SET007 Axioms: SET007+719.ax
%------------------------------------------------------------------------------
% File : SET007+719 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Full Adder Circuit. Part II
% 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_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 58 ( 7 unt; 0 def)
% Number of atoms : 463 ( 127 equ)
% Maximal formula atoms : 32 ( 7 avg)
% Number of connectives : 469 ( 64 ~; 1 |; 278 &)
% ( 5 <=>; 121 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 10 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 48 ( 46 usr; 1 prp; 0-3 aty)
% Number of functors : 71 ( 71 usr; 14 con; 0-4 aty)
% Number of variables : 190 ( 173 !; 17 ?)
% 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_2,axiom,
! [A] :
( l1_msualg_1(A)
=> ( v2_msualg_1(A)
=> ( v1_circcomb(A)
& v2_circcomb(A)
& v3_circcomb(A) ) ) ) ).
fof(rc1_facirc_2,axiom,
? [A] :
( l1_msualg_1(A)
& v1_msualg_1(A)
& v2_msualg_1(A)
& v1_circcomb(A)
& v2_circcomb(A)
& v3_circcomb(A) ) ).
fof(fc1_facirc_2,axiom,
! [A] :
( ~ v3_struct_0(k1_facirc_2(A))
& v1_msualg_1(k1_facirc_2(A))
& v2_msualg_1(k1_facirc_2(A))
& v2_msafree2(k1_facirc_2(A))
& v1_circcomb(k1_facirc_2(A))
& v2_circcomb(k1_facirc_2(A))
& v3_circcomb(k1_facirc_2(A))
& v5_circcomb(k1_facirc_2(A)) ) ).
fof(cc2_facirc_2,axiom,
! [A] :
( v1_xboole_0(A)
=> ~ v1_facirc_1(A) ) ).
fof(fc2_facirc_2,axiom,
( v1_xboole_0(k1_xboole_0)
& v1_relat_1(k1_xboole_0)
& v3_relat_1(k1_xboole_0)
& v1_funct_1(k1_xboole_0)
& v2_funct_1(k1_xboole_0)
& v1_ordinal1(k1_xboole_0)
& v2_ordinal1(k1_xboole_0)
& v3_ordinal1(k1_xboole_0)
& v4_ordinal2(k1_xboole_0)
& v1_finset_1(k1_xboole_0)
& v1_finseq_1(k1_xboole_0)
& v1_xreal_0(k1_xboole_0)
& ~ v2_xreal_0(k1_xboole_0)
& ~ v3_xreal_0(k1_xboole_0)
& v1_xcmplx_0(k1_xboole_0)
& v1_margrel1(k1_xboole_0)
& ~ v1_facirc_1(k1_xboole_0)
& ~ v2_facirc_1(k1_xboole_0)
& v3_facirc_1(k1_xboole_0) ) ).
fof(fc3_facirc_2,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v3_facirc_1(A) )
=> ~ v1_facirc_1(k1_funct_1(A,B)) ) ).
fof(fc4_facirc_2,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B)
& v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> ( ~ v1_xboole_0(k6_facirc_2(A,B,C))
& v1_facirc_1(k6_facirc_2(A,B,C)) ) ) ).
fof(t1_facirc_2,axiom,
! [A,B,C] :
~ ( A != C
& B != C
& k4_xboole_0(k2_tarski(A,B),k1_tarski(C)) != k2_tarski(A,B) ) ).
fof(t2_facirc_2,axiom,
$true ).
fof(t3_facirc_2,axiom,
! [A,B,C] :
( A != k4_tarski(k6_facirc_1(A,B),C)
& B != k4_tarski(k6_facirc_1(A,B),C) ) ).
fof(d1_facirc_2,axiom,
! [A,B] :
( ( v1_msualg_1(B)
& v2_msualg_1(B)
& l1_msualg_1(B) )
=> ( B = k1_facirc_2(A)
<=> u1_struct_0(B) = k1_tarski(A) ) ) ).
fof(d2_facirc_2,axiom,
! [A,B] :
( ( v4_msualg_1(B,k1_facirc_2(A))
& v6_circcomb(B,k1_facirc_2(A))
& l3_msualg_1(B,k1_facirc_2(A)) )
=> B = k2_facirc_2(A) ) ).
