SET007 Axioms: SET007+439.ax
%------------------------------------------------------------------------------
% File : SET007+439 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Full Adder Circuit. Part I
% Version : [Urb08] axioms.
% English :
% Refs : [Mat90] Matuszewski (1990), Formalized Mathematics
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : facirc_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 176 ( 22 unt; 0 def)
% Number of atoms : 1268 ( 164 equ)
% Maximal formula atoms : 28 ( 7 avg)
% Number of connectives : 1324 ( 232 ~; 4 |; 646 &)
% ( 9 <=>; 433 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 9 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 46 ( 45 usr; 0 prp; 1-4 aty)
% Number of functors : 77 ( 77 usr; 11 con; 0-4 aty)
% Number of variables : 631 ( 618 !; 13 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(cc1_facirc_1,axiom,
! [A] :
( v1_facirc_1(A)
=> ~ v1_xboole_0(A) ) ).
fof(fc1_facirc_1,axiom,
! [A,B] :
( ~ v1_xboole_0(k4_tarski(A,B))
& v1_facirc_1(k4_tarski(A,B)) ) ).
fof(rc1_facirc_1,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_facirc_1(A) ) ).
fof(rc2_facirc_1,axiom,
? [A] : ~ v1_facirc_1(A) ).
fof(cc2_facirc_1,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ( v1_ordinal1(A)
& v2_ordinal1(A)
& v3_ordinal1(A)
& v4_ordinal2(A)
& v1_xcmplx_0(A)
& v1_xreal_0(A)
& ~ v1_facirc_1(A) ) ) ).
fof(cc3_facirc_1,axiom,
! [A] :
( v1_xboole_0(A)
=> ~ v2_facirc_1(A) ) ).
fof(fc2_facirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ( ~ v1_xboole_0(k1_tarski(A))
& ~ v2_facirc_1(k1_tarski(A)) ) ) ).
fof(fc3_facirc_1,axiom,
! [A,B] :
( ( ~ v1_facirc_1(A)
& ~ v1_facirc_1(B) )
=> ( ~ v1_xboole_0(k2_tarski(A,B))
& ~ v2_facirc_1(k2_tarski(A,B)) ) ) ).
fof(fc4_facirc_1,axiom,
! [A,B,C] :
( ( ~ v1_facirc_1(A)
& ~ v1_facirc_1(B)
& ~ v1_facirc_1(C) )
=> ~ v2_facirc_1(k1_enumset1(A,B,C)) ) ).
fof(rc3_facirc_1,axiom,
? [A] :
( ~ v1_xboole_0(A)
& ~ v2_facirc_1(A) ) ).
fof(fc5_facirc_1,axiom,
! [A,B] :
( ( ~ v2_facirc_1(A)
& ~ v2_facirc_1(B) )
=> ~ v2_facirc_1(k2_xboole_0(A,B)) ) ).
fof(fc6_facirc_1,axiom,
! [A,B] :
( ~ v2_facirc_1(A)
=> ~ v2_facirc_1(k4_xboole_0(A,B)) ) ).
fof(fc7_facirc_1,axiom,
! [A,B] :
( ~ v2_facirc_1(A)
=> ~ v2_facirc_1(k3_xboole_0(A,B)) ) ).
fof(fc8_facirc_1,axiom,
! [A,B] :
( ~ v2_facirc_1(A)
=> ~ v2_facirc_1(k3_xboole_0(B,A)) ) ).
fof(fc9_facirc_1,axiom,
! [A] :
( v1_facirc_1(A)
=> ( ~ v1_xboole_0(k1_tarski(A))
& v1_relat_1(k1_tarski(A)) ) ) ).
fof(fc10_facirc_1,axiom,
! [A,B] :
( ( v1_facirc_1(A)
& v1_facirc_1(B) )
=> ( ~ v1_xboole_0(k2_tarski(A,B))
& v1_relat_1(k2_tarski(A,B)) ) ) ).
fof(fc11_facirc_1,axiom,
! [A,B,C] :
( ( v1_facirc_1(A)
& v1_facirc_1(B)
& v1_facirc_1(C) )
=> v1_relat_1(k1_enumset1(A,B,C)) ) ).
fof(cc4_facirc_1,axiom,
! [A] :
( ( v1_relat_1(A)
& ~ v2_facirc_1(A) )
=> ( v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v2_funct_1(A)
& v1_ordinal1(A)
& v2_ordinal1(A)
& v3_ordinal1(A)
& v4_ordinal2(A)
& v1_xcmplx_0(A)
& v1_xreal_0(A)
& ~ v2_xreal_0(A)
& ~ v3_xreal_0(A)
& ~ v2_facirc_1(A) ) ) ).
fof(fc12_facirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ( ~ v1_xboole_0(k5_finseq_1(A))
& v1_relat_1(k5_finseq_1(A))
& v1_funct_1(k5_finseq_1(A))
& v1_finset_1(k5_finseq_1(A))
& v1_finseq_1(k5_finseq_1(A))
& v3_facirc_1(k5_finseq_1(A)) ) ) ).
fof(fc13_facirc_1,axiom,
! [A,B] :
( ( ~ v1_facirc_1(A)
& ~ v1_facirc_1(B) )
=> ( v1_relat_1(k10_finseq_1(A,B))
& v1_funct_1(k10_finseq_1(A,B))
& v1_finset_1(k10_finseq_1(A,B))
& v1_finseq_1(k10_finseq_1(A,B))
& v3_facirc_1(k10_finseq_1(A,B)) ) ) ).
fof(fc14_facirc_1,axiom,
! [A,B,C] :
( ( ~ v1_facirc_1(A)
& ~ v1_facirc_1(B)
& ~ v1_facirc_1(C) )
=> ( v1_relat_1(k11_finseq_1(A,B,C))
& v1_funct_1(k11_finseq_1(A,B,C))
& v1_finset_1(k11_finseq_1(A,B,C))
& v1_finseq_1(k11_finseq_1(A,B,C))
& v3_facirc_1(k11_finseq_1(A,B,C)) ) ) ).
fof(rc4_facirc_1,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ? [B] :
( m1_circcomb(B,A)
& v1_relat_1(B)
& v1_funct_1(B)
& v2_funct_1(B)
& v1_finset_1(B)
& v1_finseq_1(B)
& v3_facirc_1(B) ) ) ).
fof(rc5_facirc_1,axiom,
? [A] :
( v1_relat_1(A)
& v1_funct_1(A)
& v2_funct_1(A)
& v1_finset_1(A)
& v1_finseq_1(A)
& v3_facirc_1(A) ) ).
fof(fc15_facirc_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v3_facirc_1(A) )
=> ~ v2_facirc_1(k2_relat_1(A)) ) ).
fof(fc16_facirc_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v5_circcomb(A)
& l1_msualg_1(A)
& m1_subset_1(B,u1_msualg_1(A)) )
=> ( v1_relat_1(k2_mcart_1(B))
& v1_funct_1(k2_mcart_1(B)) ) ) ).
fof(fc17_facirc_1,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(np__2,k10_circcomb),k10_circcomb)
& m1_relset_1(D,k4_finseq_2(np__2,k10_circcomb),k10_circcomb) )
=> ( ~ v1_xboole_0(k13_facirc_1(A,B,C,D))
& v1_facirc_1(k13_facirc_1(A,B,C,D)) ) ) ).
fof(d1_facirc_1,axiom,
! [A] :
( v1_facirc_1(A)
<=> ? [B,C] : A = k4_tarski(B,C) ) ).
fof(d2_facirc_1,axiom,
! [A] :
( v2_facirc_1(A)
<=> ? [B] :
( v1_facirc_1(B)
& r2_hidden(B,A) ) ) ).
fof(d3_facirc_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v3_facirc_1(A)
<=> ! [B] :
~ ( r2_hidden(B,k1_relat_1(A))
& v1_facirc_1(k1_funct_1(A,B)) ) ) ) ).
fof(t1_facirc_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ~ ( v3_facirc_1(A)
& v2_facirc_1(k2_relat_1(A)) ) ) ).
fof(t2_facirc_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ( ( r1_circcomb(A,B)
& v1_relat_1(k3_msafree2(A))
& v1_relat_1(k3_msafree2(B)) )
=> v1_relat_1(k3_msafree2(k3_circcomb(A,B))) ) ) ) ).
fof(t3_facirc_1,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) )
=> ( ( v1_relat_1(k3_msafree2(A))
& v1_relat_1(k3_msafree2(B)) )
=> v1_relat_1(k3_msafree2(k3_circcomb(A,B))) ) ) ) ).
fof(t4_facirc_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ( ( r1_circcomb(A,B)
& r1_xboole_0(k3_msafree2(B),k2_msafree2(A)) )
=> ( r1_tarski(k2_msafree2(A),k2_msafree2(k3_circcomb(A,B)))
& k2_msafree2(k3_circcomb(A,B)) = k2_xboole_0(k2_msafree2(A),k4_xboole_0(k2_msafree2(B),k3_msafree2(A))) ) ) ) ) ).
fof(t5_facirc_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> ( v2_facirc_1(A)
| r1_xboole_0(A,B) ) ) ).
fof(t6_facirc_1,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) )
=> ( v1_relat_1(k3_msafree2(B))
=> ( v2_facirc_1(k2_msafree2(A))
| ( r1_tarski(k2_msafree2(A),k2_msafree2(k3_circcomb(A,B)))
& k2_msafree2(k3_circcomb(A,B)) = k2_xboole_0(k2_msafree2(A),k4_xboole_0(k2_msafree2(B),k3_msafree2(A))) ) ) ) ) ) ).
fof(t7_facirc_1,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) )
=> ( ( v1_relat_1(k3_msafree2(A))
& v1_relat_1(k3_msafree2(B)) )
=> ( v2_facirc_1(k2_msafree2(A))
| v2_facirc_1(k2_msafree2(B))
| k2_msafree2(k3_circcomb(A,B)) = k2_xboole_0(k2_msafree2(A),k2_msafree2(B)) ) ) ) ) ).
fof(t8_facirc_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ~ ( r1_circcomb(A,B)
& ~ v2_facirc_1(k2_msafree2(A))
& ~ v2_facirc_1(k2_msafree2(B))
& v2_facirc_1(k2_msafree2(k3_circcomb(A,B))) ) ) ) ).
