SET007 Axioms: SET007+566.ax
%------------------------------------------------------------------------------
% File : SET007+566 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The Correspondence Between Lattices of Subalgebras
% Version : [Urb08] axioms.
% English : The Correspondence Between Lattices of Subalgebras of Universal
% Algebras and Many Sorted Algebras},
% 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 : mssublat [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 38 ( 4 unt; 0 def)
% Number of atoms : 401 ( 45 equ)
% Maximal formula atoms : 21 ( 10 avg)
% Number of connectives : 420 ( 57 ~; 0 |; 244 &)
% ( 3 <=>; 116 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 34 ( 33 usr; 0 prp; 1-3 aty)
% Number of functors : 48 ( 48 usr; 7 con; 0-4 aty)
% Number of variables : 92 ( 92 !; 0 ?)
% 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_mssublat,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ( v1_relat_1(u1_unialg_1(A))
& v2_relat_1(u1_unialg_1(A))
& v1_funct_1(u1_unialg_1(A))
& ~ v1_xboole_0(u1_unialg_1(A))
& v1_finseq_1(u1_unialg_1(A))
& v4_unialg_1(u1_unialg_1(A),u1_struct_0(A))
& v5_unialg_1(u1_unialg_1(A),u1_struct_0(A))
& v1_funcop_1(u1_unialg_1(A)) ) ) ).
fof(fc2_mssublat,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(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))
& v2_msualg_2(k7_msualg_1(A)) ) ) ).
fof(fc3_mssublat,axiom,
! [A] :
( ( v7_unialg_1(A)
& l1_unialg_1(A) )
=> ( v3_unialg_1(g1_unialg_1(u1_struct_0(A),u1_unialg_1(A)))
& v7_unialg_1(g1_unialg_1(u1_struct_0(A),u1_unialg_1(A))) ) ) ).
fof(fc4_mssublat,axiom,
! [A] :
( ( v6_unialg_1(A)
& l1_unialg_1(A) )
=> ( v3_unialg_1(g1_unialg_1(u1_struct_0(A),u1_unialg_1(A)))
& v6_unialg_1(g1_unialg_1(u1_struct_0(A),u1_unialg_1(A))) ) ) ).
fof(fc5_mssublat,axiom,
! [A] :
( ( v8_unialg_1(A)
& l1_unialg_1(A) )
=> ( v3_unialg_1(g1_unialg_1(u1_struct_0(A),u1_unialg_1(A)))
& v8_unialg_1(g1_unialg_1(u1_struct_0(A),u1_unialg_1(A))) ) ) ).
fof(fc6_mssublat,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A) )
=> ( ~ v3_struct_0(g1_unialg_1(u1_struct_0(A),u1_unialg_1(A)))
& v3_unialg_1(g1_unialg_1(u1_struct_0(A),u1_unialg_1(A)))
& v6_unialg_1(g1_unialg_1(u1_struct_0(A),u1_unialg_1(A)))
& v7_unialg_1(g1_unialg_1(u1_struct_0(A),u1_unialg_1(A)))
& v8_unialg_1(g1_unialg_1(u1_struct_0(A),u1_unialg_1(A)))
& v2_unialg_2(g1_unialg_1(u1_struct_0(A),u1_unialg_1(A))) ) ) ).
fof(t1_mssublat,axiom,
! [A] : k8_funct_2(k5_numbers,k3_finseq_2(k1_tarski(A)),k9_pboole(A),np__0) = k1_xboole_0 ).
fof(t2_mssublat,axiom,
! [A] : k8_funct_2(k5_numbers,k3_finseq_2(k1_tarski(A)),k9_pboole(A),np__1) = k9_finseq_1(A) ).
fof(t3_mssublat,axiom,
! [A] : k8_funct_2(k5_numbers,k3_finseq_2(k1_tarski(A)),k9_pboole(A),np__2) = k10_finseq_1(A,A) ).
fof(t4_mssublat,axiom,
! [A] : k8_funct_2(k5_numbers,k3_finseq_2(k1_tarski(A)),k9_pboole(A),np__3) = k11_finseq_1(A,A,A) ).
