SET007 Axioms: SET007+380.ax
%------------------------------------------------------------------------------
% File : SET007+380 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Development of Terminology for bf SCM
% 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 : scm_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 46 ( 2 unt; 0 def)
% Number of atoms : 452 ( 203 equ)
% Maximal formula atoms : 30 ( 9 avg)
% Number of connectives : 437 ( 31 ~; 4 |; 182 &)
% ( 3 <=>; 217 =>; 0 <=; 0 <~>)
% Maximal formula depth : 45 ( 14 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 23 ( 21 usr; 1 prp; 0-6 aty)
% Number of functors : 61 ( 61 usr; 14 con; 0-4 aty)
% Number of variables : 230 ( 228 !; 2 ?)
% 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(t1_scm_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,A) = k1_funct_1(A,np__0)
& k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,A) = k1_funct_1(A,k1_funct_1(A,np__0)) ) ) ).
fof(t2_scm_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,A),B)) = k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,A),B)))
& k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,A),B)) = k1_funct_1(A,k1_funct_1(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,A),B),np__0)) ) ) ) ).
fof(t3_scm_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ( ? [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
& k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,A),B))) = k5_ami_1(k1_tarski(k4_numbers),k1_ami_3) )
=> v9_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) ) ) ).
fof(t4_scm_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,A),B))) = k5_ami_1(k1_tarski(k4_numbers),k1_ami_3)
=> k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,A) = k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,A),B) ) ) ) ).
fof(t5_scm_1,axiom,
$true ).
fof(t6_scm_1,axiom,
$true ).
fof(t7_scm_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( k2_ami_1(k1_tarski(k4_numbers),k1_ami_3) != k16_ami_3(A)
& k2_ami_1(k1_tarski(k4_numbers),k1_ami_3) != k15_ami_3(A)
& k16_ami_3(A) != k15_ami_3(B) ) ) ) ).
fof(d1_scm_1,axiom,
! [A] :
( m2_finseq_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [B] :
( m2_finseq_1(B,k4_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m1_subset_1(F,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ( m1_scm_1(F,A,B,C,D,E)
<=> ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,F) = k16_ami_3(C)
& ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(k3_finseq_1(A),G)
=> k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,F,k16_ami_3(k1_nat_1(D,G))) = k1_funct_1(A,k1_nat_1(G,np__1)) ) )
& ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(k3_finseq_1(B),G)
=> k2_ami_3(F,k15_ami_3(k1_nat_1(E,G))) = k1_funct_1(B,k1_nat_1(G,np__1)) ) ) ) ) ) ) ) ) ) ) ).
fof(t8_scm_1,axiom,
! [A,B,C,D,E] :
( ( v1_relat_1(E)
& v1_funct_1(E)
& v1_finseq_1(E) )
=> ( E = k7_finseq_1(k7_finseq_1(k7_finseq_1(k9_finseq_1(A),k9_finseq_1(B)),k9_finseq_1(C)),k9_finseq_1(D))
=> ( k3_finseq_1(E) = np__4
& k1_funct_1(E,np__1) = A
& k1_funct_1(E,np__2) = B
& k1_funct_1(E,np__3) = C
& k1_funct_1(E,np__4) = D ) ) ) ).
fof(t9_scm_1,axiom,
! [A,B,C,D,E,F] :
( ( v1_relat_1(F)
& v1_funct_1(F)
& v1_finseq_1(F) )
=> ( F = k7_finseq_1(k7_finseq_1(k7_finseq_1(k7_finseq_1(k9_finseq_1(A),k9_finseq_1(B)),k9_finseq_1(C)),k9_finseq_1(D)),k9_finseq_1(E))
=> ( k3_finseq_1(F) = np__5
& k1_funct_1(F,np__1) = A
& k1_funct_1(F,np__2) = B
& k1_funct_1(F,np__3) = C
& k1_funct_1(F,np__4) = D
& k1_funct_1(F,np__5) = E ) ) ) ).
fof(t10_scm_1,axiom,
! [A,B,C,D,E,F,G] :
( ( v1_relat_1(G)
& v1_funct_1(G)
& v1_finseq_1(G) )
=> ( G = k7_finseq_1(k7_finseq_1(k7_finseq_1(k7_finseq_1(k7_finseq_1(k9_finseq_1(A),k9_finseq_1(B)),k9_finseq_1(C)),k9_finseq_1(D)),k9_finseq_1(E)),k9_finseq_1(F))
=> ( k3_finseq_1(G) = np__6
& k1_funct_1(G,np__1) = A
& k1_funct_1(G,np__2) = B
& k1_funct_1(G,np__3) = C
& k1_funct_1(G,np__4) = D
& k1_funct_1(G,np__5) = E
& k1_funct_1(G,np__6) = F ) ) ) ).