fof(t9_facirc_1,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) )
=> ~ ( ~ v2_facirc_1(k2_msafree2(A))
& ~ v2_facirc_1(k2_msafree2(B))
& v2_facirc_1(k2_msafree2(k3_circcomb(A,B))) ) ) ) ).
fof(d4_facirc_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k4_finseq_2(np__2,k10_circcomb),k10_circcomb)
& m2_relset_1(A,k4_finseq_2(np__2,k10_circcomb),k10_circcomb) )
=> ( A = k1_facirc_1
<=> ! [B] :
( m2_subset_1(B,k5_numbers,k10_circcomb)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k10_circcomb)
=> k1_funct_1(A,k10_finseq_1(B,C)) = k4_binarith(B,C) ) ) ) ) ).
fof(d5_facirc_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k4_finseq_2(np__2,k10_circcomb),k10_circcomb)
& m2_relset_1(A,k4_finseq_2(np__2,k10_circcomb),k10_circcomb) )
=> ( A = k2_facirc_1
<=> ! [B] :
( m2_subset_1(B,k5_numbers,k10_circcomb)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k10_circcomb)
=> k1_funct_1(A,k10_finseq_1(B,C)) = k3_binarith(B,C) ) ) ) ) ).
fof(d6_facirc_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k4_finseq_2(np__2,k10_circcomb),k10_circcomb)
& m2_relset_1(A,k4_finseq_2(np__2,k10_circcomb),k10_circcomb) )
=> ( A = k3_facirc_1
<=> ! [B] :
( m2_subset_1(B,k5_numbers,k10_circcomb)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k10_circcomb)
=> k1_funct_1(A,k10_finseq_1(B,C)) = k12_margrel1(B,C) ) ) ) ) ).
fof(d7_facirc_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k4_finseq_2(np__3,k10_circcomb),k10_circcomb)
& m2_relset_1(A,k4_finseq_2(np__3,k10_circcomb),k10_circcomb) )
=> ( A = k4_facirc_1
<=> ! [B] :
( m2_subset_1(B,k5_numbers,k10_circcomb)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k10_circcomb)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k10_circcomb)
=> k1_funct_1(A,k11_finseq_1(B,C,D)) = k3_binarith(k3_binarith(B,C),D) ) ) ) ) ) ).
fof(t10_facirc_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v4_msafree2(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u4_msualg_1(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_msualg_1(A))
=> k1_funct_1(k6_circuit2(A,B,C),k2_msualg_1(A,D)) = k1_funct_1(k5_msualg_1(A,D,B),k5_relat_1(k1_msualg_1(A,D),C)) ) ) ) ) ).
fof(d8_facirc_1,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] :
( m1_subset_1(E,k4_card_3(u4_msualg_1(A,B)))
=> ( E = k9_facirc_1(A,B,C,D)
<=> ? [F] :
( v1_funct_1(F)
& v1_funct_2(F,k5_numbers,k4_card_3(u4_msualg_1(A,B)))
& m2_relset_1(F,k5_numbers,k4_card_3(u4_msualg_1(A,B)))
& E = k8_funct_2(k5_numbers,k4_card_3(u4_msualg_1(A,B)),F,D)
& k8_funct_2(k5_numbers,k4_card_3(u4_msualg_1(A,B)),F,np__0) = C
& ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k4_card_3(u4_msualg_1(A,B)),F,k1_nat_1(G,np__1)) = k6_circuit2(A,B,k8_funct_2(k5_numbers,k4_card_3(u4_msualg_1(A,B)),F,G)) ) ) ) ) ) ) ) ) ).
fof(t11_facirc_1,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)))
=> k9_facirc_1(A,B,C,np__0) = C ) ) ) ).
fof(t12_facirc_1,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)
=> k9_facirc_1(A,B,C,k1_nat_1(D,np__1)) = k6_circuit2(A,B,k9_facirc_1(A,B,C,D)) ) ) ) ) ).
fof(t13_facirc_1,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)
=> k9_facirc_1(A,B,C,k1_nat_1(D,E)) = k9_facirc_1(A,B,k9_facirc_1(A,B,C,D),E) ) ) ) ) ) ).
fof(t14_facirc_1,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)))
=> k9_facirc_1(A,B,C,np__1) = k6_circuit2(A,B,C) ) ) ) ).
fof(t15_facirc_1,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)))
=> k9_facirc_1(A,B,C,np__2) = k6_circuit2(A,B,k6_circuit2(A,B,C)) ) ) ) ).
fof(t16_facirc_1,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)
=> k9_facirc_1(A,B,C,k1_nat_1(D,np__1)) = k9_facirc_1(A,B,k6_circuit2(A,B,C),D) ) ) ) ) ).
fof(d9_facirc_1,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] :
( r1_facirc_1(A,B,C,D)
<=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k1_funct_1(k9_facirc_1(A,B,C,E),D) = k1_funct_1(C,D) ) ) ) ) ) ).
fof(t17_facirc_1,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] :
( r1_facirc_1(A,B,C,D)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> r1_facirc_1(A,B,k9_facirc_1(A,B,C,E),D) ) ) ) ) ) ).
fof(t18_facirc_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v4_msafree2(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u4_msualg_1(A,B)))
=> ! [D] :
( r2_hidden(D,k2_msafree2(A))
=> r1_facirc_1(A,B,C,D) ) ) ) ) ).
fof(t19_facirc_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v4_msafree2(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u4_msualg_1(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_msualg_1(A))
=> ( ! [E] :
( r2_hidden(E,k2_relat_1(k1_msualg_1(A,D)))
=> r1_facirc_1(A,B,C,E) )
=> r1_facirc_1(A,B,k6_circuit2(A,B,C),k2_msualg_1(A,D)) ) ) ) ) ) ).
fof(t20_facirc_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,u1_struct_0(k3_circcomb(A,B)))
& r2_hidden(C,u1_struct_0(k3_circcomb(B,A))) ) ) ) ) ).
fof(t21_facirc_1,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] :
( r2_hidden(C,k3_msafree2(A))
=> ( r2_hidden(C,k3_msafree2(k3_circcomb(A,B)))
& r2_hidden(C,k3_msafree2(k3_circcomb(B,A))) ) ) ) ) ).
fof(t22_facirc_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( r2_hidden(C,k3_msafree2(B))
=> r2_hidden(C,k3_msafree2(k3_circcomb(A,B))) ) ) ) ).
fof(t23_facirc_1,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) )
=> k3_circcomb(A,B) = k3_circcomb(B,A) ) ) ).
fof(t24_facirc_1,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) )
=> k4_circcomb(A,B,C,D) = k4_circcomb(B,A,D,C) ) ) ) ) ).
fof(t25_facirc_1,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] :
( ( ~ v3_struct_0(C)
& ~ v2_msualg_1(C)
& v1_circcomb(C)
& v2_circcomb(C)
& v3_circcomb(C)
& l1_msualg_1(C) )
=> ! [D] :
( ( v4_msafree2(D,A)
& v6_circcomb(D,A)
& l3_msualg_1(D,A) )
=> ! [E] :
( ( v4_msafree2(E,B)
& v6_circcomb(E,B)
& l3_msualg_1(E,B) )
=> ! [F] :
( ( v4_msafree2(F,C)
& v6_circcomb(F,C)
& l3_msualg_1(F,C) )
=> 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(t26_facirc_1,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] :
( ( v5_msualg_1(C,A)
& v4_msafree2(C,A)
& v4_circcomb(C,A)
& v6_circcomb(C,A)
& l3_msualg_1(C,A) )
=> ! [D] :
( ( v5_msualg_1(D,B)
& 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))))
=> ( m1_subset_1(k7_relat_1(E,u1_struct_0(A)),k4_card_3(u4_msualg_1(A,C)))
& m1_subset_1(k7_relat_1(E,u1_struct_0(B)),k4_card_3(u4_msualg_1(B,D))) ) ) ) ) ) ) ).
fof(t27_facirc_1,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) )
=> k3_msafree2(k3_circcomb(A,B)) = k2_xboole_0(k3_msafree2(A),k3_msafree2(B)) ) ) ).
fof(t28_facirc_1,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) )
=> ( r1_xboole_0(k4_msafree2(B),k2_msafree2(A))
=> ! [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,k4_card_3(u4_msualg_1(A,C)))
=> ( F = k7_relat_1(E,u1_struct_0(A))
=> k7_relat_1(k6_circuit2(k3_circcomb(A,B),k4_circcomb(A,B,C,D),E),u1_struct_0(A)) = k6_circuit2(A,C,F) ) ) ) ) ) ) ) ) ).
fof(t29_facirc_1,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) )
=> ( r1_xboole_0(k4_msafree2(A),k2_msafree2(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,k4_card_3(u4_msualg_1(B,D)))
=> ( F = k7_relat_1(E,u1_struct_0(B))
=> k7_relat_1(k6_circuit2(k3_circcomb(A,B),k4_circcomb(A,B,C,D),E),u1_struct_0(B)) = k6_circuit2(B,D,F) ) ) ) ) ) ) ) ) ).
fof(t30_facirc_1,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) )
=> ( r1_xboole_0(k4_msafree2(B),k2_msafree2(A))
=> ! [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,k4_card_3(u4_msualg_1(A,C)))
=> ( F = k7_relat_1(E,u1_struct_0(A))
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> k7_relat_1(k9_facirc_1(k3_circcomb(A,B),k4_circcomb(A,B,C,D),E,G),u1_struct_0(A)) = k9_facirc_1(A,C,F,G) ) ) ) ) ) ) ) ) ) ).
fof(t31_facirc_1,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) )
=> ( r1_xboole_0(k4_msafree2(A),k2_msafree2(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,k4_card_3(u4_msualg_1(B,D)))
=> ( F = k7_relat_1(E,u1_struct_0(B))
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> k7_relat_1(k9_facirc_1(k3_circcomb(A,B),k4_circcomb(A,B,C,D),E,G),u1_struct_0(B)) = k9_facirc_1(B,D,F,G) ) ) ) ) ) ) ) ) ) ).
