SET007 Axioms: SET007+501.ax
%------------------------------------------------------------------------------
% File : SET007+501 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Institution of Many Sorted Algebras. Part I
% Version : [Urb08] axioms.
% English : Institution of Many Sorted Algebras. Part I: Signature Reduct of
% an Algebra
% 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 : instalg1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 68 ( 1 unt; 0 def)
% Number of atoms : 678 ( 56 equ)
% Maximal formula atoms : 25 ( 9 avg)
% Number of connectives : 739 ( 129 ~; 2 |; 290 &)
% ( 7 <=>; 311 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 11 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 38 ( 36 usr; 1 prp; 0-5 aty)
% Number of functors : 48 ( 48 usr; 4 con; 0-6 aty)
% Number of variables : 283 ( 276 !; 7 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(cc1_instalg1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A))
& m1_subset_1(C,u1_msualg_1(A)) )
=> ! [D] :
( m1_subset_1(D,k3_msualg_1(A,C,k11_msafree(A,B)))
=> ( v1_relat_1(D)
& v1_funct_1(D)
& v1_finseq_1(D)
& v6_trees_3(D) ) ) ) ).
fof(fc1_instalg1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ( v4_msualg_1(g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)),A)
& v5_msualg_1(g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)),A) ) ) ).
fof(cc2_instalg1,axiom,
! [A] :
( l1_msualg_1(A)
=> ( ~ v3_struct_0(A)
=> v1_instalg1(A) ) ) ).
fof(cc3_instalg1,axiom,
! [A] :
( l1_msualg_1(A)
=> ( v2_msualg_1(A)
=> v1_instalg1(A) ) ) ).
fof(cc4_instalg1,axiom,
! [A] :
( l1_msualg_1(A)
=> ( ( v3_struct_0(A)
& v1_instalg1(A) )
=> v2_msualg_1(A) ) ) ).
fof(cc5_instalg1,axiom,
! [A] :
( l1_msualg_1(A)
=> ( ( ~ v2_msualg_1(A)
& v1_instalg1(A) )
=> ~ v3_struct_0(A) ) ) ).
fof(rc1_instalg1,axiom,
? [A] :
( l1_msualg_1(A)
& ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v1_instalg1(A) ) ).
fof(cc6_instalg1,axiom,
! [A] :
( ( v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_instalg1(B,A)
=> v1_instalg1(B) ) ) ).
fof(rc2_instalg1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ? [B] :
( m1_instalg1(B,A)
& ~ v3_struct_0(B)
& v1_instalg1(B) ) ) ).
fof(rc3_instalg1,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ? [B] :
( m1_instalg1(B,A)
& ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& v1_instalg1(B) ) ) ).
fof(fc2_instalg1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A)
& ~ v3_struct_0(B)
& m1_instalg1(B,A)
& v5_msualg_1(C,A)
& l3_msualg_1(C,A) )
=> ( v4_msualg_1(k2_instalg1(A,B,C),B)
& v5_msualg_1(k2_instalg1(A,B,C),B) ) ) ).
fof(fc3_instalg1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ( v1_relat_1(k13_msafree(A,B))
& v2_relat_1(k13_msafree(A,B))
& ~ v3_relat_1(k13_msafree(A,B))
& v1_funct_1(k13_msafree(A,B))
& v1_msafree(k13_msafree(A,B),A,k11_msafree(A,B)) ) ) ).
fof(t1_instalg1,axiom,
$true ).
fof(t2_instalg1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,u1_struct_0(A)) )
=> ! [D] :
( m1_msaterm(D,A,C,k2_msaterm(A,C,B))
<=> m1_subset_1(D,k3_msualg_1(A,B,k11_msafree(A,C))) ) ) ) ) ).
fof(t3_instalg1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( l3_msualg_1(C,A)
=> ( r1_pzfmisc1(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
=> ! [D] :
( m1_subset_1(D,u1_msualg_1(A))
=> ~ ( k3_msualg_1(A,D,B) != k1_xboole_0
& k3_msualg_1(A,D,C) = k1_xboole_0 ) ) ) ) ) ) ).