fof(t11_scm_1,axiom,
! [A,B,C,D,E,F,G,H] :
( ( v1_relat_1(H)
& v1_funct_1(H)
& v1_finseq_1(H) )
=> ( H = k7_finseq_1(k7_finseq_1(k7_finseq_1(k7_finseq_1(k7_finseq_1(k7_finseq_1(k9_finseq_1(A),k9_finseq_1(B)),k9_finseq_1(C)),k9_finseq_1(D)),k9_finseq_1(E)),k9_finseq_1(F)),k9_finseq_1(G))
=> ( k3_finseq_1(H) = np__7
& k1_funct_1(H,np__1) = A
& k1_funct_1(H,np__2) = B
& k1_funct_1(H,np__3) = C
& k1_funct_1(H,np__4) = D
& k1_funct_1(H,np__5) = E
& k1_funct_1(H,np__6) = F
& k1_funct_1(H,np__7) = G ) ) ) ).
fof(t12_scm_1,axiom,
! [A,B,C,D,E,F,G,H,I] :
( ( v1_relat_1(I)
& v1_funct_1(I)
& v1_finseq_1(I) )
=> ( I = k7_finseq_1(k7_finseq_1(k7_finseq_1(k7_finseq_1(k7_finseq_1(k7_finseq_1(k7_finseq_1(k9_finseq_1(A),k9_finseq_1(B)),k9_finseq_1(C)),k9_finseq_1(D)),k9_finseq_1(E)),k9_finseq_1(F)),k9_finseq_1(G)),k9_finseq_1(H))
=> ( k3_finseq_1(I) = np__8
& k1_funct_1(I,np__1) = A
& k1_funct_1(I,np__2) = B
& k1_funct_1(I,np__3) = C
& k1_funct_1(I,np__4) = D
& k1_funct_1(I,np__5) = E
& k1_funct_1(I,np__6) = F
& k1_funct_1(I,np__7) = G
& k1_funct_1(I,np__8) = H ) ) ) ).
fof(t13_scm_1,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( ( v1_relat_1(J)
& v1_funct_1(J)
& v1_finseq_1(J) )
=> ( J = k7_finseq_1(k7_finseq_1(k7_finseq_1(k7_finseq_1(k7_finseq_1(k7_finseq_1(k7_finseq_1(k7_finseq_1(k9_finseq_1(A),k9_finseq_1(B)),k9_finseq_1(C)),k9_finseq_1(D)),k9_finseq_1(E)),k9_finseq_1(F)),k9_finseq_1(G)),k9_finseq_1(H)),k9_finseq_1(I))
=> ( k3_finseq_1(J) = np__9
& k1_funct_1(J,np__1) = A
& k1_funct_1(J,np__2) = B
& k1_funct_1(J,np__3) = C
& k1_funct_1(J,np__4) = D
& k1_funct_1(J,np__5) = E
& k1_funct_1(J,np__6) = F
& k1_funct_1(J,np__7) = G
& k1_funct_1(J,np__8) = H
& k1_funct_1(J,np__9) = I ) ) ) ).