fof(t32_facirc_1,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) )
=> ( r1_xboole_0(k4_msafree2(B),k2_msafree2(A))
=> ! [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,k4_card_3(u4_msualg_1(A,C)))
=> ( F = k7_relat_1(E,u1_struct_0(A))
=> ! [G] :
( r2_hidden(G,u1_struct_0(A))
=> ! [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
=> k1_funct_1(k9_facirc_1(k3_circcomb(A,B),k4_circcomb(A,B,C,D),E,H),G) = k1_funct_1(k9_facirc_1(A,C,F,H),G) ) ) ) ) ) ) ) ) ) ) ).
fof(t33_facirc_1,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) )
=> ( r1_xboole_0(k4_msafree2(A),k2_msafree2(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,k4_card_3(u4_msualg_1(B,D)))
=> ( F = k7_relat_1(E,u1_struct_0(B))
=> ! [G] :
( r2_hidden(G,u1_struct_0(B))
=> ! [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
=> k1_funct_1(k9_facirc_1(k3_circcomb(A,B),k4_circcomb(A,B,C,D),E,H),G) = k1_funct_1(k9_facirc_1(B,D,F,H),G) ) ) ) ) ) ) ) ) ) ) ).
fof(t34_facirc_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& v5_circcomb(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v4_msafree2(B,A)
& l3_msualg_1(B,A) )
=> ( v4_circcomb(B,A)
=> ! [C] :
( m1_subset_1(C,k4_card_3(u4_msualg_1(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_msualg_1(A))
=> k1_funct_1(k6_circuit2(A,B,C),k2_msualg_1(A,D)) = k1_funct_1(k2_mcart_1(D),k5_relat_1(k1_msualg_1(A,D),C)) ) ) ) ) ) ).
fof(t35_facirc_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v1_circcomb(A)
& v2_circcomb(A)
& v3_circcomb(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v4_msafree2(B,A)
& v4_circcomb(B,A)
& v6_circcomb(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u4_msualg_1(A,B)))
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D)
& v1_finseq_1(D) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( r2_hidden(k4_tarski(D,E),u1_msualg_1(A))
=> k1_funct_1(k6_circuit2(A,B,C),k4_tarski(D,E)) = k1_funct_1(E,k5_relat_1(D,C)) ) ) ) ) ) ) ).
fof(t36_facirc_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v1_circcomb(A)
& v2_circcomb(A)
& v3_circcomb(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v4_msafree2(B,A)
& v4_circcomb(B,A)
& v6_circcomb(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u4_msualg_1(A,B)))
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D)
& v1_finseq_1(D) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( ( r2_hidden(k4_tarski(D,E),u1_msualg_1(A))
& ! [F] :
( r2_hidden(F,k2_relat_1(D))
=> r1_facirc_1(A,B,C,F) ) )
=> r1_facirc_1(A,B,k6_circuit2(A,B,C),k4_tarski(D,E)) ) ) ) ) ) ) ).
fof(t37_facirc_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_circcomb(A)
& l1_msualg_1(A) )
=> k3_msafree2(A) = u1_msualg_1(A) ) ).
fof(t38_facirc_1,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> v1_relat_1(k4_msafree2(k7_circcomb(A,B))) ) ).
fof(t39_facirc_1,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B)
& v3_facirc_1(B) )
=> ~ v2_facirc_1(k2_msafree2(k7_circcomb(A,B))) ) ).
fof(t40_facirc_1,axiom,
! [A,B,C] : k2_msafree2(k7_circcomb(A,k6_facirc_1(B,C))) = k2_tarski(B,C) ).
fof(t41_facirc_1,axiom,
! [A,B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(C)
=> ~ v2_facirc_1(k2_msafree2(k7_circcomb(A,k6_facirc_1(B,C)))) ) ) ).
fof(t42_facirc_1,axiom,
! [A,B,C,D] : k2_msafree2(k7_circcomb(A,k7_facirc_1(B,C,D))) = k1_enumset1(B,C,D) ).
fof(t43_facirc_1,axiom,
! [A,B,C] :
( r2_hidden(A,u1_struct_0(k7_circcomb(C,k6_facirc_1(A,B))))
& r2_hidden(B,u1_struct_0(k7_circcomb(C,k6_facirc_1(A,B))))
& r2_hidden(k4_tarski(k6_facirc_1(A,B),C),u1_struct_0(k7_circcomb(C,k6_facirc_1(A,B)))) ) ).
fof(t44_facirc_1,axiom,
! [A,B,C,D] :
( r2_hidden(A,u1_struct_0(k7_circcomb(D,k7_facirc_1(A,B,C))))
& r2_hidden(B,u1_struct_0(k7_circcomb(D,k7_facirc_1(A,B,C))))
& r2_hidden(C,u1_struct_0(k7_circcomb(D,k7_facirc_1(A,B,C)))) ) ).
fof(t45_facirc_1,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> ( r2_hidden(B,u1_struct_0(k6_circcomb(A,C,B)))
& ! [D] :
( r2_hidden(D,k2_relat_1(C))
=> r2_hidden(D,u1_struct_0(k6_circcomb(A,C,B))) ) ) ) ).
fof(t46_facirc_1,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> ( v2_circcomb(k6_circcomb(A,C,B))
& v2_msafree2(k6_circcomb(A,C,B)) ) ) ).
fof(t47_facirc_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ! [B] : r2_hidden(k4_tarski(A,B),k4_msafree2(k7_circcomb(B,A))) ) ).
fof(d10_facirc_1,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k4_finseq_2(np__2,k10_circcomb),k10_circcomb)
& m2_relset_1(C,k4_finseq_2(np__2,k10_circcomb),k10_circcomb) )
=> k10_facirc_1(A,B,C) = k9_circcomb(np__2,k10_circcomb,C,k6_facirc_1(A,B)) ) ).
fof(t48_facirc_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(C)
& v1_finset_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(np__2,C),C)
& m2_relset_1(D,k4_finseq_2(np__2,C),C) )
=> ! [E] :
( m1_subset_1(E,k4_card_3(u4_msualg_1(k7_circcomb(D,k6_facirc_1(A,B)),k9_circcomb(np__2,C,D,k6_facirc_1(A,B)))))
=> ( k1_funct_1(k6_circuit2(k7_circcomb(D,k6_facirc_1(A,B)),k9_circcomb(np__2,C,D,k6_facirc_1(A,B)),E),k4_tarski(k6_facirc_1(A,B),D)) = k1_funct_1(D,k6_facirc_1(k1_funct_1(E,A),k1_funct_1(E,B)))
& k1_funct_1(k6_circuit2(k7_circcomb(D,k6_facirc_1(A,B)),k9_circcomb(np__2,C,D,k6_facirc_1(A,B)),E),A) = k1_funct_1(E,A)
& k1_funct_1(k6_circuit2(k7_circcomb(D,k6_facirc_1(A,B)),k9_circcomb(np__2,C,D,k6_facirc_1(A,B)),E),B) = k1_funct_1(E,B) ) ) ) ) ).
fof(t49_facirc_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(C)
& v1_finset_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(np__2,C),C)
& m2_relset_1(D,k4_finseq_2(np__2,C),C) )
=> ! [E] :
( m1_subset_1(E,k4_card_3(u4_msualg_1(k7_circcomb(D,k6_facirc_1(A,B)),k9_circcomb(np__2,C,D,k6_facirc_1(A,B)))))
=> v1_circuit2(k6_circuit2(k7_circcomb(D,k6_facirc_1(A,B)),k9_circcomb(np__2,C,D,k6_facirc_1(A,B)),E),k7_circcomb(D,k6_facirc_1(A,B)),k9_circcomb(np__2,C,D,k6_facirc_1(A,B))) ) ) ) ).
fof(t50_facirc_1,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k4_finseq_2(np__2,k10_circcomb),k10_circcomb)
& m2_relset_1(C,k4_finseq_2(np__2,k10_circcomb),k10_circcomb) )
=> ! [D] :
( m1_subset_1(D,k4_card_3(u4_msualg_1(k7_circcomb(C,k6_facirc_1(A,B)),k10_facirc_1(A,B,C))))
=> ( k1_funct_1(k6_circuit2(k7_circcomb(C,k6_facirc_1(A,B)),k10_facirc_1(A,B,C),D),k4_tarski(k6_facirc_1(A,B),C)) = k1_funct_1(C,k6_facirc_1(k1_funct_1(D,A),k1_funct_1(D,B)))
& k1_funct_1(k6_circuit2(k7_circcomb(C,k6_facirc_1(A,B)),k10_facirc_1(A,B,C),D),A) = k1_funct_1(D,A)
& k1_funct_1(k6_circuit2(k7_circcomb(C,k6_facirc_1(A,B)),k10_facirc_1(A,B,C),D),B) = k1_funct_1(D,B) ) ) ) ).
fof(t51_facirc_1,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k4_finseq_2(np__2,k10_circcomb),k10_circcomb)
& m2_relset_1(C,k4_finseq_2(np__2,k10_circcomb),k10_circcomb) )
=> ! [D] :
( m1_subset_1(D,k4_card_3(u4_msualg_1(k7_circcomb(C,k6_facirc_1(A,B)),k10_facirc_1(A,B,C))))
=> v1_circuit2(k6_circuit2(k7_circcomb(C,k6_facirc_1(A,B)),k10_facirc_1(A,B,C),D),k7_circcomb(C,k6_facirc_1(A,B)),k10_facirc_1(A,B,C)) ) ) ).
fof(d11_facirc_1,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(np__3,k10_circcomb),k10_circcomb)
& m2_relset_1(D,k4_finseq_2(np__3,k10_circcomb),k10_circcomb) )
=> k11_facirc_1(A,B,C,D) = k9_circcomb(np__3,k10_circcomb,D,k7_facirc_1(A,B,C)) ) ).
