SET007 Axioms: SET007+393.ax
%------------------------------------------------------------------------------
% File : SET007+393 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Many Sorted Algebras
% 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 : msualg_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 83 ( 13 unt; 0 def)
% Number of atoms : 436 ( 40 equ)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 437 ( 84 ~; 0 |; 242 &)
% ( 5 <=>; 106 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 35 ( 33 usr; 1 prp; 0-4 aty)
% Number of functors : 48 ( 48 usr; 4 con; 0-6 aty)
% Number of variables : 151 ( 139 !; 12 ?)
% 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(rc1_msualg_1,axiom,
? [A] :
( l1_msualg_1(A)
& v1_msualg_1(A) ) ).
fof(rc2_msualg_1,axiom,
? [A] :
( l1_msualg_1(A)
& ~ v3_struct_0(A)
& v1_msualg_1(A)
& v2_msualg_1(A) ) ).
fof(rc3_msualg_1,axiom,
? [A] :
( l1_msualg_1(A)
& ~ v3_struct_0(A)
& v1_msualg_1(A)
& ~ v2_msualg_1(A) ) ).
fof(rc4_msualg_1,axiom,
! [A] :
( l1_struct_0(A)
=> ? [B] :
( l2_msualg_1(B,A)
& v3_msualg_1(B,A) ) ) ).
fof(rc5_msualg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ? [B] :
( l3_msualg_1(B,A)
& v4_msualg_1(B,A) ) ) ).
fof(rc6_msualg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ? [B] :
( l3_msualg_1(B,A)
& v4_msualg_1(B,A)
& v5_msualg_1(B,A) ) ) ).
fof(rc7_msualg_1,axiom,
! [A] :
( l1_struct_0(A)
=> ? [B] :
( l2_msualg_1(B,A)
& v3_msualg_1(B,A)
& v5_msualg_1(B,A) ) ) ).
fof(fc1_msualg_1,axiom,
! [A,B] :
( ( l1_struct_0(A)
& v5_msualg_1(B,A)
& l2_msualg_1(B,A) )
=> ( v1_relat_1(u4_msualg_1(A,B))
& v2_relat_1(u4_msualg_1(A,B))
& v1_funct_1(u4_msualg_1(A,B)) ) ) ).
fof(cc1_msualg_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A)
& v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k2_relat_1(u4_msualg_1(A,B)))
=> ~ v1_xboole_0(C) ) ) ).
fof(cc2_msualg_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A)
& v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k2_relat_1(k6_pboole(u1_struct_0(A),u4_msualg_1(A,B))))
=> ~ v1_xboole_0(C) ) ) ).
fof(rc8_msualg_1,axiom,
? [A] :
( l1_msualg_1(A)
& ~ v3_struct_0(A)
& v3_realset2(A)
& v1_msualg_1(A)
& ~ v2_msualg_1(A)
& v6_msualg_1(A) ) ).
fof(fc2_msualg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ( ~ v3_struct_0(k7_msualg_1(A))
& v3_realset2(k7_msualg_1(A))
& v1_msualg_1(k7_msualg_1(A))
& ~ v2_msualg_1(k7_msualg_1(A))
& v6_msualg_1(k7_msualg_1(A)) ) ) ).
fof(fc3_msualg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ( v4_msualg_1(k10_msualg_1(A),k7_msualg_1(A))
& v5_msualg_1(k10_msualg_1(A),k7_msualg_1(A)) ) ) ).
fof(fc4_msualg_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_realset2(A)
& l1_msualg_1(A)
& v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ~ v1_xboole_0(k11_msualg_1(A,B)) ) ).
fof(d1_msualg_1,axiom,
$true ).
fof(d2_msualg_1,axiom,
$true ).
fof(d3_msualg_1,axiom,
$true ).
fof(d4_msualg_1,axiom,
$true ).
fof(d5_msualg_1,axiom,
! [A] :
( l1_msualg_1(A)
=> ( v2_msualg_1(A)
<=> u1_msualg_1(A) = k1_xboole_0 ) ) ).
