SET007 Axioms: SET007+658.ax
%------------------------------------------------------------------------------
% File : SET007+658 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The Construction and Computation of While-Loop Programs for SCMPDS
% 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 : scmpds_8 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 43 ( 0 unt; 0 def)
% Number of atoms : 610 ( 94 equ)
% Maximal formula atoms : 40 ( 14 avg)
% Number of connectives : 594 ( 27 ~; 31 |; 265 &)
% ( 3 <=>; 268 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 14 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 23 ( 22 usr; 0 prp; 1-3 aty)
% Number of functors : 70 ( 70 usr; 27 con; 0-5 aty)
% Number of variables : 210 ( 208 !; 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(fc1_scmpds_8,axiom,
! [A,B,C] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v3_scmpds_4(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_scmpds_2(B)
& v1_int_1(C) )
=> ( v1_relat_1(k2_scmpds_8(B,C,A))
& v1_funct_1(k2_scmpds_8(B,C,A))
& v1_finset_1(k2_scmpds_8(B,C,A))
& v1_ami_3(k2_scmpds_8(B,C,A),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k2_scmpds_8(B,C,A))
& v3_scmpds_4(k2_scmpds_8(B,C,A)) ) ) ).
fof(fc2_scmpds_8,axiom,
! [A,B,C] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v3_scmpds_5(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_scmpds_2(B)
& v1_int_1(C) )
=> ( v1_relat_1(k2_scmpds_8(B,C,A))
& v1_funct_1(k2_scmpds_8(B,C,A))
& v1_finset_1(k2_scmpds_8(B,C,A))
& v1_ami_3(k2_scmpds_8(B,C,A),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k2_scmpds_8(B,C,A))
& v3_scmpds_5(k2_scmpds_8(B,C,A)) ) ) ).
fof(fc3_scmpds_8,axiom,
! [A,B,C] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v3_scmpds_4(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_scmpds_2(B)
& v1_int_1(C) )
=> ( v1_relat_1(k3_scmpds_8(B,C,A))
& v1_funct_1(k3_scmpds_8(B,C,A))
& v1_finset_1(k3_scmpds_8(B,C,A))
& v1_ami_3(k3_scmpds_8(B,C,A),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k3_scmpds_8(B,C,A))
& v3_scmpds_4(k3_scmpds_8(B,C,A)) ) ) ).
fof(fc4_scmpds_8,axiom,
! [A,B,C] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v3_scmpds_5(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_scmpds_2(B)
& v1_int_1(C) )
=> ( v1_relat_1(k3_scmpds_8(B,C,A))
& v1_funct_1(k3_scmpds_8(B,C,A))
& v1_finset_1(k3_scmpds_8(B,C,A))
& v1_ami_3(k3_scmpds_8(B,C,A),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k3_scmpds_8(B,C,A))
& v3_scmpds_5(k3_scmpds_8(B,C,A)) ) ) ).
fof(t1_scmpds_8,axiom,
! [A] :
( m1_scmpds_2(A)
=> ? [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
& A = k1_scmp_gcd(B) ) ) ).
fof(d1_scmpds_8,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( B = k1_scmpds_8(A)
<=> ! [C] :
( ( r2_hidden(C,k2_ami_2)
=> k1_funct_1(B,C) = k1_funct_1(A,C) )
& ( r2_hidden(C,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> k1_funct_1(B,C) = k4_scmpds_2(np__0) )
& ( C = k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)
=> k1_funct_1(B,C) = k2_scmpds_3(np__0) ) ) ) ) ) ).
fof(t2_scmpds_8,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( k7_relat_1(A,k2_ami_2) = k7_relat_1(B,k2_ami_2)
=> k1_scmpds_8(A) = k1_scmpds_8(B) ) ) ) ).
fof(t3_scmpds_8,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ( r2_hidden(k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B),k9_domain_1(k5_numbers,np__0,np__4,np__5,np__6))
=> k1_scmpds_8(A) = k1_scmpds_8(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B,A)) ) ) ) ).
fof(t4_scmpds_8,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> k2_scmpds_2(k1_scmpds_8(B),A) = k2_scmpds_2(B,A) ) ) ).
fof(t5_scmpds_8,axiom,
! [A] :
( m1_scmpds_2(A)
=> ? [B] :
( v1_funct_1(B)
& v1_funct_2(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)),k5_numbers)
& m2_relset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)),k5_numbers)
& ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( r1_xreal_0(k2_scmpds_2(C,A),np__0)
=> k1_recdef_1(k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)),B,C) = np__0 )
& ( ~ r1_xreal_0(k2_scmpds_2(C,A),np__0)
=> k1_recdef_1(k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)),B,C) = k2_scmpds_2(C,A) ) ) ) ) ) ).
fof(d2_scmpds_8,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k2_scmpds_8(A,B,C) = k5_scmpds_4(k4_scmpds_4(k10_scmpds_2(A,B,k1_nat_1(k4_card_1(C),np__2)),C),k4_scmpds_2(k4_xcmplx_0(k1_nat_1(k4_card_1(C),np__1)))) ) ) ) ).