fof(t5_mssublat,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_1(B,k1_tarski(np__0))
=> ( B = k2_finseq_2(A,np__0)
<=> k3_finseq_1(B) = A ) ) ) ).
fof(t6_mssublat,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ( B = k8_funct_2(k5_numbers,k3_finseq_2(k1_tarski(np__0)),k9_pboole(np__0),A)
=> k3_finseq_1(B) = A ) ) ) ).
fof(t7_mssublat,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ( m3_unialg_2(A,B)
=> k7_msualg_1(A) = k7_msualg_1(B) ) ) ) ).
fof(t8_mssublat,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ( m3_unialg_2(A,B)
=> ! [C] :
( m4_pboole(C,u1_struct_0(k7_msualg_1(B)),u4_msualg_1(k7_msualg_1(B),k10_msualg_1(B)))
=> ( C = u4_msualg_1(k7_msualg_1(A),k10_msualg_1(A))
=> ! [D] :
( m1_subset_1(D,u1_msualg_1(k7_msualg_1(B)))
=> ! [E] :
( m1_subset_1(E,u1_msualg_1(k7_msualg_1(A)))
=> ( E = D
=> k5_msualg_1(k7_msualg_1(A),E,k10_msualg_1(A)) = k2_partfun1(k3_msualg_1(k7_msualg_1(B),D,k10_msualg_1(B)),k4_msualg_1(k7_msualg_1(B),D,k10_msualg_1(B)),k5_msualg_1(k7_msualg_1(B),D,k10_msualg_1(B)),k3_msualg_1(k7_msualg_1(A),E,k10_msualg_1(A))) ) ) ) ) ) ) ) ) ).
fof(t9_mssublat,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ( m3_unialg_2(A,B)
=> m4_pboole(u4_msualg_1(k7_msualg_1(A),k10_msualg_1(A)),u1_struct_0(k7_msualg_1(B)),u4_msualg_1(k7_msualg_1(B),k10_msualg_1(B))) ) ) ) ).
fof(t10_mssublat,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ( m3_unialg_2(A,B)
=> ! [C] :
( m4_pboole(C,u1_struct_0(k7_msualg_1(B)),u4_msualg_1(k7_msualg_1(B),k10_msualg_1(B)))
=> ( C = u4_msualg_1(k7_msualg_1(A),k10_msualg_1(A))
=> v3_msualg_2(C,k7_msualg_1(B),k10_msualg_1(B)) ) ) ) ) ) ).
fof(t11_mssublat,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ( m3_unialg_2(A,B)
=> ! [C] :
( m4_pboole(C,u1_struct_0(k7_msualg_1(B)),u4_msualg_1(k7_msualg_1(B),k10_msualg_1(B)))
=> ( C = u4_msualg_1(k7_msualg_1(A),k10_msualg_1(A))
=> u5_msualg_1(k7_msualg_1(A),k10_msualg_1(A)) = k4_msualg_2(k7_msualg_1(B),k10_msualg_1(B),C) ) ) ) ) ) ).
fof(t12_mssublat,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ( m3_unialg_2(A,B)
=> m1_msualg_2(k10_msualg_1(A),k7_msualg_1(B),k10_msualg_1(B)) ) ) ) ).
fof(t13_mssublat,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ( m1_msualg_2(k10_msualg_1(A),k7_msualg_1(B),k10_msualg_1(B))
=> m1_subset_1(u1_struct_0(A),k1_zfmisc_1(u1_struct_0(B))) ) ) ) ).
fof(t14_mssublat,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ( m1_msualg_2(k10_msualg_1(A),k7_msualg_1(B),k10_msualg_1(B))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
=> ( C = u1_struct_0(A)
=> v1_unialg_2(C,B) ) ) ) ) ) ).
fof(t15_mssublat,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ( m1_msualg_2(k10_msualg_1(A),k7_msualg_1(B),k10_msualg_1(B))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
=> ( C = u1_struct_0(A)
=> u1_unialg_1(A) = k3_unialg_2(B,C) ) ) ) ) ) ).
fof(t16_mssublat,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ( m1_msualg_2(k10_msualg_1(A),k7_msualg_1(B),k10_msualg_1(B))
=> m3_unialg_2(A,B) ) ) ) ).
