SET007 Axioms: SET007+391.ax
%------------------------------------------------------------------------------
% File : SET007+391 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : A Compiler of Arithmetic Expressions for 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_comp [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 49 ( 0 unt; 0 def)
% Number of atoms : 323 ( 97 equ)
% Maximal formula atoms : 37 ( 6 avg)
% Number of connectives : 298 ( 24 ~; 0 |; 112 &)
% ( 6 <=>; 156 =>; 0 <=; 0 <~>)
% Maximal formula depth : 40 ( 9 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 26 ( 25 usr; 0 prp; 1-6 aty)
% Number of functors : 73 ( 73 usr; 12 con; 0-4 aty)
% Number of variables : 160 ( 156 !; 4 ?)
% 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_comp,axiom,
! [A] :
( m2_finseq_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [B] :
( m2_finseq_1(B,u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [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)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( m1_scm_1(G,k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),A,B),C,D,E,F)
=> ( m1_scm_1(G,A,C,D,E,F)
& m1_scm_1(G,B,C,D,k1_nat_1(E,k3_finseq_1(A)),F) ) ) ) ) ) ) ) ) ).
fof(t2_scm_comp,axiom,
! [A] :
( m2_finseq_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [B] :
( m2_finseq_1(B,u4_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)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ! [H] :
( m1_scm_1(H,k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),A,B),k2_lang1(k4_numbers),C,D,E)
=> ! [I] :
( m1_subset_1(I,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ( ( I = k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,H),F)
& k16_ami_3(G) = k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,I) )
=> m1_scm_1(I,B,k2_lang1(k4_numbers),G,k1_nat_1(D,k3_finseq_1(A)),E) ) ) ) ) ) ) ) ) ) ) ).
fof(d1_scm_comp,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_lang1(A)
& v3_bintree1(A)
& v1_dtconstr(A)
& v2_dtconstr(A)
& v3_dtconstr(A)
& l1_lang1(A) )
=> ( A = k1_scm_comp
<=> ( k6_dtconstr(A) = k2_ami_2
& k7_dtconstr(A) = k2_zfmisc_1(np__1,np__5)
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_lang1(A,B,k4_lang1(u1_struct_0(A),C,D))
<=> r2_hidden(B,k2_zfmisc_1(np__1,np__5)) ) ) ) ) ) ) ) ).
fof(d2_scm_comp,axiom,
! [A] :
( m1_struct_0(A,k1_scm_comp,k6_dtconstr(k1_scm_comp))
=> k4_scm_comp(A) = A ) ).
fof(t3_scm_comp,axiom,
! [A] :
( m1_struct_0(A,k1_scm_comp,k7_dtconstr(k1_scm_comp))
=> ~ ( A != k4_tarski(np__0,np__0)
& A != k4_tarski(np__0,np__1)
& A != k4_tarski(np__0,np__2)
& A != k4_tarski(np__0,np__3)
& A != k4_tarski(np__0,np__4) ) ) ).
fof(t4_scm_comp,axiom,
( m1_struct_0(k4_tarski(np__0,np__0),k1_scm_comp,k7_dtconstr(k1_scm_comp))
& m1_struct_0(k4_tarski(np__0,np__1),k1_scm_comp,k7_dtconstr(k1_scm_comp))
& m1_struct_0(k4_tarski(np__0,np__2),k1_scm_comp,k7_dtconstr(k1_scm_comp))
& m1_struct_0(k4_tarski(np__0,np__3),k1_scm_comp,k7_dtconstr(k1_scm_comp))
& m1_struct_0(k4_tarski(np__0,np__4),k1_scm_comp,k7_dtconstr(k1_scm_comp)) ) ).
fof(d3_scm_comp,axiom,
! [A] :
( m1_dtconstr(A,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
=> ! [B] :
( m1_dtconstr(B,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
=> k5_scm_comp(A,B) = k6_trees_4(k4_tarski(np__0,np__0),A,B) ) ) ).
fof(d4_scm_comp,axiom,
! [A] :
( m1_dtconstr(A,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
=> ! [B] :
( m1_dtconstr(B,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
=> k6_scm_comp(A,B) = k6_trees_4(k4_tarski(np__0,np__1),A,B) ) ) ).
