SET007 Axioms: SET007+659.ax
%------------------------------------------------------------------------------
% File : SET007+659 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Insert Sort on 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 : scpisort [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 24 ( 0 unt; 0 def)
% Number of atoms : 298 ( 45 equ)
% Maximal formula atoms : 27 ( 12 avg)
% Number of connectives : 286 ( 12 ~; 16 |; 140 &)
% ( 1 <=>; 117 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 13 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 23 ( 22 usr; 0 prp; 1-3 aty)
% Number of functors : 64 ( 64 usr; 29 con; 0-4 aty)
% Number of variables : 92 ( 90 !; 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(d1_scpisort,axiom,
! [A] :
( m2_finseq_1(A,k4_numbers)
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_scpisort(A,B,C)
<=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(A)) )
=> k1_funct_1(A,D) = k2_scmpds_2(B,k1_scmp_gcd(k1_nat_1(C,D))) ) ) ) ) ) ) ).
fof(t1_scpisort,axiom,
! [A] :
( m2_finseq_1(A,k4_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_xreal_0(C,B)
=> r1_sfmastr3(A,B,C) ) ) ) ) ).
fof(t2_scpisort,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ? [D] :
( m2_finseq_1(D,k4_numbers)
& k3_finseq_1(D) = B
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,E)
& r1_xreal_0(E,k3_finseq_1(D)) )
=> k1_funct_1(D,E) = k2_scmpds_2(A,k1_scmp_gcd(k1_nat_1(C,E))) ) ) ) ) ) ) ).
fof(t3_scpisort,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ? [D] :
( m2_finseq_1(D,k4_numbers)
& k3_finseq_1(D) = B
& r1_scpisort(D,A,C) ) ) ) ) ).
fof(t4_scpisort,axiom,
! [A] :
( m2_finseq_1(A,k4_numbers)
=> ! [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)
=> ( ( r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(A))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(A))
& k3_finseq_1(A) = k3_finseq_1(B)
& k1_funct_1(A,C) = k1_funct_1(B,D)
& k1_funct_1(A,D) = k1_funct_1(B,C)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,E)
& r1_xreal_0(E,k3_finseq_1(A)) )
=> ( E = C
| E = D
| k1_funct_1(A,E) = k1_funct_1(B,E) ) ) ) )
=> r1_rfinseq(A,B) ) ) ) ) ) ).
fof(t5_scpisort,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)))
=> ( ! [C] :
( m1_scmpds_2(C)
=> k2_scmpds_2(A,C) = k2_scmpds_2(B,C) )
=> k1_scmpds_8(A) = k1_scmpds_8(B) ) ) ) ).
fof(t6_scpisort,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_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( ( v4_scmpds_4(C)
& v2_scmpds_5(C)
& m2_subset_1(C,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)) )
=> ( ( r1_scmpds_6(B,A)
& r2_scmpds_6(B,A) )
=> ( r1_scmpds_6(k5_scmpds_4(B,C),A)
& r2_scmpds_6(k5_scmpds_4(B,C),A) ) ) ) ) ) ).
fof(t7_scpisort,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_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(C)
& v2_scmpds_4(C)
& v3_scmpds_4(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [D] :
( m1_scmpds_2(D)
=> ( ( r1_scmpds_6(B,A)
& r2_scmpds_6(B,A) )
=> k2_scmpds_2(k9_scmpds_4(k3_scmpds_4(B,C),A),D) = k2_scmpds_2(k9_scmpds_4(C,k9_scmpds_4(B,A)),D) ) ) ) ) ) ).
fof(t8_scpisort,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)
& v2_scmpds_4(B)
& v3_scmpds_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(C)
& v3_scmpds_4(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [D] :
( m1_scmpds_2(D)
=> ( ( r1_scmpds_6(C,k9_scmpds_4(B,A))
& r2_scmpds_6(C,k9_scmpds_4(B,A)) )
=> k2_scmpds_2(k9_scmpds_4(k3_scmpds_4(B,C),A),D) = k2_scmpds_2(k9_scmpds_4(C,k9_scmpds_4(B,A)),D) ) ) ) ) ) ).
