SET007 Axioms: SET007+456.ax
%------------------------------------------------------------------------------
% File : SET007+456 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Translations, Endomorphisms, and Stable Equational Theories
% 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_6 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 101 ( 0 unt; 0 def)
% Number of atoms : 1188 ( 73 equ)
% Maximal formula atoms : 44 ( 11 avg)
% Number of connectives : 1291 ( 204 ~; 0 |; 562 &)
% ( 30 <=>; 495 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 13 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 48 ( 47 usr; 0 prp; 1-5 aty)
% Number of functors : 56 ( 56 usr; 14 con; 0-6 aty)
% Number of variables : 519 ( 487 !; 32 ?)
% 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_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ( v5_msualg_1(B,A)
=> v1_msualg_6(B,A) ) ) ) ).
fof(rc1_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ? [B] :
( l3_msualg_1(B,A)
& v5_msualg_1(B,A)
& v1_msualg_6(B,A) ) ) ).
fof(cc2_msualg_6,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) )
=> ! [C] :
( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
=> ( ( v3_msualg_4(C,A,B)
& v3_msualg_6(C,A,B) )
=> ( v1_msualg_4(C)
& v2_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B))
& v3_msualg_4(C,A,B)
& v2_msualg_6(C,A,B) ) ) ) ) ).
fof(cc3_msualg_6,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) )
=> ! [C] :
( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
=> ( ( v3_msualg_4(C,A,B)
& v2_msualg_6(C,A,B) )
=> ( v1_msualg_4(C)
& v2_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B))
& v3_msualg_4(C,A,B)
& v3_msualg_6(C,A,B) ) ) ) ) ).
fof(fc1_msualg_6,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( ~ v1_xboole_0(k6_relat_1(A))
& v1_relat_1(k6_relat_1(A))
& v1_funct_1(k6_relat_1(A))
& v1_relat_2(k6_relat_1(A))
& v3_relat_2(k6_relat_1(A))
& v4_relat_2(k6_relat_1(A))
& v8_relat_2(k6_relat_1(A)) ) ) ).
fof(cc4_msualg_6,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) )
=> ! [C] :
( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
=> ( v3_msualg_4(C,A,B)
=> ( v2_relat_1(C)
& ~ v3_relat_1(C)
& v1_msualg_4(C) ) ) ) ) ).
fof(rc2_msualg_6,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) )
=> ? [C] :
( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
& v1_relat_1(C)
& v2_relat_1(C)
& ~ v3_relat_1(C)
& v1_funct_1(C)
& v1_msualg_4(C)
& v2_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B))
& v3_msualg_4(C,A,B)
& v2_msualg_6(C,A,B)
& v3_msualg_6(C,A,B)
& v4_msualg_6(C,A,B) ) ) ).
fof(fc2_msualg_6,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v5_msualg_1(B,A)
& l3_msualg_1(B,A)
& v2_relat_1(C)
& m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ( v1_relat_1(k6_msualg_6(A,B,C))
& v2_relat_1(k6_msualg_6(A,B,C))
& ~ v3_relat_1(k6_msualg_6(A,B,C))
& v1_funct_1(k6_msualg_6(A,B,C))
& v1_msualg_4(k6_msualg_6(A,B,C))
& v3_msualg_6(k6_msualg_6(A,B,C),A,B) ) ) ).
fof(fc3_msualg_6,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v5_msualg_1(B,A)
& l3_msualg_1(B,A)
& v2_relat_1(C)
& m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ( v1_relat_1(k7_msualg_6(A,B,C))
& v2_relat_1(k7_msualg_6(A,B,C))
& ~ v3_relat_1(k7_msualg_6(A,B,C))
& v1_funct_1(k7_msualg_6(A,B,C))
& v1_msualg_4(k7_msualg_6(A,B,C))
& v4_msualg_6(k7_msualg_6(A,B,C),A,B) ) ) ).
fof(fc4_msualg_6,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v5_msualg_1(B,A)
& l3_msualg_1(B,A)
& v2_relat_1(C)
& m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ( v1_relat_1(k8_msualg_6(A,B,C))
& v2_relat_1(k8_msualg_6(A,B,C))
& ~ v3_relat_1(k8_msualg_6(A,B,C))
& v1_funct_1(k8_msualg_6(A,B,C))
& v1_msualg_4(k8_msualg_6(A,B,C))
& v3_msualg_6(k8_msualg_6(A,B,C),A,B)
& v4_msualg_6(k8_msualg_6(A,B,C),A,B) ) ) ).
fof(fc5_msualg_6,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v5_msualg_1(B,A)
& l3_msualg_1(B,A)
& v4_msualg_6(C,A,B)
& m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ( v1_relat_1(k9_msualg_6(A,B,C))
& v2_relat_1(k9_msualg_6(A,B,C))
& ~ v3_relat_1(k9_msualg_6(A,B,C))
& v1_funct_1(k9_msualg_6(A,B,C))
& v1_msualg_4(k9_msualg_6(A,B,C))
& v2_msualg_4(k9_msualg_6(A,B,C),u1_struct_0(A),u4_msualg_1(A,B))
& v3_msualg_4(k9_msualg_6(A,B,C),A,B)
& v4_msualg_6(k9_msualg_6(A,B,C),A,B) ) ) ).
fof(fc6_msualg_6,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v5_msualg_1(B,A)
& l3_msualg_1(B,A)
& v3_msualg_6(C,A,B)
& m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ( v1_relat_1(k9_msualg_6(A,B,C))
& v2_relat_1(k9_msualg_6(A,B,C))
& ~ v3_relat_1(k9_msualg_6(A,B,C))
& v1_funct_1(k9_msualg_6(A,B,C))
& v1_msualg_4(k9_msualg_6(A,B,C))
& v2_msualg_4(k9_msualg_6(A,B,C),u1_struct_0(A),u4_msualg_1(A,B))
& v3_msualg_4(k9_msualg_6(A,B,C),A,B)
& v2_msualg_6(k9_msualg_6(A,B,C),A,B)
& v3_msualg_6(k9_msualg_6(A,B,C),A,B) ) ) ).