fof(t4_facirc_2,axiom,
! [A,B] :
( l1_msualg_1(B)
=> r1_circcomb(k1_facirc_2(A),B) ) ).
fof(t5_facirc_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ( r2_hidden(A,u1_struct_0(B))
=> k3_circcomb(k1_facirc_2(A),B) = g1_msualg_1(u1_struct_0(B),u1_msualg_1(B),u2_msualg_1(B),u3_msualg_1(B)) ) ) ).
fof(t6_facirc_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v1_msualg_1(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v6_circcomb(C,B)
& l3_msualg_1(C,B) )
=> ( r2_hidden(A,u1_struct_0(B))
=> k4_circcomb(k1_facirc_2(A),B,k2_facirc_2(A),C) = g3_msualg_1(B,u4_msualg_1(B,C),u5_msualg_1(B,C)) ) ) ) ).
fof(d3_facirc_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [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) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v1_msualg_1(D)
& ~ v2_msualg_1(D)
& v1_circcomb(D)
& v2_circcomb(D)
& v3_circcomb(D)
& l1_msualg_1(D) )
=> ( D = k4_facirc_2(A,B,C)
<=> ? [E] :
( m1_pboole(E,k5_numbers)
& ? [F] :
( m1_pboole(F,k5_numbers)
& D = k1_funct_1(E,A)
& k1_funct_1(E,np__0) = k7_circcomb(k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1),k3_facirc_2)
& k1_funct_1(F,np__0) = k4_tarski(k3_facirc_2,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1))
& ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ! [H] :
( ( ~ v3_struct_0(H)
& l1_msualg_1(H) )
=> ! [I] :
( ( H = k1_funct_1(E,G)
& I = k1_funct_1(F,G) )
=> ( k1_funct_1(E,k1_nat_1(G,np__1)) = k3_circcomb(H,k23_facirc_1(k1_funct_1(B,k1_nat_1(G,np__1)),k1_funct_1(C,k1_nat_1(G,np__1)),I))
& k1_funct_1(F,k1_nat_1(G,np__1)) = k21_facirc_1(k1_funct_1(B,k1_nat_1(G,np__1)),k1_funct_1(C,k1_nat_1(G,np__1)),I) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d4_facirc_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [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) )
=> ! [D] :
( ( v4_msualg_1(D,k4_facirc_2(A,B,C))
& v4_msafree2(D,k4_facirc_2(A,B,C))
& v4_circcomb(D,k4_facirc_2(A,B,C))
& v6_circcomb(D,k4_facirc_2(A,B,C))
& l3_msualg_1(D,k4_facirc_2(A,B,C)) )
=> ( D = k5_facirc_2(A,B,C)
<=> ? [E] :
( m1_pboole(E,k5_numbers)
& ? [F] :
( m1_pboole(F,k5_numbers)
& ? [G] :
( m1_pboole(G,k5_numbers)
& k4_facirc_2(A,B,C) = k1_funct_1(E,A)
& D = k1_funct_1(F,A)
& k1_funct_1(E,np__0) = k7_circcomb(k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1),k3_facirc_2)
& k1_funct_1(F,np__0) = k9_circcomb(np__0,k10_circcomb,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1),k3_facirc_2)
& k1_funct_1(G,np__0) = k4_tarski(k3_facirc_2,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1))
& ! [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
=> ! [I] :
( ( ~ v3_struct_0(I)
& l1_msualg_1(I) )
=> ! [J] :
( ( v5_msualg_1(J,I)
& l3_msualg_1(J,I) )
=> ! [K] :
( ( I = k1_funct_1(E,H)
& J = k1_funct_1(F,H)
& K = k1_funct_1(G,H) )
=> ( k1_funct_1(E,k1_nat_1(H,np__1)) = k3_circcomb(I,k23_facirc_1(k1_funct_1(B,k1_nat_1(H,np__1)),k1_funct_1(C,k1_nat_1(H,np__1)),K))