fof(t9_scpisort,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] :
( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(C)
& v2_scmpds_4(C)
& v3_scmpds_4(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( ( r1_scmpds_6(B,A)
& r2_scmpds_6(B,A) )
=> ( r1_scmpds_6(k3_scmpds_4(B,C),A)
& r2_scmpds_6(k3_scmpds_4(B,C),A) ) ) ) ) ) ).
fof(t10_scpisort,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)
& v2_scmpds_4(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(C)
& v3_scmpds_4(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( ( r1_scmpds_6(C,k9_scmpds_4(B,A))
& r2_scmpds_6(C,k9_scmpds_4(B,A)) )
=> ( r1_scmpds_6(k3_scmpds_4(B,C),A)
& r2_scmpds_6(k3_scmpds_4(B,C),A) ) ) ) ) ) ).
fof(t11_scpisort,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] :
( ( v4_scmpds_4(C)
& v2_scmpds_5(C)
& m2_subset_1(C,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)) )
=> ( ( r1_scmpds_6(B,A)
& r2_scmpds_6(B,A) )
=> ( r1_scmpds_6(k5_scmpds_4(B,C),A)
& r2_scmpds_6(k5_scmpds_4(B,C),A) ) ) ) ) ) ).
fof(t12_scpisort,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] :
( m1_scmpds_2(D)
=> ! [E] :
( m1_scmpds_2(E)
=> ! [F] :
( v1_int_1(F)
=> ! [G] :
( v1_int_1(G)
=> ! [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(k2_xcmplx_0(k2_scmpds_2(A,E),G),k2_scmpds_2(A,D))
& ! [I] :
( m1_subset_1(I,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( r1_xreal_0(k2_xcmplx_0(k2_scmpds_2(I,E),G),k2_scmpds_2(I,D))
& 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),F)),np__0)
| ( k2_scmpds_2(k9_scmpds_4(k5_scmpds_4(B,k12_scmpds_2(C,F,k4_xcmplx_0(H))),I),C) = k2_scmpds_2(I,C)
& k2_scmpds_2(k9_scmpds_4(k5_scmpds_4(B,k12_scmpds_2(C,F,k4_xcmplx_0(H))),I),k3_scmpds_2(k2_scmpds_2(A,C),F)) = k6_xcmplx_0(k2_scmpds_2(I,k3_scmpds_2(k2_scmpds_2(A,C),F)),H)
& r1_scmpds_6(B,I)
& r2_scmpds_6(B,I)
& r1_xreal_0(k2_xcmplx_0(k2_scmpds_2(k9_scmpds_4(k5_scmpds_4(B,k12_scmpds_2(C,F,k4_xcmplx_0(H))),I),E),G),k2_scmpds_2(k9_scmpds_4(k5_scmpds_4(B,k12_scmpds_2(C,F,k4_xcmplx_0(H))),I),D)) ) ) ) ) )
=> ( r1_xreal_0(H,np__0)
| ( r1_scmpds_6(k2_scmpds_7(C,F,H,B),A)
& r2_scmpds_6(k2_scmpds_7(C,F,H,B),A) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t13_scpisort,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] :
( m1_scmpds_2(D)
=> ! [E] :
( m1_scmpds_2(E)
=> ! [F] :
( v1_int_1(F)
=> ! [G] :
( v1_int_1(G)
=> ! [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(k2_xcmplx_0(k2_scmpds_2(A,E),G),k2_scmpds_2(A,D))
& ! [I] :
( m1_subset_1(I,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( r1_xreal_0(k2_xcmplx_0(k2_scmpds_2(I,E),G),k2_scmpds_2(I,D))