fof(d5_scm_comp,axiom,
! [A] :
( m1_dtconstr(A,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
=> ! [B] :
( m1_dtconstr(B,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
=> k7_scm_comp(A,B) = k6_trees_4(k4_tarski(np__0,np__2),A,B) ) ) ).
fof(d6_scm_comp,axiom,
! [A] :
( m1_dtconstr(A,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
=> ! [B] :
( m1_dtconstr(B,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
=> k8_scm_comp(A,B) = k6_trees_4(k4_tarski(np__0,np__3),A,B) ) ) ).
fof(d7_scm_comp,axiom,
! [A] :
( m1_dtconstr(A,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
=> ! [B] :
( m1_dtconstr(B,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
=> k9_scm_comp(A,B) = k6_trees_4(k4_tarski(np__0,np__4),A,B) ) ) ).
fof(t5_scm_comp,axiom,
! [A] :
( m1_dtconstr(A,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
=> ~ ( ! [B] :
( m1_struct_0(B,k1_scm_comp,k6_dtconstr(k1_scm_comp))
=> A != k3_scm_comp(B) )
& ! [B] :
( m1_dtconstr(B,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
=> ( A != k5_scm_comp(B,C)
& A != k6_scm_comp(B,C)
& A != k7_scm_comp(B,C)
& A != k8_scm_comp(B,C)
& A != k9_scm_comp(B,C) ) ) ) ) ) ).
fof(d8_scm_comp,axiom,
! [A] :
( m1_struct_0(A,k1_scm_comp,k7_dtconstr(k1_scm_comp))
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( v1_int_1(C)
=> ( ( A = k4_tarski(np__0,np__0)
=> k10_scm_comp(A,B,C) = k2_xcmplx_0(B,C) )
& ( A = k4_tarski(np__0,np__1)
=> k10_scm_comp(A,B,C) = k6_xcmplx_0(B,C) )
& ( A = k4_tarski(np__0,np__2)
=> k10_scm_comp(A,B,C) = k3_xcmplx_0(B,C) )
& ( A = k4_tarski(np__0,np__3)
=> k10_scm_comp(A,B,C) = k5_int_1(B,C) )
& ( A = k4_tarski(np__0,np__4)
=> k10_scm_comp(A,B,C) = k6_int_1(B,C) ) ) ) ) ) ).
fof(d9_scm_comp,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [B] :
( m1_dtconstr(B,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
=> ! [C] :
( v1_int_1(C)
=> ( C = k13_scm_comp(A,B)
<=> ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,k4_dtconstr(k1_scm_comp),k4_numbers)
& m2_relset_1(D,k4_dtconstr(k1_scm_comp),k4_numbers)
& C = k8_funct_2(k4_dtconstr(k1_scm_comp),k4_numbers,D,B)
& ! [E] :
( m1_struct_0(E,k1_scm_comp,k6_dtconstr(k1_scm_comp))
=> k8_funct_2(k4_dtconstr(k1_scm_comp),k4_numbers,D,k3_scm_comp(E)) = k11_scm_comp(A,E) )
& ! [E] :
( m1_struct_0(E,k1_scm_comp,k7_dtconstr(k1_scm_comp))
=> ! [F] :
( m1_dtconstr(F,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
=> ! [G] :
( m1_dtconstr(G,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k1_scm_comp))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(k1_scm_comp))
=> ( ( H = k1_bintree1(u1_struct_0(k1_scm_comp),F)
& I = k1_bintree1(u1_struct_0(k1_scm_comp),G)
& r1_lang1(k1_scm_comp,E,k4_lang1(u1_struct_0(k1_scm_comp),H,I)) )
=> ! [J] :
( m1_subset_1(J,k4_numbers)
=> ! [K] :
( m1_subset_1(K,k4_numbers)
=> ( ( J = k8_funct_2(k4_dtconstr(k1_scm_comp),k4_numbers,D,F)
& K = k8_funct_2(k4_dtconstr(k1_scm_comp),k4_numbers,D,G) )
=> k8_funct_2(k4_dtconstr(k1_scm_comp),k4_numbers,D,k2_scm_comp(E,F,G)) = k10_scm_comp(E,J,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t6_scm_comp,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [B] :
( m1_struct_0(B,k1_scm_comp,k6_dtconstr(k1_scm_comp))
=> k13_scm_comp(A,k3_scm_comp(B)) = k11_scm_comp(A,B) ) ) ).