fof(t6_scmpds_8,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k4_card_1(k2_scmpds_8(A,B,C)) = k1_nat_1(k4_card_1(C),np__2) ) ) ) ).
fof(t7_scmpds_8,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(D)
& m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( ~ r1_xreal_0(k1_nat_1(k4_card_1(D),np__2),C)
<=> r2_hidden(k2_scmpds_3(C),k1_relat_1(k2_scmpds_8(A,B,D))) ) ) ) ) ) ).
fof(t8_scmpds_8,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( k1_funct_1(k2_scmpds_8(A,B,C),k2_scmpds_3(np__0)) = k10_scmpds_2(A,B,k1_nat_1(k4_card_1(C),np__2))
& k1_funct_1(k2_scmpds_8(A,B,C),k2_scmpds_3(k1_nat_1(k4_card_1(C),np__1))) = k4_scmpds_2(k4_xcmplx_0(k1_nat_1(k4_card_1(C),np__1))) ) ) ) ) ).
fof(t9_scmpds_8,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)))
=> ( r1_scmpds_6(k2_scmpds_8(C,D,B),A)
& r2_scmpds_6(k2_scmpds_8(C,D,B),A) ) ) ) ) ) ) ).
fof(t10_scmpds_8,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( v1_int_1(E)
=> ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)))
=> k9_scmpds_4(k2_scmpds_8(C,E,B),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k4_card_1(B),np__2)))) ) ) ) ) ) ) ).
fof(t11_scmpds_8,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)))
=> k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(k2_scmpds_8(C,D,B),A)) = k2_scmpds_3(k1_nat_1(k4_card_1(B),np__2)) ) ) ) ) ) ).
fof(t12_scmpds_8,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( v1_int_1(E)
=> ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)))
=> k2_scmpds_2(k9_scmpds_4(k2_scmpds_8(C,E,B),A),D) = k2_scmpds_2(A,D) ) ) ) ) ) ) ).
fof(t13_scmpds_8,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& v3_scmpds_4(B)
& v3_scmpds_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ! [E,F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)),k5_numbers)
& m2_relset_1(F,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)),k5_numbers) )
=> ( ( ! [G] :
( m1_subset_1(G,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( k1_recdef_1(k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)),F,k1_scmpds_8(G)) = np__0
=> r1_xreal_0(np__0,k2_scmpds_2(G,k3_scmpds_2(k2_scmpds_2(A,C),D))) ) )
& ! [G] :
( m1_subset_1(G,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( ! [H] :
( m1_scmpds_2(H)
=> ( r2_hidden(H,E)
=> k2_scmpds_2(G,H) = k2_scmpds_2(A,H) ) )
& k2_scmpds_2(G,C) = k2_scmpds_2(A,C) )
=> ( r1_xreal_0(np__0,k2_scmpds_2(G,k3_scmpds_2(k2_scmpds_2(A,C),D)))
| ( k2_scmpds_2(k9_scmpds_4(B,G),C) = k2_scmpds_2(G,C)
& ~ r1_xreal_0(k1_recdef_1(k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)),F,k1_scmpds_8(G)),k1_recdef_1(k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)),F,k1_scmpds_8(k9_scmpds_4(B,G))))
& r1_scmpds_6(B,G)
& r2_scmpds_6(B,G)
& ! [H] :
( m1_scmpds_2(H)
=> ( r2_hidden(H,E)
=> k2_scmpds_2(k9_scmpds_4(B,G),H) = k2_scmpds_2(G,H) ) ) ) ) ) ) )
=> ( r1_xreal_0(k4_card_1(B),np__0)
| ( r1_scmpds_6(k2_scmpds_8(C,D,B),A)
& r2_scmpds_6(k2_scmpds_8(C,D,B),A) ) ) ) ) ) ) ) ) ).
fof(t14_scmpds_8,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& v3_scmpds_4(B)
& v3_scmpds_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ! [E,F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)),k5_numbers)
& m2_relset_1(F,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)),k5_numbers) )
=> ( ( ! [G] :
( m1_subset_1(G,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( k1_recdef_1(k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)),F,k1_scmpds_8(G)) = np__0
=> r1_xreal_0(np__0,k2_scmpds_2(G,k3_scmpds_2(k2_scmpds_2(A,C),D))) ) )
& ! [G] :
( m1_subset_1(G,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( ! [H] :
( m1_scmpds_2(H)
=> ( r2_hidden(H,E)
=> k2_scmpds_2(G,H) = k2_scmpds_2(A,H) ) )
& k2_scmpds_2(G,C) = k2_scmpds_2(A,C) )
=> ( r1_xreal_0(np__0,k2_scmpds_2(G,k3_scmpds_2(k2_scmpds_2(A,C),D)))
| ( k2_scmpds_2(k9_scmpds_4(B,G),C) = k2_scmpds_2(G,C)
& r1_scmpds_6(B,G)
& r2_scmpds_6(B,G)
& ~ r1_xreal_0(k1_recdef_1(k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)),F,k1_scmpds_8(G)),k1_recdef_1(k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)),F,k1_scmpds_8(k9_scmpds_4(B,G))))
& ! [H] :
( m1_scmpds_2(H)
=> ( r2_hidden(H,E)
=> k2_scmpds_2(k9_scmpds_4(B,G),H) = k2_scmpds_2(G,H) ) ) ) ) ) ) )
=> ( r1_xreal_0(k4_card_1(B),np__0)
| r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)))
| k9_scmpds_4(k2_scmpds_8(C,D,B),A) = k9_scmpds_4(k2_scmpds_8(C,D,B),k9_scmpds_4(B,A)) ) ) ) ) ) ) ) ).