fof(t14_scm_1,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [C] :
( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [D] :
( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [E] :
( m2_subset_1(E,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [F] :
( m2_subset_1(F,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [G] :
( m2_subset_1(G,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [H] :
( m2_subset_1(H,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [I] :
( m2_subset_1(I,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [J] :
( v1_int_1(J)
=> ! [K] :
( v1_int_1(K)
=> ! [L] :
( v1_int_1(L)
=> ! [M] :
( v1_int_1(M)
=> ! [N] :
( m2_subset_1(N,k1_numbers,k5_numbers)
=> ! [O] :
( m1_scm_1(O,k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),A),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),B)),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),C)),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),D)),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),E)),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),F)),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),G)),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),H)),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),I)),k8_finseq_1(k4_numbers,k8_finseq_1(k4_numbers,k8_finseq_1(k4_numbers,k1_scm_1(J),k1_scm_1(K)),k1_scm_1(L)),k1_scm_1(M)),N,np__0,np__0)
=> ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,O) = k16_ami_3(N)
& k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__0)) = A
& k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__1)) = B
& k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__2)) = C
& k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__3)) = D
& k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__4)) = E
& k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__5)) = F
& k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__6)) = G
& k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__7)) = H
& k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__8)) = I
& k2_ami_3(O,k15_ami_3(np__0)) = J
& k2_ami_3(O,k15_ami_3(np__1)) = K
& k2_ami_3(O,k15_ami_3(np__2)) = L
& k2_ami_3(O,k15_ami_3(np__3)) = M ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t15_scm_1,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( v1_int_1(D)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m1_scm_1(F,k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),A),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),B)),k8_finseq_1(k4_numbers,k1_scm_1(C),k1_scm_1(D)),E,np__0,np__0)
=> ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,F) = k16_ami_3(E)
& k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,F,k16_ami_3(np__0)) = A
& k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,F,k16_ami_3(np__1)) = B
& k2_ami_3(F,k15_ami_3(np__0)) = C
& k2_ami_3(F,k15_ami_3(np__1)) = D ) ) ) ) ) ) ) ).
fof(d2_scm_1,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v4_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
=> ( v9_ami_1(C,A,B)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( D = k2_scm_1(A,B,C)
<=> ( k8_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),D)) = k5_ami_1(A,B)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( k8_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),E)) = k5_ami_1(A,B)
=> r1_xreal_0(D,E) ) ) ) ) ) ) ) ) ) ).
fof(t16_scm_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,A),k1_nat_1(B,np__1)))) = k5_ami_1(k1_tarski(k4_numbers),k1_ami_3)
=> ( k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,A),B))) = k5_ami_1(k1_tarski(k4_numbers),k1_ami_3)
| ( k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,A) = k1_nat_1(B,np__1)
& v9_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) ) ) )
& ( ( k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,A) = k1_nat_1(B,np__1)
& v9_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) )
=> ( k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,A),B))) != k5_ami_1(k1_tarski(k4_numbers),k1_ami_3)
& k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,A),k1_nat_1(B,np__1)))) = k5_ami_1(k1_tarski(k4_numbers),k1_ami_3) ) ) ) ) ) ).
fof(t17_scm_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,A),k1_nat_1(B,np__1)))) = k5_ami_1(k1_tarski(k4_numbers),k1_ami_3)
=> ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,A),B)) = k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,A),k1_nat_1(B,np__1)))
| k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,A) = k1_nat_1(B,np__1) ) ) ) ) ).
fof(t18_scm_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [D] :
( m1_ami_3(D)
=> ! [E] :
( m1_ami_3(E)
=> ( ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A)) = k16_ami_3(B)
& k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,C,k16_ami_3(B)) = k3_ami_3(D,E) )
=> ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1))) = k16_ami_3(k1_nat_1(B,np__1))
& k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1)),D) = k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),E)
& ! [F] :
( m1_ami_3(F)
=> ( F != D
=> k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1)),F) = k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),F) ) ) ) ) ) ) ) ) ) ).
fof(t19_scm_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [D] :
( m1_ami_3(D)
=> ! [E] :
( m1_ami_3(E)
=> ( ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A)) = k16_ami_3(B)
& k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,C,k16_ami_3(B)) = k4_ami_3(D,E) )
=> ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1))) = k16_ami_3(k1_nat_1(B,np__1))
& k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1)),D) = k2_xcmplx_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),D),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),E))
& ! [F] :
( m1_ami_3(F)
=> ( F != D
=> k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1)),F) = k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),F) ) ) ) ) ) ) ) ) ) ).
fof(t20_scm_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [D] :
( m1_ami_3(D)
=> ! [E] :
( m1_ami_3(E)
=> ( ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A)) = k16_ami_3(B)
& k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,C,k16_ami_3(B)) = k5_ami_3(D,E) )
=> ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1))) = k16_ami_3(k1_nat_1(B,np__1))
& k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1)),D) = k6_xcmplx_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),D),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),E))
& ! [F] :
( m1_ami_3(F)
=> ( F != D
=> k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1)),F) = k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),F) ) ) ) ) ) ) ) ) ) ).