fof(t4_instalg1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,u1_struct_0(A)) )
=> ! [D] :
( m1_subset_1(D,k3_msualg_1(A,B,k11_msafree(A,C)))
=> k8_funct_2(k3_msualg_1(A,B,k11_msafree(A,C)),k4_msualg_1(A,B,k11_msafree(A,C)),k5_msualg_1(A,B,k11_msafree(A,C)),D) = k4_trees_4(k4_tarski(B,u1_struct_0(A)),D) ) ) ) ) ).
fof(t5_instalg1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( l3_msualg_1(C,A)
=> ( g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)) = g3_msualg_1(A,u4_msualg_1(A,C),u5_msualg_1(A,C))
=> ! [D] :
( m1_subset_1(D,u1_msualg_1(A))
=> k5_msualg_1(A,D,B) = k5_msualg_1(A,D,C) ) ) ) ) ) ).
fof(t6_instalg1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( l3_msualg_1(C,A)
=> ! [D] :
( l3_msualg_1(D,A)
=> ! [E] :
( l3_msualg_1(E,A)
=> ( ( g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)) = g3_msualg_1(A,u4_msualg_1(A,D),u5_msualg_1(A,D))
& g3_msualg_1(A,u4_msualg_1(A,C),u5_msualg_1(A,C)) = g3_msualg_1(A,u4_msualg_1(A,E),u5_msualg_1(A,E)) )
=> ! [F] :
( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
=> ! [G] :
( m3_pboole(G,u1_struct_0(A),u4_msualg_1(A,D),u4_msualg_1(A,E))
=> ( r6_pboole(u1_struct_0(A),F,G)
=> ! [H] :
( m1_subset_1(H,u1_msualg_1(A))
=> ~ ( k3_msualg_1(A,H,B) != k1_xboole_0
& k3_msualg_1(A,H,C) != k1_xboole_0
& ? [I] :
( m1_subset_1(I,k3_msualg_1(A,H,B))
& ? [J] :
( m1_subset_1(J,k3_msualg_1(A,H,D))
& I = J
& k5_msualg_3(A,B,C,H,F,I) != k5_msualg_3(A,D,E,H,G,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t7_instalg1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( l3_msualg_1(C,A)
=> ! [D] :
( l3_msualg_1(D,A)
=> ! [E] :
( l3_msualg_1(E,A)
=> ( ( g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)) = g3_msualg_1(A,u4_msualg_1(A,D),u5_msualg_1(A,D))
& g3_msualg_1(A,u4_msualg_1(A,C),u5_msualg_1(A,C)) = g3_msualg_1(A,u4_msualg_1(A,E),u5_msualg_1(A,E))
& r1_pzfmisc1(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) )
=> ! [F] :
( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
=> ~ ( r1_msualg_3(A,B,C,F)
& ! [G] :
( m3_pboole(G,u1_struct_0(A),u4_msualg_1(A,D),u4_msualg_1(A,E))
=> ~ ( r6_pboole(u1_struct_0(A),G,F)
& r1_msualg_3(A,D,E,G) ) ) ) ) ) ) ) ) ) ) ).
fof(d1_instalg1,axiom,
! [A] :
( l1_msualg_1(A)
=> ( v1_instalg1(A)
<=> ( u1_struct_0(A) = k1_xboole_0
=> u1_msualg_1(A) = k1_xboole_0 ) ) ) ).
fof(t8_instalg1,axiom,
! [A] :
( l1_msualg_1(A)
=> ( v1_instalg1(A)
<=> k1_relat_1(u3_msualg_1(A)) = u1_msualg_1(A) ) ) ).
fof(t9_instalg1,axiom,
! [A] :
( ( v1_instalg1(A)
& l1_msualg_1(A) )
=> r3_pua2mss1(A,A,k6_partfun1(u1_struct_0(A)),k6_partfun1(u1_msualg_1(A))) ) ).