fof(t52_facirc_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(D)
& v1_finset_1(D) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k4_finseq_2(np__3,D),D)
& m2_relset_1(E,k4_finseq_2(np__3,D),D) )
=> ! [F] :
( m1_subset_1(F,k4_card_3(u4_msualg_1(k7_circcomb(E,k7_facirc_1(A,B,C)),k9_circcomb(np__3,D,E,k7_facirc_1(A,B,C)))))
=> ( k1_funct_1(k6_circuit2(k7_circcomb(E,k7_facirc_1(A,B,C)),k9_circcomb(np__3,D,E,k7_facirc_1(A,B,C)),F),k4_tarski(k7_facirc_1(A,B,C),E)) = k1_funct_1(E,k7_facirc_1(k1_funct_1(F,A),k1_funct_1(F,B),k1_funct_1(F,C)))
& k1_funct_1(k6_circuit2(k7_circcomb(E,k7_facirc_1(A,B,C)),k9_circcomb(np__3,D,E,k7_facirc_1(A,B,C)),F),A) = k1_funct_1(F,A)
& k1_funct_1(k6_circuit2(k7_circcomb(E,k7_facirc_1(A,B,C)),k9_circcomb(np__3,D,E,k7_facirc_1(A,B,C)),F),B) = k1_funct_1(F,B)
& k1_funct_1(k6_circuit2(k7_circcomb(E,k7_facirc_1(A,B,C)),k9_circcomb(np__3,D,E,k7_facirc_1(A,B,C)),F),C) = k1_funct_1(F,C) ) ) ) ) ).
fof(t53_facirc_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(D)
& v1_finset_1(D) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k4_finseq_2(np__3,D),D)
& m2_relset_1(E,k4_finseq_2(np__3,D),D) )
=> ! [F] :
( m1_subset_1(F,k4_card_3(u4_msualg_1(k7_circcomb(E,k7_facirc_1(A,B,C)),k9_circcomb(np__3,D,E,k7_facirc_1(A,B,C)))))
=> v1_circuit2(k6_circuit2(k7_circcomb(E,k7_facirc_1(A,B,C)),k9_circcomb(np__3,D,E,k7_facirc_1(A,B,C)),F),k7_circcomb(E,k7_facirc_1(A,B,C)),k9_circcomb(np__3,D,E,k7_facirc_1(A,B,C))) ) ) ) ).
fof(t54_facirc_1,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(np__3,k10_circcomb),k10_circcomb)
& m2_relset_1(D,k4_finseq_2(np__3,k10_circcomb),k10_circcomb) )
=> ! [E] :
( m1_subset_1(E,k4_card_3(u4_msualg_1(k7_circcomb(D,k7_facirc_1(A,B,C)),k11_facirc_1(A,B,C,D))))
=> ( k1_funct_1(k6_circuit2(k7_circcomb(D,k7_facirc_1(A,B,C)),k11_facirc_1(A,B,C,D),E),k4_tarski(k7_facirc_1(A,B,C),D)) = k1_funct_1(D,k7_facirc_1(k1_funct_1(E,A),k1_funct_1(E,B),k1_funct_1(E,C)))
& k1_funct_1(k6_circuit2(k7_circcomb(D,k7_facirc_1(A,B,C)),k11_facirc_1(A,B,C,D),E),A) = k1_funct_1(E,A)
& k1_funct_1(k6_circuit2(k7_circcomb(D,k7_facirc_1(A,B,C)),k11_facirc_1(A,B,C,D),E),B) = k1_funct_1(E,B)
& k1_funct_1(k6_circuit2(k7_circcomb(D,k7_facirc_1(A,B,C)),k11_facirc_1(A,B,C,D),E),C) = k1_funct_1(E,C) ) ) ) ).
fof(t55_facirc_1,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(np__3,k10_circcomb),k10_circcomb)
& m2_relset_1(D,k4_finseq_2(np__3,k10_circcomb),k10_circcomb) )
=> ! [E] :
( m1_subset_1(E,k4_card_3(u4_msualg_1(k7_circcomb(D,k7_facirc_1(A,B,C)),k11_facirc_1(A,B,C,D))))
=> v1_circuit2(k6_circuit2(k7_circcomb(D,k7_facirc_1(A,B,C)),k11_facirc_1(A,B,C,D),E),k7_circcomb(D,k7_facirc_1(A,B,C)),k11_facirc_1(A,B,C,D)) ) ) ).
fof(d12_facirc_1,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(np__2,k10_circcomb),k10_circcomb)
& m2_relset_1(D,k4_finseq_2(np__2,k10_circcomb),k10_circcomb) )
=> k12_facirc_1(A,B,C,D) = k3_circcomb(k7_circcomb(D,k6_facirc_1(A,B)),k7_circcomb(D,k6_facirc_1(k4_tarski(k6_facirc_1(A,B),D),C))) ) ).
fof(d13_facirc_1,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(np__2,k10_circcomb),k10_circcomb)
& m2_relset_1(D,k4_finseq_2(np__2,k10_circcomb),k10_circcomb) )
=> k13_facirc_1(A,B,C,D) = k4_tarski(k6_facirc_1(k4_tarski(k6_facirc_1(A,B),D),C),D) ) ).
fof(t56_facirc_1,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(np__2,k10_circcomb),k10_circcomb)
& m2_relset_1(D,k4_finseq_2(np__2,k10_circcomb),k10_circcomb) )
=> k4_msafree2(k12_facirc_1(A,B,C,D)) = k2_tarski(k4_tarski(k6_facirc_1(A,B),D),k13_facirc_1(A,B,C,D)) ) ).
fof(t57_facirc_1,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(np__2,k10_circcomb),k10_circcomb)
& m2_relset_1(D,k4_finseq_2(np__2,k10_circcomb),k10_circcomb) )
=> ( A != k4_tarski(k6_facirc_1(B,C),D)
=> k2_msafree2(k12_facirc_1(B,C,A,D)) = k1_enumset1(B,C,A) ) ) ).
fof(d14_facirc_1,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(np__2,k10_circcomb),k10_circcomb)
& m2_relset_1(D,k4_finseq_2(np__2,k10_circcomb),k10_circcomb) )
=> k14_facirc_1(A,B,C,D) = k4_circcomb(k7_circcomb(D,k6_facirc_1(A,B)),k7_circcomb(D,k6_facirc_1(k4_tarski(k6_facirc_1(A,B),D),C)),k10_facirc_1(A,B,D),k10_facirc_1(k4_tarski(k6_facirc_1(A,B),D),C,D)) ) ).
fof(t58_facirc_1,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(np__2,k10_circcomb),k10_circcomb)
& m2_relset_1(D,k4_finseq_2(np__2,k10_circcomb),k10_circcomb) )
=> v1_relat_1(k4_msafree2(k12_facirc_1(A,B,C,D))) ) ).
fof(t59_facirc_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k4_finseq_2(np__2,k10_circcomb),k10_circcomb)
& m2_relset_1(A,k4_finseq_2(np__2,k10_circcomb),k10_circcomb) )
=> ! [B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(C)
=> ! [D] :
( ~ v1_facirc_1(D)
=> ~ v2_facirc_1(k2_msafree2(k12_facirc_1(B,C,D,A))) ) ) ) ) ).
fof(t60_facirc_1,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(np__2,k10_circcomb),k10_circcomb)
& m2_relset_1(D,k4_finseq_2(np__2,k10_circcomb),k10_circcomb) )
=> ( r2_hidden(A,u1_struct_0(k12_facirc_1(A,B,C,D)))
& r2_hidden(B,u1_struct_0(k12_facirc_1(A,B,C,D)))
& r2_hidden(C,u1_struct_0(k12_facirc_1(A,B,C,D))) ) ) ).
fof(t61_facirc_1,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(np__2,k10_circcomb),k10_circcomb)
& m2_relset_1(D,k4_finseq_2(np__2,k10_circcomb),k10_circcomb) )
=> ( r2_hidden(k4_tarski(k6_facirc_1(A,B),D),u1_struct_0(k12_facirc_1(A,B,C,D)))
& r2_hidden(k4_tarski(k6_facirc_1(k4_tarski(k6_facirc_1(A,B),D),C),D),u1_struct_0(k12_facirc_1(A,B,C,D))) ) ) ).
fof(t62_facirc_1,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(np__2,k10_circcomb),k10_circcomb)
& m2_relset_1(D,k4_finseq_2(np__2,k10_circcomb),k10_circcomb) )
=> ! [E] :
( m1_subset_1(E,k4_card_3(u4_msualg_1(k12_facirc_1(B,C,A,D),k14_facirc_1(B,C,A,D))))
=> ( A != k4_tarski(k6_facirc_1(B,C),D)
=> ( k15_facirc_1(k12_facirc_1(B,C,A,D),k14_facirc_1(B,C,A,D),k9_facirc_1(k12_facirc_1(B,C,A,D),k14_facirc_1(B,C,A,D),E,np__2),k13_facirc_1(B,C,A,D)) = k1_funct_1(D,k6_facirc_1(k1_funct_1(D,k6_facirc_1(k1_funct_1(E,B),k1_funct_1(E,C))),k1_funct_1(E,A)))
& k1_funct_1(k9_facirc_1(k12_facirc_1(B,C,A,D),k14_facirc_1(B,C,A,D),E,np__2),k4_tarski(k6_facirc_1(B,C),D)) = k1_funct_1(D,k6_facirc_1(k1_funct_1(E,B),k1_funct_1(E,C)))
& k1_funct_1(k9_facirc_1(k12_facirc_1(B,C,A,D),k14_facirc_1(B,C,A,D),E,np__2),B) = k1_funct_1(E,B)
& k1_funct_1(k9_facirc_1(k12_facirc_1(B,C,A,D),k14_facirc_1(B,C,A,D),E,np__2),C) = k1_funct_1(E,C)
& k1_funct_1(k9_facirc_1(k12_facirc_1(B,C,A,D),k14_facirc_1(B,C,A,D),E,np__2),A) = k1_funct_1(E,A) ) ) ) ) ).
fof(t63_facirc_1,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(np__2,k10_circcomb),k10_circcomb)
& m2_relset_1(D,k4_finseq_2(np__2,k10_circcomb),k10_circcomb) )
=> ! [E] :
( m1_subset_1(E,k4_card_3(u4_msualg_1(k12_facirc_1(B,C,A,D),k14_facirc_1(B,C,A,D))))
=> ( A != k4_tarski(k6_facirc_1(B,C),D)
=> v1_circuit2(k9_facirc_1(k12_facirc_1(B,C,A,D),k14_facirc_1(B,C,A,D),E,np__2),k12_facirc_1(B,C,A,D),k14_facirc_1(B,C,A,D)) ) ) ) ).