fof(t15_scmpds_8,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& v3_scmpds_4(B)
& v3_scmpds_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ! [E] :
( ! [F] :
( m1_subset_1(F,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( ! [G] :
( m1_scmpds_2(G)
=> ( r2_hidden(G,E)
=> k2_scmpds_2(F,G) = k2_scmpds_2(A,G) ) )
& k2_scmpds_2(F,C) = k2_scmpds_2(A,C) )
=> ( r1_xreal_0(np__0,k2_scmpds_2(F,k3_scmpds_2(k2_scmpds_2(A,C),D)))
| ( k2_scmpds_2(k9_scmpds_4(B,F),C) = k2_scmpds_2(F,C)
& ~ r1_xreal_0(k2_scmpds_2(k9_scmpds_4(B,F),k3_scmpds_2(k2_scmpds_2(A,C),D)),k2_scmpds_2(F,k3_scmpds_2(k2_scmpds_2(A,C),D)))
& r1_scmpds_6(B,F)
& r2_scmpds_6(B,F)
& ! [G] :
( m1_scmpds_2(G)
=> ( r2_hidden(G,E)
=> k2_scmpds_2(k9_scmpds_4(B,F),G) = k2_scmpds_2(F,G) ) ) ) ) ) )
=> ( r1_xreal_0(k4_card_1(B),np__0)
| ( r1_scmpds_6(k2_scmpds_8(C,D,B),A)
& r2_scmpds_6(k2_scmpds_8(C,D,B),A) ) ) ) ) ) ) ) ).
fof(t16_scmpds_8,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& v3_scmpds_4(B)
& v3_scmpds_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ! [E] :
( ! [F] :
( m1_subset_1(F,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( ! [G] :
( m1_scmpds_2(G)
=> ( r2_hidden(G,E)
=> k2_scmpds_2(F,G) = k2_scmpds_2(A,G) ) )
& k2_scmpds_2(F,C) = k2_scmpds_2(A,C) )
=> ( r1_xreal_0(np__0,k2_scmpds_2(F,k3_scmpds_2(k2_scmpds_2(A,C),D)))
| ( k2_scmpds_2(k9_scmpds_4(B,F),C) = k2_scmpds_2(F,C)
& ~ r1_xreal_0(k2_scmpds_2(k9_scmpds_4(B,F),k3_scmpds_2(k2_scmpds_2(A,C),D)),k2_scmpds_2(F,k3_scmpds_2(k2_scmpds_2(A,C),D)))
& r1_scmpds_6(B,F)
& r2_scmpds_6(B,F)
& ! [G] :
( m1_scmpds_2(G)
=> ( r2_hidden(G,E)
=> k2_scmpds_2(k9_scmpds_4(B,F),G) = k2_scmpds_2(F,G) ) ) ) ) ) )
=> ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)))
| r1_xreal_0(k4_card_1(B),np__0)
| k9_scmpds_4(k2_scmpds_8(C,D,B),A) = k9_scmpds_4(k2_scmpds_8(C,D,B),k9_scmpds_4(B,A)) ) ) ) ) ) ) ).
fof(d3_scmpds_8,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k3_scmpds_8(A,B,C) = k5_scmpds_4(k4_scmpds_4(k9_scmpds_2(A,B,k1_nat_1(k4_card_1(C),np__2)),C),k4_scmpds_2(k4_xcmplx_0(k1_nat_1(k4_card_1(C),np__1)))) ) ) ) ).
fof(t17_scmpds_8,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k4_card_1(k3_scmpds_8(A,B,C)) = k1_nat_1(k4_card_1(C),np__2) ) ) ) ).
fof(t18_scmpds_8,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(D)
& m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( ~ r1_xreal_0(k1_nat_1(k4_card_1(D),np__2),C)
<=> r2_hidden(k2_scmpds_3(C),k1_relat_1(k3_scmpds_8(A,B,D))) ) ) ) ) ) ).
fof(t19_scmpds_8,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( k1_funct_1(k3_scmpds_8(A,B,C),k2_scmpds_3(np__0)) = k9_scmpds_2(A,B,k1_nat_1(k4_card_1(C),np__2))
& k1_funct_1(k3_scmpds_8(A,B,C),k2_scmpds_3(k1_nat_1(k4_card_1(C),np__1))) = k4_scmpds_2(k4_xcmplx_0(k1_nat_1(k4_card_1(C),np__1))) ) ) ) ) ).