fof(t7_scm_comp,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [B] :
( m1_struct_0(B,k1_scm_comp,k7_dtconstr(k1_scm_comp))
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
=> ! [D] :
( m1_dtconstr(D,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
=> k13_scm_comp(A,k2_scm_comp(B,C,D)) = k10_scm_comp(B,k13_scm_comp(A,C),k13_scm_comp(A,D)) ) ) ) ) ).
fof(t8_scm_comp,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [B] :
( m1_dtconstr(B,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
=> ( k13_scm_comp(A,k5_scm_comp(B,C)) = k2_xcmplx_0(k13_scm_comp(A,B),k13_scm_comp(A,C))
& k13_scm_comp(A,k6_scm_comp(B,C)) = k6_xcmplx_0(k13_scm_comp(A,B),k13_scm_comp(A,C))
& k13_scm_comp(A,k7_scm_comp(B,C)) = k3_xcmplx_0(k13_scm_comp(A,B),k13_scm_comp(A,C))
& k13_scm_comp(A,k8_scm_comp(B,C)) = k5_int_1(k13_scm_comp(A,B),k13_scm_comp(A,C))
& k13_scm_comp(A,k9_scm_comp(B,C)) = k6_int_1(k13_scm_comp(A,B),k13_scm_comp(A,C)) ) ) ) ) ).
fof(d10_scm_comp,axiom,
! [A] :
( m1_struct_0(A,k1_scm_comp,k7_dtconstr(k1_scm_comp))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( A = k4_tarski(np__0,np__0)
=> k14_scm_comp(A,B) = k3_lang1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k4_ami_3(k15_ami_3(B),k15_ami_3(k1_nat_1(B,np__1)))) )
& ( A = k4_tarski(np__0,np__1)
=> k14_scm_comp(A,B) = k3_lang1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k5_ami_3(k15_ami_3(B),k15_ami_3(k1_nat_1(B,np__1)))) )
& ( A = k4_tarski(np__0,np__2)
=> k14_scm_comp(A,B) = k3_lang1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k6_ami_3(k15_ami_3(B),k15_ami_3(k1_nat_1(B,np__1)))) )
& ( A = k4_tarski(np__0,np__3)
=> k14_scm_comp(A,B) = k3_lang1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k7_ami_3(k15_ami_3(B),k15_ami_3(k1_nat_1(B,np__1)))) )
& ( A = k4_tarski(np__0,np__4)
=> k14_scm_comp(A,B) = k4_lang1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k7_ami_3(k15_ami_3(B),k15_ami_3(k1_nat_1(B,np__1))),k3_ami_3(k15_ami_3(B),k15_ami_3(k1_nat_1(B,np__1)))) ) ) ) ) ).
fof(d11_scm_comp,axiom,
! [A] :
( m1_dtconstr(A,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_1(C,u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ( C = k15_scm_comp(A,B)
<=> ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,k4_dtconstr(k1_scm_comp),k1_fraenkel(k5_numbers,k3_finseq_2(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))))
& m2_relset_1(D,k4_dtconstr(k1_scm_comp),k1_fraenkel(k5_numbers,k3_finseq_2(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))))
& C = k8_funct_2(k5_numbers,k3_finseq_2(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)),k8_funct_2(k4_dtconstr(k1_scm_comp),k1_fraenkel(k5_numbers,k3_finseq_2(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))),D,A),B)
& ! [E] :
( m1_struct_0(E,k1_scm_comp,k6_dtconstr(k1_scm_comp))
=> ? [F] :
( v1_funct_1(F)
& v1_funct_2(F,k5_numbers,k3_finseq_2(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
& m2_relset_1(F,k5_numbers,k3_finseq_2(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
& F = k8_funct_2(k4_dtconstr(k1_scm_comp),k1_fraenkel(k5_numbers,k3_finseq_2(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))),D,k3_scm_comp(E))
& ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k3_finseq_2(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)),F,G) = k3_lang1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k3_ami_3(k15_ami_3(G),k4_scm_comp(E))) ) ) )
& ! [E] :
( m1_struct_0(E,k1_scm_comp,k7_dtconstr(k1_scm_comp))
=> ! [F] :
( m1_dtconstr(F,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
=> ! [G] :
( m1_dtconstr(G,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k1_scm_comp))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(k1_scm_comp))
=> ~ ( H = k1_bintree1(u1_struct_0(k1_scm_comp),F)
& I = k1_bintree1(u1_struct_0(k1_scm_comp),G)
& r1_lang1(k1_scm_comp,E,k4_lang1(u1_struct_0(k1_scm_comp),H,I))
& ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,k5_numbers,k3_finseq_2(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