fof(t1_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ! [D] :
( r2_hidden(D,k3_msualg_1(A,C,B))
=> ( v1_relat_1(D)
& v1_funct_1(D) ) ) ) ) ) ).
fof(t2_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( r2_hidden(D,k3_msualg_1(A,C,B))
=> ( k1_relat_1(D) = k4_finseq_1(k1_msualg_1(A,C))
& ! [E] :
( r2_hidden(E,k4_finseq_1(k1_msualg_1(A,C)))
=> r2_hidden(k1_funct_1(D,E),k1_funct_1(u4_msualg_1(A,B),k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,C),E))) ) ) ) ) ) ) ) ).
fof(d1_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ( v1_msualg_6(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ~ ( k3_msualg_1(A,C,B) != k1_xboole_0
& k4_msualg_1(A,C,B) = k1_xboole_0 ) ) ) ) ) ).
fof(t3_msualg_6,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_xboole_0
<=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(D,k4_finseq_1(k1_msualg_1(A,B)))
& k1_funct_1(u4_msualg_1(A,C),k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,B),D)) = k1_xboole_0 ) ) ) ) ) ) ).
fof(d2_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m3_pboole(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
=> ( m1_msualg_6(C,A,B)
<=> r1_msualg_3(A,B,B,C) ) ) ) ) ).
fof(t4_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> m1_msualg_6(k2_msualg_3(u1_struct_0(A),u4_msualg_1(A,B)),A,B) ) ) ).
fof(t5_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m3_pboole(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
=> ! [D] :
( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
=> ! [E] :
( m1_subset_1(E,u1_msualg_1(A))
=> ! [F] :
( m1_subset_1(F,k3_msualg_1(A,E,B))
=> ( r2_hidden(F,k3_msualg_1(A,E,B))
=> k5_msualg_3(A,B,B,E,D,k5_msualg_3(A,B,B,E,C,F)) = k5_msualg_3(A,B,B,E,k1_msualg_6(u1_struct_0(A),u4_msualg_1(A,B),C,D),F) ) ) ) ) ) ) ) ).
fof(t6_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m1_msualg_6(C,A,B)
=> ! [D] :
( m1_msualg_6(D,A,B)
=> m1_msualg_6(k1_msualg_6(u1_struct_0(A),u4_msualg_1(A,B),C,D),A,B) ) ) ) ) ).
fof(d3_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ( B = k3_msualg_6(A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(k4_tarski(C,D),B)
<=> ? [E] :
( m1_subset_1(E,u1_msualg_1(A))
& k2_msualg_1(A,E) = D
& ? [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
& r2_hidden(F,k4_finseq_1(k1_msualg_1(A,E)))
& k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,E),F) = C ) ) ) ) ) ) ) ) ).
fof(t7_msualg_6,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)
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( r2_hidden(D,k3_msualg_1(A,B,C))
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,C),k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,B),E)))
=> r2_hidden(k2_funct_7(D,E,F),k3_msualg_1(A,B,C)) ) ) ) ) ) ) ) ).
fof(t8_msualg_6,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] :
( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
=> ! [E] :
( m1_subset_1(E,u1_msualg_1(A))
=> ~ ( k3_msualg_1(A,E,B) != k1_xboole_0
& k3_msualg_1(A,E,C) != k1_xboole_0
& ? [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
& r2_hidden(F,k4_finseq_1(k1_msualg_1(A,E)))
& ~ ! [G] :
( m1_subset_1(G,k1_funct_1(u4_msualg_1(A,B),k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,E),F)))
=> r2_hidden(k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,E),F)),G),k1_funct_1(u4_msualg_1(A,C),k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,E),F))) ) ) ) ) ) ) ) ) ).
fof(t9_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r2_hidden(C,k4_finseq_1(k1_msualg_1(A,B)))
=> ! [D] :
( l3_msualg_1(D,A)
=> ! [E] :
( l3_msualg_1(E,A)
=> ! [F] :
( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,D),u4_msualg_1(A,E))
=> ! [G] :
( m1_subset_1(G,k3_msualg_1(A,B,D))
=> ! [H] :
( m1_subset_1(H,k3_msualg_1(A,B,D))
=> ( ( r2_hidden(G,k3_msualg_1(A,B,D))
& r2_hidden(k5_msualg_3(A,D,E,B,F,G),k3_msualg_1(A,B,E)) )
=> ! [I] :
( ( v1_relat_1(I)
& v1_funct_1(I) )
=> ! [J] :
( ( v1_relat_1(J)
& v1_funct_1(J) )
=> ! [K] :
( ( v1_relat_1(K)
& v1_funct_1(K) )
=> ( ( I = G
& J = k5_msualg_3(A,D,E,B,F,G)
& K = k5_msualg_3(A,D,E,B,F,H) )
=> ! [L] :
( m1_subset_1(L,k1_funct_1(u4_msualg_1(A,D),k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,B),C)))
=> ( H = k2_funct_7(I,C,L)
=> ( k1_funct_1(K,C) = k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,D),u4_msualg_1(A,E),F,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,B),C)),L)
& k5_msualg_3(A,D,E,B,F,H) = k2_funct_7(J,C,k1_funct_1(K,C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d4_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( l3_msualg_1(D,A)
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ! [F] :
( ( v1_relat_1(F)
& v1_funct_1(F) )
=> ( F = k4_msualg_6(A,B,C,D,E)
<=> ( k1_relat_1(F) = k1_funct_1(u4_msualg_1(A,D),k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,B),C))
& ! [G] :
( r2_hidden(G,k1_funct_1(u4_msualg_1(A,D),k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,B),C)))
=> k1_funct_1(F,G) = k1_funct_1(k5_msualg_1(A,B,D),k2_funct_7(E,C,G)) ) ) ) ) ) ) ) ) ) ).
