SET007 Axioms: SET007+425.ax
%------------------------------------------------------------------------------
% File : SET007+425 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Introduction to Circuits, 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 : circuit1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 40 ( 1 unt; 0 def)
% Number of atoms : 503 ( 39 equ)
% Maximal formula atoms : 22 ( 12 avg)
% Number of connectives : 561 ( 98 ~; 1 |; 312 &)
% ( 10 <=>; 140 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 13 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 1 prp; 0-4 aty)
% Number of functors : 51 ( 51 usr; 5 con; 0-4 aty)
% Number of variables : 167 ( 160 !; 7 ?)
% 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_circuit1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& v5_msafree2(A)
& l1_msualg_1(A)
& v5_msualg_1(B,A)
& v4_msafree2(B,A)
& l3_msualg_1(B,A)
& m1_subset_1(C,u1_struct_0(A)) )
=> ! [D] :
( m1_subset_1(D,k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),C))
=> ( ~ v1_xboole_0(D)
& v1_relat_1(D)
& v1_funct_1(D)
& v1_finset_1(D) ) ) ) ).
fof(cc2_circuit1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& v5_msafree2(A)
& l1_msualg_1(A)
& v5_msualg_1(B,A)
& v4_msafree2(B,A)
& l3_msualg_1(B,A)
& m1_subset_1(C,u1_struct_0(A)) )
=> ! [D] :
( m1_subset_1(D,k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),C))
=> ( ~ v1_xboole_0(D)
& v1_relat_1(D)
& v1_funct_1(D)
& v1_finset_1(D)
& v3_trees_2(D) ) ) ) ).
fof(fc1_circuit1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v5_msafree2(A)
& l1_msualg_1(A)
& v5_msualg_1(B,A)
& v4_msafree2(B,A)
& l3_msualg_1(B,A)
& m1_subset_1(C,u1_struct_0(A)) )
=> ( ~ v1_xboole_0(k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),C))
& v1_finset_1(k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),C)) ) ) ).
fof(d1_circuit1,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_pboole(C,k1_msafree2(A))
=> ( C = k1_circuit1(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(D,k1_relat_1(C))
=> r2_hidden(k1_funct_1(C,D),k1_msualg_2(A,B,D)) ) ) ) ) ) ) ).
fof(t1_circuit1,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,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_funct_1(u4_msualg_1(A,B),C))
=> ( ( r2_hidden(C,k1_msafree2(A))
& r2_hidden(D,k1_msualg_2(A,B,C)) )
=> k1_funct_1(k1_circuit1(A,B),C) = D ) ) ) ) ) ).
fof(t2_circuit1,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] :
( m3_pboole(C,k2_msafree2(A),k2_pre_circ(k2_msafree2(A),k5_numbers),k3_pre_circ(u1_struct_0(A),u4_msualg_1(A,B),k2_msafree2(A)))
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( v1_msafree2(A)
=> m1_msafree2(k1_funct_1(k10_funct_6(C),D),A,B) ) ) ) ) ) ).
fof(d2_circuit1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& l1_msualg_1(A) )
=> ( v1_msafree2(A)
=> ! [B] :
( ( v5_msualg_1(B,A)
& v4_msafree2(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m3_pboole(C,k2_msafree2(A),k2_pre_circ(k2_msafree2(A),k5_numbers),k3_pre_circ(u1_struct_0(A),u4_msualg_1(A,B),k2_msafree2(A)))
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_circuit1(A,B,C,D) = k1_funct_1(k10_funct_6(C),D) ) ) ) ) ) ).
fof(t3_circuit1,axiom,
$true ).
fof(t4_circuit1,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)))
=> k1_relat_1(C) = u1_struct_0(A) ) ) ) ).
fof(t5_circuit1,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_struct_0(A))
=> r2_hidden(k1_funct_1(C,D),k1_funct_1(u4_msualg_1(A,B),D)) ) ) ) ) ).
fof(d3_circuit1,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))
=> k3_circuit1(A,B,C,D) = k5_relat_1(k1_msualg_1(A,D),C) ) ) ) ) ).