fof(t64_facirc_1,axiom,
! [A,B,C] :
( A != k4_tarski(k6_facirc_1(B,C),k1_facirc_1)
=> ! [D] :
( m1_subset_1(D,k4_card_3(u4_msualg_1(k12_facirc_1(B,C,A,k1_facirc_1),k14_facirc_1(B,C,A,k1_facirc_1))))
=> ! [E] :
( m2_subset_1(E,k5_numbers,k10_circcomb)
=> ! [F] :
( m2_subset_1(F,k5_numbers,k10_circcomb)
=> ! [G] :
( m2_subset_1(G,k5_numbers,k10_circcomb)
=> ( ( E = k1_funct_1(D,B)
& F = k1_funct_1(D,C)
& G = k1_funct_1(D,A) )
=> k15_facirc_1(k12_facirc_1(B,C,A,k1_facirc_1),k14_facirc_1(B,C,A,k1_facirc_1),k9_facirc_1(k12_facirc_1(B,C,A,k1_facirc_1),k14_facirc_1(B,C,A,k1_facirc_1),D,np__2),k13_facirc_1(B,C,A,k1_facirc_1)) = k4_binarith(k4_binarith(E,F),G) ) ) ) ) ) ) ).
fof(t65_facirc_1,axiom,
! [A,B,C] :
( A != k4_tarski(k6_facirc_1(B,C),k2_facirc_1)
=> ! [D] :
( m1_subset_1(D,k4_card_3(u4_msualg_1(k12_facirc_1(B,C,A,k2_facirc_1),k14_facirc_1(B,C,A,k2_facirc_1))))
=> ! [E] :
( m2_subset_1(E,k5_numbers,k10_circcomb)
=> ! [F] :
( m2_subset_1(F,k5_numbers,k10_circcomb)
=> ! [G] :
( m2_subset_1(G,k5_numbers,k10_circcomb)
=> ( ( E = k1_funct_1(D,B)
& F = k1_funct_1(D,C)
& G = k1_funct_1(D,A) )
=> k15_facirc_1(k12_facirc_1(B,C,A,k2_facirc_1),k14_facirc_1(B,C,A,k2_facirc_1),k9_facirc_1(k12_facirc_1(B,C,A,k2_facirc_1),k14_facirc_1(B,C,A,k2_facirc_1),D,np__2),k13_facirc_1(B,C,A,k2_facirc_1)) = k3_binarith(k3_binarith(E,F),G) ) ) ) ) ) ) ).
fof(t66_facirc_1,axiom,
! [A,B,C] :
( A != k4_tarski(k6_facirc_1(B,C),k3_facirc_1)
=> ! [D] :
( m1_subset_1(D,k4_card_3(u4_msualg_1(k12_facirc_1(B,C,A,k3_facirc_1),k14_facirc_1(B,C,A,k3_facirc_1))))
=> ! [E] :
( m2_subset_1(E,k5_numbers,k10_circcomb)
=> ! [F] :
( m2_subset_1(F,k5_numbers,k10_circcomb)
=> ! [G] :
( m2_subset_1(G,k5_numbers,k10_circcomb)
=> ( ( E = k1_funct_1(D,B)
& F = k1_funct_1(D,C)
& G = k1_funct_1(D,A) )
=> k15_facirc_1(k12_facirc_1(B,C,A,k3_facirc_1),k14_facirc_1(B,C,A,k3_facirc_1),k9_facirc_1(k12_facirc_1(B,C,A,k3_facirc_1),k14_facirc_1(B,C,A,k3_facirc_1),D,np__2),k13_facirc_1(B,C,A,k3_facirc_1)) = k12_margrel1(k12_margrel1(E,F),G) ) ) ) ) ) ) ).
fof(d15_facirc_1,axiom,
! [A,B,C] : k16_facirc_1(A,B,C) = k13_facirc_1(A,B,C,k1_facirc_1) ).
fof(d16_facirc_1,axiom,
! [A,B,C] : k17_facirc_1(A,B,C) = k14_facirc_1(A,B,C,k1_facirc_1) ).
fof(d17_facirc_1,axiom,
! [A,B,C] : k18_facirc_1(A,B,C) = k3_circcomb(k3_circcomb(k7_circcomb(k3_facirc_1,k6_facirc_1(A,B)),k7_circcomb(k3_facirc_1,k6_facirc_1(B,C))),k7_circcomb(k3_facirc_1,k6_facirc_1(C,A))) ).
fof(d18_facirc_1,axiom,
! [A,B,C] : k19_facirc_1(A,B,C) = k3_circcomb(k18_facirc_1(A,B,C),k7_circcomb(k4_facirc_1,k7_facirc_1(k4_tarski(k6_facirc_1(A,B),k3_facirc_1),k4_tarski(k6_facirc_1(B,C),k3_facirc_1),k4_tarski(k6_facirc_1(C,A),k3_facirc_1)))) ).
fof(d19_facirc_1,axiom,
! [A,B,C] : k20_facirc_1(A,B,C) = k4_circcomb(k3_circcomb(k7_circcomb(k3_facirc_1,k6_facirc_1(A,B)),k7_circcomb(k3_facirc_1,k6_facirc_1(B,C))),k7_circcomb(k3_facirc_1,k6_facirc_1(C,A)),k4_circcomb(k7_circcomb(k3_facirc_1,k6_facirc_1(A,B)),k7_circcomb(k3_facirc_1,k6_facirc_1(B,C)),k10_facirc_1(A,B,k3_facirc_1),k10_facirc_1(B,C,k3_facirc_1)),k10_facirc_1(C,A,k3_facirc_1)) ).
fof(t67_facirc_1,axiom,
! [A,B,C] : v1_relat_1(k4_msafree2(k19_facirc_1(A,B,C))) ).
fof(t68_facirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ! [B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(C)
=> ~ v2_facirc_1(k2_msafree2(k19_facirc_1(A,B,C))) ) ) ) ).
fof(t69_facirc_1,axiom,
! [A,B,C,D] :
( m1_subset_1(D,k4_card_3(u4_msualg_1(k18_facirc_1(A,B,C),k20_facirc_1(A,B,C))))
=> ! [E] :
( m2_subset_1(E,k5_numbers,k10_circcomb)
=> ! [F] :
( m2_subset_1(F,k5_numbers,k10_circcomb)
=> ( ( E = k1_funct_1(D,A)
& F = k1_funct_1(D,B) )
=> k1_funct_1(k6_circuit2(k18_facirc_1(A,B,C),k20_facirc_1(A,B,C),D),k4_tarski(k6_facirc_1(A,B),k3_facirc_1)) = k12_margrel1(E,F) ) ) ) ) ).
fof(t70_facirc_1,axiom,
! [A,B,C,D] :
( m1_subset_1(D,k4_card_3(u4_msualg_1(k18_facirc_1(A,B,C),k20_facirc_1(A,B,C))))
=> ! [E] :
( m2_subset_1(E,k5_numbers,k10_circcomb)
=> ! [F] :
( m2_subset_1(F,k5_numbers,k10_circcomb)
=> ( ( E = k1_funct_1(D,B)
& F = k1_funct_1(D,C) )
=> k1_funct_1(k6_circuit2(k18_facirc_1(A,B,C),k20_facirc_1(A,B,C),D),k4_tarski(k6_facirc_1(B,C),k3_facirc_1)) = k12_margrel1(E,F) ) ) ) ) ).
fof(t71_facirc_1,axiom,
! [A,B,C,D] :
( m1_subset_1(D,k4_card_3(u4_msualg_1(k18_facirc_1(A,B,C),k20_facirc_1(A,B,C))))
=> ! [E] :
( m2_subset_1(E,k5_numbers,k10_circcomb)
=> ! [F] :
( m2_subset_1(F,k5_numbers,k10_circcomb)
=> ( ( E = k1_funct_1(D,C)
& F = k1_funct_1(D,A) )
=> k1_funct_1(k6_circuit2(k18_facirc_1(A,B,C),k20_facirc_1(A,B,C),D),k4_tarski(k6_facirc_1(C,A),k3_facirc_1)) = k12_margrel1(E,F) ) ) ) ) ).
fof(d20_facirc_1,axiom,
! [A,B,C] : k21_facirc_1(A,B,C) = k4_tarski(k7_facirc_1(k4_tarski(k6_facirc_1(A,B),k3_facirc_1),k4_tarski(k6_facirc_1(B,C),k3_facirc_1),k4_tarski(k6_facirc_1(C,A),k3_facirc_1)),k4_facirc_1) ).
fof(d21_facirc_1,axiom,
! [A,B,C] : k22_facirc_1(A,B,C) = k4_circcomb(k18_facirc_1(A,B,C),k7_circcomb(k4_facirc_1,k7_facirc_1(k4_tarski(k6_facirc_1(A,B),k3_facirc_1),k4_tarski(k6_facirc_1(B,C),k3_facirc_1),k4_tarski(k6_facirc_1(C,A),k3_facirc_1))),k20_facirc_1(A,B,C),k11_facirc_1(k4_tarski(k6_facirc_1(A,B),k3_facirc_1),k4_tarski(k6_facirc_1(B,C),k3_facirc_1),k4_tarski(k6_facirc_1(C,A),k3_facirc_1),k4_facirc_1)) ).
fof(t72_facirc_1,axiom,
! [A,B,C] :
( r2_hidden(A,u1_struct_0(k19_facirc_1(A,B,C)))
& r2_hidden(B,u1_struct_0(k19_facirc_1(A,B,C)))
& r2_hidden(C,u1_struct_0(k19_facirc_1(A,B,C))) ) ).
fof(t73_facirc_1,axiom,
! [A,B,C] :
( r2_hidden(k4_tarski(k6_facirc_1(A,B),k3_facirc_1),k4_msafree2(k19_facirc_1(A,B,C)))
& r2_hidden(k4_tarski(k6_facirc_1(B,C),k3_facirc_1),k4_msafree2(k19_facirc_1(A,B,C)))
& r2_hidden(k4_tarski(k6_facirc_1(C,A),k3_facirc_1),k4_msafree2(k19_facirc_1(A,B,C))) ) ).
