = F
=> k5_msualg_1(k3_circcomb(A,B),E,k4_circcomb(A,B,C,D)) = k5_msualg_1(B,F,D) ) ) ) ) ) ) ) ) ).
fof(t35_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v5_msualg_1(C,A)
& l3_msualg_1(C,A) )
=> ! [D] :
( ( v5_msualg_1(D,B)
& l3_msualg_1(D,B) )
=> ( ( r1_partfun1(u4_msualg_1(A,C),u4_msualg_1(B,D))
& r1_partfun1(u5_msualg_1(A,C),u5_msualg_1(B,D)) )
=> ! [E] :
( m1_subset_1(E,u1_msualg_1(k3_circcomb(A,B)))
=> ! [F] :
( m1_subset_1(F,u1_msualg_1(A))
=> ( E = F
=> k5_msualg_1(k3_circcomb(A,B),E,k4_circcomb(A,B,C,D)) = k5_msualg_1(A,F,C) ) ) ) ) ) ) ) ) ).
fof(t36_circcomb,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) )
=> ! [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] :
( m1_subset_1(I,u1_msualg_1(C))
=> ! [J] :
( m1_subset_1(J,u1_msualg_1(B))
=> ( I = J
=> k3_circuit1(C,F,G,I) = k3_circuit1(B,E,H,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t37_circcomb,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)
& r1_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) )
=> ! [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,u1_msualg_1(C))
=> ! [J] :
( m1_subset_1(J,u1_msualg_1(A))
=> ( I = J
=> k3_circuit1(C,F,G,I) = k3_circuit1(A,D,H,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t38_circcomb,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,u1_struct_0(C))
=> ( ! [I] :
( m1_subset_1(I,k4_card_3(u4_msualg_1(A,D)))
=> ( I = k7_relat_1(G,u1_struct_0(A))
=> ( ( ~ r2_hidden(H,k4_msafree2(A))
& ~ ( r2_hidden(H,u1_struct_0(A))
& r2_hidden(H,k2_msafree2(C)) ) )
| k1_funct_1(k6_circuit2(C,F,G),H) = k1_funct_1(k6_circuit2(A,D,I),H) ) ) )
& ! [I] :
( m1_subset_1(I,k4_card_3(u4_msualg_1(B,E)))
=> ( I = k7_relat_1(G,u1_struct_0(B))
=> ( ( ~ r2_hidden(H,k4_msafree2(B))
& ~ ( r2_hidden(H,u1_struct_0(B))
& r2_hidden(H,k2_msafree2(C)) ) )
| k1_funct_1(k6_circuit2(C,F,G),H) = k1_funct_1(k6_circuit2(B,E,I),H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t39_circcomb,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(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)) )
=> k6_circuit2(C,F,G) = k1_funct_4(k6_circuit2(A,D,H),k6_circuit2(B,E,I)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t40_circcomb,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(B),k2_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)))
=> ! [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)) )
=> k6_circuit2(C,F,G) = k1_funct_4(k6_circuit2(B,E,I),k6_circuit2(A,D,H)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t41_circcomb,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_tarski(k2_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(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)) )
=> k6_circuit2(C,F,G) = k1_funct_4(k6_circuit2(B,E,I),k6_circuit2(A,D,H)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t42_circcomb,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_tarski(k2_msafree2(B),k2_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)))
=> ! [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)) )
=> k6_circuit2(C,F,G) = k1_funct_4(k6_circuit2(A,D,H),k6_circuit2(B,E,I)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d5_circcomb,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ! [C,D] :
( ( v1_msualg_1(D)
& ~ v2_msualg_1(D)
& l1_msualg_1(D) )
=> ( D = k6_circcomb(A,B,C)
<=> ( u1_struct_0(D) = k2_xboole_0(k2_relat_1(B),k1_tarski(C))
& u1_msualg_1(D) = k1_tarski(k4_tarski(B,A))
& k1_funct_1(u2_msualg_1(D),k4_tarski(B,A)) = B
& k1_funct_1(u3_msualg_1(D),k4_tarski(B,A)) = C ) ) ) ) ).
fof(t43_circcomb,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> ( u2_msualg_1(k6_circcomb(A,C,B)) = k2_pre_circ(k1_tarski(k4_tarski(C,A)),C)
& u3_msualg_1(k6_circcomb(A,C,B)) = k2_pre_circ(k1_tarski(k4_tarski(C,A)),B) ) ) ).