fof(t6_circuit1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& v5_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,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),C))
=> ! [F] :
( ( v1_relat_1(F)
& v1_funct_1(F)
& v1_finseq_1(F)
& v6_trees_3(F) )
=> ( ( r2_hidden(C,k4_msafree2(A))
& E = k4_trees_4(k4_tarski(k5_msafree2(A,C),u1_struct_0(A)),F) )
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ( ( r2_hidden(G,k4_finseq_1(F))
& r2_hidden(k1_funct_1(F,G),k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),D)) )
=> D = k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,k5_msafree2(A,C)),G) ) ) ) ) ) ) ) ) ) ).
fof(t7_circuit1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& v5_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,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),C))
=> ! [F] :
( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),D))
=> ! [G] :
( ( v1_relat_1(G)
& v1_funct_1(G)
& v1_finseq_1(G)
& v6_trees_3(G) )
=> ! [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
=> ( ( r2_hidden(C,k6_subset_1(u1_struct_0(A),k4_msafree2(A),k1_msafree2(A)))
& E = k4_trees_4(k4_tarski(k5_msafree2(A,C),u1_struct_0(A)),G)
& r2_hidden(k1_nat_1(H,np__1),k4_finseq_1(G))
& r2_hidden(k1_funct_1(G,k1_nat_1(H,np__1)),k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),D)) )
=> r2_hidden(k8_trees_2(E,k3_lang1(k5_numbers,H),F),k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),C)) ) ) ) ) ) ) ) ) ) ).
fof(t8_circuit1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& v5_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,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),C))
=> ~ ( ~ r1_xreal_0(k4_card_1(D),np__1)
& ! [E] :
( m1_subset_1(E,u1_msualg_1(A))
=> k1_funct_1(D,k1_xboole_0) != k4_tarski(E,u1_struct_0(A)) ) ) ) ) ) ) ).
fof(t9_circuit1,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))
=> r2_hidden(k1_funct_1(k5_msualg_1(A,D,B),k3_circuit1(A,B,C,D)),k1_funct_1(u4_msualg_1(A,B),k2_msualg_1(A,D))) ) ) ) ) ).
fof(t10_circuit1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& v5_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,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),C))
=> ~ ( k1_funct_1(D,k1_xboole_0) = k4_tarski(k5_msafree2(A,C),u1_struct_0(A))
& ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E)
& v1_finseq_1(E)
& v6_trees_3(E) )
=> D != k4_trees_4(k4_tarski(k5_msafree2(A,C),u1_struct_0(A)),E) ) ) ) ) ) ) ).
fof(t11_circuit1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& v5_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,u1_struct_0(A))
=> ( k4_circuit1(A,B,C) = np__1
<=> r2_hidden(C,k4_subset_1(u1_struct_0(A),k2_msafree2(A),k1_msafree2(A))) ) ) ) ) ).
fof(t12_circuit1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& v5_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,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),C))
=> ! [F] :
( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),D))
=> ! [G] :
( ( v1_relat_1(G)
& v1_funct_1(G)
& v1_finseq_1(G)
& v6_trees_3(G) )
=> ( ( r2_hidden(C,k6_subset_1(u1_struct_0(A),k4_msafree2(A),k1_msafree2(A)))
& k4_card_1(E) = k4_circuit1(A,B,C)
& E = k4_trees_4(k4_tarski(k5_msafree2(A,C),u1_struct_0(A)),G)
& r2_hidden(F,k2_relat_1(G)) )
=> k4_card_1(F) = k4_circuit1(A,B,D) ) ) ) ) ) ) ) ) ).
fof(t13_circuit1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& v5_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,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),C))
=> ~ ( r2_hidden(C,k6_subset_1(u1_struct_0(A),k4_msafree2(A),k1_msafree2(A)))
& k4_card_1(D) = k4_circuit1(A,B,C)
& ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E)
& v1_finseq_1(E)
& v6_trees_3(E) )
=> D != k4_trees_4(k4_tarski(k5_msafree2(A,C),u1_struct_0(A)),E) ) ) ) ) ) ) ).