fof(t21_scm_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [D] :
( m1_ami_3(D)
=> ! [E] :
( m1_ami_3(E)
=> ( ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A)) = k16_ami_3(B)
& k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,C,k16_ami_3(B)) = k6_ami_3(D,E) )
=> ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1))) = k16_ami_3(k1_nat_1(B,np__1))
& k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1)),D) = k3_xcmplx_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),D),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),E))
& ! [F] :
( m1_ami_3(F)
=> ( F != D
=> k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1)),F) = k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),F) ) ) ) ) ) ) ) ) ) ).
fof(t22_scm_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [D] :
( m1_ami_3(D)
=> ! [E] :
( m1_ami_3(E)
=> ( ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A)) = k16_ami_3(B)
& k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,C,k16_ami_3(B)) = k7_ami_3(D,E) )
=> ( D = E
| ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1))) = k16_ami_3(k1_nat_1(B,np__1))
& k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1)),D) = k5_int_1(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),D),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),E))
& k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1)),E) = k6_int_1(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),D),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),E))
& ! [F] :
( m1_ami_3(F)
=> ~ ( F != D
& F != E
& k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1)),F) != k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),F) ) ) ) ) ) ) ) ) ) ) ).
fof(t23_scm_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [D] :
( m1_struct_0(D,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ( ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A)) = k16_ami_3(B)
& k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,C,k16_ami_3(B)) = k8_ami_3(D) )
=> ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1))) = D
& ! [E] :
( m1_ami_3(E)
=> k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1)),E) = k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),E) ) ) ) ) ) ) ) ).
fof(t24_scm_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [D] :
( m1_ami_3(D)
=> ! [E] :
( m1_struct_0(E,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ( ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A)) = k16_ami_3(B)
& k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,C,k16_ami_3(B)) = k9_ami_3(E,D) )
=> ( ( k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),D) = np__0
=> k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1))) = E )
& ( k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),D) != np__0
=> k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1))) = k16_ami_3(k1_nat_1(B,np__1)) )
& ! [F] :
( m1_ami_3(F)
=> k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1)),F) = k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),F) ) ) ) ) ) ) ) ) ).
fof(t25_scm_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [D] :
( m1_ami_3(D)
=> ! [E] :
( m1_struct_0(E,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ( ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A)) = k16_ami_3(B)
& k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,C,k16_ami_3(B)) = k10_ami_3(E,D) )
=> ( ( ~ r1_xreal_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),D),np__0)
=> k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1))) = E )
& ( r1_xreal_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),D),np__0)
=> k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1))) = k16_ami_3(k1_nat_1(B,np__1)) )
& ! [F] :
( m1_ami_3(F)
=> k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1)),F) = k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),F) ) ) ) ) ) ) ) ) ).
fof(t26_scm_1,axiom,
( k1_mcart_1(k5_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = np__0
& ! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> k1_mcart_1(k3_ami_3(A,B)) = np__1 ) )
& ! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> k1_mcart_1(k4_ami_3(A,B)) = np__2 ) )
& ! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> k1_mcart_1(k5_ami_3(A,B)) = np__3 ) )
& ! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> k1_mcart_1(k6_ami_3(A,B)) = np__4 ) )
& ! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> k1_mcart_1(k7_ami_3(A,B)) = np__5 ) )
& ! [A] :
( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> k1_mcart_1(k8_ami_3(A)) = np__6 )
& ! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> k1_mcart_1(k9_ami_3(B,A)) = np__7 ) )
& ! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> k1_mcart_1(k10_ami_3(B,A)) = np__8 ) ) ) ).
fof(t27_scm_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_setfam_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v4_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( v9_ami_1(C,A,B)
<=> v9_ami_1(k11_ami_1(A,B,k10_ami_1(A,B,C),D),A,B) ) ) ) ) ) ).
fof(t28_scm_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( B = k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,A),C)
& k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,B) = D
& v9_ami_1(B,k1_tarski(k4_numbers),k1_ami_3) )
=> ( r1_xreal_0(D,np__0)
| k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,A) = k1_nat_1(C,D) ) ) ) ) ) ) ).
fof(t29_scm_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( B = k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,A),C)
& v9_ami_1(B,k1_tarski(k4_numbers),k1_ami_3) )
=> k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,B) = k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,A) ) ) ) ) ).