fof(t44_circcomb,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> ! [D] :
( m1_subset_1(D,u1_msualg_1(k6_circcomb(A,C,B)))
=> ( D = k4_tarski(C,A)
& k1_msualg_1(k6_circcomb(A,C,B),D) = C
& k2_msualg_1(k6_circcomb(A,C,B),D) = B ) ) ) ).
fof(t45_circcomb,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> ( k2_msafree2(k6_circcomb(A,C,B)) = k4_xboole_0(k2_relat_1(C),k1_tarski(B))
& k4_msafree2(k6_circcomb(A,C,B)) = k1_tarski(B) ) ) ).
fof(d6_circcomb,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ! [C] :
( ( v1_msualg_1(C)
& ~ v2_msualg_1(C)
& l1_msualg_1(C) )
=> ( C = k7_circcomb(A,B)
<=> ( u1_struct_0(C) = k2_xboole_0(k2_relat_1(B),k1_tarski(k4_tarski(B,A)))
& u1_msualg_1(C) = k1_tarski(k4_tarski(B,A))
& k1_funct_1(u2_msualg_1(C),k4_tarski(B,A)) = B
& k1_funct_1(u3_msualg_1(C),k4_tarski(B,A)) = k4_tarski(B,A) ) ) ) ) ).
fof(t46_circcomb,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> k7_circcomb(A,B) = k6_circcomb(A,B,k4_tarski(B,A)) ) ).
fof(t47_circcomb,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ( u2_msualg_1(k7_circcomb(A,B)) = k2_pre_circ(k1_tarski(k4_tarski(B,A)),B)
& u3_msualg_1(k7_circcomb(A,B)) = k2_pre_circ(k1_tarski(k4_tarski(B,A)),k4_tarski(B,A)) ) ) ).
fof(t48_circcomb,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(k7_circcomb(A,B)))
=> ( C = k4_tarski(B,A)
& k1_msualg_1(k7_circcomb(A,B),C) = B
& k2_msualg_1(k7_circcomb(A,B),C) = C ) ) ) ).
fof(t49_circcomb,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ( k2_msafree2(k7_circcomb(A,B)) = k2_relat_1(B)
& k4_msafree2(k7_circcomb(A,B)) = k1_tarski(k4_tarski(B,A)) ) ) ).
fof(t50_circcomb,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ! [C] :
( r2_hidden(C,k2_relat_1(B))
=> r2_hidden(k6_classes1(C),k6_classes1(k4_tarski(B,A))) ) ) ).
fof(t51_circcomb,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> r1_circcomb(k7_circcomb(A,B),k7_circcomb(A,C)) ) ) ).
fof(d7_circcomb,axiom,
! [A] :
( l1_msualg_1(A)
=> ( v1_circcomb(A)
<=> u3_msualg_1(A) = k6_partfun1(u1_msualg_1(A)) ) ) ).
fof(d8_circcomb,axiom,
! [A] :
( l1_msualg_1(A)
=> ( v2_circcomb(A)
<=> ! [B] :
( r2_hidden(B,u1_msualg_1(A))
=> B = k4_tarski(k1_funct_1(u2_msualg_1(A),B),k2_mcart_1(B)) ) ) ) ).
fof(d9_circcomb,axiom,
! [A] :
( l1_msualg_1(A)
=> ( v3_circcomb(A)
<=> ! [B] :
( r2_hidden(B,u1_msualg_1(A))
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> ~ ( C = k1_funct_1(u2_msualg_1(A),B)
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(k3_finseq_1(C),k6_margrel1),k6_margrel1)
& m2_relset_1(D,k4_finseq_2(k3_finseq_1(C),k6_margrel1),k6_margrel1) )
=> B != k4_tarski(k1_mcart_1(B),D) ) ) ) ) ) ) ).
fof(d10_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ( v4_circcomb(B,A)
<=> ! [C] :
( r2_hidden(C,u1_msualg_1(A))
=> C = k4_tarski(k1_mcart_1(C),k1_funct_1(u5_msualg_1(A,B),C)) ) ) ) ) ).
fof(d11_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ( v5_circcomb(A)
<=> ? [B] :
( l3_msualg_1(B,A)
& v4_circcomb(B,A) ) ) ) ).
fof(t52_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ( v1_circcomb(A)
<=> ! [B] :
( r2_hidden(B,u1_msualg_1(A))
=> k1_funct_1(u3_msualg_1(A),B) = B ) ) ) ).