fof(t14_circuit1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& v5_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,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),C))
=> ~ ( r2_hidden(C,k6_subset_1(u1_struct_0(A),k4_msafree2(A),k1_msafree2(A)))
& k4_card_1(D) = k4_circuit1(A,B,C)
& ! [E] :
( m1_subset_1(E,u1_msualg_1(A))
=> k1_funct_1(D,k1_xboole_0) != k4_tarski(E,u1_struct_0(A)) ) ) ) ) ) ) ).
fof(d5_circuit1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(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,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),C))
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( E = k5_circuit1(A,B,C,D)
<=> ? [F] :
( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,k11_msafree(A,u4_msualg_1(A,B))),C))
& D = F
& E = k9_msafree2(A,u4_msualg_1(A,B),C,F) ) ) ) ) ) ) ) ).
fof(t15_circuit1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& v5_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,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(C,k4_msafree2(A))
& r2_hidden(D,k5_relset_1(k5_numbers,u1_struct_0(A),k1_msualg_1(A,k5_msafree2(A,C))))
& r1_xreal_0(k4_circuit1(A,B,C),k4_circuit1(A,B,D)) ) ) ) ) ) ).
fof(t16_circuit1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& v5_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,u1_struct_0(A))
=> ~ r1_xreal_0(k4_circuit1(A,B,C),np__0) ) ) ) ).
fof(t17_circuit1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& v5_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,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),C))
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E)
& v1_finseq_1(E)
& v6_trees_3(E) )
=> ( ( r2_hidden(C,k4_msafree2(A))
& D = k4_trees_4(k4_tarski(k5_msafree2(A,C),u1_struct_0(A)),E)
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(F,k4_finseq_1(E))
& ! [G] :
( m1_subset_1(G,k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,k5_msafree2(A,C)),F)))
=> ~ ( G = k1_funct_1(E,F)
& k4_card_1(G) = k4_circuit1(A,B,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,k5_msafree2(A,C)),F)) ) ) ) ) )
=> k4_card_1(D) = k4_circuit1(A,B,C) ) ) ) ) ) ) ).
fof(t18_circuit1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_group_1(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& v5_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,u1_struct_0(A))
=> r1_xreal_0(k6_circuit1(A,B,C),k7_circuit1(A,B)) ) ) ) ).
fof(t19_circuit1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& v5_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,u1_struct_0(A))
=> ( k6_circuit1(A,B,C) = np__0
<=> ( r2_hidden(C,k2_msafree2(A))
| r2_hidden(C,k1_msafree2(A)) ) ) ) ) ) ).
fof(t20_circuit1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& v5_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,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(C,k4_msafree2(A))
& r2_hidden(D,k5_relset_1(k5_numbers,u1_struct_0(A),k1_msualg_1(A,k5_msafree2(A,C))))
& r1_xreal_0(k6_circuit1(A,B,C),k6_circuit1(A,B,D)) ) ) ) ) ) ).
fof(dt_k1_circuit1,axiom,
! [A,B] :
( ( ~ 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_pboole(k1_circuit1(A,B),k1_msafree2(A)) ) ).
fof(dt_k2_circuit1,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)
& m3_pboole(C,k2_msafree2(A),k2_pre_circ(k2_msafree2(A),k5_numbers),k3_pre_circ(u1_struct_0(A),u4_msualg_1(A,B),k2_msafree2(A)))
& m1_subset_1(D,k5_numbers) )
=> m1_msafree2(k2_circuit1(A,B,C,D),A,B) ) ).
fof(dt_k3_circuit1,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,u1_msualg_1(A)) )
=> m1_subset_1(k3_circuit1(A,B,C,D),k3_msualg_1(A,D,B)) ) ).
fof(dt_k4_circuit1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& v5_msafree2(A)
& l1_msualg_1(A)
& v5_msualg_1(B,A)
& v4_msafree2(B,A)
& l3_msualg_1(B,A)
& m1_subset_1(C,u1_struct_0(A)) )
=> v4_ordinal2(k4_circuit1(A,B,C)) ) ).