fof(t10_instalg1,axiom,
! [A] :
( l1_msualg_1(A)
=> ! [B] :
( l1_msualg_1(B)
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( r3_pua2mss1(A,B,C,D)
=> ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(D)
& v1_funct_2(D,u1_msualg_1(A),u1_msualg_1(B))
& m2_relset_1(D,u1_msualg_1(A),u1_msualg_1(B)) ) ) ) ) ) ) ).
fof(d2_instalg1,axiom,
! [A] :
( ( v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l1_msualg_1(B)
=> ( m1_instalg1(B,A)
<=> r3_pua2mss1(B,A,k6_partfun1(u1_struct_0(B)),k6_partfun1(u1_msualg_1(B))) ) ) ) ).
fof(t11_instalg1,axiom,
! [A] :
( ( v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_instalg1(B,A)
=> ( r1_tarski(u1_struct_0(B),u1_struct_0(A))
& r1_tarski(u1_msualg_1(B),u1_msualg_1(A)) ) ) ) ).
fof(t12_instalg1,axiom,
! [A] :
( ( v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_instalg1(B,A)
=> ( r1_tarski(u3_msualg_1(B),u3_msualg_1(A))
& r1_tarski(u2_msualg_1(B),u2_msualg_1(A)) ) ) ) ).
fof(t13_instalg1,axiom,
! [A] :
( ( v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_instalg1(B,A)
=> ( u2_msualg_1(B) = k2_partfun1(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),u1_msualg_1(B))
& u3_msualg_1(B) = k2_partfun1(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u1_msualg_1(B)) ) ) ) ).
fof(t14_instalg1,axiom,
! [A] :
( ( v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v1_instalg1(B)
& l1_msualg_1(B) )
=> ( ( r1_tarski(u1_struct_0(B),u1_struct_0(A))
& r1_tarski(u2_msualg_1(B),u2_msualg_1(A))
& r1_tarski(u3_msualg_1(B),u3_msualg_1(A)) )
=> m1_instalg1(B,A) ) ) ) ).
fof(t15_instalg1,axiom,
! [A] :
( ( v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v1_instalg1(B)
& l1_msualg_1(B) )
=> ( ( r1_tarski(u1_struct_0(B),u1_struct_0(A))
& u2_msualg_1(B) = k2_partfun1(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),u1_msualg_1(B))
& u3_msualg_1(B) = k2_partfun1(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u1_msualg_1(B)) )
=> m1_instalg1(B,A) ) ) ) ).
fof(t16_instalg1,axiom,
! [A] :
( ( v1_instalg1(A)
& l1_msualg_1(A) )
=> m1_instalg1(A,A) ) ).
fof(t17_instalg1,axiom,
! [A] :
( ( v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_instalg1(B,A)
=> ! [C] :
( m1_instalg1(C,B)
=> m1_instalg1(C,A) ) ) ) ).
fof(t18_instalg1,axiom,
! [A] :
( ( v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_instalg1(B,A)
=> ( m1_instalg1(A,B)
=> g1_msualg_1(u1_struct_0(A),u1_msualg_1(A),u2_msualg_1(A),u3_msualg_1(A)) = g1_msualg_1(u1_struct_0(B),u1_msualg_1(B),u2_msualg_1(B),u3_msualg_1(B)) ) ) ) ).
fof(t19_instalg1,axiom,
! [A] :
( ( v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_instalg1(B,A)
=> ! [C] :
( l1_msualg_1(C)
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( r3_pua2mss1(A,C,D,E)
=> r3_pua2mss1(B,C,k7_relat_1(D,u1_struct_0(B)),k7_relat_1(E,u1_msualg_1(B))) ) ) ) ) ) ) ).
fof(t20_instalg1,axiom,
! [A] :
( l1_msualg_1(A)
=> ! [B] :
( ( v1_instalg1(B)
& l1_msualg_1(B) )
=> ! [C] :
( m1_instalg1(C,B)
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( r3_pua2mss1(A,C,D,E)
=> r3_pua2mss1(A,B,D,E) ) ) ) ) ) ) ).