& k1_funct_1(F,k1_nat_1(H,np__1)) = k4_circcomb(I,k23_facirc_1(k1_funct_1(B,k1_nat_1(H,np__1)),k1_funct_1(C,k1_nat_1(H,np__1)),K),J,k24_facirc_1(k1_funct_1(B,k1_nat_1(H,np__1)),k1_funct_1(C,k1_nat_1(H,np__1)),K))
& k1_funct_1(G,k1_nat_1(H,np__1)) = k21_facirc_1(k1_funct_1(B,k1_nat_1(H,np__1)),k1_funct_1(C,k1_nat_1(H,np__1)),K) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d5_facirc_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [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) )
=> ! [D] :
( m1_struct_0(D,k4_facirc_2(A,B,C),k4_msafree2(k4_facirc_2(A,B,C)))
=> ( D = k6_facirc_2(A,B,C)
<=> ? [E] :
( m1_pboole(E,k5_numbers)
& D = k1_funct_1(E,A)
& k1_funct_1(E,np__0) = k4_tarski(k3_facirc_2,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1))
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( G = k1_funct_1(E,F)
=> k1_funct_1(E,k1_nat_1(F,np__1)) = k21_facirc_1(k1_funct_1(B,k1_nat_1(F,np__1)),k1_funct_1(C,k1_nat_1(F,np__1)),G) ) ) ) ) ) ) ) ) ).
fof(t7_facirc_2,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ! [C] :
( m1_pboole(C,k5_numbers)
=> ! [D] :
( m1_pboole(D,k5_numbers)
=> ! [E] :
( m1_pboole(E,k5_numbers)
=> ( ( k1_funct_1(C,np__0) = k7_circcomb(k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1),k3_facirc_2)
& k1_funct_1(D,np__0) = k9_circcomb(np__0,k10_circcomb,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1),k3_facirc_2)
& k1_funct_1(E,np__0) = k4_tarski(k3_facirc_2,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1))
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( ( ~ v3_struct_0(G)
& l1_msualg_1(G) )
=> ! [H] :
( ( v5_msualg_1(H,G)
& l3_msualg_1(H,G) )
=> ! [I] :
( ( G = k1_funct_1(C,F)
& H = k1_funct_1(D,F)
& I = k1_funct_1(E,F) )
=> ( k1_funct_1(C,k1_nat_1(F,np__1)) = k3_circcomb(G,k23_facirc_1(k1_funct_1(A,k1_nat_1(F,np__1)),k1_funct_1(B,k1_nat_1(F,np__1)),I))
& k1_funct_1(D,k1_nat_1(F,np__1)) = k4_circcomb(G,k23_facirc_1(k1_funct_1(A,k1_nat_1(F,np__1)),k1_funct_1(B,k1_nat_1(F,np__1)),I),H,k24_facirc_1(k1_funct_1(A,k1_nat_1(F,np__1)),k1_funct_1(B,k1_nat_1(F,np__1)),I))
& k1_funct_1(E,k1_nat_1(F,np__1)) = k21_facirc_1(k1_funct_1(A,k1_nat_1(F,np__1)),k1_funct_1(B,k1_nat_1(F,np__1)),I) ) ) ) ) ) )
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( k4_facirc_2(F,A,B) = k1_funct_1(C,F)
& k5_facirc_2(F,A,B) = k1_funct_1(D,F)
& k6_facirc_2(F,A,B) = k1_funct_1(E,F) ) ) ) ) ) ) ) ) ).
fof(t8_facirc_2,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ( k4_facirc_2(np__0,A,B) = k7_circcomb(k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1),k3_facirc_2)
& k5_facirc_2(np__0,A,B) = k9_circcomb(np__0,k10_circcomb,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1),k3_facirc_2)
& k6_facirc_2(np__0,A,B) = k4_tarski(k3_facirc_2,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1)) ) ) ) ).