& 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),F)),np__0)
| ( k2_scmpds_2(k9_scmpds_4(k5_scmpds_4(B,k12_scmpds_2(C,F,k4_xcmplx_0(H))),I),C) = k2_scmpds_2(I,C)
& k2_scmpds_2(k9_scmpds_4(k5_scmpds_4(B,k12_scmpds_2(C,F,k4_xcmplx_0(H))),I),k3_scmpds_2(k2_scmpds_2(A,C),F)) = k6_xcmplx_0(k2_scmpds_2(I,k3_scmpds_2(k2_scmpds_2(A,C),F)),H)
& r1_scmpds_6(B,I)
& r2_scmpds_6(B,I)
& r1_xreal_0(k2_xcmplx_0(k2_scmpds_2(k9_scmpds_4(k5_scmpds_4(B,k12_scmpds_2(C,F,k4_xcmplx_0(H))),I),E),G),k2_scmpds_2(k9_scmpds_4(k5_scmpds_4(B,k12_scmpds_2(C,F,k4_xcmplx_0(H))),I),D)) ) ) ) ) )
=> ( r1_xreal_0(H,np__0)
| r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),F)),np__0)
| k9_scmpds_4(k2_scmpds_7(C,F,H,B),A) = k9_scmpds_4(k2_scmpds_7(C,F,H,B),k9_scmpds_4(k5_scmpds_4(B,k12_scmpds_2(C,F,k4_xcmplx_0(H))),A)) ) ) ) ) ) ) ) ) ) ) ).
fof(t14_scpisort,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] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ! [F] :
( m1_subset_1(F,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( k2_scmpds_2(F,C) = k2_scmpds_2(A,C)
=> ( k2_scmpds_2(k9_scmpds_4(B,F),C) = k2_scmpds_2(F,C)
& 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) ) ) )
=> ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
| r1_xreal_0(E,np__0)
| r1_xreal_0(k4_card_1(B),np__0)
| C = k3_scmpds_2(k2_scmpds_2(A,C),D)
| ( r1_scmpds_6(k2_scmpds_7(C,D,E,B),A)
& r2_scmpds_6(k2_scmpds_7(C,D,E,B),A) ) ) ) ) ) ) ) ) ).
fof(d2_scpisort,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k1_scpisort(A,B) = k3_scmpds_4(k5_scmpds_4(k5_scmpds_4(k6_scmpds_4(k6_scmpds_2(k2_scmp_gcd,np__0),k11_scmpds_2(k2_scmp_gcd,np__1,np__0)),k11_scmpds_2(k2_scmp_gcd,np__2,k6_xcmplx_0(A,np__1))),k11_scmpds_2(k2_scmp_gcd,np__3,B)),k2_scmpds_7(k2_scmp_gcd,np__2,np__1,k3_scmpds_4(k5_scmpds_4(k5_scmpds_4(k6_scmpds_4(k12_scmpds_2(k2_scmp_gcd,np__3,np__1),k17_scmpds_2(k2_scmp_gcd,k2_scmp_gcd,np__4,np__3)),k12_scmpds_2(k2_scmp_gcd,np__1,np__1)),k17_scmpds_2(k2_scmp_gcd,k2_scmp_gcd,np__6,np__1)),k3_scmpds_8(k2_scmp_gcd,np__6,k3_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(np__4),np__5,k4_xcmplx_0(np__1)),k14_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(np__4),np__5,np__0)),k3_scmpds_6(k2_scmp_gcd,np__5,k5_scmpds_4(k5_scmpds_4(k5_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(np__4),np__5,k4_xcmplx_0(np__1)),k17_scmpds_2(k1_scmp_gcd(np__4),k1_scmp_gcd(np__4),k4_xcmplx_0(np__1),np__0)),k17_scmpds_2(k1_scmp_gcd(np__4),k2_scmp_gcd,np__0,np__5)),k12_scmpds_2(k2_scmp_gcd,np__4,k4_xcmplx_0(np__1))),k12_scmpds_2(k2_scmp_gcd,np__6,k4_xcmplx_0(np__1))),k1_scmpds_4(k11_scmpds_2(k2_scmp_gcd,np__6,np__0)))))))) ) ) ).