fof(t21_instalg1,axiom,
! [A] :
( l1_msualg_1(A)
=> ! [B] :
( ( v1_instalg1(B)
& l1_msualg_1(B) )
=> ! [C] :
( m1_instalg1(C,B)
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( ( r3_pua2mss1(A,B,D,E)
& r1_tarski(k2_relat_1(D),u1_struct_0(C))
& r1_tarski(k2_relat_1(E),u1_msualg_1(C)) )
=> r3_pua2mss1(A,C,D,E) ) ) ) ) ) ) ).
fof(d3_instalg1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( l3_msualg_1(C,B)
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( r3_pua2mss1(A,B,D,E)
=> ! [F] :
( ( v4_msualg_1(F,A)
& l3_msualg_1(F,A) )
=> ( F = k1_instalg1(A,B,C,D,E)
<=> ( u4_msualg_1(A,F) = k5_relat_1(D,u4_msualg_1(B,C))
& u5_msualg_1(A,F) = k5_relat_1(E,u5_msualg_1(B,C)) ) ) ) ) ) ) ) ) ) ).
fof(d4_instalg1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( l3_msualg_1(C,A)
=> k2_instalg1(A,B,C) = k1_instalg1(B,A,C,k6_partfun1(u1_struct_0(B)),k6_partfun1(u1_msualg_1(B))) ) ) ) ).
fof(t22_instalg1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( l3_msualg_1(C,B)
=> ! [D] :
( l3_msualg_1(D,B)
=> ( g3_msualg_1(B,u4_msualg_1(B,C),u5_msualg_1(B,C)) = g3_msualg_1(B,u4_msualg_1(B,D),u5_msualg_1(B,D))
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ! [F] :
( ( v1_relat_1(F)
& v1_funct_1(F) )
=> ( r3_pua2mss1(A,B,E,F)
=> k1_instalg1(A,B,C,E,F) = k1_instalg1(A,B,D,E,F) ) ) ) ) ) ) ) ) ).
fof(t23_instalg1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v5_msualg_1(C,B)
& l3_msualg_1(C,B) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( r3_pua2mss1(A,B,D,E)
=> v5_msualg_1(k1_instalg1(A,B,C,D,E),A) ) ) ) ) ) ) ).
fof(t24_instalg1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( r3_pua2mss1(A,B,C,D)
=> ! [E] :
( l3_msualg_1(E,B)
=> ! [F] :
( m1_subset_1(F,u1_msualg_1(A))
=> ! [G] :
( m1_subset_1(G,u1_msualg_1(B))
=> ( G = k1_funct_1(D,F)
=> k5_msualg_1(A,F,k1_instalg1(A,B,E,C,D)) = k5_msualg_1(B,G,E) ) ) ) ) ) ) ) ) ) ).
fof(t25_instalg1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( r3_pua2mss1(A,B,C,D)
=> ! [E] :
( l3_msualg_1(E,B)
=> ! [F] :
( m1_subset_1(F,u1_msualg_1(A))
=> ! [G] :
( m1_subset_1(G,u1_msualg_1(B))
=> ( G = k1_funct_1(D,F)
=> ( k3_msualg_1(B,G,E) = k3_msualg_1(A,F,k1_instalg1(A,B,E,C,D))
& k4_msualg_1(A,F,k1_instalg1(A,B,E,C,D)) = k4_msualg_1(B,G,E) ) ) ) ) ) ) ) ) ) ) ).
fof(t26_instalg1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> k1_instalg1(A,A,B,k6_partfun1(u1_struct_0(A)),k6_partfun1(u1_msualg_1(A))) = g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)) ) ) ).
fof(t27_instalg1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> k2_instalg1(A,A,B) = g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)) ) ) ).
fof(t28_instalg1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_msualg_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( r3_pua2mss1(A,B,D,E)
=> ! [F] :
( ( v1_relat_1(F)
& v1_funct_1(F) )
=> ! [G] :
( ( v1_relat_1(G)
& v1_funct_1(G) )
=> ( r3_pua2mss1(B,C,F,G)
=> ! [H] :
( l3_msualg_1(H,C)
=> k1_instalg1(A,C,H,k5_relat_1(D,F),k5_relat_1(E,G)) = k1_instalg1(A,B,k1_instalg1(B,C,H,F,G),D,E) ) ) ) ) ) ) ) ) ) ) ).