fof(t17_mssublat,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) )
=> ! [C] :
( ( v5_msualg_1(C,A)
& m1_msualg_2(C,A,B) )
=> m1_subset_1(u1_struct_0(k13_msualg_1(A,C)),k1_zfmisc_1(u1_struct_0(k13_msualg_1(A,B)))) ) ) ) ).
fof(t18_mssublat,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) )
=> ! [C] :
( ( v5_msualg_1(C,A)
& m1_msualg_2(C,A,B) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k13_msualg_1(A,B)))) )
=> ( D = u1_struct_0(k13_msualg_1(A,C))
=> v1_unialg_2(D,k13_msualg_1(A,B)) ) ) ) ) ) ).
fof(t19_mssublat,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) )
=> ! [C] :
( ( v5_msualg_1(C,A)
& m1_msualg_2(C,A,B) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k13_msualg_1(A,B)))) )
=> ( D = u1_struct_0(k13_msualg_1(A,C))
=> u1_unialg_1(k13_msualg_1(A,C)) = k3_unialg_2(k13_msualg_1(A,B),D) ) ) ) ) ) ).
fof(t20_mssublat,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) )
=> ! [C] :
( ( v5_msualg_1(C,A)
& m1_msualg_2(C,A,B) )
=> m3_unialg_2(k13_msualg_1(A,C),k13_msualg_1(A,B)) ) ) ) ).
fof(t21_mssublat,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)
=> ( m1_msualg_2(B,A,C)
<=> m1_msualg_2(B,A,g3_msualg_1(A,u4_msualg_1(A,C),u5_msualg_1(A,C))) ) ) ) ) ).
fof(t22_mssublat,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ( k6_msualg_1(A) = k6_msualg_1(B)
<=> k7_msualg_1(A) = k7_msualg_1(B) ) ) ) ).
fof(t23_mssublat,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) )
=> ( u1_struct_0(A) = k1_tarski(np__0)
=> k7_msualg_1(k13_msualg_1(A,B)) = g1_msualg_1(u1_struct_0(A),u1_msualg_1(A),u2_msualg_1(A),u3_msualg_1(A)) ) ) ) ).
fof(t24_mssublat,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) )
=> ! [C] :
( ( v5_msualg_1(C,A)
& l3_msualg_1(C,A) )
=> ( ( u1_struct_0(A) = k1_tarski(np__0)
& k13_msualg_1(A,B) = k13_msualg_1(A,C) )
=> 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)) ) ) ) ) ).
fof(t25_mssublat,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) )
=> ( u1_struct_0(A) = k1_tarski(np__0)
=> u4_msualg_1(A,B) = u4_msualg_1(k7_msualg_1(k13_msualg_1(A,B)),k10_msualg_1(k13_msualg_1(A,B))) ) ) ) ).
fof(t26_mssublat,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) )
=> ( u1_struct_0(A) = k1_tarski(np__0)
=> k10_msualg_1(k13_msualg_1(A,B)) = g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)) ) ) ) ).
fof(t27_mssublat,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( v4_msualg_1(B,k7_msualg_1(A))
& v5_msualg_1(B,k7_msualg_1(A))
& m1_msualg_2(B,k7_msualg_1(A),k10_msualg_1(A)) )
=> ( u1_struct_0(k7_msualg_1(A)) = k1_tarski(np__0)
=> m3_unialg_2(k13_msualg_1(k7_msualg_1(A),B),A) ) ) ) ).
fof(t28_mssublat,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( v3_unialg_1(B)
& v8_unialg_1(B)
& m3_unialg_2(B,A) )
=> ! [C] :
( ( v3_unialg_1(C)
& v8_unialg_1(C)
& m3_unialg_2(C,A) )
=> ! [D] :
( ( v4_msualg_1(D,k7_msualg_1(A))
& v5_msualg_1(D,k7_msualg_1(A))
& m1_msualg_2(D,k7_msualg_1(A),k10_msualg_1(A)) )
=> ! [E] :
( ( v4_msualg_1(E,k7_msualg_1(A))
& v5_msualg_1(E,k7_msualg_1(A))
& m1_msualg_2(E,k7_msualg_1(A),k10_msualg_1(A)) )
=> ( ( D = k10_msualg_1(B)
& E = k10_msualg_1(C) )
=> k2_pboole(u1_struct_0(k7_msualg_1(A)),u4_msualg_1(k7_msualg_1(A),D),u4_msualg_1(k7_msualg_1(A),E)) = k3_cqc_lang(np__0,k2_xboole_0(u1_struct_0(B),u1_struct_0(C))) ) ) ) ) ) ) ).