fof(t10_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r2_hidden(C,k4_finseq_1(k1_msualg_1(A,B)))
=> ! [D] :
( ( v1_msualg_6(D,A)
& l3_msualg_1(D,A) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( r2_hidden(E,k3_msualg_1(A,B,D))
=> ( v1_funct_1(k4_msualg_6(A,B,C,D,E))
& v1_funct_2(k4_msualg_6(A,B,C,D,E),k1_funct_1(u4_msualg_1(A,D),k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,B),C)),k1_funct_1(u4_msualg_1(A,D),k2_msualg_1(A,B)))
& m2_relset_1(k4_msualg_6(A,B,C,D,E),k1_funct_1(u4_msualg_1(A,D),k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,B),C)),k1_funct_1(u4_msualg_1(A,D),k2_msualg_1(A,B))) ) ) ) ) ) ) ) ) ).
fof(d5_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( l3_msualg_1(D,A)
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( r1_msualg_6(A,B,C,D,E)
<=> ? [F] :
( m1_subset_1(F,u1_msualg_1(A))
& k2_msualg_1(A,F) = C
& ? [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
& r2_hidden(G,k4_finseq_1(k1_msualg_1(A,F)))
& k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,F),G) = B
& ? [H] :
( v1_relat_1(H)
& v1_funct_1(H)
& r2_hidden(H,k3_msualg_1(A,F,D))
& E = k4_msualg_6(A,F,G,D,H) ) ) ) ) ) ) ) ) ) ).
fof(t11_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_msualg_6(D,A)
& l3_msualg_1(D,A) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( r1_msualg_6(A,B,C,D,E)
=> ( v1_funct_1(E)
& v1_funct_2(E,k1_funct_1(u4_msualg_1(A,D),B),k1_funct_1(u4_msualg_1(A,D),C))
& m2_relset_1(E,k1_funct_1(u4_msualg_1(A,D),B),k1_funct_1(u4_msualg_1(A,D),C))
& k1_funct_1(u4_msualg_1(A,D),B) != k1_xboole_0
& k1_funct_1(u4_msualg_1(A,D),C) != k1_xboole_0 ) ) ) ) ) ) ) ).
fof(t12_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( l3_msualg_1(D,A)
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( r1_msualg_6(A,B,C,D,E)
=> r2_hidden(k4_tarski(B,C),k3_msualg_6(A)) ) ) ) ) ) ) ).
fof(t13_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v5_msualg_1(D,A)
& l3_msualg_1(D,A) )
=> ~ ( r2_hidden(k4_tarski(B,C),k3_msualg_6(A))
& ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ~ r1_msualg_6(A,B,C,D,E) ) ) ) ) ) ) ).
fof(t14_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v1_msualg_6(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_rewrite1(k3_msualg_6(A),C,D)
=> ! [E] :
( m1_rewrite1(E,k3_msualg_6(A))
=> ! [F] :
( ( v1_relat_1(F)
& v1_funct_1(F)
& v1_finseq_1(F)
& v1_funcop_1(F) )
=> ( ( k3_finseq_1(E) = k1_nat_1(k3_finseq_1(F),np__1)
& C = k1_funct_1(E,np__1)
& D = k1_funct_1(E,k3_finseq_1(E))
& ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ! [H] :
( ( v1_relat_1(H)
& v1_funct_1(H) )
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ( ( r2_hidden(G,k4_finseq_1(F))
& H = k1_funct_1(F,G)
& I = k1_funct_1(E,G)
& J = k1_funct_1(E,k1_nat_1(G,np__1)) )
=> r1_msualg_6(A,I,J,B,H) ) ) ) ) ) )
=> ( v1_funct_1(k4_funct_7(k1_funct_1(u4_msualg_1(A,B),C),F))
& v1_funct_2(k4_funct_7(k1_funct_1(u4_msualg_1(A,B),C),F),k1_funct_1(u4_msualg_1(A,B),C),k1_funct_1(u4_msualg_1(A,B),D))
& m2_relset_1(k4_funct_7(k1_funct_1(u4_msualg_1(A,B),C),F),k1_funct_1(u4_msualg_1(A,B),C),k1_funct_1(u4_msualg_1(A,B),D))
& ( F != k1_xboole_0
=> ( k1_funct_1(u4_msualg_1(A,B),C) != k1_xboole_0
& k1_funct_1(u4_msualg_1(A,B),D) != k1_xboole_0 ) ) ) ) ) ) ) ) ) ) ) ).
fof(d6_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_rewrite1(k3_msualg_6(A),C,D)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k1_funct_1(u4_msualg_1(A,B),C),k1_funct_1(u4_msualg_1(A,B),D))
& m2_relset_1(E,k1_funct_1(u4_msualg_1(A,B),C),k1_funct_1(u4_msualg_1(A,B),D)) )
=> ( m2_msualg_6(E,A,B,C,D)
<=> ? [F] :
( m1_rewrite1(F,k3_msualg_6(A))
& ? [G] :
( v1_relat_1(G)
& v1_funct_1(G)
& v1_finseq_1(G)
& v1_funcop_1(G)
& E = k4_funct_7(k1_funct_1(u4_msualg_1(A,B),C),G)
& k3_finseq_1(F) = k1_nat_1(k3_finseq_1(G),np__1)
& C = k1_funct_1(F,np__1)
& D = k1_funct_1(F,k3_finseq_1(F))
& ! [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
=> ! [I] :
( ( v1_relat_1(I)
& v1_funct_1(I) )
=> ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ! [K] :
( m1_subset_1(K,u1_struct_0(A))
=> ( ( r2_hidden(H,k4_finseq_1(G))
& I = k1_funct_1(G,H)
& J = k1_funct_1(F,H)
& K = k1_funct_1(F,k1_nat_1(H,np__1)) )
=> r1_msualg_6(A,J,K,B,I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t15_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_rewrite1(k3_msualg_6(A),C,D)
=> ! [E] :
( m1_rewrite1(E,k3_msualg_6(A))
=> ! [F] :
( ( v1_relat_1(F)
& v1_funct_1(F)
& v1_finseq_1(F)
& v1_funcop_1(F) )
=> ( ( k3_finseq_1(E) = k1_nat_1(k3_finseq_1(F),np__1)
& C = k1_funct_1(E,np__1)
& D = k1_funct_1(E,k3_finseq_1(E))
& ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ! [H] :
( ( v1_relat_1(H)
& v1_funct_1(H) )
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ( ( r2_hidden(G,k4_finseq_1(F))
& H = k1_funct_1(F,G)
& I = k1_funct_1(E,G)
& J = k1_funct_1(E,k1_nat_1(G,np__1)) )
=> r1_msualg_6(A,I,J,B,H) ) ) ) ) ) )
=> m2_msualg_6(k4_funct_7(k1_funct_1(u4_msualg_1(A,B),C),F),A,B,C,D) ) ) ) ) ) ) ) ) ).