fof(t29_instalg1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_instalg1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& m1_instalg1(C,B) )
=> ! [D] :
( l3_msualg_1(D,A)
=> k2_instalg1(A,C,D) = k2_instalg1(B,C,k2_instalg1(A,B,D)) ) ) ) ) ).
fof(t30_instalg1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( r3_pua2mss1(A,B,C,D)
=> ! [E] :
( l3_msualg_1(E,B)
=> ! [F] :
( l3_msualg_1(F,B)
=> ! [G] :
( m3_pboole(G,u1_struct_0(B),u4_msualg_1(B,E),u4_msualg_1(B,F))
=> m3_pboole(k7_pboole(u1_struct_0(A),u1_struct_0(B),C,G),u1_struct_0(A),u4_msualg_1(A,k1_instalg1(A,B,E,C,D)),u4_msualg_1(A,k1_instalg1(A,B,F,C,D))) ) ) ) ) ) ) ) ) ).
fof(t31_instalg1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_instalg1(B,A) )
=> ! [C] :
( l3_msualg_1(C,A)
=> ! [D] :
( l3_msualg_1(D,A)
=> ! [E] :
( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
=> m3_pboole(k7_relat_1(E,u1_struct_0(B)),u1_struct_0(B),u4_msualg_1(B,k2_instalg1(A,B,C)),u4_msualg_1(B,k2_instalg1(A,B,D))) ) ) ) ) ) ).
fof(t32_instalg1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( r3_pua2mss1(A,B,C,D)
=> ! [E] :
( l3_msualg_1(E,B)
=> k5_relat_1(C,k2_msualg_3(u1_struct_0(B),u4_msualg_1(B,E))) = k2_msualg_3(u1_struct_0(A),u4_msualg_1(A,k1_instalg1(A,B,E,C,D))) ) ) ) ) ) ) ).
fof(t33_instalg1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_instalg1(B,A) )
=> ! [C] :
( l3_msualg_1(C,A)
=> k7_relat_1(k2_msualg_3(u1_struct_0(A),u4_msualg_1(A,C)),u1_struct_0(B)) = k2_msualg_3(u1_struct_0(B),u4_msualg_1(B,k2_instalg1(A,B,C))) ) ) ) ).
fof(t34_instalg1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( r3_pua2mss1(A,B,C,D)
=> ! [E] :
( l3_msualg_1(E,B)
=> ! [F] :
( l3_msualg_1(F,B)
=> ! [G] :
( m3_pboole(G,u1_struct_0(B),u4_msualg_1(B,E),u4_msualg_1(B,F))
=> ! [H] :
( m3_pboole(H,u1_struct_0(A),u4_msualg_1(A,k1_instalg1(A,B,E,C,D)),u4_msualg_1(A,k1_instalg1(A,B,F,C,D)))
=> ( H = k5_relat_1(C,G)
=> ! [I] :
( m1_subset_1(I,u1_msualg_1(A))
=> ! [J] :
( m1_subset_1(J,u1_msualg_1(B))
=> ( J = k1_funct_1(D,I)
=> ( k3_msualg_1(B,J,E) = k1_xboole_0
| k3_msualg_1(B,J,F) = k1_xboole_0
| ! [K] :
( m1_subset_1(K,k3_msualg_1(B,J,E))
=> ! [L] :
( m1_subset_1(L,k3_msualg_1(A,I,k1_instalg1(A,B,E,C,D)))
=> ( K = L
=> k5_msualg_3(A,k1_instalg1(A,B,E,C,D),k1_instalg1(A,B,F,C,D),I,H,L) = k5_msualg_3(B,E,F,J,G,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t35_instalg1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) )
=> ! [C] :
( l3_msualg_1(C,A)
=> ! [D] :
( l3_msualg_1(D,A)
=> ( r1_pzfmisc1(u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
=> ! [E] :
( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
=> ( r1_msualg_3(A,C,D,E)
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(F,u1_struct_0(B),u1_struct_0(A)) )
=> ! [G] :
( ( v1_relat_1(G)
& v1_funct_1(G) )