fof(t15_scpisort,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k4_card_1(k1_scpisort(A,B)) = np__23 ) ) ).
fof(t16_scpisort,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r1_xreal_0(np__7,A)
=> v2_scmpds_4(k1_scpisort(B,A)) ) ) ) ).
fof(t17_scpisort,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( m2_finseq_1(B,k4_numbers)
=> ! [C] :
( m2_finseq_1(C,k4_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(k2_xcmplx_0(np__7,k2_scmpds_2(A,k1_scmp_gcd(np__6))),k2_scmpds_2(A,k1_scmp_gcd(np__4)))
& k2_scmpds_2(A,k2_scmp_gcd) = np__0
& E = k2_scmpds_2(A,k1_scmp_gcd(np__6))
& D = k6_xcmplx_0(k6_xcmplx_0(k2_scmpds_2(A,k1_scmp_gcd(np__4)),k2_scmpds_2(A,k1_scmp_gcd(np__6))),np__1)
& r1_scpisort(B,A,D)
& r1_scpisort(C,k9_scmpds_4(k3_scmpds_8(k2_scmp_gcd,np__6,k3_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(np__4),np__5,k4_xcmplx_0(np__1)),k14_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(np__4),np__5,np__0)),k3_scmpds_6(k2_scmp_gcd,np__5,k5_scmpds_4(k5_scmpds_4(k5_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(np__4),np__5,k4_xcmplx_0(np__1)),k17_scmpds_2(k1_scmp_gcd(np__4),k1_scmp_gcd(np__4),k4_xcmplx_0(np__1),np__0)),k17_scmpds_2(k1_scmp_gcd(np__4),k2_scmp_gcd,np__0,np__5)),k12_scmpds_2(k2_scmp_gcd,np__4,k4_xcmplx_0(np__1))),k12_scmpds_2(k2_scmp_gcd,np__6,k4_xcmplx_0(np__1))),k1_scmpds_4(k11_scmpds_2(k2_scmp_gcd,np__6,np__0))))),A),D)
& k3_finseq_1(B) = k3_finseq_1(C)
& r1_sfmastr3(B,np__1,E) )
=> ( r1_xreal_0(k3_finseq_1(B),E)
| ( r1_rfinseq(B,C)
& r1_sfmastr3(C,np__1,k1_nat_1(E,np__1))
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( r1_xreal_0(F,k3_finseq_1(B))
=> ( r1_xreal_0(F,k1_nat_1(E,np__1))
| k1_funct_1(B,F) = k1_funct_1(C,F) ) ) )
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,F)
& r1_xreal_0(F,k1_nat_1(E,np__1))
& ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,G)
& r1_xreal_0(G,k1_nat_1(E,np__1))
& k1_funct_1(C,F) = k1_funct_1(B,G) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t18_scpisort,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( m2_finseq_1(B,k4_numbers)
=> ! [C] :
( m2_finseq_1(C,k4_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__6,D)
& k3_finseq_1(B) = E
& k3_finseq_1(C) = E
& r1_scpisort(B,A,D)
& r1_scpisort(C,k9_scmpds_4(k1_scpisort(E,k1_nat_1(D,np__1)),A),D) )
=> ( r1_rfinseq(B,C)
& r1_sfmastr3(C,np__1,E) ) ) ) ) ) ) ) ).