fof(t16_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> m2_msualg_6(k6_partfun1(k1_funct_1(u4_msualg_1(A,B),C)),A,B,C,C) ) ) ) ).
fof(t17_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( r1_msualg_6(A,C,D,B,E)
=> ( r1_rewrite1(k3_msualg_6(A),C,D)
& m2_msualg_6(E,A,B,C,D) ) ) ) ) ) ) ) ).
fof(t18_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( r1_rewrite1(k3_msualg_6(A),C,D)
& r1_rewrite1(k3_msualg_6(A),D,E) )
=> ! [F] :
( m2_msualg_6(F,A,B,C,D)
=> ! [G] :
( m2_msualg_6(G,A,B,D,E)
=> m2_msualg_6(k7_funct_2(k1_funct_1(u4_msualg_1(A,B),C),k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,B),E),F,G),A,B,C,E) ) ) ) ) ) ) ) ) ).
fof(t19_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r1_rewrite1(k3_msualg_6(A),C,D)
=> ! [F] :
( m2_msualg_6(F,A,B,C,D)
=> ! [G] :
( ( v1_relat_1(G)
& v1_funct_1(G) )
=> ( r1_msualg_6(A,D,E,B,G)
=> m2_msualg_6(k5_relat_1(F,G),A,B,C,E) ) ) ) ) ) ) ) ) ) ).
fof(t20_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r1_rewrite1(k3_msualg_6(A),D,E)
=> ! [F] :
( ( v1_relat_1(F)
& v1_funct_1(F) )
=> ( r1_msualg_6(A,C,D,B,F)
=> ! [G] :
( m2_msualg_6(G,A,B,D,E)
=> m2_msualg_6(k5_relat_1(F,G),A,B,C,E) ) ) ) ) ) ) ) ) ) ).
fof(t21_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_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) )
=> ! [D] :
( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
=> ( r1_msualg_3(A,B,C,D)
=> ! [E] :
( m1_subset_1(E,u1_msualg_1(A))
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( r2_hidden(F,k4_finseq_1(k1_msualg_1(A,E)))
=> ! [G] :
( m1_subset_1(G,k3_msualg_1(A,E,B))
=> k5_relat_1(k4_msualg_6(A,E,F,B,G),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D,k2_msualg_1(A,E))) = k5_relat_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,E),F)),k4_msualg_6(A,E,F,C,k6_msualg_3(A,B,C,E,D,G))) ) ) ) ) ) ) ) ) ) ).
fof(t22_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_msualg_6(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_msualg_1(A))
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(E,k4_finseq_1(k1_msualg_1(A,D)))
=> ! [F] :
( m1_subset_1(F,k3_msualg_1(A,D,B))
=> k5_relat_1(k4_msualg_6(A,D,E,B,F),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,k2_msualg_1(A,D))) = k5_relat_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,D),E)),k4_msualg_6(A,D,E,B,k6_msualg_3(A,B,B,D,C,F))) ) ) ) ) ) ) ) ).
fof(t23_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_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) )
=> ! [D] :
( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
=> ( r1_msualg_3(A,B,C,D)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( ( v1_relat_1(G)
& v1_funct_1(G) )
=> ~ ( r1_msualg_6(A,E,F,B,G)
& ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,k1_funct_1(u4_msualg_1(A,C),E),k1_funct_1(u4_msualg_1(A,C),F))
& m2_relset_1(H,k1_funct_1(u4_msualg_1(A,C),E),k1_funct_1(u4_msualg_1(A,C),F)) )
=> ~ ( r1_msualg_6(A,E,F,C,H)
& k7_funct_2(k1_funct_1(u4_msualg_1(A,B),E),k1_funct_1(u4_msualg_1(A,C),E),k1_funct_1(u4_msualg_1(A,C),F),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D,E),H) = k5_relat_1(G,k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D,F)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t24_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_msualg_6(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( ( v1_relat_1(F)
& v1_funct_1(F) )
=> ~ ( r1_msualg_6(A,D,E,B,F)
& ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,B),E))
& m2_relset_1(G,k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,B),E)) )
=> ~ ( r1_msualg_6(A,D,E,B,G)
& k7_funct_2(k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,B),E),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,D),G) = k5_relat_1(F,k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,E)) ) ) ) ) ) ) ) ) ) ).
fof(t25_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_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) )
=> ! [D] :
( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
=> ( r1_msualg_3(A,B,C,D)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( r1_rewrite1(k3_msualg_6(A),E,F)
=> ! [G] :
( m2_msualg_6(G,A,B,E,F)
=> ? [H] :
( m2_msualg_6(H,A,C,E,F)
& k7_funct_2(k1_funct_1(u4_msualg_1(A,B),E),k1_funct_1(u4_msualg_1(A,C),E),k1_funct_1(u4_msualg_1(A,C),F),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D,E),H) = k7_funct_2(k1_funct_1(u4_msualg_1(A,B),E),k1_funct_1(u4_msualg_1(A,B),F),k1_funct_1(u4_msualg_1(A,C),F),G,k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D,F)) ) ) ) ) ) ) ) ) ) ) ).