fof(t74_facirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ! [B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(C)
=> ( r2_hidden(A,k2_msafree2(k19_facirc_1(A,B,C)))
& r2_hidden(B,k2_msafree2(k19_facirc_1(A,B,C)))
& r2_hidden(C,k2_msafree2(k19_facirc_1(A,B,C))) ) ) ) ) ).
fof(t75_facirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ! [B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(C)
=> ( k2_msafree2(k19_facirc_1(A,B,C)) = k1_enumset1(A,B,C)
& k4_msafree2(k19_facirc_1(A,B,C)) = k2_xboole_0(k1_enumset1(k4_tarski(k6_facirc_1(A,B),k3_facirc_1),k4_tarski(k6_facirc_1(B,C),k3_facirc_1),k4_tarski(k6_facirc_1(C,A),k3_facirc_1)),k1_struct_0(k19_facirc_1(A,B,C),k21_facirc_1(A,B,C))) ) ) ) ) ).
fof(t76_facirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ! [B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(C)
=> ! [D] :
( m1_subset_1(D,k4_card_3(u4_msualg_1(k19_facirc_1(A,B,C),k22_facirc_1(A,B,C))))
=> ! [E] :
( m2_subset_1(E,k5_numbers,k10_circcomb)
=> ! [F] :
( m2_subset_1(F,k5_numbers,k10_circcomb)
=> ( ( E = k1_funct_1(D,A)
& F = k1_funct_1(D,B) )
=> k1_funct_1(k6_circuit2(k19_facirc_1(A,B,C),k22_facirc_1(A,B,C),D),k4_tarski(k6_facirc_1(A,B),k3_facirc_1)) = k12_margrel1(E,F) ) ) ) ) ) ) ) ).
fof(t77_facirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ! [B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(C)
=> ! [D] :
( m1_subset_1(D,k4_card_3(u4_msualg_1(k19_facirc_1(A,B,C),k22_facirc_1(A,B,C))))
=> ! [E] :
( m2_subset_1(E,k5_numbers,k10_circcomb)
=> ! [F] :
( m2_subset_1(F,k5_numbers,k10_circcomb)
=> ( ( E = k1_funct_1(D,B)
& F = k1_funct_1(D,C) )
=> k1_funct_1(k6_circuit2(k19_facirc_1(A,B,C),k22_facirc_1(A,B,C),D),k4_tarski(k6_facirc_1(B,C),k3_facirc_1)) = k12_margrel1(E,F) ) ) ) ) ) ) ) ).
fof(t78_facirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ! [B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(C)
=> ! [D] :
( m1_subset_1(D,k4_card_3(u4_msualg_1(k19_facirc_1(A,B,C),k22_facirc_1(A,B,C))))
=> ! [E] :
( m2_subset_1(E,k5_numbers,k10_circcomb)
=> ! [F] :
( m2_subset_1(F,k5_numbers,k10_circcomb)
=> ( ( E = k1_funct_1(D,A)
& F = k1_funct_1(D,C) )
=> k1_funct_1(k6_circuit2(k19_facirc_1(A,B,C),k22_facirc_1(A,B,C),D),k4_tarski(k6_facirc_1(C,A),k3_facirc_1)) = k12_margrel1(F,E) ) ) ) ) ) ) ) ).
fof(t79_facirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ! [B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(C)
=> ! [D] :
( m1_subset_1(D,k4_card_3(u4_msualg_1(k19_facirc_1(A,B,C),k22_facirc_1(A,B,C))))
=> ! [E] :
( m2_subset_1(E,k5_numbers,k10_circcomb)
=> ! [F] :
( m2_subset_1(F,k5_numbers,k10_circcomb)
=> ! [G] :
( m2_subset_1(G,k5_numbers,k10_circcomb)
=> ( ( E = k1_funct_1(D,k4_tarski(k6_facirc_1(A,B),k3_facirc_1))
& F = k1_funct_1(D,k4_tarski(k6_facirc_1(B,C),k3_facirc_1))
& G = k1_funct_1(D,k4_tarski(k6_facirc_1(C,A),k3_facirc_1)) )
=> k15_facirc_1(k19_facirc_1(A,B,C),k22_facirc_1(A,B,C),k6_circuit2(k19_facirc_1(A,B,C),k22_facirc_1(A,B,C),D),k21_facirc_1(A,B,C)) = k3_binarith(k3_binarith(E,F),G) ) ) ) ) ) ) ) ) ).
fof(t80_facirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ! [B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(C)
=> ! [D] :
( m1_subset_1(D,k4_card_3(u4_msualg_1(k19_facirc_1(A,B,C),k22_facirc_1(A,B,C))))
=> ! [E] :
( m2_subset_1(E,k5_numbers,k10_circcomb)
=> ! [F] :
( m2_subset_1(F,k5_numbers,k10_circcomb)
=> ( ( E = k1_funct_1(D,A)
& F = k1_funct_1(D,B) )
=> k1_funct_1(k9_facirc_1(k19_facirc_1(A,B,C),k22_facirc_1(A,B,C),D,np__2),k4_tarski(k6_facirc_1(A,B),k3_facirc_1)) = k12_margrel1(E,F) ) ) ) ) ) ) ) ).
fof(t81_facirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ! [B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(C)
=> ! [D] :
( m1_subset_1(D,k4_card_3(u4_msualg_1(k19_facirc_1(A,B,C),k22_facirc_1(A,B,C))))
=> ! [E] :
( m2_subset_1(E,k5_numbers,k10_circcomb)
=> ! [F] :
( m2_subset_1(F,k5_numbers,k10_circcomb)
=> ( ( E = k1_funct_1(D,B)
& F = k1_funct_1(D,C) )
=> k1_funct_1(k9_facirc_1(k19_facirc_1(A,B,C),k22_facirc_1(A,B,C),D,np__2),k4_tarski(k6_facirc_1(B,C),k3_facirc_1)) = k12_margrel1(E,F) ) ) ) ) ) ) ) ).
fof(t82_facirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ! [B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(C)
=> ! [D] :
( m1_subset_1(D,k4_card_3(u4_msualg_1(k19_facirc_1(A,B,C),k22_facirc_1(A,B,C))))
=> ! [E] :
( m2_subset_1(E,k5_numbers,k10_circcomb)
=> ! [F] :
( m2_subset_1(F,k5_numbers,k10_circcomb)
=> ( ( E = k1_funct_1(D,A)
& F = k1_funct_1(D,C) )
=> k1_funct_1(k9_facirc_1(k19_facirc_1(A,B,C),k22_facirc_1(A,B,C),D,np__2),k4_tarski(k6_facirc_1(C,A),k3_facirc_1)) = k12_margrel1(F,E) ) ) ) ) ) ) ) ).
fof(t83_facirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ! [B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(C)
=> ! [D] :
( m1_subset_1(D,k4_card_3(u4_msualg_1(k19_facirc_1(A,B,C),k22_facirc_1(A,B,C))))
=> ! [E] :
( m2_subset_1(E,k5_numbers,k10_circcomb)
=> ! [F] :
( m2_subset_1(F,k5_numbers,k10_circcomb)
=> ! [G] :
( m2_subset_1(G,k5_numbers,k10_circcomb)
=> ( ( E = k1_funct_1(D,A)
& F = k1_funct_1(D,B)
& G = k1_funct_1(D,C) )
=> k15_facirc_1(k19_facirc_1(A,B,C),k22_facirc_1(A,B,C),k9_facirc_1(k19_facirc_1(A,B,C),k22_facirc_1(A,B,C),D,np__2),k21_facirc_1(A,B,C)) = k3_binarith(k3_binarith(k12_margrel1(E,F),k12_margrel1(F,G)),k12_margrel1(G,E)) ) ) ) ) ) ) ) ) ).
fof(t84_facirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ! [B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(C)
=> ! [D] :
( m1_subset_1(D,k4_card_3(u4_msualg_1(k19_facirc_1(A,B,C),k22_facirc_1(A,B,C))))
=> v1_circuit2(k9_facirc_1(k19_facirc_1(A,B,C),k22_facirc_1(A,B,C),D,np__2),k19_facirc_1(A,B,C),k22_facirc_1(A,B,C)) ) ) ) ) ).
fof(d22_facirc_1,axiom,
! [A,B,C] : k23_facirc_1(A,B,C) = k3_circcomb(k12_facirc_1(A,B,C,k1_facirc_1),k19_facirc_1(A,B,C)) ).
fof(t85_facirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ! [B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(C)
=> k2_msafree2(k23_facirc_1(A,B,C)) = k1_enumset1(A,B,C) ) ) ) ).
fof(t86_facirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ! [B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(C)
=> k4_msafree2(k23_facirc_1(A,B,C)) = k2_xboole_0(k2_xboole_0(k2_tarski(k4_tarski(k6_facirc_1(A,B),k1_facirc_1),k13_facirc_1(A,B,C,k1_facirc_1)),k1_enumset1(k4_tarski(k6_facirc_1(A,B),k3_facirc_1),k4_tarski(k6_facirc_1(B,C),k3_facirc_1),k4_tarski(k6_facirc_1(C,A),k3_facirc_1))),k1_struct_0(k19_facirc_1(A,B,C),k21_facirc_1(A,B,C))) ) ) ) ).
fof(t87_facirc_1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(D)
& l1_msualg_1(D) )
=> ( D = k23_facirc_1(A,B,C)
=> ( r2_hidden(A,u1_struct_0(D))
& r2_hidden(B,u1_struct_0(D))
& r2_hidden(C,u1_struct_0(D)) ) ) ) ).
fof(d23_facirc_1,axiom,
! [A,B,C] : k24_facirc_1(A,B,C) = k4_circcomb(k12_facirc_1(A,B,C,k1_facirc_1),k19_facirc_1(A,B,C),k17_facirc_1(A,B,C),k22_facirc_1(A,B,C)) ).
fof(t88_facirc_1,axiom,
! [A,B,C] : v1_relat_1(k4_msafree2(k23_facirc_1(A,B,C))) ).
fof(t89_facirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ! [B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(C)
=> ~ v2_facirc_1(k2_msafree2(k23_facirc_1(A,B,C))) ) ) ) ).