fof(s1_scpisort,axiom,
( ( ~ r1_xreal_0(f5_s1_scpisort,np__0)
& p1_s1_scpisort(k1_scmpds_8(f1_s1_scpisort))
& ! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( p1_s1_scpisort(k1_scmpds_8(A))
& k2_scmpds_2(A,f3_s1_scpisort) = k2_scmpds_2(f1_s1_scpisort,f3_s1_scpisort) )
=> ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(f1_s1_scpisort,f3_s1_scpisort),f4_s1_scpisort)),np__0)
| ( k2_scmpds_2(k9_scmpds_4(k5_scmpds_4(f2_s1_scpisort,k12_scmpds_2(f3_s1_scpisort,f4_s1_scpisort,k4_xcmplx_0(f5_s1_scpisort))),A),f3_s1_scpisort) = k2_scmpds_2(A,f3_s1_scpisort)
& k2_scmpds_2(k9_scmpds_4(k5_scmpds_4(f2_s1_scpisort,k12_scmpds_2(f3_s1_scpisort,f4_s1_scpisort,k4_xcmplx_0(f5_s1_scpisort))),A),k3_scmpds_2(k2_scmpds_2(f1_s1_scpisort,f3_s1_scpisort),f4_s1_scpisort)) = k6_xcmplx_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(f1_s1_scpisort,f3_s1_scpisort),f4_s1_scpisort)),f5_s1_scpisort)
& r1_scmpds_6(f2_s1_scpisort,A)
& r2_scmpds_6(f2_s1_scpisort,A)
& p1_s1_scpisort(k1_scmpds_8(k9_scmpds_4(k5_scmpds_4(f2_s1_scpisort,k12_scmpds_2(f3_s1_scpisort,f4_s1_scpisort,k4_xcmplx_0(f5_s1_scpisort))),A))) ) ) ) ) )
=> ( ~ ( ~ p1_s1_scpisort(f1_s1_scpisort)
& p1_s1_scpisort(f1_s1_scpisort) )
& r1_scmpds_6(k2_scmpds_7(f3_s1_scpisort,f4_s1_scpisort,f5_s1_scpisort,f2_s1_scpisort),f1_s1_scpisort)
& r2_scmpds_6(k2_scmpds_7(f3_s1_scpisort,f4_s1_scpisort,f5_s1_scpisort,f2_s1_scpisort),f1_s1_scpisort) ) ) ).
fof(s2_scpisort,axiom,
( ( ~ r1_xreal_0(f5_s2_scpisort,np__0)
& ~ r1_xreal_0(k2_scmpds_2(f1_s2_scpisort,k3_scmpds_2(k2_scmpds_2(f1_s2_scpisort,f3_s2_scpisort),f4_s2_scpisort)),np__0)
& p1_s2_scpisort(k1_scmpds_8(f1_s2_scpisort))
& ! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( p1_s2_scpisort(k1_scmpds_8(A))
& k2_scmpds_2(A,f3_s2_scpisort) = k2_scmpds_2(f1_s2_scpisort,f3_s2_scpisort) )
=> ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(f1_s2_scpisort,f3_s2_scpisort),f4_s2_scpisort)),np__0)
| ( k2_scmpds_2(k9_scmpds_4(k5_scmpds_4(f2_s2_scpisort,k12_scmpds_2(f3_s2_scpisort,f4_s2_scpisort,k4_xcmplx_0(f5_s2_scpisort))),A),f3_s2_scpisort) = k2_scmpds_2(A,f3_s2_scpisort)
& k2_scmpds_2(k9_scmpds_4(k5_scmpds_4(f2_s2_scpisort,k12_scmpds_2(f3_s2_scpisort,f4_s2_scpisort,k4_xcmplx_0(f5_s2_scpisort))),A),k3_scmpds_2(k2_scmpds_2(f1_s2_scpisort,f3_s2_scpisort),f4_s2_scpisort)) = k6_xcmplx_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(f1_s2_scpisort,f3_s2_scpisort),f4_s2_scpisort)),f5_s2_scpisort)
& r1_scmpds_6(f2_s2_scpisort,A)
& r2_scmpds_6(f2_s2_scpisort,A)
& p1_s2_scpisort(k1_scmpds_8(k9_scmpds_4(k5_scmpds_4(f2_s2_scpisort,k12_scmpds_2(f3_s2_scpisort,f4_s2_scpisort,k4_xcmplx_0(f5_s2_scpisort))),A))) ) ) ) ) )
=> ( ~ ( ~ p1_s2_scpisort(f1_s2_scpisort)
& p1_s2_scpisort(f1_s2_scpisort) )
& k9_scmpds_4(k2_scmpds_7(f3_s2_scpisort,f4_s2_scpisort,f5_s2_scpisort,f2_s2_scpisort),f1_s2_scpisort) = k9_scmpds_4(k2_scmpds_7(f3_s2_scpisort,f4_s2_scpisort,f5_s2_scpisort,f2_s2_scpisort),k9_scmpds_4(k5_scmpds_4(f2_s2_scpisort,k12_scmpds_2(f3_s2_scpisort,f4_s2_scpisort,k4_xcmplx_0(f5_s2_scpisort))),f1_s2_scpisort)) ) ) ).