fof(t26_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_msualg_6(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r1_rewrite1(k3_msualg_6(A),D,E)
=> ! [F] :
( m2_msualg_6(F,A,B,D,E)
=> ? [G] :
( m2_msualg_6(G,A,B,D,E)
& k7_funct_2(k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,B),E),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,D),G) = k7_funct_2(k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,B),E),k1_funct_1(u4_msualg_1(A,B),E),F,k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,E)) ) ) ) ) ) ) ) ) ).
fof(d7_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
=> ( v2_msualg_6(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_msualg_1(A))
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ! [F] :
( ( v1_relat_1(F)
& v1_funct_1(F) )
=> ( ( r2_hidden(E,k3_msualg_1(A,D,B))
& r2_hidden(F,k3_msualg_1(A,D,B))
& ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ( r2_hidden(G,k4_finseq_1(k1_msualg_1(A,D)))
=> r2_hidden(k4_tarski(k1_funct_1(E,G),k1_funct_1(F,G)),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,D),G))) ) ) )
=> r2_hidden(k4_tarski(k1_funct_1(k5_msualg_1(A,D,B),E),k1_funct_1(k5_msualg_1(A,D,B),F)),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,k2_msualg_1(A,D))) ) ) ) ) ) ) ) ) ).
fof(d8_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
=> ( v3_msualg_6(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( ( v1_relat_1(F)
& v1_funct_1(F) )
=> ( r1_msualg_6(A,D,E,B,F)
=> ! [G,H] :
( r2_hidden(k4_tarski(G,H),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,D))
=> r2_hidden(k4_tarski(k1_funct_1(F,G),k1_funct_1(F,H)),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,E)) ) ) ) ) ) ) ) ) ) ).
fof(d9_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
=> ( v4_msualg_6(C,A,B)
<=> ! [D] :
( m1_msualg_6(D,A,B)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F,G] :
( r2_hidden(k4_tarski(F,G),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,E))
=> r2_hidden(k4_tarski(k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),D,E),F),k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),D,E),G)),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,E)) ) ) ) ) ) ) ) ).
fof(t27_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v3_msualg_4(C,A,B)
& m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ( v2_msualg_6(C,A,B)
<=> ( v3_msualg_4(C,A,B)
& v4_msualg_4(C,A,B)
& m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) ) ) ) ).
fof(t28_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
=> ( v3_msualg_6(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r1_rewrite1(k3_msualg_6(A),D,E)
=> ! [F] :
( m2_msualg_6(F,A,B,D,E)
=> ! [G,H] :
( r2_hidden(k4_tarski(G,H),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,D))
=> r2_hidden(k4_tarski(k1_funct_1(F,G),k1_funct_1(F,H)),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,E)) ) ) ) ) ) ) ) ) ) ).
fof(d10_msualg_6,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_msualg_4(C,A,B,B)
=> ( C = k5_msualg_6(A,B)
<=> ! [D] :
( r2_hidden(D,A)
=> k1_funct_1(C,D) = k6_partfun1(k1_funct_1(B,D)) ) ) ) ) ).
fof(d11_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
=> ! [D] :
( ( v3_msualg_6(D,A,B)
& m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ( D = k6_msualg_6(A,B,C)
<=> ( r2_pboole(u1_struct_0(A),C,D)
& ! [E] :
( ( v3_msualg_6(E,A,B)
& m1_msualg_4(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ( r2_pboole(u1_struct_0(A),C,E)
=> r2_pboole(u1_struct_0(A),D,E) ) ) ) ) ) ) ) ) ).
fof(t29_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k1_funct_1(u4_msualg_1(A,B),D))
=> ! [F] :
( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,B),D))
=> ( r2_hidden(k4_tarski(E,F),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),k6_msualg_6(A,B,C),D))
<=> ? [G] :
( m1_subset_1(G,u1_struct_0(A))
& ? [H] :
( m1_subset_1(H,k1_funct_1(u4_msualg_1(A,B),G))
& ? [I] :
( m1_subset_1(I,k1_funct_1(u4_msualg_1(A,B),G))
& ? [J] :
( m2_msualg_6(J,A,B,G,D)
& r1_rewrite1(k3_msualg_6(A),G,D)
& r2_hidden(k4_tarski(H,I),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,G))
& E = k8_funct_2(k1_funct_1(u4_msualg_1(A,B),G),k1_funct_1(u4_msualg_1(A,B),D),J,H)
& F = k8_funct_2(k1_funct_1(u4_msualg_1(A,B),G),k1_funct_1(u4_msualg_1(A,B),D),J,I) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t30_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v4_msualg_6(C,A,B)
& m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> v4_msualg_6(k6_msualg_6(A,B,C),A,B) ) ) ) ).
fof(d12_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
=> ! [D] :
( ( v4_msualg_6(D,A,B)
& m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ( D = k7_msualg_6(A,B,C)
<=> ( r2_pboole(u1_struct_0(A),C,D)
& ! [E] :
( ( v4_msualg_6(E,A,B)
& m1_msualg_4(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ( r2_pboole(u1_struct_0(A),C,E)
=> r2_pboole(u1_struct_0(A),D,E) ) ) ) ) ) ) ) ) ).
fof(t31_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k1_funct_1(u4_msualg_1(A,B),D))
=> ! [F] :
( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,B),D))
=> ( r2_hidden(k4_tarski(E,F),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),k7_msualg_6(A,B,C),D))
<=> ? [G] :
( m1_subset_1(G,k1_funct_1(u4_msualg_1(A,B),D))
& ? [H] :
( m1_subset_1(H,k1_funct_1(u4_msualg_1(A,B),D))
& ? [I] :
( m1_msualg_6(I,A,B)
& r2_hidden(k4_tarski(G,H),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,D))
& E = k8_funct_2(k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,B),D),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),I,D),G)
& F = k8_funct_2(k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,B),D),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),I,D),H) ) ) ) ) ) ) ) ) ) ) ).