fof(t9_facirc_2,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ! [C] :
( C = k4_tarski(k3_facirc_2,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1))
=> ( k4_facirc_2(np__1,A,B) = k3_circcomb(k7_circcomb(k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1),k3_facirc_2),k23_facirc_1(k1_funct_1(A,np__1),k1_funct_1(B,np__1),C))
& k5_facirc_2(np__1,A,B) = k4_circcomb(k7_circcomb(k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1),k3_facirc_2),k23_facirc_1(k1_funct_1(A,np__1),k1_funct_1(B,np__1),C),k9_circcomb(np__0,k10_circcomb,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1),k3_facirc_2),k24_facirc_1(k1_funct_1(A,np__1),k1_funct_1(B,np__1),C))
& k6_facirc_2(np__1,A,B) = k21_facirc_1(k1_funct_1(A,np__1),k1_funct_1(B,np__1),C) ) ) ) ) ).
fof(t10_facirc_2,axiom,
! [A,B,C] :
( C = k4_tarski(k3_facirc_2,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1))
=> ( k4_facirc_2(np__1,k5_facirc_1(A),k5_facirc_1(B)) = k3_circcomb(k7_circcomb(k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1),k3_facirc_2),k23_facirc_1(A,B,C))
& k5_facirc_2(np__1,k5_facirc_1(A),k5_facirc_1(B)) = k4_circcomb(k7_circcomb(k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1),k3_facirc_2),k23_facirc_1(A,B,C),k9_circcomb(np__0,k10_circcomb,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1),k3_facirc_2),k24_facirc_1(A,B,C))
& k6_facirc_2(np__1,k5_facirc_1(A),k5_facirc_1(B)) = k21_facirc_1(A,B,C) ) ) ).
fof(t11_facirc_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_circcomb(B,A)
=> ! [C] :
( m1_circcomb(C,A)
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D)
& v1_finseq_1(D) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E)
& v1_finseq_1(E) )
=> ! [F] :
( ( v1_relat_1(F)
& v1_funct_1(F)
& v1_finseq_1(F) )
=> ! [G] :
( ( v1_relat_1(G)
& v1_funct_1(G)
& v1_finseq_1(G) )
=> ( k4_facirc_2(A,k7_finseq_1(B,D),k7_finseq_1(C,F)) = k4_facirc_2(A,k7_finseq_1(B,E),k7_finseq_1(C,G))
& k5_facirc_2(A,k7_finseq_1(B,D),k7_finseq_1(C,F)) = k5_facirc_2(A,k7_finseq_1(B,E),k7_finseq_1(C,G))
& k6_facirc_2(A,k7_finseq_1(B,D),k7_finseq_1(C,F)) = k6_facirc_2(A,k7_finseq_1(B,E),k7_finseq_1(C,G)) ) ) ) ) ) ) ) ) ).
fof(t12_facirc_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_circcomb(B,A)
=> ! [C] :
( m1_circcomb(C,A)
=> ! [D,E] :
( k4_facirc_2(k1_nat_1(A,np__1),k8_facirc_1(A,np__1,B,k5_facirc_1(D)),k8_facirc_1(A,np__1,C,k5_facirc_1(E))) = k3_circcomb(k4_facirc_2(A,B,C),k23_facirc_1(D,E,k6_facirc_2(A,B,C)))
& k5_facirc_2(k1_nat_1(A,np__1),k8_facirc_1(A,np__1,B,k5_facirc_1(D)),k8_facirc_1(A,np__1,C,k5_facirc_1(E))) = k4_circcomb(k4_facirc_2(A,B,C),k23_facirc_1(D,E,k6_facirc_2(A,B,C)),k5_facirc_2(A,B,C),k24_facirc_1(D,E,k6_facirc_2(A,B,C)))
& k6_facirc_2(k1_nat_1(A,np__1),k8_facirc_1(A,np__1,B,k5_facirc_1(D)),k8_facirc_1(A,np__1,C,k5_facirc_1(E))) = k21_facirc_1(D,E,k6_facirc_2(A,B,C)) ) ) ) ) ).