fof(t20_scmpds_8,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
=> ( r1_scmpds_6(k3_scmpds_8(C,D,B),A)
& r2_scmpds_6(k3_scmpds_8(C,D,B),A) ) ) ) ) ) ) ).
fof(t21_scmpds_8,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( v1_int_1(E)
=> ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)),np__0)
=> k9_scmpds_4(k3_scmpds_8(C,E,B),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k4_card_1(B),np__2)))) ) ) ) ) ) ) ).
fof(t22_scmpds_8,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
=> k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(k3_scmpds_8(C,D,B),A)) = k2_scmpds_3(k1_nat_1(k4_card_1(B),np__2)) ) ) ) ) ) ).
fof(t23_scmpds_8,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( v1_int_1(E)
=> ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)),np__0)
=> k2_scmpds_2(k9_scmpds_4(k3_scmpds_8(C,E,B),A),D) = k2_scmpds_2(A,D) ) ) ) ) ) ) ).
fof(t24_scmpds_8,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& v3_scmpds_4(B)
& v3_scmpds_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ! [E] :
( v1_int_1(E)
=> ! [F,G,H] :
( ( v1_funct_1(H)
& v1_funct_2(H,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)),k5_numbers)
& m2_relset_1(H,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)),k5_numbers) )
=> ( ( ! [I] :
( m1_subset_1(I,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( k1_recdef_1(k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)),H,k1_scmpds_8(I)) = np__0
=> r1_xreal_0(k2_scmpds_2(I,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0) ) )
& ! [I] :
( m1_scmpds_2(I)
=> ( r2_hidden(I,F)
=> r1_xreal_0(k2_xcmplx_0(E,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D))),k2_scmpds_2(A,I)) ) )
& ! [I] :
( m1_subset_1(I,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( ! [J] :
( m1_scmpds_2(J)
=> ( r2_hidden(J,F)
=> r1_xreal_0(k2_xcmplx_0(E,k2_scmpds_2(I,k3_scmpds_2(k2_scmpds_2(A,C),D))),k2_scmpds_2(I,J)) ) )
& ! [J] :
( m1_scmpds_2(J)
=> ( r2_hidden(J,G)
=> k2_scmpds_2(I,J) = k2_scmpds_2(A,J) ) )
& k2_scmpds_2(I,C) = k2_scmpds_2(A,C) )
=> ( r1_xreal_0(k2_scmpds_2(I,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
| ( k2_scmpds_2(k9_scmpds_4(B,I),C) = k2_scmpds_2(I,C)
& r1_scmpds_6(B,I)
& r2_scmpds_6(B,I)
& ~ r1_xreal_0(k1_recdef_1(k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)),H,k1_scmpds_8(I)),k1_recdef_1(k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)),H,k1_scmpds_8(k9_scmpds_4(B,I))))
& ! [J] :
( m1_scmpds_2(J)
=> ( r2_hidden(J,F)
=> r1_xreal_0(k2_xcmplx_0(E,k2_scmpds_2(k9_scmpds_4(B,I),k3_scmpds_2(k2_scmpds_2(A,C),D))),k2_scmpds_2(k9_scmpds_4(B,I),J)) ) )
& ! [J] :
( m1_scmpds_2(J)
=> ( r2_hidden(J,G)
=> k2_scmpds_2(k9_scmpds_4(B,I),J) = k2_scmpds_2(I,J) ) ) ) ) ) ) )
=> ( r1_xreal_0(k4_card_1(B),np__0)
| ( r1_scmpds_6(k3_scmpds_8(C,D,B),A)
& r2_scmpds_6(k3_scmpds_8(C,D,B),A) ) ) ) ) ) ) ) ) ) ).