fof(t32_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
=> v4_msualg_6(k6_msualg_6(A,B,k7_msualg_6(A,B,C)),A,B) ) ) ) ).
fof(d13_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
=> ! [D] :
( ( v3_msualg_6(D,A,B)
& v4_msualg_6(D,A,B)
& m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ( D = k8_msualg_6(A,B,C)
<=> ( r2_pboole(u1_struct_0(A),C,D)
& ! [E] :
( ( v3_msualg_6(E,A,B)
& v4_msualg_6(E,A,B)
& m1_msualg_4(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ( r2_pboole(u1_struct_0(A),C,E)
=> r2_pboole(u1_struct_0(A),D,E) ) ) ) ) ) ) ) ) ).
fof(t33_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v3_msualg_6(C,A,B)
& m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> r6_pboole(u1_struct_0(A),k6_msualg_6(A,B,C),C) ) ) ) ).
fof(t34_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v4_msualg_6(C,A,B)
& m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> r6_pboole(u1_struct_0(A),k7_msualg_6(A,B,C),C) ) ) ) ).
fof(t35_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v3_msualg_6(C,A,B)
& v4_msualg_6(C,A,B)
& m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> r6_pboole(u1_struct_0(A),k8_msualg_6(A,B,C),C) ) ) ) ).
fof(t36_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
=> ( r2_pboole(u1_struct_0(A),k7_msualg_6(A,B,C),k8_msualg_6(A,B,C))
& r2_pboole(u1_struct_0(A),k6_msualg_6(A,B,C),k8_msualg_6(A,B,C))
& r2_pboole(u1_struct_0(A),k7_msualg_6(A,B,k6_msualg_6(A,B,C)),k8_msualg_6(A,B,C)) ) ) ) ) ).
fof(t37_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
=> r6_pboole(u1_struct_0(A),k6_msualg_6(A,B,k7_msualg_6(A,B,C)),k8_msualg_6(A,B,C)) ) ) ) ).
fof(t38_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k1_funct_1(u4_msualg_1(A,B),D))
=> ! [F] :
( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,B),D))
=> ( r2_hidden(k4_tarski(E,F),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),k8_msualg_6(A,B,C),D))
<=> ? [G] :
( m1_subset_1(G,u1_struct_0(A))
& r1_rewrite1(k3_msualg_6(A),G,D)
& ? [H] :
( m1_subset_1(H,k1_funct_1(u4_msualg_1(A,B),G))
& ? [I] :
( m1_subset_1(I,k1_funct_1(u4_msualg_1(A,B),G))
& ? [J] :
( m1_msualg_6(J,A,B)
& ? [K] :
( m2_msualg_6(K,A,B,G,D)
& r2_hidden(k4_tarski(H,I),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,G))
& E = k8_funct_2(k1_funct_1(u4_msualg_1(A,B),G),k1_funct_1(u4_msualg_1(A,B),D),K,k8_funct_2(k1_funct_1(u4_msualg_1(A,B),G),k1_funct_1(u4_msualg_1(A,B),G),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),J,G),H))
& F = k8_funct_2(k1_funct_1(u4_msualg_1(A,B),G),k1_funct_1(u4_msualg_1(A,B),D),K,k8_funct_2(k1_funct_1(u4_msualg_1(A,B),G),k1_funct_1(u4_msualg_1(A,B),G),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),J,G),I)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t39_msualg_6,axiom,
! [A,B] :
( m2_relset_1(B,A,A)
=> ! [C] :
( m2_relset_1(C,A,A)
=> ( ! [D,E] :
( ( r2_hidden(D,A)
& r2_hidden(E,A) )
=> ( r2_hidden(k4_tarski(D,E),C)
<=> r2_rewrite1(B,D,E) ) )
=> ( v1_partfun1(C,A,A)
& v3_relat_2(C)
& v8_relat_2(C) ) ) ) ) ).
fof(t40_msualg_6,axiom,
! [A,B] :
( m2_relset_1(B,A,A)
=> ! [C] :
( ( v1_partfun1(C,A,A)
& v3_relat_2(C)
& v8_relat_2(C)
& m2_relset_1(C,A,A) )
=> ( r1_tarski(B,C)
=> ! [D,E] :
( ( r2_hidden(D,A)
& r2_hidden(E,A)
& r2_rewrite1(B,D,E) )
=> r2_hidden(k4_tarski(D,E),C) ) ) ) ) ).
fof(t41_msualg_6,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_relset_1(B,A,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,A)
=> ( r2_hidden(k4_tarski(C,D),k1_msualg_5(A,B))
<=> r2_rewrite1(B,C,D) ) ) ) ) ) ).
fof(t42_msualg_6,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,A) )
=> ! [C] :
( m1_msualg_4(C,A,B,B)
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,k1_funct_1(B,D))
=> ! [F] :
( m1_subset_1(F,k1_funct_1(B,D))
=> ( r2_hidden(k4_tarski(E,F),k1_msualg_4(A,B,B,k3_msualg_5(A,B,C),D))
<=> r2_rewrite1(k1_msualg_4(A,B,B,C,D),E,F) ) ) ) ) ) ) ) ).
fof(d14_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
=> k9_msualg_6(A,B,C) = k3_msualg_5(u1_struct_0(A),u4_msualg_1(A,B),C) ) ) ) ).
fof(t43_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
=> r2_pboole(u1_struct_0(A),C,k9_msualg_6(A,B,C)) ) ) ) ).
fof(t44_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
=> ! [D] :
( ( v3_msualg_4(D,A,B)
& m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ( r2_pboole(u1_struct_0(A),C,D)
=> r2_pboole(u1_struct_0(A),k9_msualg_6(A,B,C),D) ) ) ) ) ) ).