& m2_relset_1(J,k5_numbers,k3_finseq_2(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))) )
=> ! [K] :
( ( v1_funct_1(K)
& v1_funct_2(K,k5_numbers,k3_finseq_2(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
& m2_relset_1(K,k5_numbers,k3_finseq_2(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))) )
=> ! [L] :
( ( v1_funct_1(L)
& v1_funct_2(L,k5_numbers,k3_finseq_2(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
& m2_relset_1(L,k5_numbers,k3_finseq_2(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))) )
=> ~ ( J = k8_funct_2(k4_dtconstr(k1_scm_comp),k1_fraenkel(k5_numbers,k3_finseq_2(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))),D,k2_scm_comp(E,F,G))
& K = k8_funct_2(k4_dtconstr(k1_scm_comp),k1_fraenkel(k5_numbers,k3_finseq_2(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))),D,F)
& L = k8_funct_2(k4_dtconstr(k1_scm_comp),k1_fraenkel(k5_numbers,k3_finseq_2(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))),D,G)
& ! [M] :
( m2_subset_1(M,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k3_finseq_2(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)),J,M) = k1_lang1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k1_lang1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_funct_2(k5_numbers,k3_finseq_2(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)),K,M),k8_funct_2(k5_numbers,k3_finseq_2(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)),L,k1_nat_1(M,np__1))),k14_scm_comp(E,M)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t9_scm_comp,axiom,
! [A] :
( m1_struct_0(A,k1_scm_comp,k6_dtconstr(k1_scm_comp))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k15_scm_comp(k3_scm_comp(A),B) = k3_lang1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k3_ami_3(k15_ami_3(B),k4_scm_comp(A))) ) ) ).
fof(t10_scm_comp,axiom,
! [A] :
( m1_struct_0(A,k1_scm_comp,k7_dtconstr(k1_scm_comp))
=> ! [B] :
( m1_dtconstr(B,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k1_scm_comp))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k1_scm_comp))
=> ( ( E = k1_bintree1(u1_struct_0(k1_scm_comp),B)
& F = k1_bintree1(u1_struct_0(k1_scm_comp),C)
& r1_lang1(k1_scm_comp,A,k4_lang1(u1_struct_0(k1_scm_comp),E,F)) )
=> k15_scm_comp(k2_scm_comp(A,B,C),D) = 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),k15_scm_comp(B,D),k15_scm_comp(C,k1_nat_1(D,np__1))),k14_scm_comp(A,D)) ) ) ) ) ) ) ) ).
fof(d12_scm_comp,axiom,
! [A] :
( m1_struct_0(A,k1_scm_comp,k6_dtconstr(k1_scm_comp))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( B = k16_scm_comp(A)
<=> k15_ami_3(B) = A ) ) ) ).
fof(d13_scm_comp,axiom,
! [A] :
( m1_dtconstr(A,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( B = k17_scm_comp(A)
<=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,k4_dtconstr(k1_scm_comp),k5_numbers)
& m2_relset_1(C,k4_dtconstr(k1_scm_comp),k5_numbers)
& B = k8_funct_2(k4_dtconstr(k1_scm_comp),k5_numbers,C,A)
& ! [D] :
( m1_struct_0(D,k1_scm_comp,k6_dtconstr(k1_scm_comp))
=> k8_funct_2(k4_dtconstr(k1_scm_comp),k5_numbers,C,k3_scm_comp(D)) = k16_scm_comp(D) )
& ! [D] :
( m1_struct_0(D,k1_scm_comp,k7_dtconstr(k1_scm_comp))
=> ! [E] :
( m1_dtconstr(E,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
=> ! [F] :
( m1_dtconstr(F,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k1_scm_comp))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k1_scm_comp))
=> ( ( G = k1_bintree1(u1_struct_0(k1_scm_comp),E)
& H = k1_bintree1(u1_struct_0(k1_scm_comp),F)
& r1_lang1(k1_scm_comp,D,k4_lang1(u1_struct_0(k1_scm_comp),G,H)) )
=> ! [I] :
( m2_subset_1(I,k1_numbers,k5_numbers)
=> ! [J] :
( m2_subset_1(J,k1_numbers,k5_numbers)
=> ( ( I = k8_funct_2(k4_dtconstr(k1_scm_comp),k5_numbers,C,E)
& J = k8_funct_2(k4_dtconstr(k1_scm_comp),k5_numbers,C,F) )
=> k8_funct_2(k4_dtconstr(k1_scm_comp),k5_numbers,C,k2_scm_comp(D,E,F)) = k1_limfunc1(I,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t11_scm_comp,axiom,
! [A] :
( m1_struct_0(A,k1_scm_comp,k6_dtconstr(k1_scm_comp))
=> k17_scm_comp(k3_scm_comp(A)) = k16_scm_comp(A) ) ).