=> ~ ( r3_pua2mss1(B,A,F,G)
& ! [H] :
( m3_pboole(H,u1_struct_0(B),u4_msualg_1(B,k1_instalg1(B,A,C,F,G)),u4_msualg_1(B,k1_instalg1(B,A,D,F,G)))
=> ~ ( r6_pboole(u1_struct_0(B),H,k7_pboole(u1_struct_0(B),u1_struct_0(A),F,E))
& r1_msualg_3(B,k1_instalg1(B,A,C,F,G),k1_instalg1(B,A,D,F,G),H) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t36_instalg1,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v2_msualg_1(B)
& m1_instalg1(B,A) )
=> ! [C] :
( l3_msualg_1(C,A)
=> ! [D] :
( l3_msualg_1(D,A)
=> ( r1_pzfmisc1(u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
=> ! [E] :
( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
=> ~ ( r1_msualg_3(A,C,D,E)
& ! [F] :
( m3_pboole(F,u1_struct_0(B),u4_msualg_1(B,k2_instalg1(A,B,C)),u4_msualg_1(B,k2_instalg1(A,B,D)))
=> ~ ( F = k7_relat_1(E,u1_struct_0(B))
& r1_msualg_3(B,k2_instalg1(A,B,C),k2_instalg1(A,B,D),F) ) ) ) ) ) ) ) ) ) ).
fof(t37_instalg1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v5_msualg_1(C,A)
& l3_msualg_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( r3_pua2mss1(B,A,D,E)
=> ! [F] :
( ( v5_msualg_1(F,B)
& l3_msualg_1(F,B) )
=> ( F = k1_instalg1(B,A,C,D,E)
=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(B))
=> ! [I] :
( ( v1_relat_1(I)
& v1_funct_1(I) )
=> ( r1_msualg_6(B,G,H,F,I)
=> r1_msualg_6(A,k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,G),k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,H),C,I) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t38_instalg1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( r3_pua2mss1(B,A,C,D)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( r1_rewrite1(k3_msualg_6(B),E,F)
=> r1_rewrite1(k3_msualg_6(A),k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,E),k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,F)) ) ) ) ) ) ) ) ) ).
fof(t39_instalg1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v5_msualg_1(C,A)
& l3_msualg_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( r3_pua2mss1(B,A,D,E)
=> ! [F] :
( ( v5_msualg_1(F,B)
& l3_msualg_1(F,B) )
=> ( F = k1_instalg1(B,A,C,D,E)
=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(B))
=> ( r1_rewrite1(k3_msualg_6(B),G,H)
=> ! [I] :
( m2_msualg_6(I,B,F,G,H)
=> m2_msualg_6(I,A,C,k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,G),k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,H)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t40_instalg1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m4_pboole(D,A,B)
=> ! [E] :
( m3_pboole(E,A,B,C)
=> ! [F] :
( r2_hidden(F,A)
=> ! [G] :
( ( v1_relat_1(G)
& v1_funct_1(G) )
=> ! [H] :
( ( v1_relat_1(H)
& v1_funct_1(H) )
=> ( ( G = k1_funct_1(E,F)
& H = k1_funct_1(k1_msafree(A,B,C,D,E),F) )
=> ! [I] :
( r2_hidden(I,k1_funct_1(D,F))
=> k1_funct_1(H,I) = k1_funct_1(G,I) ) ) ) ) ) ) ) ) ) ).