fof(t45_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v4_msualg_6(C,A,B)
& m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k1_funct_1(u4_msualg_1(A,B),D))
=> ! [F] :
( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,B),D))
=> ( r2_rewrite1(k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,D),E,F)
=> ! [G] :
( m1_msualg_6(G,A,B)
=> r2_rewrite1(k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,D),k8_funct_2(k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,B),D),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),G,D),E),k8_funct_2(k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,B),D),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),G,D),F)) ) ) ) ) ) ) ) ) ).
fof(t46_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v4_msualg_6(C,A,B)
& m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> v4_msualg_6(k9_msualg_6(A,B,C),A,B) ) ) ) ).
fof(t47_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v3_msualg_6(C,A,B)
& m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,B),D))
=> ! [G] :
( m1_subset_1(G,k1_funct_1(u4_msualg_1(A,B),D))
=> ( r2_rewrite1(k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,D),F,G)
=> ! [H] :
( ( v1_relat_1(H)
& v1_funct_1(H) )
=> ( r1_msualg_6(A,D,E,B,H)
=> r2_rewrite1(k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,E),k1_funct_1(H,F),k1_funct_1(H,G)) ) ) ) ) ) ) ) ) ) ) ).
fof(t48_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v3_msualg_6(C,A,B)
& m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> v3_msualg_6(k9_msualg_6(A,B,C),A,B) ) ) ) ).
fof(t49_msualg_6,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,A) )
=> ! [C] :
( m1_msualg_4(C,A,B,B)
=> ! [D] :
( m1_msualg_4(D,A,B,B)
=> ( ! [E] :
( m1_subset_1(E,A)
=> ! [F] :
( m1_subset_1(F,k1_funct_1(B,E))
=> ! [G] :
( m1_subset_1(G,k1_funct_1(B,E))
=> ( r2_hidden(k4_tarski(F,G),k1_msualg_4(A,B,B,D,E))
<=> r2_rewrite1(k1_msualg_4(A,B,B,C,E),F,G) ) ) ) )
=> v2_msualg_4(D,A,B) ) ) ) ) ) ).
fof(t50_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
=> ! [D] :
( m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
=> ( ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,B),E))
=> ! [G] :
( m1_subset_1(G,k1_funct_1(u4_msualg_1(A,B),E))
=> ( r2_hidden(k4_tarski(F,G),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),D,E))
<=> r2_rewrite1(k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),k8_msualg_6(A,B,C),E),F,G) ) ) ) )
=> ( v3_msualg_4(D,A,B)
& v3_msualg_6(D,A,B)
& v4_msualg_6(D,A,B)
& m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) ) ) ) ) ).
fof(t51_msualg_6,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,A) )
=> ! [C] :
( m1_msualg_4(C,A,B,B)
=> ! [D] :
( ( v2_msualg_4(D,A,B)
& m1_msualg_4(D,A,B,B) )
=> ( r2_pboole(A,C,D)
=> ! [E] :
( m1_subset_1(E,A)
=> ! [F] :
( m1_subset_1(F,k1_funct_1(B,E))
=> ! [G] :
( m1_subset_1(G,k1_funct_1(B,E))
=> ( r2_rewrite1(k1_msualg_4(A,B,B,C,E),F,G)
=> r2_hidden(k4_tarski(F,G),k1_msualg_4(A,B,B,D,E)) ) ) ) ) ) ) ) ) ) ).
fof(d15_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
=> ! [D] :
( ( v3_msualg_4(D,A,B)
& v3_msualg_6(D,A,B)
& v4_msualg_6(D,A,B)
& m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ( D = k10_msualg_6(A,B,C)
<=> ( r2_pboole(u1_struct_0(A),C,D)
& ! [E] :
( ( v3_msualg_4(E,A,B)
& v3_msualg_6(E,A,B)
& v4_msualg_6(E,A,B)
& m1_msualg_4(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ( r2_pboole(u1_struct_0(A),C,E)
=> r2_pboole(u1_struct_0(A),D,E) ) ) ) ) ) ) ) ) ).
fof(t52_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
=> ( r2_pboole(u1_struct_0(A),k9_msualg_6(A,B,C),k10_msualg_6(A,B,C))
& r2_pboole(u1_struct_0(A),k6_msualg_6(A,B,C),k10_msualg_6(A,B,C))
& r2_pboole(u1_struct_0(A),k7_msualg_6(A,B,C),k10_msualg_6(A,B,C))
& r2_pboole(u1_struct_0(A),k8_msualg_6(A,B,C),k10_msualg_6(A,B,C)) ) ) ) ) ).
fof(t53_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k1_funct_1(u4_msualg_1(A,B),D))
=> ! [F] :
( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,B),D))
=> ( r2_hidden(k4_tarski(E,F),k2_msualg_4(A,B,k10_msualg_6(A,B,C),D))
<=> r2_rewrite1(k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),k8_msualg_6(A,B,C),D),E,F) ) ) ) ) ) ) ) ).
fof(t54_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
=> r6_pboole(u1_struct_0(A),k10_msualg_6(A,B,C),k9_msualg_6(A,B,k8_msualg_6(A,B,C))) ) ) ) ).
fof(s1_msualg_6,axiom,
( ( ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s1_msualg_6))
=> p1_s1_msualg_6(k6_partfun1(k1_funct_1(u4_msualg_1(f1_s1_msualg_6,f2_s1_msualg_6),A)),A,A) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s1_msualg_6))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s1_msualg_6))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(f1_s1_msualg_6))
=> ( r1_rewrite1(k3_msualg_6(f1_s1_msualg_6),A,B)
=> ! [D] :
( m2_msualg_6(D,f1_s1_msualg_6,f2_s1_msualg_6,A,B)
=> ( p1_s1_msualg_6(D,A,B)
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( r1_msualg_6(f1_s1_msualg_6,B,C,f2_s1_msualg_6,E)
=> p1_s1_msualg_6(k5_relat_1(D,E),A,C) ) ) ) ) ) ) ) ) )
=> ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s1_msualg_6))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s1_msualg_6))
=> ( r1_rewrite1(k3_msualg_6(f1_s1_msualg_6),A,B)
=> ! [C] :
( m2_msualg_6(C,f1_s1_msualg_6,f2_s1_msualg_6,A,B)
=> p1_s1_msualg_6(C,A,B) ) ) ) ) ) ).