fof(t53_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ( v1_circcomb(A)
=> r1_tarski(u1_msualg_1(A),u1_struct_0(A)) ) ) ).
fof(t54_circcomb,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ( v1_circcomb(k7_circcomb(A,B))
& v2_circcomb(k7_circcomb(A,B)) ) ) ).
fof(t55_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_circcomb(A)
& v2_circcomb(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_circcomb(B)
& v2_circcomb(B)
& l1_msualg_1(B) )
=> r1_circcomb(A,B) ) ) ).
fof(t56_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( l3_msualg_1(C,A)
=> ! [D] :
( l3_msualg_1(D,B)
=> ( ( v4_circcomb(C,A)
& v4_circcomb(D,B) )
=> r1_partfun1(u5_msualg_1(A,C),u5_msualg_1(B,D)) ) ) ) ) ) ).
fof(t57_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_circcomb(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_circcomb(B)
& l1_msualg_1(B) )
=> v1_circcomb(k3_circcomb(A,B)) ) ) ).
fof(t58_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_circcomb(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_circcomb(B)
& l1_msualg_1(B) )
=> v2_circcomb(k3_circcomb(A,B)) ) ) ).
fof(t59_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ( ( v3_circcomb(A)
& v3_circcomb(B) )
=> v3_circcomb(k3_circcomb(A,B)) ) ) ) ).
fof(d12_circcomb,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ( m1_circcomb(B,A)
<=> k3_finseq_1(B) = A ) ) ) ).
fof(d13_circcomb,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(A,B),C)
& m2_relset_1(D,k4_finseq_2(A,B),C) )
=> ! [E] :
( m1_circcomb(E,A)
=> ! [F] :
( ( r2_hidden(F,k2_relat_1(E))
=> B = C )
=> ! [G] :
( ( v4_msualg_1(G,k6_circcomb(D,E,F))
& v5_msualg_1(G,k6_circcomb(D,E,F))
& l3_msualg_1(G,k6_circcomb(D,E,F)) )
=> ( G = k8_circcomb(A,B,C,D,E,F)
<=> ( u4_msualg_1(k6_circcomb(D,E,F),G) = k1_circcomb(k2_relat_1(E),k1_tarski(F),k2_pre_circ(k2_relat_1(E),B),k2_pre_circ(k1_tarski(F),C))
& k1_funct_1(u5_msualg_1(k6_circcomb(D,E,F),G),k4_tarski(E,D)) = D ) ) ) ) ) ) ) ) ) ).
fof(d14_circcomb,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(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] :
( ( v4_msualg_1(E,k7_circcomb(C,D))
& v5_msualg_1(E,k7_circcomb(C,D))
& l3_msualg_1(E,k7_circcomb(C,D)) )
=> ( E = k9_circcomb(A,B,C,D)
<=> ( r6_pboole(u1_struct_0(k7_circcomb(C,D)),u4_msualg_1(k7_circcomb(C,D),E),k2_pre_circ(u1_struct_0(k7_circcomb(C,D)),B))
& k1_funct_1(u5_msualg_1(k7_circcomb(C,D),E),k4_tarski(D,C)) = C ) ) ) ) ) ) ) ).
fof(t60_circcomb,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(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)
=> ( v4_circcomb(k9_circcomb(A,B,C,D),k7_circcomb(C,D))
& v5_circcomb(k7_circcomb(C,D)) ) ) ) ) ) ).
fof(t61_circcomb,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_circcomb(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k4_finseq_2(A,k6_margrel1),k6_margrel1)
& m2_relset_1(C,k4_finseq_2(A,k6_margrel1),k6_margrel1) )
=> v3_circcomb(k7_circcomb(C,B)) ) ) ) ).
fof(t62_circcomb,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(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)
=> ( u5_msualg_1(k7_circcomb(C,D),k9_circcomb(A,B,C,D)) = k2_pre_circ(k1_tarski(k4_tarski(D,C)),C)
& ! [E] :
( m1_subset_1(E,u1_struct_0(k7_circcomb(C,D)))
=> k1_funct_1(u4_msualg_1(k7_circcomb(C,D),k9_circcomb(A,B,C,D)),E) = B ) ) ) ) ) ) ).
fof(t63_circcomb,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(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_circcomb(E,A)
=> r2_circcomb(k7_circcomb(C,D),k7_circcomb(C,E),k9_circcomb(A,B,C,D),k9_circcomb(A,B,C,E)) ) ) ) ) ) ).