fof(dt_k5_circuit1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v5_msualg_1(B,A)
& v4_msafree2(B,A)
& l3_msualg_1(B,A)
& m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(D,k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),C)) )
=> m2_subset_1(k5_circuit1(A,B,C,D),k1_numbers,k5_numbers) ) ).
fof(dt_k6_circuit1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v5_msafree2(A)
& l1_msualg_1(A)
& v5_msualg_1(B,A)
& v4_msafree2(B,A)
& l3_msualg_1(B,A)
& m1_subset_1(C,u1_struct_0(A)) )
=> v4_ordinal2(k6_circuit1(A,B,C)) ) ).
fof(dt_k7_circuit1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v6_group_1(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& v5_msafree2(A)
& l1_msualg_1(A)
& v5_msualg_1(B,A)
& v4_msafree2(B,A)
& l3_msualg_1(B,A) )
=> v4_ordinal2(k7_circuit1(A,B)) ) ).
fof(d4_circuit1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& v5_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,u1_struct_0(A))
=> ! [D] :
( v4_ordinal2(D)
=> ( D = k4_circuit1(A,B,C)
<=> ? [E] :
( ~ v1_xboole_0(E)
& v1_finset_1(E)
& m1_subset_1(E,k1_zfmisc_1(k5_numbers))
& E = a_3_0_circuit1(A,B,C)
& D = k1_pre_circ(E) ) ) ) ) ) ) ).
fof(d6_circuit1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v5_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,u1_struct_0(A))
=> ! [D] :
( v4_ordinal2(D)
=> ( D = k6_circuit1(A,B,C)
<=> ? [E] :
( ~ v1_xboole_0(E)
& v1_finset_1(E)
& m1_subset_1(E,k1_zfmisc_1(k5_numbers))
& E = a_3_1_circuit1(A,B,C)
& D = k1_pre_circ(E) ) ) ) ) ) ) ).
fof(d7_circuit1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_group_1(A)
& ~ v2_msualg_1(A)
& v2_msafree2(A)
& v5_msafree2(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v4_msafree2(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( v4_ordinal2(C)
=> ( C = k7_circuit1(A,B)
<=> ? [D] :
( ~ v1_xboole_0(D)
& v1_finset_1(D)
& m1_subset_1(D,k1_zfmisc_1(k5_numbers))
& D = a_2_0_circuit1(A,B)
& C = k1_pre_circ(D) ) ) ) ) ) ).
fof(fraenkel_a_3_0_circuit1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& v2_msafree2(B)
& v5_msafree2(B)
& l1_msualg_1(B)
& v5_msualg_1(C,B)
& v4_msafree2(C,B)
& l3_msualg_1(C,B)
& m1_subset_1(D,u1_struct_0(B)) )
=> ( r2_hidden(A,a_3_0_circuit1(B,C,D))
<=> ? [E] :
( m1_subset_1(E,k1_funct_1(u4_msualg_1(B,k6_msafree2(B,C)),D))
& A = k4_card_1(E) ) ) ) ).
fof(fraenkel_a_3_1_circuit1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& v5_msafree2(B)
& l1_msualg_1(B)
& v5_msualg_1(C,B)
& v4_msafree2(C,B)
& l3_msualg_1(C,B)
& m1_subset_1(D,u1_struct_0(B)) )
=> ( r2_hidden(A,a_3_1_circuit1(B,C,D))
<=> ? [E] :
( m1_subset_1(E,k1_funct_1(u4_msualg_1(B,k6_msafree2(B,C)),D))
& A = k5_circuit1(B,C,D,E) ) ) ) ).
fof(fraenkel_a_2_0_circuit1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v6_group_1(B)
& ~ v2_msualg_1(B)
& v2_msafree2(B)
& v5_msafree2(B)
& l1_msualg_1(B)
& v5_msualg_1(C,B)
& v4_msafree2(C,B)
& l3_msualg_1(C,B) )
=> ( r2_hidden(A,a_2_0_circuit1(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = k6_circuit1(B,C,D)
& r2_hidden(D,u1_struct_0(B)) ) ) ) ).
%------------------------------------------------------------------------------