fof(t30_scm_1,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [C] :
( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [D] :
( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [E] :
( m2_subset_1(E,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [F] :
( m2_subset_1(F,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [G] :
( m2_subset_1(G,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [H] :
( m2_subset_1(H,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [I] :
( m2_subset_1(I,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [J] :
( v1_int_1(J)
=> ! [K] :
( v1_int_1(K)
=> ! [L] :
( v1_int_1(L)
=> ! [M] :
( v1_int_1(M)
=> ! [N] :
( m2_subset_1(N,k1_numbers,k5_numbers)
=> ! [O] :
( m1_subset_1(O,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ( ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,O) = k16_ami_3(N)
& k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__0)) = A
& k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__1)) = B
& k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__2)) = C
& k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__3)) = D
& k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__4)) = E
& k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__5)) = F
& k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__6)) = G
& k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__7)) = H
& k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__8)) = I
& k2_ami_3(O,k15_ami_3(np__0)) = J
& k2_ami_3(O,k15_ami_3(np__1)) = K
& k2_ami_3(O,k15_ami_3(np__2)) = L
& k2_ami_3(O,k15_ami_3(np__3)) = M )
=> m1_scm_1(O,k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),A),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),B)),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),C)),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),D)),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),E)),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),F)),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),G)),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),H)),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),I)),k8_finseq_1(k4_numbers,k8_finseq_1(k4_numbers,k8_finseq_1(k4_numbers,k1_scm_1(J),k1_scm_1(K)),k1_scm_1(L)),k1_scm_1(M)),N,np__0,np__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t31_scm_1,axiom,
! [A] :
( m1_scm_1(A,k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k5_ami_1(k1_tarski(k4_numbers),k1_ami_3)),k6_finseq_1(k4_numbers),np__0,np__0,np__0)
=> ( v9_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
& k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,A) = np__0
& k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,A) = A ) ) ).
fof(t32_scm_1,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m1_scm_1(C,k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k3_ami_3(k15_ami_3(np__0),k15_ami_3(np__1))),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k5_ami_1(k1_tarski(k4_numbers),k1_ami_3))),k8_finseq_1(k4_numbers,k1_scm_1(A),k1_scm_1(B)),np__0,np__0,np__0)
=> ( v9_ami_1(C,k1_tarski(k4_numbers),k1_ami_3)
& k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,C) = np__1
& k2_ami_3(k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k15_ami_3(np__0)) = B
& ! [D] :
( m1_ami_3(D)
=> ( D != k15_ami_3(np__0)
=> k2_ami_3(k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D) = k2_ami_3(C,D) ) ) ) ) ) ) ).
fof(t33_scm_1,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m1_scm_1(C,k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k4_ami_3(k15_ami_3(np__0),k15_ami_3(np__1))),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k5_ami_1(k1_tarski(k4_numbers),k1_ami_3))),k8_finseq_1(k4_numbers,k1_scm_1(A),k1_scm_1(B)),np__0,np__0,np__0)
=> ( v9_ami_1(C,k1_tarski(k4_numbers),k1_ami_3)
& k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,C) = np__1
& k2_ami_3(k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k15_ami_3(np__0)) = k2_xcmplx_0(A,B)
& ! [D] :
( m1_ami_3(D)
=> ( D != k15_ami_3(np__0)
=> k2_ami_3(k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D) = k2_ami_3(C,D) ) ) ) ) ) ) ).
fof(t34_scm_1,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m1_scm_1(C,k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k5_ami_3(k15_ami_3(np__0),k15_ami_3(np__1))),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k5_ami_1(k1_tarski(k4_numbers),k1_ami_3))),k8_finseq_1(k4_numbers,k1_scm_1(A),k1_scm_1(B)),np__0,np__0,np__0)
=> ( v9_ami_1(C,k1_tarski(k4_numbers),k1_ami_3)
& k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,C) = np__1
& k2_ami_3(k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k15_ami_3(np__0)) = k6_xcmplx_0(A,B)
& ! [D] :
( m1_ami_3(D)
=> ( D != k15_ami_3(np__0)
=> k2_ami_3(k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D) = k2_ami_3(C,D) ) ) ) ) ) ) ).
fof(t35_scm_1,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m1_scm_1(C,k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k6_ami_3(k15_ami_3(np__0),k15_ami_3(np__1))),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k5_ami_1(k1_tarski(k4_numbers),k1_ami_3))),k8_finseq_1(k4_numbers,k1_scm_1(A),k1_scm_1(B)),np__0,np__0,np__0)
=> ( v9_ami_1(C,k1_tarski(k4_numbers),k1_ami_3)
& k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,C) = np__1
& k2_ami_3(k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k15_ami_3(np__0)) = k3_xcmplx_0(A,B)
& ! [D] :
( m1_ami_3(D)
=> ( D != k15_ami_3(np__0)
=> k2_ami_3(k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D) = k2_ami_3(C,D) ) ) ) ) ) ) ).