fof(t64_circcomb,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),k4_tarski(D,C)) = k1_funct_1(C,k5_relat_1(D,E)) ) ) ) ) ) ).
fof(d15_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ( v6_circcomb(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k1_funct_1(u4_msualg_1(A,B),C) = k10_circcomb ) ) ) ) ).
fof(t65_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ( v6_circcomb(B,A)
<=> r6_pboole(u1_struct_0(A),u4_msualg_1(A,B),k2_pre_circ(u1_struct_0(A),k10_circcomb)) ) ) ) ).
fof(t66_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ( v6_circcomb(B,A)
<=> r1_tarski(k2_relat_1(u4_msualg_1(A,B)),k1_tarski(k10_circcomb)) ) ) ) ).
fof(t67_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( l3_msualg_1(C,A)
=> ! [D] :
( l3_msualg_1(D,B)
=> ( ( v6_circcomb(C,A)
& v6_circcomb(D,B) )
=> r1_partfun1(u4_msualg_1(A,C),u4_msualg_1(B,D)) ) ) ) ) ) ).
fof(t68_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_circcomb(A)
& v2_circcomb(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_circcomb(B)
& v2_circcomb(B)
& l1_msualg_1(B) )
=> ! [C] :
( l3_msualg_1(C,A)
=> ! [D] :
( l3_msualg_1(D,B)
=> ( ( v6_circcomb(C,A)
& v4_circcomb(C,A)
& v6_circcomb(D,B)
& v4_circcomb(D,B) )
=> r2_circcomb(A,B,C,D) ) ) ) ) ) ).
fof(t69_circcomb,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k4_finseq_2(A,k10_circcomb),k10_circcomb)
& m2_relset_1(B,k4_finseq_2(A,k10_circcomb),k10_circcomb) )
=> ! [C] :
( m1_circcomb(C,A)
=> v6_circcomb(k9_circcomb(A,k10_circcomb,B,C),k7_circcomb(B,C)) ) ) ) ).
fof(t70_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v6_circcomb(C,A)
& l3_msualg_1(C,A) )
=> ! [D] :
( ( v6_circcomb(D,B)
& l3_msualg_1(D,B) )
=> v6_circcomb(k4_circcomb(A,B,C,D),k3_circcomb(A,B)) ) ) ) ) ).
fof(t71_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v5_msualg_1(C,A)
& l3_msualg_1(C,A) )
=> ! [D] :
( ( v5_msualg_1(D,B)
& l3_msualg_1(D,B) )
=> ( ( v4_circcomb(C,A)
& v4_circcomb(D,B)
& r1_partfun1(u4_msualg_1(A,C),u4_msualg_1(B,D)) )
=> v4_circcomb(k4_circcomb(A,B,C,D),k3_circcomb(A,B)) ) ) ) ) ) ).
fof(t72_circcomb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v1_circcomb(A)
& v2_circcomb(A)
& v3_circcomb(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& v1_circcomb(B)
& v2_circcomb(B)
& v3_circcomb(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v4_msafree2(C,A)
& v4_circcomb(C,A)
& v6_circcomb(C,A)
& l3_msualg_1(C,A) )
=> ! [D] :
( ( v4_msafree2(D,B)
& v4_circcomb(D,B)
& v6_circcomb(D,B)
& l3_msualg_1(D,B) )
=> ! [E] :
( m1_subset_1(E,k4_card_3(u4_msualg_1(k3_circcomb(A,B),k4_circcomb(A,B,C,D))))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k3_circcomb(A,B)))
=> ( ! [G] :
( m1_subset_1(G,k4_card_3(u4_msualg_1(A,C)))
=> ( G = k7_relat_1(E,u1_struct_0(A))
=> ( ( ~ r2_hidden(F,k4_msafree2(A))
& ~ ( r2_hidden(F,u1_struct_0(A))
& r2_hidden(F,k2_msafree2(k3_circcomb(A,B))) ) )
| k1_funct_1(k6_circuit2(k3_circcomb(A,B),k4_circcomb(A,B,C,D),E),F) = k1_funct_1(k6_circuit2(A,C,G),F) ) ) )
& ! [G] :
( m1_subset_1(G,k4_card_3(u4_msualg_1(B,D)))
=> ( G = k7_relat_1(E,u1_struct_0(B))
=> ( ( ~ r2_hidden(F,k4_msafree2(B))
& ~ ( r2_hidden(F,u1_struct_0(B))
& r2_hidden(F,k2_msafree2(k3_circcomb(A,B))) ) )
| k1_funct_1(k6_circuit2(k3_circcomb(A,B),k4_circcomb(A,B,C,D),E),F) = k1_funct_1(k6_circuit2(B,D,G),F) ) ) ) ) ) ) ) ) ) ) ).