fof(t13_facirc_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [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) )
=> ( k4_facirc_2(k1_nat_1(A,np__1),B,C) = k3_circcomb(k4_facirc_2(A,B,C),k23_facirc_1(k1_funct_1(B,k1_nat_1(A,np__1)),k1_funct_1(C,k1_nat_1(A,np__1)),k6_facirc_2(A,B,C)))
& k5_facirc_2(k1_nat_1(A,np__1),B,C) = k4_circcomb(k4_facirc_2(A,B,C),k23_facirc_1(k1_funct_1(B,k1_nat_1(A,np__1)),k1_funct_1(C,k1_nat_1(A,np__1)),k6_facirc_2(A,B,C)),k5_facirc_2(A,B,C),k24_facirc_1(k1_funct_1(B,k1_nat_1(A,np__1)),k1_funct_1(C,k1_nat_1(A,np__1)),k6_facirc_2(A,B,C)))
& k6_facirc_2(k1_nat_1(A,np__1),B,C) = k21_facirc_1(k1_funct_1(B,k1_nat_1(A,np__1)),k1_funct_1(C,k1_nat_1(A,np__1)),k6_facirc_2(A,B,C)) ) ) ) ) ).
fof(t14_facirc_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r1_xreal_0(A,B)
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D)
& v1_finseq_1(D) )
=> r1_tarski(k4_msafree2(k4_facirc_2(A,C,D)),k4_msafree2(k4_facirc_2(B,C,D))) ) ) ) ) ) ).
fof(t15_facirc_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [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) )
=> k4_msafree2(k4_facirc_2(k1_nat_1(A,np__1),B,C)) = k2_xboole_0(k4_msafree2(k4_facirc_2(A,B,C)),k4_msafree2(k23_facirc_1(k1_funct_1(B,k1_nat_1(A,np__1)),k1_funct_1(C,k1_nat_1(A,np__1)),k6_facirc_2(A,B,C)))) ) ) ) ).
fof(d6_facirc_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D)
& v1_finseq_1(D) )
=> ! [E] :
( m1_struct_0(E,k4_facirc_2(B,C,D),k4_msafree2(k4_facirc_2(B,C,D)))
=> ( E = k7_facirc_2(A,B,C,D)
<=> ? [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
& A = k1_nat_1(F,np__1)
& E = k16_facirc_1(k1_funct_1(C,A),k1_funct_1(D,A),k6_facirc_2(F,C,D)) ) ) ) ) ) ) ) ) ).
fof(t16_facirc_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(A,B)
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D)
& v1_finseq_1(D) )
=> k7_facirc_2(k1_nat_1(B,np__1),A,C,D) = k16_facirc_1(k1_funct_1(C,k1_nat_1(B,np__1)),k1_funct_1(D,k1_nat_1(B,np__1)),k6_facirc_2(B,C,D)) ) ) ) ) ) ).
fof(t17_facirc_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [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) )
=> v1_relat_1(k4_msafree2(k4_facirc_2(A,B,C))) ) ) ) ).
fof(t18_facirc_2,axiom,
! [A,B,C] : k4_msafree2(k18_facirc_1(A,B,C)) = 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)) ).
fof(t19_facirc_2,axiom,
! [A,B,C] :
~ ( A != k4_tarski(k6_facirc_1(B,C),k3_facirc_1)
& B != k4_tarski(k6_facirc_1(C,A),k3_facirc_1)
& C != k4_tarski(k6_facirc_1(A,B),k3_facirc_1)
& k2_msafree2(k18_facirc_1(A,B,C)) != k1_enumset1(A,B,C) ) ).
fof(t20_facirc_2,axiom,
! [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(t21_facirc_2,axiom,
! [A,B,C] :
~ ( A != k4_tarski(k6_facirc_1(B,C),k3_facirc_1)
& B != k4_tarski(k6_facirc_1(C,A),k3_facirc_1)
& C != k4_tarski(k6_facirc_1(A,B),k3_facirc_1)
& k2_msafree2(k19_facirc_1(A,B,C)) != k1_enumset1(A,B,C) ) ).
fof(t22_facirc_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ( ( r1_circcomb(A,B)
& k2_msafree2(A) = k2_msafree2(B) )
=> k2_msafree2(k3_circcomb(A,B)) = k2_msafree2(A) ) ) ) ).