fof(d5_instalg1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( r3_pua2mss1(A,B,D,E)
=> ! [F] :
( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,k11_msafree(A,k8_pboole(u1_struct_0(A),u1_struct_0(B),D,C))),u4_msualg_1(A,k1_instalg1(A,B,k11_msafree(B,C),D,E)))
=> ( F = k3_instalg1(A,B,C,D,E)
<=> ( r1_msualg_3(A,k11_msafree(A,k8_pboole(u1_struct_0(A),u1_struct_0(B),D,C)),k1_instalg1(A,B,k11_msafree(B,C),D,E),F)
& ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ! [H] :
( m1_subset_1(H,k1_funct_1(k8_pboole(u1_struct_0(A),u1_struct_0(B),D,C),G))
=> k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,k11_msafree(A,k8_pboole(u1_struct_0(A),u1_struct_0(B),D,C))),u4_msualg_1(A,k1_instalg1(A,B,k11_msafree(B,C),D,E)),F,G),k1_trees_4(k4_tarski(H,G))) = k1_trees_4(k4_tarski(H,k8_funct_2(u1_struct_0(A),u1_struct_0(B),D,G))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t41_instalg1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( r3_pua2mss1(A,B,D,E)
=> ! [F] :
( m1_subset_1(F,u1_msualg_1(A))
=> ! [G] :
( m1_subset_1(G,k3_msualg_1(A,F,k11_msafree(A,k8_pboole(u1_struct_0(A),u1_struct_0(B),D,C))))
=> ! [H] :
( ( v1_relat_1(H)
& v1_funct_1(H)
& v1_finseq_1(H) )
=> ( H = k5_msualg_3(A,k11_msafree(A,k8_pboole(u1_struct_0(A),u1_struct_0(B),D,C)),k1_instalg1(A,B,k11_msafree(B,C),D,E),F,k3_instalg1(A,B,C,D,E),G)
=> k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,k11_msafree(A,k8_pboole(u1_struct_0(A),u1_struct_0(B),D,C))),u4_msualg_1(A,k1_instalg1(A,B,k11_msafree(B,C),D,E)),k3_instalg1(A,B,C,D,E),k2_msualg_1(A,F)),k4_trees_4(k4_tarski(F,u1_struct_0(A)),G)) = k4_trees_4(k4_tarski(k1_funct_1(E,F),u1_struct_0(B)),H) ) ) ) ) ) ) ) ) ) ) ).
fof(t42_instalg1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( r3_pua2mss1(A,B,D,E)
=> ! [F] :
( m1_dtconstr(F,u1_struct_0(k5_msafree(A,k8_pboole(u1_struct_0(A),u1_struct_0(B),D,C))),k5_trees_3(u1_struct_0(k5_msafree(A,k8_pboole(u1_struct_0(A),u1_struct_0(B),D,C)))),k1_msaterm(A,k8_pboole(u1_struct_0(A),u1_struct_0(B),D,C)))
=> ( m2_msaterm(k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,k11_msafree(A,k8_pboole(u1_struct_0(A),u1_struct_0(B),D,C))),u4_msualg_1(A,k1_instalg1(A,B,k11_msafree(B,C),D,E)),k3_instalg1(A,B,C,D,E),k7_msaterm(A,k8_pboole(u1_struct_0(A),u1_struct_0(B),D,C),F)),F),B,C)
<=> m2_msaterm(F,A,k8_pboole(u1_struct_0(A),u1_struct_0(B),D,C)) ) ) ) ) ) ) ) ) ).
fof(t43_instalg1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E)
& v2_funct_1(E) )
=> ( r3_pua2mss1(A,B,D,E)
=> r3_msualg_3(A,k11_msafree(A,k8_pboole(u1_struct_0(A),u1_struct_0(B),D,C)),k1_instalg1(A,B,k11_msafree(B,C),D,E),k3_instalg1(A,B,C,D,E)) ) ) ) ) ) ) ).
fof(t44_instalg1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> r6_pboole(u1_struct_0(A),k3_instalg1(A,A,B,k6_partfun1(u1_struct_0(A)),k6_partfun1(u1_msualg_1(A))),k2_msualg_3(u1_struct_0(A),u4_msualg_1(A,k11_msafree(A,B)))) ) ) ).