fof(d6_msualg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> k1_msualg_1(A,B) = k1_funct_1(u2_msualg_1(A),B) ) ) ).
fof(d7_msualg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> k2_msualg_1(A,B) = k1_funct_1(u3_msualg_1(A),B) ) ) ).
fof(d8_msualg_1,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l2_msualg_1(B,A)
=> ( v5_msualg_1(B,A)
<=> v2_relat_1(u4_msualg_1(A,B)) ) ) ) ).
fof(d9_msualg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( l3_msualg_1(C,A)
=> k3_msualg_1(A,B,C) = k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),u4_msualg_1(A,C))),B) ) ) ) ).
fof(d10_msualg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( l3_msualg_1(C,A)
=> k4_msualg_1(A,B,C) = k1_funct_1(k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,C)),B) ) ) ) ).
fof(d11_msualg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( l3_msualg_1(C,A)
=> k5_msualg_1(A,B,C) = k1_funct_1(u5_msualg_1(A,C),B) ) ) ) ).
fof(t1_msualg_1,axiom,
$true ).
fof(t2_msualg_1,axiom,
$true ).
fof(t3_msualg_1,axiom,
$true ).
fof(t4_msualg_1,axiom,
$true ).
fof(t5_msualg_1,axiom,
$true ).
fof(t6_msualg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( ( v5_msualg_1(C,A)
& l3_msualg_1(C,A) )
=> ~ v1_xboole_0(k5_msualg_1(A,B,C)) ) ) ) ).
fof(t7_msualg_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,B,C)
& m2_relset_1(E,B,C) )
=> ( v1_funct_1(k1_partfun1(A,B,B,C,D,E))
& v1_funct_2(k1_partfun1(A,B,B,C,D,E),k1_relat_1(D),C)
& m2_relset_1(k1_partfun1(A,B,B,C,D,E),k1_relat_1(D),C) ) ) ) ) ) ).
fof(t8_msualg_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& ~ v1_xboole_0(B)
& v1_unialg_1(B,A)
& v2_unialg_1(B,A)
& m2_relset_1(B,k3_finseq_2(A),A) )
=> k1_relat_1(B) = k1_funct_2(k2_finseq_1(k2_unialg_1(A,B)),A) ) ) ).
fof(t9_msualg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ~ v1_xboole_0(k3_unialg_1(A)) ) ).
fof(d12_msualg_1,axiom,
! [A] :
( l1_msualg_1(A)
=> ( v6_msualg_1(A)
<=> ? [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
& u1_msualg_1(A) = k2_finseq_1(B) ) ) ) ).
fof(t10_msualg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ( v3_realset2(A)
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m1_subset_1(C,k2_relat_1(u4_msualg_1(A,B)))
=> ! [D] :
( m1_subset_1(D,k2_relat_1(u4_msualg_1(A,B)))
=> C = D ) ) ) ) ) ).
fof(d13_msualg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( v3_realset2(B)
& v1_msualg_1(B)
& ~ v2_msualg_1(B)
& v6_msualg_1(B)
& l1_msualg_1(B) )
=> ( B = k7_msualg_1(A)
<=> ( u1_struct_0(B) = k1_tarski(np__0)
& u1_msualg_1(B) = k4_finseq_1(k6_msualg_1(A))
& u2_msualg_1(B) = k1_partfun1(k5_numbers,k5_numbers,k5_numbers,k3_finseq_2(k1_tarski(np__0)),k6_msualg_1(A),k9_pboole(np__0))
& u3_msualg_1(B) = k10_pboole(k4_finseq_1(k6_msualg_1(A)),np__0) ) ) ) ) ).
fof(d14_msualg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> k8_msualg_1(A) = k10_pboole(k1_tarski(np__0),u1_struct_0(A)) ) ).
fof(d15_msualg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> k9_msualg_1(A) = u1_unialg_1(A) ) ).