fof(t25_scmpds_8,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& v3_scmpds_4(B)
& v3_scmpds_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ! [E] :
( v1_int_1(E)
=> ! [F,G,H] :
( ( v1_funct_1(H)
& v1_funct_2(H,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)),k5_numbers)
& m2_relset_1(H,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)),k5_numbers) )
=> ( ( ! [I] :
( m1_subset_1(I,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( k1_recdef_1(k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)),H,k1_scmpds_8(I)) = np__0
=> r1_xreal_0(k2_scmpds_2(I,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0) ) )
& ! [I] :
( m1_scmpds_2(I)
=> ( r2_hidden(I,F)
=> r1_xreal_0(k2_xcmplx_0(E,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D))),k2_scmpds_2(A,I)) ) )
& ! [I] :
( m1_subset_1(I,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( ! [J] :
( m1_scmpds_2(J)
=> ( r2_hidden(J,F)
=> r1_xreal_0(k2_xcmplx_0(E,k2_scmpds_2(I,k3_scmpds_2(k2_scmpds_2(A,C),D))),k2_scmpds_2(I,J)) ) )
& ! [J] :
( m1_scmpds_2(J)
=> ( r2_hidden(J,G)
=> k2_scmpds_2(I,J) = k2_scmpds_2(A,J) ) )
& k2_scmpds_2(I,C) = k2_scmpds_2(A,C) )
=> ( r1_xreal_0(k2_scmpds_2(I,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
| ( k2_scmpds_2(k9_scmpds_4(B,I),C) = k2_scmpds_2(I,C)
& r1_scmpds_6(B,I)
& r2_scmpds_6(B,I)
& ~ r1_xreal_0(k1_recdef_1(k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)),H,k1_scmpds_8(I)),k1_recdef_1(k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)),H,k1_scmpds_8(k9_scmpds_4(B,I))))
& ! [J] :
( m1_scmpds_2(J)
=> ( r2_hidden(J,F)
=> r1_xreal_0(k2_xcmplx_0(E,k2_scmpds_2(k9_scmpds_4(B,I),k3_scmpds_2(k2_scmpds_2(A,C),D))),k2_scmpds_2(k9_scmpds_4(B,I),J)) ) )
& ! [J] :
( m1_scmpds_2(J)
=> ( r2_hidden(J,G)
=> k2_scmpds_2(k9_scmpds_4(B,I),J) = k2_scmpds_2(I,J) ) ) ) ) ) ) )
=> ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
| r1_xreal_0(k4_card_1(B),np__0)
| k9_scmpds_4(k3_scmpds_8(C,D,B),A) = k9_scmpds_4(k3_scmpds_8(C,D,B),k9_scmpds_4(B,A)) ) ) ) ) ) ) ) ) ).
fof(t26_scmpds_8,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& v3_scmpds_4(B)
& v3_scmpds_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ! [E,F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)),k5_numbers)
& m2_relset_1(F,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)),k5_numbers) )
=> ( ( ! [G] :
( m1_subset_1(G,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( k1_recdef_1(k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)),F,k1_scmpds_8(G)) = np__0
=> r1_xreal_0(k2_scmpds_2(G,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0) ) )
& ! [G] :
( m1_subset_1(G,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( ! [H] :
( m1_scmpds_2(H)
=> ( r2_hidden(H,E)
=> k2_scmpds_2(G,H) = k2_scmpds_2(A,H) ) )
& k2_scmpds_2(G,C) = k2_scmpds_2(A,C) )
=> ( r1_xreal_0(k2_scmpds_2(G,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
| ( k2_scmpds_2(k9_scmpds_4(B,G),C) = k2_scmpds_2(G,C)
& r1_scmpds_6(B,G)
& r2_scmpds_6(B,G)
& ~ r1_xreal_0(k1_recdef_1(k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)),F,k1_scmpds_8(G)),k1_recdef_1(k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)),F,k1_scmpds_8(k9_scmpds_4(B,G))))
& ! [H] :
( m1_scmpds_2(H)
=> ( r2_hidden(H,E)
=> k2_scmpds_2(k9_scmpds_4(B,G),H) = k2_scmpds_2(G,H) ) ) ) ) ) ) )
=> ( r1_xreal_0(k4_card_1(B),np__0)
| ( r1_scmpds_6(k3_scmpds_8(C,D,B),A)
& r2_scmpds_6(k3_scmpds_8(C,D,B),A)
& ( ~ r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
=> k9_scmpds_4(k3_scmpds_8(C,D,B),A) = k9_scmpds_4(k3_scmpds_8(C,D,B),k9_scmpds_4(B,A)) ) ) ) ) ) ) ) ) ) ).
fof(t27_scmpds_8,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& v3_scmpds_4(B)
& v3_scmpds_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ! [E] :
( v1_int_1(E)
=> ! [F,G] :
( ( ! [H] :
( m1_scmpds_2(H)
=> ( r2_hidden(H,F)
=> r1_xreal_0(k2_xcmplx_0(E,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D))),k2_scmpds_2(A,H)) ) )
& ! [H] :
( m1_subset_1(H,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( ! [I] :
( m1_scmpds_2(I)
=> ( r2_hidden(I,F)
=> r1_xreal_0(k2_xcmplx_0(E,k2_scmpds_2(H,k3_scmpds_2(k2_scmpds_2(A,C),D))),k2_scmpds_2(H,I)) ) )
& ! [I] :
( m1_scmpds_2(I)
=> ( r2_hidden(I,G)
=> k2_scmpds_2(H,I) = k2_scmpds_2(A,I) ) )
& k2_scmpds_2(H,C) = k2_scmpds_2(A,C) )
=> ( r1_xreal_0(k2_scmpds_2(H,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
| ( k2_scmpds_2(k9_scmpds_4(B,H),C) = k2_scmpds_2(H,C)
& r1_scmpds_6(B,H)
& r2_scmpds_6(B,H)
& ~ r1_xreal_0(k2_scmpds_2(H,k3_scmpds_2(k2_scmpds_2(A,C),D)),k2_scmpds_2(k9_scmpds_4(B,H),k3_scmpds_2(k2_scmpds_2(A,C),D)))
& ! [I] :
( m1_scmpds_2(I)
=> ( r2_hidden(I,F)
=> r1_xreal_0(k2_xcmplx_0(E,k2_scmpds_2(k9_scmpds_4(B,H),k3_scmpds_2(k2_scmpds_2(A,C),D))),k2_scmpds_2(k9_scmpds_4(B,H),I)) ) )
& ! [I] :
( m1_scmpds_2(I)
=> ( r2_hidden(I,G)
=> k2_scmpds_2(k9_scmpds_4(B,H),I) = k2_scmpds_2(H,I) ) ) ) ) ) ) )
=> ( r1_xreal_0(k4_card_1(B),np__0)
| ( r1_scmpds_6(k3_scmpds_8(C,D,B),A)
& r2_scmpds_6(k3_scmpds_8(C,D,B),A)
& ( ~ r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
=> k9_scmpds_4(k3_scmpds_8(C,D,B),A) = k9_scmpds_4(k3_scmpds_8(C,D,B),k9_scmpds_4(B,A)) ) ) ) ) ) ) ) ) ) ).