fof(t36_scm_1,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m1_scm_1(C,k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k7_ami_3(k15_ami_3(np__0),k15_ami_3(np__1))),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k5_ami_1(k1_tarski(k4_numbers),k1_ami_3))),k8_finseq_1(k4_numbers,k1_scm_1(A),k1_scm_1(B)),np__0,np__0,np__0)
=> ( v9_ami_1(C,k1_tarski(k4_numbers),k1_ami_3)
& k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,C) = np__1
& k2_ami_3(k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k15_ami_3(np__0)) = k5_int_1(A,B)
& k2_ami_3(k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k15_ami_3(np__1)) = k6_int_1(A,B)
& ! [D] :
( m1_ami_3(D)
=> ~ ( D != k15_ami_3(np__0)
& D != k15_ami_3(np__1)
& k2_ami_3(k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D) != k2_ami_3(C,D) ) ) ) ) ) ) ).
fof(t37_scm_1,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m1_scm_1(C,k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_ami_3(k16_ami_3(np__1))),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k5_ami_1(k1_tarski(k4_numbers),k1_ami_3))),k8_finseq_1(k4_numbers,k1_scm_1(A),k1_scm_1(B)),np__0,np__0,np__0)
=> ( v9_ami_1(C,k1_tarski(k4_numbers),k1_ami_3)
& k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,C) = np__1
& ! [D] :
( m1_ami_3(D)
=> k2_ami_3(k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D) = k2_ami_3(C,D) ) ) ) ) ) ).
fof(t38_scm_1,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m1_scm_1(C,k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k9_ami_3(k16_ami_3(np__1),k15_ami_3(np__0))),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k5_ami_1(k1_tarski(k4_numbers),k1_ami_3))),k8_finseq_1(k4_numbers,k1_scm_1(A),k1_scm_1(B)),np__0,np__0,np__0)
=> ( v9_ami_1(C,k1_tarski(k4_numbers),k1_ami_3)
& k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,C) = np__1
& ! [D] :
( m1_ami_3(D)
=> k2_ami_3(k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D) = k2_ami_3(C,D) ) ) ) ) ) ).
fof(t39_scm_1,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m1_scm_1(C,k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k10_ami_3(k16_ami_3(np__1),k15_ami_3(np__0))),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k5_ami_1(k1_tarski(k4_numbers),k1_ami_3))),k8_finseq_1(k4_numbers,k1_scm_1(A),k1_scm_1(B)),np__0,np__0,np__0)
=> ( v9_ami_1(C,k1_tarski(k4_numbers),k1_ami_3)
& k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,C) = np__1
& ! [D] :
( m1_ami_3(D)
=> k2_ami_3(k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D) = k2_ami_3(C,D) ) ) ) ) ) ).
fof(dt_m1_scm_1,axiom,
! [A,B,C,D,E] :
( ( m1_finseq_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
& m1_finseq_1(B,k4_numbers)
& m1_subset_1(C,k5_numbers)
& m1_subset_1(D,k5_numbers)
& m1_subset_1(E,k5_numbers) )
=> ! [F] :
( m1_scm_1(F,A,B,C,D,E)
=> m1_subset_1(F,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) ) ) ).
fof(existence_m1_scm_1,axiom,
! [A,B,C,D,E] :
( ( m1_finseq_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
& m1_finseq_1(B,k4_numbers)
& m1_subset_1(C,k5_numbers)
& m1_subset_1(D,k5_numbers)
& m1_subset_1(E,k5_numbers) )
=> ? [F] : m1_scm_1(F,A,B,C,D,E) ) ).
fof(dt_k1_scm_1,axiom,
! [A] :
( v1_int_1(A)
=> m2_finseq_1(k1_scm_1(A),k4_numbers) ) ).
fof(redefinition_k1_scm_1,axiom,
! [A] :
( v1_int_1(A)
=> k1_scm_1(A) = k5_finseq_1(A) ) ).
fof(dt_k2_scm_1,axiom,
! [A,B,C] :
( ( v1_setfam_1(A)
& ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v4_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A)
& m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) )
=> m2_subset_1(k2_scm_1(A,B,C),k1_numbers,k5_numbers) ) ).
%------------------------------------------------------------------------------