fof(d16_msualg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> k10_msualg_1(A) = g3_msualg_1(k7_msualg_1(A),k8_msualg_1(A),k9_msualg_1(A)) ) ).
fof(d17_msualg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_realset2(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( C = k11_msualg_1(A,B)
<=> m1_subset_1(C,k2_relat_1(u4_msualg_1(A,B))) ) ) ) ).
fof(t11_msualg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_realset2(A)
& ~ v2_msualg_1(A)
& v6_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( ( v5_msualg_1(C,A)
& l3_msualg_1(C,A) )
=> k3_msualg_1(A,B,C) = k4_finseq_2(k3_finseq_1(k1_msualg_1(A,B)),k11_msualg_1(A,C)) ) ) ) ).
fof(t12_msualg_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> r1_tarski(k4_finseq_2(B,A),k3_finseq_2(A)) ) ) ).
fof(t13_msualg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_realset2(A)
& ~ v2_msualg_1(A)
& v6_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( ( v5_msualg_1(C,A)
& l3_msualg_1(C,A) )
=> r1_tarski(k3_msualg_1(A,B,C),k3_finseq_2(k11_msualg_1(A,C))) ) ) ) ).
fof(t14_msualg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_realset2(A)
& ~ v2_msualg_1(A)
& v6_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> m2_finseq_1(u5_msualg_1(A,B),k4_partfun1(k3_finseq_2(k11_msualg_1(A,B)),k11_msualg_1(A,B))) ) ) ).
fof(d18_msualg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_realset2(A)
& ~ v2_msualg_1(A)
& v6_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> k12_msualg_1(A,B) = u5_msualg_1(A,B) ) ) ).
fof(d19_msualg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_realset2(A)
& ~ v2_msualg_1(A)
& v6_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> k13_msualg_1(A,B) = g1_unialg_1(k11_msualg_1(A,B),k12_msualg_1(A,B)) ) ) ).
fof(t15_msualg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_unialg_1(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> A = k13_msualg_1(k7_msualg_1(A),k10_msualg_1(A)) ) ).
fof(t16_msualg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k4_finseq_1(k6_msualg_1(A)),k3_finseq_2(k1_tarski(np__0)))
& m2_relset_1(B,k4_finseq_1(k6_msualg_1(A)),k3_finseq_2(k1_tarski(np__0))) )
=> ( B = k1_partfun1(k5_numbers,k5_numbers,k5_numbers,k3_finseq_2(k1_tarski(np__0)),k6_msualg_1(A),k9_pboole(np__0))
=> k7_msualg_1(A) = g1_msualg_1(k1_tarski(np__0),k4_finseq_1(k6_msualg_1(A)),B,k10_pboole(k4_finseq_1(k6_msualg_1(A)),np__0)) ) ) ) ).
fof(dt_l1_msualg_1,axiom,
! [A] :
( l1_msualg_1(A)
=> l1_struct_0(A) ) ).
fof(existence_l1_msualg_1,axiom,
? [A] : l1_msualg_1(A) ).
fof(dt_l2_msualg_1,axiom,
$true ).
fof(existence_l2_msualg_1,axiom,
! [A] :
( l1_struct_0(A)
=> ? [B] : l2_msualg_1(B,A) ) ).
fof(dt_l3_msualg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> l2_msualg_1(B,A) ) ) ).
fof(existence_l3_msualg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ? [B] : l3_msualg_1(B,A) ) ).
fof(abstractness_v1_msualg_1,axiom,
! [A] :
( l1_msualg_1(A)
=> ( v1_msualg_1(A)
=> A = g1_msualg_1(u1_struct_0(A),u1_msualg_1(A),u2_msualg_1(A),u3_msualg_1(A)) ) ) ).
fof(abstractness_v3_msualg_1,axiom,
! [A,B] :
( ( l1_struct_0(A)
& l2_msualg_1(B,A) )
=> ( v3_msualg_1(B,A)
=> B = g2_msualg_1(A,u4_msualg_1(A,B)) ) ) ).