fof(t28_scmpds_8,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& v3_scmpds_4(B)
& v3_scmpds_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ! [E] :
( ! [F] :
( m1_subset_1(F,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( ! [G] :
( m1_scmpds_2(G)
=> ( r2_hidden(G,E)
=> k2_scmpds_2(F,G) = k2_scmpds_2(A,G) ) )
& k2_scmpds_2(F,C) = k2_scmpds_2(A,C) )
=> ( r1_xreal_0(k2_scmpds_2(F,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
| ( k2_scmpds_2(k9_scmpds_4(B,F),C) = k2_scmpds_2(F,C)
& r1_scmpds_6(B,F)
& r2_scmpds_6(B,F)
& ~ r1_xreal_0(k2_scmpds_2(F,k3_scmpds_2(k2_scmpds_2(A,C),D)),k2_scmpds_2(k9_scmpds_4(B,F),k3_scmpds_2(k2_scmpds_2(A,C),D)))
& ! [G] :
( m1_scmpds_2(G)
=> ( r2_hidden(G,E)
=> k2_scmpds_2(k9_scmpds_4(B,F),G) = k2_scmpds_2(F,G) ) ) ) ) ) )
=> ( r1_xreal_0(k4_card_1(B),np__0)
| ( r1_scmpds_6(k3_scmpds_8(C,D,B),A)
& r2_scmpds_6(k3_scmpds_8(C,D,B),A)
& ( ~ r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
=> k9_scmpds_4(k3_scmpds_8(C,D,B),A) = k9_scmpds_4(k3_scmpds_8(C,D,B),k9_scmpds_4(B,A)) ) ) ) ) ) ) ) ) ).
fof(t29_scmpds_8,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& v3_scmpds_4(B)
& v3_scmpds_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ! [E] :
( v1_int_1(E)
=> ! [F] :
( ( ! [G] :
( m1_scmpds_2(G)
=> ( r2_hidden(G,F)
=> r1_xreal_0(k2_xcmplx_0(E,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D))),k2_scmpds_2(A,G)) ) )
& ! [G] :
( m1_subset_1(G,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( ! [H] :
( m1_scmpds_2(H)
=> ( r2_hidden(H,F)
=> r1_xreal_0(k2_xcmplx_0(E,k2_scmpds_2(G,k3_scmpds_2(k2_scmpds_2(A,C),D))),k2_scmpds_2(G,H)) ) )
& k2_scmpds_2(G,C) = k2_scmpds_2(A,C) )
=> ( r1_xreal_0(k2_scmpds_2(G,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
| ( k2_scmpds_2(k9_scmpds_4(B,G),C) = k2_scmpds_2(G,C)
& r1_scmpds_6(B,G)
& r2_scmpds_6(B,G)
& ~ r1_xreal_0(k2_scmpds_2(G,k3_scmpds_2(k2_scmpds_2(A,C),D)),k2_scmpds_2(k9_scmpds_4(B,G),k3_scmpds_2(k2_scmpds_2(A,C),D)))
& ! [H] :
( m1_scmpds_2(H)
=> ( r2_hidden(H,F)
=> r1_xreal_0(k2_xcmplx_0(E,k2_scmpds_2(k9_scmpds_4(B,G),k3_scmpds_2(k2_scmpds_2(A,C),D))),k2_scmpds_2(k9_scmpds_4(B,G),H)) ) ) ) ) ) ) )
=> ( r1_xreal_0(k4_card_1(B),np__0)
| ( r1_scmpds_6(k3_scmpds_8(C,D,B),A)
& r2_scmpds_6(k3_scmpds_8(C,D,B),A)
& ( ~ r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
=> k9_scmpds_4(k3_scmpds_8(C,D,B),A) = k9_scmpds_4(k3_scmpds_8(C,D,B),k9_scmpds_4(B,A)) ) ) ) ) ) ) ) ) ) ).