fof(t12_scm_comp,axiom,
! [A] :
( m1_struct_0(A,k1_scm_comp,k7_dtconstr(k1_scm_comp))
=> ! [B] :
( m1_dtconstr(B,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
=> k17_scm_comp(k2_scm_comp(A,B,C)) = k1_limfunc1(k17_scm_comp(B),k17_scm_comp(C)) ) ) ) ).
fof(t13_scm_comp,axiom,
! [A] :
( m1_dtconstr(A,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_xreal_0(D,k17_scm_comp(A))
=> k2_ami_3(B,k15_ami_3(D)) = k2_ami_3(C,k15_ami_3(D)) ) )
=> k13_scm_comp(B,A) = k13_scm_comp(C,A) ) ) ) ) ).
fof(t14_scm_comp,axiom,
! [A] :
( m1_dtconstr(A,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m1_scm_1(E,k15_scm_comp(A,B),k2_lang1(k4_numbers),C,C,D)
=> ~ ( ~ r1_xreal_0(B,k17_scm_comp(A))
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( m1_subset_1(G,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ~ ( G = k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,E),k1_nat_1(F,np__1))
& k1_nat_1(F,np__1) = k3_finseq_1(k15_scm_comp(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,E),F)) = k16_ami_3(k1_nat_1(C,F))
& k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,G) = k16_ami_3(k1_nat_1(C,k1_nat_1(F,np__1)))
& k2_ami_3(G,k15_ami_3(B)) = k13_scm_comp(E,A)
& ! [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(B,H)
=> k2_ami_3(E,k15_ami_3(H)) = k2_ami_3(G,k15_ami_3(H)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t15_scm_comp,axiom,
! [A] :
( m1_dtconstr(A,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m1_scm_1(E,k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k15_scm_comp(A,B),k3_lang1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k5_ami_1(k1_tarski(k4_numbers),k1_ami_3))),k2_lang1(k4_numbers),C,C,D)
=> ( ~ r1_xreal_0(B,k17_scm_comp(A))
=> ( v9_ami_1(E,k1_tarski(k4_numbers),k1_ami_3)
& k2_ami_3(k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,E),k15_ami_3(B)) = k13_scm_comp(E,A)
& k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,E) = k3_finseq_1(k15_scm_comp(A,B)) ) ) ) ) ) ) ) ).
fof(dt_k1_scm_comp,axiom,
( ~ v3_struct_0(k1_scm_comp)
& v1_lang1(k1_scm_comp)
& v3_bintree1(k1_scm_comp)
& v1_dtconstr(k1_scm_comp)
& v2_dtconstr(k1_scm_comp)
& v3_dtconstr(k1_scm_comp)
& l1_lang1(k1_scm_comp) ) ).
fof(dt_k2_scm_comp,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k7_dtconstr(k1_scm_comp))
& m1_subset_1(B,k4_dtconstr(k1_scm_comp))
& m1_subset_1(C,k4_dtconstr(k1_scm_comp)) )
=> m1_dtconstr(k2_scm_comp(A,B,C),u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) ) ).
fof(redefinition_k2_scm_comp,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k7_dtconstr(k1_scm_comp))
& m1_subset_1(B,k4_dtconstr(k1_scm_comp))
& m1_subset_1(C,k4_dtconstr(k1_scm_comp)) )
=> k2_scm_comp(A,B,C) = k6_trees_4(A,B,C) ) ).