fof(t90_facirc_1,axiom,
! [A,B,C] :
( r2_hidden(k16_facirc_1(A,B,C),k4_msafree2(k23_facirc_1(A,B,C)))
& r2_hidden(k21_facirc_1(A,B,C),k4_msafree2(k23_facirc_1(A,B,C))) ) ).
fof(t91_facirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ! [B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(C)
=> ! [D] :
( m1_subset_1(D,k4_card_3(u4_msualg_1(k23_facirc_1(A,B,C),k24_facirc_1(A,B,C))))
=> ! [E] :
( m2_subset_1(E,k5_numbers,k10_circcomb)
=> ! [F] :
( m2_subset_1(F,k5_numbers,k10_circcomb)
=> ! [G] :
( m2_subset_1(G,k5_numbers,k10_circcomb)
=> ( ( E = k1_funct_1(D,A)
& F = k1_funct_1(D,B)
& G = k1_funct_1(D,C) )
=> ( k1_funct_1(k9_facirc_1(k23_facirc_1(A,B,C),k24_facirc_1(A,B,C),D,np__2),k16_facirc_1(A,B,C)) = k4_binarith(k4_binarith(E,F),G)
& k1_funct_1(k9_facirc_1(k23_facirc_1(A,B,C),k24_facirc_1(A,B,C),D,np__2),k21_facirc_1(A,B,C)) = k3_binarith(k3_binarith(k12_margrel1(E,F),k12_margrel1(F,G)),k12_margrel1(G,E)) ) ) ) ) ) ) ) ) ) ).
fof(t92_facirc_1,axiom,
! [A] :
( ~ v1_facirc_1(A)
=> ! [B] :
( ~ v1_facirc_1(B)
=> ! [C] :
( ~ v1_facirc_1(C)
=> ! [D] :
( m1_subset_1(D,k4_card_3(u4_msualg_1(k23_facirc_1(A,B,C),k24_facirc_1(A,B,C))))
=> v1_circuit2(k9_facirc_1(k23_facirc_1(A,B,C),k24_facirc_1(A,B,C),D,np__2),k23_facirc_1(A,B,C),k24_facirc_1(A,B,C)) ) ) ) ) ).
fof(s1_facirc_1,axiom,
? [A] :
( v1_funct_1(A)
& v1_funct_2(A,k4_finseq_2(np__2,k10_circcomb),k10_circcomb)
& m2_relset_1(A,k4_finseq_2(np__2,k10_circcomb),k10_circcomb)
& ! [B] :
( m2_subset_1(B,k5_numbers,k10_circcomb)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k10_circcomb)
=> k1_funct_1(A,k10_finseq_1(B,C)) = f1_s1_facirc_1(B,C) ) ) ) ).
fof(s2_facirc_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k4_finseq_2(np__2,k10_circcomb),k10_circcomb)
& m2_relset_1(A,k4_finseq_2(np__2,k10_circcomb),k10_circcomb) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k4_finseq_2(np__2,k10_circcomb),k10_circcomb)
& m2_relset_1(B,k4_finseq_2(np__2,k10_circcomb),k10_circcomb) )
=> ( ( ! [C] :
( m2_subset_1(C,k5_numbers,k10_circcomb)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k10_circcomb)
=> k1_funct_1(A,k10_finseq_1(C,D)) = f1_s2_facirc_1(C,D) ) )
& ! [C] :
( m2_subset_1(C,k5_numbers,k10_circcomb)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k10_circcomb)
=> k1_funct_1(B,k10_finseq_1(C,D)) = f1_s2_facirc_1(C,D) ) ) )
=> A = B ) ) ) ).
fof(s3_facirc_1,axiom,
( ? [A] :
( v1_funct_1(A)
& v1_funct_2(A,k4_finseq_2(np__2,k10_circcomb),k10_circcomb)
& m2_relset_1(A,k4_finseq_2(np__2,k10_circcomb),k10_circcomb)
& ! [B] :
( m2_subset_1(B,k5_numbers,k10_circcomb)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k10_circcomb)
=> k1_funct_1(A,k10_finseq_1(B,C)) = f1_s3_facirc_1(B,C) ) ) )
& ! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k4_finseq_2(np__2,k10_circcomb),k10_circcomb)
& m2_relset_1(A,k4_finseq_2(np__2,k10_circcomb),k10_circcomb) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k4_finseq_2(np__2,k10_circcomb),k10_circcomb)
& m2_relset_1(B,k4_finseq_2(np__2,k10_circcomb),k10_circcomb) )
=> ( ( ! [C] :
( m2_subset_1(C,k5_numbers,k10_circcomb)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k10_circcomb)
=> k1_funct_1(A,k10_finseq_1(C,D)) = f1_s3_facirc_1(C,D) ) )
& ! [C] :
( m2_subset_1(C,k5_numbers,k10_circcomb)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k10_circcomb)
=> k1_funct_1(B,k10_finseq_1(C,D)) = f1_s3_facirc_1(C,D) ) ) )
=> A = B ) ) ) ) ).
fof(s4_facirc_1,axiom,
? [A] :
( v1_funct_1(A)
& v1_funct_2(A,k4_finseq_2(np__3,k10_circcomb),k10_circcomb)
& m2_relset_1(A,k4_finseq_2(np__3,k10_circcomb),k10_circcomb)
& ! [B] :
( m2_subset_1(B,k5_numbers,k10_circcomb)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k10_circcomb)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k10_circcomb)
=> k1_funct_1(A,k11_finseq_1(B,C,D)) = f1_s4_facirc_1(B,C,D) ) ) ) ) ).
fof(s5_facirc_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k4_finseq_2(np__3,k10_circcomb),k10_circcomb)
& m2_relset_1(A,k4_finseq_2(np__3,k10_circcomb),k10_circcomb) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k4_finseq_2(np__3,k10_circcomb),k10_circcomb)
& m2_relset_1(B,k4_finseq_2(np__3,k10_circcomb),k10_circcomb) )
=> ( ( ! [C] :
( m2_subset_1(C,k5_numbers,k10_circcomb)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k10_circcomb)
=> ! [E] :
( m2_subset_1(E,k5_numbers,k10_circcomb)
=> k1_funct_1(A,k11_finseq_1(C,D,E)) = f1_s5_facirc_1(C,D,E) ) ) )
& ! [C] :
( m2_subset_1(C,k5_numbers,k10_circcomb)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k10_circcomb)
=> ! [E] :
( m2_subset_1(E,k5_numbers,k10_circcomb)
=> k1_funct_1(B,k11_finseq_1(C,D,E)) = f1_s5_facirc_1(C,D,E) ) ) ) )
=> A = B ) ) ) ).
fof(s6_facirc_1,axiom,
( ? [A] :
( v1_funct_1(A)
& v1_funct_2(A,k4_finseq_2(np__3,k10_circcomb),k10_circcomb)
& m2_relset_1(A,k4_finseq_2(np__3,k10_circcomb),k10_circcomb)
& ! [B] :
( m2_subset_1(B,k5_numbers,k10_circcomb)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k10_circcomb)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k10_circcomb)
=> k1_funct_1(A,k11_finseq_1(B,C,D)) = f1_s6_facirc_1(B,C,D) ) ) ) )
& ! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k4_finseq_2(np__3,k10_circcomb),k10_circcomb)
& m2_relset_1(A,k4_finseq_2(np__3,k10_circcomb),k10_circcomb) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k4_finseq_2(np__3,k10_circcomb),k10_circcomb)
& m2_relset_1(B,k4_finseq_2(np__3,k10_circcomb),k10_circcomb) )
=> ( ( ! [C] :
( m2_subset_1(C,k5_numbers,k10_circcomb)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k10_circcomb)
=> ! [E] :
( m2_subset_1(E,k5_numbers,k10_circcomb)
=> k1_funct_1(A,k11_finseq_1(C,D,E)) = f1_s6_facirc_1(C,D,E) ) ) )
& ! [C] :
( m2_subset_1(C,k5_numbers,k10_circcomb)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k10_circcomb)
=> ! [E] :
( m2_subset_1(E,k5_numbers,k10_circcomb)
=> k1_funct_1(B,k11_finseq_1(C,D,E)) = f1_s6_facirc_1(C,D,E) ) ) ) )
=> A = B ) ) ) ) ).
fof(dt_k1_facirc_1,axiom,
( v1_funct_1(k1_facirc_1)
& v1_funct_2(k1_facirc_1,k4_finseq_2(np__2,k10_circcomb),k10_circcomb)
& m2_relset_1(k1_facirc_1,k4_finseq_2(np__2,k10_circcomb),k10_circcomb) ) ).
fof(dt_k2_facirc_1,axiom,
( v1_funct_1(k2_facirc_1)
& v1_funct_2(k2_facirc_1,k4_finseq_2(np__2,k10_circcomb),k10_circcomb)
& m2_relset_1(k2_facirc_1,k4_finseq_2(np__2,k10_circcomb),k10_circcomb) ) ).
fof(dt_k3_facirc_1,axiom,
( v1_funct_1(k3_facirc_1)
& v1_funct_2(k3_facirc_1,k4_finseq_2(np__2,k10_circcomb),k10_circcomb)
& m2_relset_1(k3_facirc_1,k4_finseq_2(np__2,k10_circcomb),k10_circcomb) ) ).
fof(dt_k4_facirc_1,axiom,
( v1_funct_1(k4_facirc_1)
& v1_funct_2(k4_facirc_1,k4_finseq_2(np__3,k10_circcomb),k10_circcomb)
& m2_relset_1(k4_facirc_1,k4_finseq_2(np__3,k10_circcomb),k10_circcomb) ) ).
fof(dt_k5_facirc_1,axiom,
! [A] : m1_circcomb(k5_facirc_1(A),np__1) ).
fof(redefinition_k5_facirc_1,axiom,
! [A] : k5_facirc_1(A) = k5_finseq_1(A) ).
fof(dt_k6_facirc_1,axiom,
! [A,B] : m1_circcomb(k6_facirc_1(A,B),np__2) ).
fof(redefinition_k6_facirc_1,axiom,
! [A,B] : k6_facirc_1(A,B) = k10_finseq_1(A,B) ).
fof(dt_k7_facirc_1,axiom,
! [A,B,C] : m1_circcomb(k7_facirc_1(A,B,C),np__3) ).