fof(s1_scmpds_8,axiom,
( ( ~ r1_xreal_0(k4_card_1(f3_s1_scmpds_8),np__0)
& ! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( p1_s1_scmpds_8(k1_scmpds_8(A))
& f1_s1_scmpds_8(k1_scmpds_8(A)) = np__0 )
=> r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(f2_s1_scmpds_8,f4_s1_scmpds_8),f5_s1_scmpds_8))) ) )
& p1_s1_scmpds_8(k1_scmpds_8(f2_s1_scmpds_8))
& ! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( p1_s1_scmpds_8(k1_scmpds_8(A))
& k2_scmpds_2(A,f4_s1_scmpds_8) = k2_scmpds_2(f2_s1_scmpds_8,f4_s1_scmpds_8) )
=> ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(f2_s1_scmpds_8,f4_s1_scmpds_8),f5_s1_scmpds_8)))
| ( k2_scmpds_2(k9_scmpds_4(f3_s1_scmpds_8,A),f4_s1_scmpds_8) = k2_scmpds_2(A,f4_s1_scmpds_8)
& r1_scmpds_6(f3_s1_scmpds_8,A)
& r2_scmpds_6(f3_s1_scmpds_8,A)
& ~ r1_xreal_0(f1_s1_scmpds_8(k1_scmpds_8(A)),f1_s1_scmpds_8(k1_scmpds_8(k9_scmpds_4(f3_s1_scmpds_8,A))))
& p1_s1_scmpds_8(k1_scmpds_8(k9_scmpds_4(f3_s1_scmpds_8,A))) ) ) ) ) )
=> ( ( f1_s1_scmpds_8(f2_s1_scmpds_8) = f1_s1_scmpds_8(f2_s1_scmpds_8)
| p1_s1_scmpds_8(f2_s1_scmpds_8) )
& r1_scmpds_6(k2_scmpds_8(f4_s1_scmpds_8,f5_s1_scmpds_8,f3_s1_scmpds_8),f2_s1_scmpds_8)
& r2_scmpds_6(k2_scmpds_8(f4_s1_scmpds_8,f5_s1_scmpds_8,f3_s1_scmpds_8),f2_s1_scmpds_8) ) ) ).
fof(s2_scmpds_8,axiom,
( ( ~ r1_xreal_0(k4_card_1(f3_s2_scmpds_8),np__0)
& ~ r1_xreal_0(np__0,k2_scmpds_2(f2_s2_scmpds_8,k3_scmpds_2(k2_scmpds_2(f2_s2_scmpds_8,f4_s2_scmpds_8),f5_s2_scmpds_8)))
& ! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( p1_s2_scmpds_8(k1_scmpds_8(A))
& f1_s2_scmpds_8(k1_scmpds_8(A)) = np__0 )
=> r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(f2_s2_scmpds_8,f4_s2_scmpds_8),f5_s2_scmpds_8))) ) )
& p1_s2_scmpds_8(k1_scmpds_8(f2_s2_scmpds_8))
& ! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( p1_s2_scmpds_8(k1_scmpds_8(A))
& k2_scmpds_2(A,f4_s2_scmpds_8) = k2_scmpds_2(f2_s2_scmpds_8,f4_s2_scmpds_8) )
=> ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(f2_s2_scmpds_8,f4_s2_scmpds_8),f5_s2_scmpds_8)))
| ( k2_scmpds_2(k9_scmpds_4(f3_s2_scmpds_8,A),f4_s2_scmpds_8) = k2_scmpds_2(A,f4_s2_scmpds_8)
& r1_scmpds_6(f3_s2_scmpds_8,A)
& r2_scmpds_6(f3_s2_scmpds_8,A)
& ~ r1_xreal_0(f1_s2_scmpds_8(k1_scmpds_8(A)),f1_s2_scmpds_8(k1_scmpds_8(k9_scmpds_4(f3_s2_scmpds_8,A))))
& p1_s2_scmpds_8(k1_scmpds_8(k9_scmpds_4(f3_s2_scmpds_8,A))) ) ) ) ) )
=> ( ( f1_s2_scmpds_8(f2_s2_scmpds_8) = f1_s2_scmpds_8(f2_s2_scmpds_8)
| p1_s2_scmpds_8(f2_s2_scmpds_8) )
& k9_scmpds_4(k2_scmpds_8(f4_s2_scmpds_8,f5_s2_scmpds_8,f3_s2_scmpds_8),f2_s2_scmpds_8) = k9_scmpds_4(k2_scmpds_8(f4_s2_scmpds_8,f5_s2_scmpds_8,f3_s2_scmpds_8),k9_scmpds_4(f3_s2_scmpds_8,f2_s2_scmpds_8)) ) ) ).