fof(abstractness_v4_msualg_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A)
& l3_msualg_1(B,A) )
=> ( v4_msualg_1(B,A)
=> B = g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)) ) ) ).
fof(dt_k1_msualg_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& m1_subset_1(B,u1_msualg_1(A)) )
=> m2_finseq_2(k1_msualg_1(A,B),u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) ) ).
fof(dt_k2_msualg_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& m1_subset_1(B,u1_msualg_1(A)) )
=> m1_subset_1(k2_msualg_1(A,B),u1_struct_0(A)) ) ).
fof(dt_k3_msualg_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& m1_subset_1(B,u1_msualg_1(A))
& l3_msualg_1(C,A) )
=> m1_subset_1(k3_msualg_1(A,B,C),k2_relat_1(k6_pboole(u1_struct_0(A),u4_msualg_1(A,C)))) ) ).
fof(dt_k4_msualg_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& m1_subset_1(B,u1_msualg_1(A))
& l3_msualg_1(C,A) )
=> m1_subset_1(k4_msualg_1(A,B,C),k2_relat_1(u4_msualg_1(A,C))) ) ).
fof(dt_k5_msualg_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& m1_subset_1(B,u1_msualg_1(A))
& l3_msualg_1(C,A) )
=> ( v1_funct_1(k5_msualg_1(A,B,C))
& v1_funct_2(k5_msualg_1(A,B,C),k3_msualg_1(A,B,C),k4_msualg_1(A,B,C))
& m2_relset_1(k5_msualg_1(A,B,C),k3_msualg_1(A,B,C),k4_msualg_1(A,B,C)) ) ) ).
fof(dt_k6_msualg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> m2_finseq_1(k6_msualg_1(A),k5_numbers) ) ).
fof(redefinition_k6_msualg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> k6_msualg_1(A) = k3_unialg_1(A) ) ).
fof(dt_k7_msualg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ( v3_realset2(k7_msualg_1(A))
& v1_msualg_1(k7_msualg_1(A))
& ~ v2_msualg_1(k7_msualg_1(A))
& v6_msualg_1(k7_msualg_1(A))
& l1_msualg_1(k7_msualg_1(A)) ) ) ).
fof(dt_k8_msualg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ( v2_relat_1(k8_msualg_1(A))
& m1_pboole(k8_msualg_1(A),u1_struct_0(k7_msualg_1(A))) ) ) ).
fof(dt_k9_msualg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> m3_pboole(k9_msualg_1(A),u1_msualg_1(k7_msualg_1(A)),k8_pboole(u1_msualg_1(k7_msualg_1(A)),k3_finseq_2(u1_struct_0(k7_msualg_1(A))),u2_msualg_1(k7_msualg_1(A)),k6_pboole(u1_struct_0(k7_msualg_1(A)),k8_msualg_1(A))),k8_pboole(u1_msualg_1(k7_msualg_1(A)),u1_struct_0(k7_msualg_1(A)),u3_msualg_1(k7_msualg_1(A)),k8_msualg_1(A))) ) ).
fof(dt_k10_msualg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ( v4_msualg_1(k10_msualg_1(A),k7_msualg_1(A))
& l3_msualg_1(k10_msualg_1(A),k7_msualg_1(A)) ) ) ).
fof(dt_k11_msualg_1,axiom,
$true ).
fof(dt_k12_msualg_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_realset2(A)
& ~ v2_msualg_1(A)
& v6_msualg_1(A)
& l1_msualg_1(A)
& v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> m2_finseq_1(k12_msualg_1(A,B),k4_partfun1(k13_finseq_1(k11_msualg_1(A,B)),k11_msualg_1(A,B))) ) ).