fof(t23_facirc_2,axiom,
! [A,B,C] :
~ ( A != k4_tarski(k6_facirc_1(B,C),k3_facirc_1)
& B != k4_tarski(k6_facirc_1(C,A),k3_facirc_1)
& C != k4_tarski(k6_facirc_1(A,B),k3_facirc_1)
& C != k4_tarski(k6_facirc_1(A,B),k1_facirc_1)
& k2_msafree2(k23_facirc_1(A,B,C)) != k1_enumset1(A,B,C) ) ).
fof(t24_facirc_2,axiom,
! [A,B,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(t25_facirc_2,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( k1_mcart_1(k6_facirc_2(C,A,B)) = k3_facirc_2
& k2_mcart_1(k6_facirc_2(C,A,B)) = k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k7_margrel1)
& k1_funct_5(k2_mcart_1(k6_facirc_2(C,A,B))) = k4_finseq_2(np__0,k10_circcomb) )
| ( k1_card_1(k1_mcart_1(k6_facirc_2(C,A,B))) = np__3
& k2_mcart_1(k6_facirc_2(C,A,B)) = k4_facirc_1
& k1_funct_5(k2_mcart_1(k6_facirc_2(C,A,B))) = k4_finseq_2(np__3,k10_circcomb) ) ) ) ) ) ).
fof(t26_facirc_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [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) )
=> ! [D] :
( k6_facirc_2(A,B,C) != k4_tarski(D,k3_facirc_1)
& k6_facirc_2(A,B,C) != k4_tarski(D,k1_facirc_1) ) ) ) ) ).
fof(t27_facirc_2,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A)
& v3_facirc_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B)
& v3_facirc_1(B) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( k2_msafree2(k4_facirc_2(k1_nat_1(C,np__1),A,B)) = k2_xboole_0(k2_msafree2(k4_facirc_2(C,A,B)),k4_xboole_0(k2_msafree2(k23_facirc_1(k1_funct_1(A,k1_nat_1(C,np__1)),k1_funct_1(B,k1_nat_1(C,np__1)),k6_facirc_2(C,A,B))),k1_struct_0(k4_facirc_2(C,A,B),k6_facirc_2(C,A,B))))
& v1_relat_1(k4_msafree2(k4_facirc_2(C,A,B)))
& ~ v2_facirc_1(k2_msafree2(k4_facirc_2(C,A,B))) ) ) ) ) ).
fof(t28_facirc_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v3_facirc_1(B)
& m1_circcomb(B,A) )
=> ! [C] :
( ( v3_facirc_1(C)
& m1_circcomb(C,A) )
=> k2_msafree2(k4_facirc_2(A,B,C)) = k2_xboole_0(k2_relat_1(B),k2_relat_1(C)) ) ) ) ).
fof(t29_facirc_2,axiom,
! [A,B,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(t30_facirc_2,axiom,
! [A,B,C] :
~ ( A != k4_tarski(k6_facirc_1(B,C),k3_facirc_1)
& B != k4_tarski(k6_facirc_1(C,A),k3_facirc_1)
& C != k4_tarski(k6_facirc_1(A,B),k3_facirc_1)
& C != k4_tarski(k6_facirc_1(A,B),k1_facirc_1)
& ~ ! [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(t31_facirc_2,axiom,
! [A,B,C] :
~ ( A != k4_tarski(k6_facirc_1(B,C),k3_facirc_1)
& B != k4_tarski(k6_facirc_1(C,A),k3_facirc_1)
& C != k4_tarski(k6_facirc_1(A,B),k3_facirc_1)
& C != k4_tarski(k6_facirc_1(A,B),k1_facirc_1)
& ? [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(t32_facirc_2,axiom,
! [A,B,C] :
~ ( A != k4_tarski(k6_facirc_1(B,C),k3_facirc_1)
& B != k4_tarski(k6_facirc_1(C,A),k3_facirc_1)
& C != k4_tarski(k6_facirc_1(A,B),k3_facirc_1)
& C != k4_tarski(k6_facirc_1(A,B),k1_facirc_1)
& ~ ! [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(t33_facirc_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v3_facirc_1(B)
& m1_circcomb(B,A) )
=> ! [C] :
( ( v3_facirc_1(C)
& m1_circcomb(C,A) )
=> ! [D] :
( m1_subset_1(D,k4_card_3(u4_msualg_1(k4_facirc_2(A,B,C),k5_facirc_2(A,B,C))))
=> v1_circuit2(k9_facirc_1(k4_facirc_2(A,B,C),k5_facirc_2(A,B,C),D,k1_nat_1(np__1,k2_nat_1(np__2,A))),k4_facirc_2(A,B,C),k5_facirc_2(A,B,C)) ) ) ) ) ).