fof(t45_instalg1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& ~ v2_msualg_1(C)
& l1_msualg_1(C) )
=> ! [D] :
( ( v2_relat_1(D)
& m1_pboole(D,u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
=> ! [F] :
( ( v1_relat_1(F)
& v1_funct_1(F) )
=> ( r3_pua2mss1(A,B,E,F)
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(G,u1_struct_0(B),u1_struct_0(C)) )
=> ! [H] :
( ( v1_relat_1(H)
& v1_funct_1(H) )
=> ( r3_pua2mss1(B,C,G,H)
=> k3_instalg1(A,C,D,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),E,G),k5_relat_1(F,H)) = k13_pboole(k3_instalg1(A,B,k8_pboole(u1_struct_0(B),u1_struct_0(C),G,D),E,F),k7_pboole(u1_struct_0(A),u1_struct_0(B),E,k3_instalg1(B,C,D,G,H))) ) ) ) ) ) ) ) ) ) ) ).
fof(s1_instalg1,axiom,
( ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s1_instalg1))
=> ! [B] :
( m1_subset_1(B,k1_funct_1(f3_s1_instalg1,A))
=> r2_hidden(f4_s1_instalg1(B,A),k1_funct_1(u4_msualg_1(f1_s1_instalg1,f2_s1_instalg1),A)) ) )
=> ? [A] :
( m3_pboole(A,u1_struct_0(f1_s1_instalg1),u4_msualg_1(f1_s1_instalg1,k11_msafree(f1_s1_instalg1,f3_s1_instalg1)),u4_msualg_1(f1_s1_instalg1,f2_s1_instalg1))
& r1_msualg_3(f1_s1_instalg1,k11_msafree(f1_s1_instalg1,f3_s1_instalg1),f2_s1_instalg1,A)
& ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s1_instalg1))
=> ! [C] :
( m1_subset_1(C,k1_funct_1(f3_s1_instalg1,B))
=> k1_funct_1(k1_msualg_3(u1_struct_0(f1_s1_instalg1),u4_msualg_1(f1_s1_instalg1,k11_msafree(f1_s1_instalg1,f3_s1_instalg1)),u4_msualg_1(f1_s1_instalg1,f2_s1_instalg1),A,B),k1_trees_4(k4_tarski(C,B))) = f4_s1_instalg1(C,B) ) ) ) ) ).
fof(dt_m1_instalg1,axiom,
! [A] :
( ( v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_instalg1(B,A)
=> l1_msualg_1(B) ) ) ).
fof(existence_m1_instalg1,axiom,
! [A] :
( ( v1_instalg1(A)
& l1_msualg_1(A) )
=> ? [B] : m1_instalg1(B,A) ) ).
fof(dt_k1_instalg1,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A)
& ~ v3_struct_0(B)
& l1_msualg_1(B)
& l3_msualg_1(C,B)
& v1_relat_1(D)
& v1_funct_1(D)
& v1_relat_1(E)
& v1_funct_1(E) )
=> ( v4_msualg_1(k1_instalg1(A,B,C,D,E),A)
& l3_msualg_1(k1_instalg1(A,B,C,D,E),A) ) ) ).
fof(dt_k2_instalg1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A)
& ~ v3_struct_0(B)
& l1_msualg_1(B)
& l3_msualg_1(C,A) )
=> ( v4_msualg_1(k2_instalg1(A,B,C),B)
& l3_msualg_1(k2_instalg1(A,B,C),B) ) ) ).
fof(dt_k3_instalg1,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B)
& v2_relat_1(C)
& m1_pboole(C,u1_struct_0(B))
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(D,u1_struct_0(A),u1_struct_0(B))
& v1_relat_1(E)
& v1_funct_1(E) )
=> m3_pboole(k3_instalg1(A,B,C,D,E),u1_struct_0(A),u4_msualg_1(A,k11_msafree(A,k8_pboole(u1_struct_0(A),u1_struct_0(B),D,C))),u4_msualg_1(A,k1_instalg1(A,B,k11_msafree(B,C),D,E))) ) ).
%------------------------------------------------------------------------------