fof(s3_scmpds_8,axiom,
( ( ~ r1_xreal_0(k4_card_1(f3_s3_scmpds_8),np__0)
& ! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( p1_s3_scmpds_8(k1_scmpds_8(A))
& f1_s3_scmpds_8(k1_scmpds_8(A)) = np__0 )
=> r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(f2_s3_scmpds_8,f4_s3_scmpds_8),f5_s3_scmpds_8)),np__0) ) )
& p1_s3_scmpds_8(k1_scmpds_8(f2_s3_scmpds_8))
& ! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( p1_s3_scmpds_8(k1_scmpds_8(A))
& k2_scmpds_2(A,f4_s3_scmpds_8) = k2_scmpds_2(f2_s3_scmpds_8,f4_s3_scmpds_8) )
=> ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(f2_s3_scmpds_8,f4_s3_scmpds_8),f5_s3_scmpds_8)),np__0)
| ( k2_scmpds_2(k9_scmpds_4(f3_s3_scmpds_8,A),f4_s3_scmpds_8) = k2_scmpds_2(A,f4_s3_scmpds_8)
& r1_scmpds_6(f3_s3_scmpds_8,A)
& r2_scmpds_6(f3_s3_scmpds_8,A)
& ~ r1_xreal_0(f1_s3_scmpds_8(k1_scmpds_8(A)),f1_s3_scmpds_8(k1_scmpds_8(k9_scmpds_4(f3_s3_scmpds_8,A))))
& p1_s3_scmpds_8(k1_scmpds_8(k9_scmpds_4(f3_s3_scmpds_8,A))) ) ) ) ) )
=> ( ( f1_s3_scmpds_8(f2_s3_scmpds_8) = f1_s3_scmpds_8(f2_s3_scmpds_8)
| p1_s3_scmpds_8(f2_s3_scmpds_8) )
& r1_scmpds_6(k3_scmpds_8(f4_s3_scmpds_8,f5_s3_scmpds_8,f3_s3_scmpds_8),f2_s3_scmpds_8)
& r2_scmpds_6(k3_scmpds_8(f4_s3_scmpds_8,f5_s3_scmpds_8,f3_s3_scmpds_8),f2_s3_scmpds_8) ) ) ).
fof(s4_scmpds_8,axiom,
( ( ~ r1_xreal_0(k4_card_1(f3_s4_scmpds_8),np__0)
& ~ r1_xreal_0(k2_scmpds_2(f2_s4_scmpds_8,k3_scmpds_2(k2_scmpds_2(f2_s4_scmpds_8,f4_s4_scmpds_8),f5_s4_scmpds_8)),np__0)
& ! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( p1_s4_scmpds_8(k1_scmpds_8(A))
& f1_s4_scmpds_8(k1_scmpds_8(A)) = np__0 )
=> r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(f2_s4_scmpds_8,f4_s4_scmpds_8),f5_s4_scmpds_8)),np__0) ) )
& p1_s4_scmpds_8(k1_scmpds_8(f2_s4_scmpds_8))
& ! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( p1_s4_scmpds_8(k1_scmpds_8(A))
& k2_scmpds_2(A,f4_s4_scmpds_8) = k2_scmpds_2(f2_s4_scmpds_8,f4_s4_scmpds_8) )
=> ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(f2_s4_scmpds_8,f4_s4_scmpds_8),f5_s4_scmpds_8)),np__0)
| ( k2_scmpds_2(k9_scmpds_4(f3_s4_scmpds_8,A),f4_s4_scmpds_8) = k2_scmpds_2(A,f4_s4_scmpds_8)
& r1_scmpds_6(f3_s4_scmpds_8,A)
& r2_scmpds_6(f3_s4_scmpds_8,A)
& ~ r1_xreal_0(f1_s4_scmpds_8(k1_scmpds_8(A)),f1_s4_scmpds_8(k1_scmpds_8(k9_scmpds_4(f3_s4_scmpds_8,A))))
& p1_s4_scmpds_8(k1_scmpds_8(k9_scmpds_4(f3_s4_scmpds_8,A))) ) ) ) ) )
=> ( ( f1_s4_scmpds_8(f2_s4_scmpds_8) = f1_s4_scmpds_8(f2_s4_scmpds_8)
| p1_s4_scmpds_8(f2_s4_scmpds_8) )
& k9_scmpds_4(k3_scmpds_8(f4_s4_scmpds_8,f5_s4_scmpds_8,f3_s4_scmpds_8),f2_s4_scmpds_8) = k9_scmpds_4(k3_scmpds_8(f4_s4_scmpds_8,f5_s4_scmpds_8,f3_s4_scmpds_8),k9_scmpds_4(f3_s4_scmpds_8,f2_s4_scmpds_8)) ) ) ).
fof(dt_k1_scmpds_8,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> m1_subset_1(k1_scmpds_8(A),k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) ) ).
fof(dt_k2_scmpds_8,axiom,
! [A,B,C] :
( ( m1_scmpds_2(A)
& v1_int_1(B)
& v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( v1_ami_3(k2_scmpds_8(A,B,C),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k2_scmpds_8(A,B,C))
& m1_ami_1(k2_scmpds_8(A,B,C),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
fof(dt_k3_scmpds_8,axiom,
! [A,B,C] :
( ( m1_scmpds_2(A)
& v1_int_1(B)
& v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( v1_ami_3(k3_scmpds_8(A,B,C),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k3_scmpds_8(A,B,C))
& m1_ami_1(k3_scmpds_8(A,B,C),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
%------------------------------------------------------------------------------