fof(dt_k13_msualg_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_realset2(A)
& ~ v2_msualg_1(A)
& v6_msualg_1(A)
& l1_msualg_1(A)
& v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ( ~ v3_struct_0(k13_msualg_1(A,B))
& v3_unialg_1(k13_msualg_1(A,B))
& v6_unialg_1(k13_msualg_1(A,B))
& v7_unialg_1(k13_msualg_1(A,B))
& v8_unialg_1(k13_msualg_1(A,B))
& l1_unialg_1(k13_msualg_1(A,B)) ) ) ).
fof(dt_u1_msualg_1,axiom,
$true ).
fof(dt_u2_msualg_1,axiom,
! [A] :
( l1_msualg_1(A)
=> ( v1_funct_1(u2_msualg_1(A))
& v1_funct_2(u2_msualg_1(A),u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)))
& m2_relset_1(u2_msualg_1(A),u1_msualg_1(A),k3_finseq_2(u1_struct_0(A))) ) ) ).
fof(dt_u3_msualg_1,axiom,
! [A] :
( l1_msualg_1(A)
=> ( v1_funct_1(u3_msualg_1(A))
& v1_funct_2(u3_msualg_1(A),u1_msualg_1(A),u1_struct_0(A))
& m2_relset_1(u3_msualg_1(A),u1_msualg_1(A),u1_struct_0(A)) ) ) ).
fof(dt_u4_msualg_1,axiom,
! [A,B] :
( ( l1_struct_0(A)
& l2_msualg_1(B,A) )
=> m1_pboole(u4_msualg_1(A,B),u1_struct_0(A)) ) ).
fof(dt_u5_msualg_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A)
& l3_msualg_1(B,A) )
=> m3_pboole(u5_msualg_1(A,B),u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),u4_msualg_1(A,B))),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,B))) ) ).
fof(dt_g1_msualg_1,axiom,
! [A,B,C,D] :
( ( v1_funct_1(C)
& v1_funct_2(C,B,k3_finseq_2(A))
& m1_relset_1(C,B,k3_finseq_2(A))
& v1_funct_1(D)
& v1_funct_2(D,B,A)
& m1_relset_1(D,B,A) )
=> ( v1_msualg_1(g1_msualg_1(A,B,C,D))
& l1_msualg_1(g1_msualg_1(A,B,C,D)) ) ) ).
fof(free_g1_msualg_1,axiom,
! [A,B,C,D] :
( ( v1_funct_1(C)
& v1_funct_2(C,B,k3_finseq_2(A))
& m1_relset_1(C,B,k3_finseq_2(A))
& v1_funct_1(D)
& v1_funct_2(D,B,A)
& m1_relset_1(D,B,A) )
=> ! [E,F,G,H] :
( g1_msualg_1(A,B,C,D) = g1_msualg_1(E,F,G,H)
=> ( A = E
& B = F
& C = G
& D = H ) ) ) ).
fof(dt_g2_msualg_1,axiom,
! [A,B] :
( ( l1_struct_0(A)
& m1_pboole(B,u1_struct_0(A)) )
=> ( v3_msualg_1(g2_msualg_1(A,B),A)
& l2_msualg_1(g2_msualg_1(A,B),A) ) ) ).
fof(free_g2_msualg_1,axiom,
! [A,B] :
( ( l1_struct_0(A)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C,D] :
( g2_msualg_1(A,B) = g2_msualg_1(C,D)
=> ( A = C
& B = D ) ) ) ).
fof(dt_g3_msualg_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A)
& m1_pboole(B,u1_struct_0(A))
& m3_pboole(C,u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),B)),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),B)) )
=> ( v4_msualg_1(g3_msualg_1(A,B,C),A)
& l3_msualg_1(g3_msualg_1(A,B,C),A) ) ) ).
fof(free_g3_msualg_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A)
& m1_pboole(B,u1_struct_0(A))
& m3_pboole(C,u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),B)),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),B)) )
=> ! [D,E,F] :
( g3_msualg_1(A,B,C) = g3_msualg_1(D,E,F)
=> ( A = D
& B = E
& C = F ) ) ) ).
%------------------------------------------------------------------------------