fof(s1_circcomb,axiom,
? [A] :
( m1_pboole(A,f1_s1_circcomb)
& ! [B,C] :
( m1_subset_1(C,f2_s1_circcomb)
=> ( ( r2_hidden(B,f1_s1_circcomb)
& C = k1_funct_1(f3_s1_circcomb,B) )
=> k1_funct_1(A,B) = f4_s1_circcomb(B,C) ) ) ) ).
fof(s2_circcomb,axiom,
( ! [A,B] :
( m2_finseq_2(B,u1_struct_0(f1_s2_circcomb),k3_finseq_2(u1_struct_0(f1_s2_circcomb)))
=> ( ( r2_hidden(A,u1_msualg_1(f1_s2_circcomb))
& B = k1_funct_1(u2_msualg_1(f1_s2_circcomb),A) )
=> ( v1_funct_1(f2_s2_circcomb(A,B))
& v1_funct_2(f2_s2_circcomb(A,B),k4_finseq_2(k3_finseq_1(B),k6_margrel1),k6_margrel1)
& m2_relset_1(f2_s2_circcomb(A,B),k4_finseq_2(k3_finseq_1(B),k6_margrel1),k6_margrel1) ) ) )
=> ? [A] :
( v4_msualg_1(A,f1_s2_circcomb)
& l3_msualg_1(A,f1_s2_circcomb)
& r6_pboole(u1_struct_0(f1_s2_circcomb),u4_msualg_1(f1_s2_circcomb,A),k2_pre_circ(u1_struct_0(f1_s2_circcomb),k6_margrel1))
& ! [B,C] :
( m2_finseq_2(C,u1_struct_0(f1_s2_circcomb),k3_finseq_2(u1_struct_0(f1_s2_circcomb)))
=> ( ( r2_hidden(B,u1_msualg_1(f1_s2_circcomb))
& C = k1_funct_1(u2_msualg_1(f1_s2_circcomb),B) )
=> k1_funct_1(u5_msualg_1(f1_s2_circcomb,A),B) = f2_s2_circcomb(B,C) ) ) ) ) ).
fof(dt_m1_circcomb,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ! [B] :
( m1_circcomb(B,A)
=> ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) ) ) ) ).
fof(existence_m1_circcomb,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ? [B] : m1_circcomb(B,A) ) ).
fof(symmetry_r1_circcomb,axiom,
! [A,B] :
( ( l1_msualg_1(A)
& l1_msualg_1(B) )
=> ( r1_circcomb(A,B)
=> r1_circcomb(B,A) ) ) ).
fof(reflexivity_r1_circcomb,axiom,
! [A,B] :
( ( l1_msualg_1(A)
& l1_msualg_1(B) )
=> r1_circcomb(A,A) ) ).
fof(dt_k1_circcomb,axiom,
! [A,B,C,D] :
( ( m1_pboole(C,A)
& m1_pboole(D,B) )
=> m1_pboole(k1_circcomb(A,B,C,D),k2_xboole_0(A,B)) ) ).
fof(idempotence_k1_circcomb,axiom,
! [A,B,C,D] :
( ( m1_pboole(C,A)
& m1_pboole(D,B) )
=> k1_circcomb(A,B,C,C) = C ) ).
fof(redefinition_k1_circcomb,axiom,
! [A,B,C,D] :
( ( m1_pboole(C,A)
& m1_pboole(D,B) )
=> k1_circcomb(A,B,C,D) = k1_funct_4(C,D) ) ).
fof(dt_k2_circcomb,axiom,
! [A,B,C,D,E,F,G,H] :
( ( v2_relat_1(B)
& m1_pboole(B,A)
& v2_relat_1(C)
& m1_pboole(C,A)
& v2_relat_1(E)
& m1_pboole(E,D)
& v2_relat_1(F)
& m1_pboole(F,D)
& m3_pboole(G,A,B,C)
& m3_pboole(H,D,E,F) )
=> m3_pboole(k2_circcomb(A,B,C,D,E,F,G,H),k2_xboole_0(A,D),k1_circcomb(A,D,B,E),k1_circcomb(A,D,C,F)) ) ).