fof(redefinition_k7_facirc_1,axiom,
! [A,B,C] : k7_facirc_1(A,B,C) = k11_finseq_1(A,B,C) ).
fof(dt_k8_facirc_1,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers)
& m1_circcomb(C,A)
& m1_circcomb(D,B) )
=> m1_circcomb(k8_facirc_1(A,B,C,D),k1_nat_1(A,B)) ) ).
fof(redefinition_k8_facirc_1,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers)
& m1_circcomb(C,A)
& m1_circcomb(D,B) )
=> k8_facirc_1(A,B,C,D) = k7_finseq_1(C,D) ) ).
fof(dt_k9_facirc_1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& l1_msualg_1(A)
& v5_msualg_1(B,A)
& v4_msafree2(B,A)
& l3_msualg_1(B,A)
& m1_subset_1(C,k4_card_3(u4_msualg_1(A,B)))
& m1_subset_1(D,k5_numbers) )
=> m1_subset_1(k9_facirc_1(A,B,C,D),k4_card_3(u4_msualg_1(A,B))) ) ).
fof(dt_k10_facirc_1,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k4_finseq_2(np__2,k10_circcomb),k10_circcomb)
& m1_relset_1(C,k4_finseq_2(np__2,k10_circcomb),k10_circcomb) )
=> ( v4_msualg_1(k10_facirc_1(A,B,C),k7_circcomb(C,k6_facirc_1(A,B)))
& v4_msafree2(k10_facirc_1(A,B,C),k7_circcomb(C,k6_facirc_1(A,B)))
& v4_circcomb(k10_facirc_1(A,B,C),k7_circcomb(C,k6_facirc_1(A,B)))
& v6_circcomb(k10_facirc_1(A,B,C),k7_circcomb(C,k6_facirc_1(A,B)))
& l3_msualg_1(k10_facirc_1(A,B,C),k7_circcomb(C,k6_facirc_1(A,B))) ) ) ).
fof(dt_k11_facirc_1,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(np__3,k10_circcomb),k10_circcomb)
& m1_relset_1(D,k4_finseq_2(np__3,k10_circcomb),k10_circcomb) )
=> ( v4_msualg_1(k11_facirc_1(A,B,C,D),k7_circcomb(D,k7_facirc_1(A,B,C)))
& v4_msafree2(k11_facirc_1(A,B,C,D),k7_circcomb(D,k7_facirc_1(A,B,C)))
& v4_circcomb(k11_facirc_1(A,B,C,D),k7_circcomb(D,k7_facirc_1(A,B,C)))
& v6_circcomb(k11_facirc_1(A,B,C,D),k7_circcomb(D,k7_facirc_1(A,B,C)))
& l3_msualg_1(k11_facirc_1(A,B,C,D),k7_circcomb(D,k7_facirc_1(A,B,C))) ) ) ).
fof(dt_k12_facirc_1,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(np__2,k10_circcomb),k10_circcomb)
& m1_relset_1(D,k4_finseq_2(np__2,k10_circcomb),k10_circcomb) )
=> ( ~ v3_struct_0(k12_facirc_1(A,B,C,D))
& v1_msualg_1(k12_facirc_1(A,B,C,D))
& ~ v2_msualg_1(k12_facirc_1(A,B,C,D))
& v1_circcomb(k12_facirc_1(A,B,C,D))
& v2_circcomb(k12_facirc_1(A,B,C,D))
& v3_circcomb(k12_facirc_1(A,B,C,D))
& l1_msualg_1(k12_facirc_1(A,B,C,D)) ) ) ).
fof(dt_k13_facirc_1,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(np__2,k10_circcomb),k10_circcomb)
& m1_relset_1(D,k4_finseq_2(np__2,k10_circcomb),k10_circcomb) )
=> m1_struct_0(k13_facirc_1(A,B,C,D),k12_facirc_1(A,B,C,D),k4_msafree2(k12_facirc_1(A,B,C,D))) ) ).
fof(dt_k14_facirc_1,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(np__2,k10_circcomb),k10_circcomb)
& m1_relset_1(D,k4_finseq_2(np__2,k10_circcomb),k10_circcomb) )
=> ( v4_msualg_1(k14_facirc_1(A,B,C,D),k12_facirc_1(A,B,C,D))
& v4_msafree2(k14_facirc_1(A,B,C,D),k12_facirc_1(A,B,C,D))
& v4_circcomb(k14_facirc_1(A,B,C,D),k12_facirc_1(A,B,C,D))
& v6_circcomb(k14_facirc_1(A,B,C,D),k12_facirc_1(A,B,C,D))
& l3_msualg_1(k14_facirc_1(A,B,C,D),k12_facirc_1(A,B,C,D)) ) ) ).
fof(dt_k15_facirc_1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v1_circcomb(A)
& l1_msualg_1(A)
& v4_msafree2(B,A)
& v6_circcomb(B,A)
& l3_msualg_1(B,A)
& m1_subset_1(C,k4_card_3(u4_msualg_1(A,B)))
& m1_subset_1(D,u1_struct_0(A)) )
=> m2_subset_1(k15_facirc_1(A,B,C,D),k5_numbers,k10_circcomb) ) ).
fof(redefinition_k15_facirc_1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v1_circcomb(A)
& l1_msualg_1(A)
& v4_msafree2(B,A)
& v6_circcomb(B,A)
& l3_msualg_1(B,A)
& m1_subset_1(C,k4_card_3(u4_msualg_1(A,B)))
& m1_subset_1(D,u1_struct_0(A)) )
=> k15_facirc_1(A,B,C,D) = k1_funct_1(C,D) ) ).
fof(dt_k16_facirc_1,axiom,
! [A,B,C] : m1_struct_0(k16_facirc_1(A,B,C),k12_facirc_1(A,B,C,k1_facirc_1),k4_msafree2(k12_facirc_1(A,B,C,k1_facirc_1))) ).
fof(dt_k17_facirc_1,axiom,
! [A,B,C] :
( v4_msualg_1(k17_facirc_1(A,B,C),k12_facirc_1(A,B,C,k1_facirc_1))
& v4_msafree2(k17_facirc_1(A,B,C),k12_facirc_1(A,B,C,k1_facirc_1))
& v4_circcomb(k17_facirc_1(A,B,C),k12_facirc_1(A,B,C,k1_facirc_1))
& v6_circcomb(k17_facirc_1(A,B,C),k12_facirc_1(A,B,C,k1_facirc_1))
& l3_msualg_1(k17_facirc_1(A,B,C),k12_facirc_1(A,B,C,k1_facirc_1)) ) ).
fof(dt_k18_facirc_1,axiom,
! [A,B,C] :
( ~ v3_struct_0(k18_facirc_1(A,B,C))
& v1_msualg_1(k18_facirc_1(A,B,C))
& ~ v2_msualg_1(k18_facirc_1(A,B,C))
& v1_circcomb(k18_facirc_1(A,B,C))
& v2_circcomb(k18_facirc_1(A,B,C))
& v3_circcomb(k18_facirc_1(A,B,C))
& l1_msualg_1(k18_facirc_1(A,B,C)) ) ).
fof(dt_k19_facirc_1,axiom,
! [A,B,C] :
( ~ v3_struct_0(k19_facirc_1(A,B,C))
& v1_msualg_1(k19_facirc_1(A,B,C))
& ~ v2_msualg_1(k19_facirc_1(A,B,C))
& v1_circcomb(k19_facirc_1(A,B,C))
& v2_circcomb(k19_facirc_1(A,B,C))
& v3_circcomb(k19_facirc_1(A,B,C))
& l1_msualg_1(k19_facirc_1(A,B,C)) ) ).
fof(dt_k20_facirc_1,axiom,
! [A,B,C] :
( v4_msualg_1(k20_facirc_1(A,B,C),k18_facirc_1(A,B,C))
& v4_msafree2(k20_facirc_1(A,B,C),k18_facirc_1(A,B,C))
& v4_circcomb(k20_facirc_1(A,B,C),k18_facirc_1(A,B,C))
& v6_circcomb(k20_facirc_1(A,B,C),k18_facirc_1(A,B,C))
& l3_msualg_1(k20_facirc_1(A,B,C),k18_facirc_1(A,B,C)) ) ).
fof(dt_k21_facirc_1,axiom,
! [A,B,C] : m1_struct_0(k21_facirc_1(A,B,C),k19_facirc_1(A,B,C),k4_msafree2(k19_facirc_1(A,B,C))) ).
fof(dt_k22_facirc_1,axiom,
! [A,B,C] :
( v4_msualg_1(k22_facirc_1(A,B,C),k19_facirc_1(A,B,C))
& v4_msafree2(k22_facirc_1(A,B,C),k19_facirc_1(A,B,C))
& v4_circcomb(k22_facirc_1(A,B,C),k19_facirc_1(A,B,C))
& v6_circcomb(k22_facirc_1(A,B,C),k19_facirc_1(A,B,C))
& l3_msualg_1(k22_facirc_1(A,B,C),k19_facirc_1(A,B,C)) ) ).
fof(dt_k23_facirc_1,axiom,
! [A,B,C] :
( ~ v3_struct_0(k23_facirc_1(A,B,C))
& v1_msualg_1(k23_facirc_1(A,B,C))
& ~ v2_msualg_1(k23_facirc_1(A,B,C))
& v1_circcomb(k23_facirc_1(A,B,C))
& v2_circcomb(k23_facirc_1(A,B,C))
& v3_circcomb(k23_facirc_1(A,B,C))
& l1_msualg_1(k23_facirc_1(A,B,C)) ) ).
fof(dt_k24_facirc_1,axiom,
! [A,B,C] :
( v4_msualg_1(k24_facirc_1(A,B,C),k23_facirc_1(A,B,C))
& v4_msafree2(k24_facirc_1(A,B,C),k23_facirc_1(A,B,C))
& v4_circcomb(k24_facirc_1(A,B,C),k23_facirc_1(A,B,C))
& v6_circcomb(k24_facirc_1(A,B,C),k23_facirc_1(A,B,C))
& l3_msualg_1(k24_facirc_1(A,B,C),k23_facirc_1(A,B,C)) ) ).
%------------------------------------------------------------------------------