fof(s3_scpisort,axiom,
( ( ~ r1_xreal_0(f5_s3_scpisort,np__0)
& p1_s3_scpisort(k1_scmpds_8(f1_s3_scpisort))
& ! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( p1_s3_scpisort(k1_scmpds_8(A))
& k2_scmpds_2(A,f3_s3_scpisort) = k2_scmpds_2(f1_s3_scpisort,f3_s3_scpisort) )
=> ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(f1_s3_scpisort,f3_s3_scpisort),f4_s3_scpisort)),np__0)
| ( k2_scmpds_2(k9_scmpds_4(k5_scmpds_4(f2_s3_scpisort,k12_scmpds_2(f3_s3_scpisort,f4_s3_scpisort,k4_xcmplx_0(f5_s3_scpisort))),A),f3_s3_scpisort) = k2_scmpds_2(A,f3_s3_scpisort)
& k2_scmpds_2(k9_scmpds_4(k5_scmpds_4(f2_s3_scpisort,k12_scmpds_2(f3_s3_scpisort,f4_s3_scpisort,k4_xcmplx_0(f5_s3_scpisort))),A),k3_scmpds_2(k2_scmpds_2(f1_s3_scpisort,f3_s3_scpisort),f4_s3_scpisort)) = k6_xcmplx_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(f1_s3_scpisort,f3_s3_scpisort),f4_s3_scpisort)),f5_s3_scpisort)
& r1_scmpds_6(f2_s3_scpisort,A)
& r2_scmpds_6(f2_s3_scpisort,A)
& p1_s3_scpisort(k1_scmpds_8(k9_scmpds_4(k5_scmpds_4(f2_s3_scpisort,k12_scmpds_2(f3_s3_scpisort,f4_s3_scpisort,k4_xcmplx_0(f5_s3_scpisort))),A))) ) ) ) ) )
=> ( ~ ( ~ p1_s3_scpisort(f1_s3_scpisort)
& p1_s3_scpisort(f1_s3_scpisort) )
& r1_xreal_0(k2_scmpds_2(k9_scmpds_4(k2_scmpds_7(f3_s3_scpisort,f4_s3_scpisort,f5_s3_scpisort,f2_s3_scpisort),f1_s3_scpisort),k3_scmpds_2(k2_scmpds_2(f1_s3_scpisort,f3_s3_scpisort),f4_s3_scpisort)),np__0)
& p1_s3_scpisort(k1_scmpds_8(k9_scmpds_4(k2_scmpds_7(f3_s3_scpisort,f4_s3_scpisort,f5_s3_scpisort,f2_s3_scpisort),f1_s3_scpisort))) ) ) ).
fof(dt_k1_scpisort,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers) )
=> ( v1_ami_3(k1_scpisort(A,B),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k1_scpisort(A,B))
& m1_ami_1(k1_scpisort(A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
%------------------------------------------------------------------------------