fof(t29_mssublat,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( v3_unialg_1(B)
& v8_unialg_1(B)
& m3_unialg_2(B,A) )
=> ! [C] :
( ( v3_unialg_1(C)
& v8_unialg_1(C)
& m3_unialg_2(C,A) )
=> ! [D] :
( ( v4_msualg_1(D,k7_msualg_1(A))
& v5_msualg_1(D,k7_msualg_1(A))
& m1_msualg_2(D,k7_msualg_1(A),k10_msualg_1(A)) )
=> ! [E] :
( ( v4_msualg_1(E,k7_msualg_1(A))
& v5_msualg_1(E,k7_msualg_1(A))
& m1_msualg_2(E,k7_msualg_1(A),k10_msualg_1(A)) )
=> ( ( D = k10_msualg_1(B)
& E = k10_msualg_1(C) )
=> k3_pboole(u1_struct_0(k7_msualg_1(A)),u4_msualg_1(k7_msualg_1(A),D),u4_msualg_1(k7_msualg_1(A),E)) = k3_cqc_lang(np__0,k3_xboole_0(u1_struct_0(B),u1_struct_0(C))) ) ) ) ) ) ) ).
fof(t30_mssublat,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) )
=> ! [B] :
( ( v3_unialg_1(B)
& v8_unialg_1(B)
& m3_unialg_2(B,A) )
=> ! [C] :
( ( v3_unialg_1(C)
& v8_unialg_1(C)
& m3_unialg_2(C,A) )
=> ! [D] :
( ( v4_msualg_1(D,k7_msualg_1(A))
& v5_msualg_1(D,k7_msualg_1(A))
& m1_msualg_2(D,k7_msualg_1(A),k10_msualg_1(A)) )
=> ! [E] :
( ( v4_msualg_1(E,k7_msualg_1(A))
& v5_msualg_1(E,k7_msualg_1(A))
& m1_msualg_2(E,k7_msualg_1(A),k10_msualg_1(A)) )
=> ( ( D = k10_msualg_1(B)
& E = k10_msualg_1(C) )
=> k10_msualg_1(k8_unialg_2(A,B,C)) = k13_msualg_2(k7_msualg_1(A),k10_msualg_1(A),D,E) ) ) ) ) ) ) ).
fof(t31_mssublat,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( v3_unialg_1(B)
& v8_unialg_1(B)
& m3_unialg_2(B,A) )
=> ! [C] :
( ( v3_unialg_1(C)
& v8_unialg_1(C)
& m3_unialg_2(C,A) )
=> ! [D] :
( ( v4_msualg_1(D,k7_msualg_1(A))
& v5_msualg_1(D,k7_msualg_1(A))
& m1_msualg_2(D,k7_msualg_1(A),k10_msualg_1(A)) )
=> ! [E] :
( ( v4_msualg_1(E,k7_msualg_1(A))
& v5_msualg_1(E,k7_msualg_1(A))
& m1_msualg_2(E,k7_msualg_1(A),k10_msualg_1(A)) )
=> ( ( D = k10_msualg_1(B)
& E = k10_msualg_1(C) )
=> k10_msualg_1(k5_unialg_2(A,B,C)) = k11_msualg_2(k7_msualg_1(A),k10_msualg_1(A),D,E) ) ) ) ) ) ) ).
fof(t32_mssublat,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A) )
=> r1_filter_1(k12_unialg_2(g1_unialg_1(u1_struct_0(A),u1_unialg_1(A))),k17_msualg_2(k7_msualg_1(g1_unialg_1(u1_struct_0(A),u1_unialg_1(A))),k10_msualg_1(g1_unialg_1(u1_struct_0(A),u1_unialg_1(A))))) ) ).
%------------------------------------------------------------------------------