fof(idempotence_k2_circcomb,axiom,
! [A,B,C,D,E,F,G,H] :
( ( v2_relat_1(B)
& m1_pboole(B,A)
& v2_relat_1(C)
& m1_pboole(C,A)
& v2_relat_1(E)
& m1_pboole(E,D)
& v2_relat_1(F)
& m1_pboole(F,D)
& m3_pboole(G,A,B,C)
& m3_pboole(H,D,E,F) )
=> k2_circcomb(A,B,C,D,E,F,G,G) = G ) ).
fof(redefinition_k2_circcomb,axiom,
! [A,B,C,D,E,F,G,H] :
( ( v2_relat_1(B)
& m1_pboole(B,A)
& v2_relat_1(C)
& m1_pboole(C,A)
& v2_relat_1(E)
& m1_pboole(E,D)
& v2_relat_1(F)
& m1_pboole(F,D)
& m3_pboole(G,A,B,C)
& m3_pboole(H,D,E,F) )
=> k2_circcomb(A,B,C,D,E,F,G,H) = k1_funct_4(G,H) ) ).
fof(dt_k3_circcomb,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A)
& ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ( ~ v3_struct_0(k3_circcomb(A,B))
& v1_msualg_1(k3_circcomb(A,B))
& l1_msualg_1(k3_circcomb(A,B)) ) ) ).
fof(dt_k4_circcomb,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A)
& ~ v3_struct_0(B)
& l1_msualg_1(B)
& v5_msualg_1(C,A)
& l3_msualg_1(C,A)
& v5_msualg_1(D,B)
& l3_msualg_1(D,B) )
=> ( v4_msualg_1(k4_circcomb(A,B,C,D),k3_circcomb(A,B))
& v5_msualg_1(k4_circcomb(A,B,C,D),k3_circcomb(A,B))
& l3_msualg_1(k4_circcomb(A,B,C,D),k3_circcomb(A,B)) ) ) ).
fof(dt_k5_circcomb,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& m1_subset_1(C,A) )
=> ( v1_funct_1(k5_circcomb(A,B,C))
& v1_funct_2(k5_circcomb(A,B,C),B,A)
& m2_relset_1(k5_circcomb(A,B,C),B,A) ) ) ).
fof(redefinition_k5_circcomb,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& m1_subset_1(C,A) )
=> k5_circcomb(A,B,C) = k2_funcop_1(B,C) ) ).
fof(dt_k6_circcomb,axiom,
! [A,B,C] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ( v1_msualg_1(k6_circcomb(A,B,C))
& ~ v2_msualg_1(k6_circcomb(A,B,C))
& l1_msualg_1(k6_circcomb(A,B,C)) ) ) ).
fof(dt_k7_circcomb,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ( v1_msualg_1(k7_circcomb(A,B))
& ~ v2_msualg_1(k7_circcomb(A,B))
& l1_msualg_1(k7_circcomb(A,B)) ) ) ).
fof(dt_k8_circcomb,axiom,
! [A,B,C,D,E,F] :
( ( m1_subset_1(A,k5_numbers)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(A,B),C)
& m1_relset_1(D,k4_finseq_2(A,B),C)
& m1_circcomb(E,A) )
=> ( v4_msualg_1(k8_circcomb(A,B,C,D,E,F),k6_circcomb(D,E,F))
& v5_msualg_1(k8_circcomb(A,B,C,D,E,F),k6_circcomb(D,E,F))
& l3_msualg_1(k8_circcomb(A,B,C,D,E,F),k6_circcomb(D,E,F)) ) ) ).
fof(dt_k9_circcomb,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& ~ v1_xboole_0(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(k9_circcomb(A,B,C,D),k7_circcomb(C,D))
& v5_msualg_1(k9_circcomb(A,B,C,D),k7_circcomb(C,D))
& l3_msualg_1(k9_circcomb(A,B,C,D),k7_circcomb(C,D)) ) ) ).
fof(dt_k10_circcomb,axiom,
( ~ v1_xboole_0(k10_circcomb)
& v1_finset_1(k10_circcomb)
& m1_subset_1(k10_circcomb,k1_zfmisc_1(k5_numbers)) ) ).
fof(redefinition_k10_circcomb,axiom,
k10_circcomb = k6_margrel1 ).
%------------------------------------------------------------------------------