fof(dt_k3_scm_comp,axiom,
! [A] :
( m1_subset_1(A,k6_dtconstr(k1_scm_comp))
=> m1_dtconstr(k3_scm_comp(A),u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) ) ).
fof(redefinition_k3_scm_comp,axiom,
! [A] :
( m1_subset_1(A,k6_dtconstr(k1_scm_comp))
=> k3_scm_comp(A) = k1_trees_4(A) ) ).
fof(dt_k4_scm_comp,axiom,
! [A] :
( m1_subset_1(A,k6_dtconstr(k1_scm_comp))
=> m1_ami_3(k4_scm_comp(A)) ) ).
fof(dt_k5_scm_comp,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_dtconstr(k1_scm_comp))
& m1_subset_1(B,k4_dtconstr(k1_scm_comp)) )
=> m1_dtconstr(k5_scm_comp(A,B),u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) ) ).
fof(dt_k6_scm_comp,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_dtconstr(k1_scm_comp))
& m1_subset_1(B,k4_dtconstr(k1_scm_comp)) )
=> m1_dtconstr(k6_scm_comp(A,B),u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) ) ).
fof(dt_k7_scm_comp,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_dtconstr(k1_scm_comp))
& m1_subset_1(B,k4_dtconstr(k1_scm_comp)) )
=> m1_dtconstr(k7_scm_comp(A,B),u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) ) ).
fof(dt_k8_scm_comp,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_dtconstr(k1_scm_comp))
& m1_subset_1(B,k4_dtconstr(k1_scm_comp)) )
=> m1_dtconstr(k8_scm_comp(A,B),u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) ) ).
fof(dt_k9_scm_comp,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_dtconstr(k1_scm_comp))
& m1_subset_1(B,k4_dtconstr(k1_scm_comp)) )
=> m1_dtconstr(k9_scm_comp(A,B),u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) ) ).
fof(dt_k10_scm_comp,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k7_dtconstr(k1_scm_comp))
& v1_int_1(B)
& v1_int_1(C) )
=> v1_int_1(k10_scm_comp(A,B,C)) ) ).
fof(dt_k11_scm_comp,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
& m1_subset_1(B,k6_dtconstr(k1_scm_comp)) )
=> v1_int_1(k11_scm_comp(A,B)) ) ).
fof(redefinition_k11_scm_comp,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
& m1_subset_1(B,k6_dtconstr(k1_scm_comp)) )
=> k11_scm_comp(A,B) = k1_funct_1(A,B) ) ).
fof(dt_k12_scm_comp,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& v1_funct_2(B,k4_numbers,A)
& m1_relset_1(B,k4_numbers,A)
& v1_int_1(C) )
=> m1_subset_1(k12_scm_comp(A,B,C),A) ) ).
fof(redefinition_k12_scm_comp,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& v1_funct_2(B,k4_numbers,A)
& m1_relset_1(B,k4_numbers,A)
& v1_int_1(C) )
=> k12_scm_comp(A,B,C) = k1_funct_1(B,C) ) ).
fof(dt_k13_scm_comp,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
& m1_subset_1(B,k4_dtconstr(k1_scm_comp)) )
=> v1_int_1(k13_scm_comp(A,B)) ) ).
fof(dt_k14_scm_comp,axiom,
! [A,B] :
( ( m1_subset_1(A,k7_dtconstr(k1_scm_comp))
& m1_subset_1(B,k5_numbers) )
=> m2_finseq_2(k14_scm_comp(A,B),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k3_finseq_2(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))) ) ).
fof(dt_k15_scm_comp,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_dtconstr(k1_scm_comp))
& m1_subset_1(B,k5_numbers) )
=> m2_finseq_1(k15_scm_comp(A,B),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ).
fof(dt_k16_scm_comp,axiom,
! [A] :
( m1_subset_1(A,k6_dtconstr(k1_scm_comp))
=> m2_subset_1(k16_scm_comp(A),k1_numbers,k5_numbers) ) ).
fof(dt_k17_scm_comp,axiom,
! [A] :
( m1_subset_1(A,k4_dtconstr(k1_scm_comp))
=> m2_subset_1(k17_scm_comp(A),k1_numbers,k5_numbers) ) ).
%------------------------------------------------------------------------------