fof(t34_facirc_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_circcomb(B,k1_nat_1(A,np__1))
=> ? [C] :
( m1_circcomb(C,A)
& ? [D] : B = k8_facirc_1(A,np__1,C,k5_facirc_1(D)) ) ) ) ).
fof(t35_facirc_2,axiom,
$true ).
fof(t36_facirc_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v3_facirc_1(B)
& m1_circcomb(B,k1_nat_1(A,np__1)) )
=> ? [C] :
( v3_facirc_1(C)
& m1_circcomb(C,A)
& ? [D] :
( ~ v1_facirc_1(D)
& B = k8_facirc_1(A,np__1,C,k5_facirc_1(D)) ) ) ) ) ).
fof(t37_facirc_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ? [B] :
( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k5_numbers)
& m2_relset_1(B,k5_numbers,k5_numbers)
& k8_funct_2(k5_numbers,k5_numbers,B,np__0) = np__1
& k8_funct_2(k5_numbers,k5_numbers,B,np__1) = np__2
& k8_funct_2(k5_numbers,k5_numbers,B,np__2) = A ) ) ).
fof(dt_k1_facirc_2,axiom,
! [A] :
( v1_msualg_1(k1_facirc_2(A))
& v2_msualg_1(k1_facirc_2(A))
& l1_msualg_1(k1_facirc_2(A)) ) ).
fof(dt_k2_facirc_2,axiom,
! [A] :
( v4_msualg_1(k2_facirc_2(A),k1_facirc_2(A))
& v6_circcomb(k2_facirc_2(A),k1_facirc_2(A))
& l3_msualg_1(k2_facirc_2(A),k1_facirc_2(A)) ) ).
fof(dt_k3_facirc_2,axiom,
m1_circcomb(k3_facirc_2,np__0) ).
fof(redefinition_k3_facirc_2,axiom,
k3_facirc_2 = k1_xboole_0 ).
fof(dt_k4_facirc_2,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B)
& v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> ( ~ v3_struct_0(k4_facirc_2(A,B,C))
& v1_msualg_1(k4_facirc_2(A,B,C))
& ~ v2_msualg_1(k4_facirc_2(A,B,C))
& v1_circcomb(k4_facirc_2(A,B,C))
& v2_circcomb(k4_facirc_2(A,B,C))
& v3_circcomb(k4_facirc_2(A,B,C))
& l1_msualg_1(k4_facirc_2(A,B,C)) ) ) ).
fof(dt_k5_facirc_2,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B)
& v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> ( v4_msualg_1(k5_facirc_2(A,B,C),k4_facirc_2(A,B,C))
& v4_msafree2(k5_facirc_2(A,B,C),k4_facirc_2(A,B,C))
& v4_circcomb(k5_facirc_2(A,B,C),k4_facirc_2(A,B,C))
& v6_circcomb(k5_facirc_2(A,B,C),k4_facirc_2(A,B,C))
& l3_msualg_1(k5_facirc_2(A,B,C),k4_facirc_2(A,B,C)) ) ) ).
fof(dt_k6_facirc_2,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B)
& v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> m1_struct_0(k6_facirc_2(A,B,C),k4_facirc_2(A,B,C),k4_msafree2(k4_facirc_2(A,B,C))) ) ).
fof(dt_k7_facirc_2,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers)
& v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C)
& v1_relat_1(D)
& v1_funct_1(D)
& v1_finseq_1(D) )
=> m1_struct_0(k7_facirc_2(A,B,C,D),k4_facirc_2(B,C,D),k4_msafree2(k4_facirc_2(B,C,D))) ) ).
%------------------------------------------------------------------------------