fof(s2_msualg_6,axiom,
? [A] :
( m1_msualg_4(A,f1_s2_msualg_6,f2_s2_msualg_6,f2_s2_msualg_6)
& ! [B] :
( m1_subset_1(B,f1_s2_msualg_6)
=> ! [C] :
( m1_subset_1(C,k1_funct_1(f2_s2_msualg_6,B))
=> ! [D] :
( m1_subset_1(D,k1_funct_1(f2_s2_msualg_6,B))
=> ( r2_hidden(k4_tarski(C,D),k1_msualg_4(f1_s2_msualg_6,f2_s2_msualg_6,f2_s2_msualg_6,A,B))
<=> p1_s2_msualg_6(B,C,D) ) ) ) ) ) ).
fof(s3_msualg_6,axiom,
( ! [A] :
( r2_hidden(A,f1_s3_msualg_6)
=> m2_relset_1(f3_s3_msualg_6(A),k1_funct_1(f2_s3_msualg_6,A),k1_funct_1(f2_s3_msualg_6,A)) )
=> ( ? [A] :
( m1_msualg_4(A,f1_s3_msualg_6,f2_s3_msualg_6,f2_s3_msualg_6)
& ! [B] :
( r2_hidden(B,f1_s3_msualg_6)
=> k1_funct_1(A,B) = f3_s3_msualg_6(B) ) )
& ! [A] :
( m1_msualg_4(A,f1_s3_msualg_6,f2_s3_msualg_6,f2_s3_msualg_6)
=> ! [B] :
( m1_msualg_4(B,f1_s3_msualg_6,f2_s3_msualg_6,f2_s3_msualg_6)
=> ( ( ! [C] :
( r2_hidden(C,f1_s3_msualg_6)
=> k1_funct_1(A,C) = f3_s3_msualg_6(C) )
& ! [C] :
( r2_hidden(C,f1_s3_msualg_6)
=> k1_funct_1(B,C) = f3_s3_msualg_6(C) ) )
=> r6_pboole(f1_s3_msualg_6,A,B) ) ) ) ) ) ).
fof(s4_msualg_6,axiom,
( ( ! [A] :
( m1_msualg_4(A,u1_struct_0(f1_s4_msualg_6),u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6))
=> ( p2_s4_msualg_6(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s4_msualg_6))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(f1_s4_msualg_6))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),B),k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),C))
& m2_relset_1(D,k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),B),k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),C)) )
=> ( p1_s4_msualg_6(D,B,C)
=> ! [E,F] :
( r2_hidden(k4_tarski(E,F),k1_msualg_4(u1_struct_0(f1_s4_msualg_6),u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),A,B))
=> r2_hidden(k4_tarski(k1_funct_1(D,E),k1_funct_1(D,F)),k1_msualg_4(u1_struct_0(f1_s4_msualg_6),u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),A,C)) ) ) ) ) ) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s4_msualg_6))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s4_msualg_6))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(f1_s4_msualg_6))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),A),k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),B))
& m2_relset_1(D,k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),A),k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),B)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),B),k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),C))
& m2_relset_1(E,k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),B),k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),C)) )
=> ( ( p1_s4_msualg_6(D,A,B)
& p1_s4_msualg_6(E,B,C) )
=> p1_s4_msualg_6(k7_funct_2(k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),A),k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),B),k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),C),D,E),A,C) ) ) ) ) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s4_msualg_6))
=> p1_s4_msualg_6(k6_partfun1(k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),A)),A,A) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s4_msualg_6))
=> ! [B] :
( m1_subset_1(B,k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),A))
=> ! [C] :
( m1_subset_1(C,k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),A))
=> ( r2_hidden(k4_tarski(B,C),k1_msualg_4(u1_struct_0(f1_s4_msualg_6),u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),f4_s4_msualg_6,A))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(f1_s4_msualg_6))
& ? [E] :
( v1_funct_1(E)
& v1_funct_2(E,k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),D),k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),A))
& m2_relset_1(E,k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),D),k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),A))
& ? [F] :
( m1_subset_1(F,k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),D))
& ? [G] :
( m1_subset_1(G,k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),D))
& p1_s4_msualg_6(E,D,A)
& r2_hidden(k4_tarski(F,G),k1_msualg_4(u1_struct_0(f1_s4_msualg_6),u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),f3_s4_msualg_6,D))
& B = k8_funct_2(k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),D),k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),A),E,F)
& C = k8_funct_2(k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),D),k1_funct_1(u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),A),E,G) ) ) ) ) ) ) ) ) )
=> ( p2_s4_msualg_6(f4_s4_msualg_6)
& r2_pboole(u1_struct_0(f1_s4_msualg_6),f3_s4_msualg_6,f4_s4_msualg_6)
& ! [A] :
( m1_msualg_4(A,u1_struct_0(f1_s4_msualg_6),u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6),u4_msualg_1(f1_s4_msualg_6,f2_s4_msualg_6))
=> ( ( p2_s4_msualg_6(A)
& r2_pboole(u1_struct_0(f1_s4_msualg_6),f3_s4_msualg_6,A) )
=> r2_pboole(u1_struct_0(f1_s4_msualg_6),f4_s4_msualg_6,A) ) ) ) ) ).
fof(dt_m1_msualg_6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_msualg_6(C,A,B)
=> m3_pboole(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) ).
fof(existence_m1_msualg_6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& l3_msualg_1(B,A) )
=> ? [C] : m1_msualg_6(C,A,B) ) ).
fof(dt_m2_msualg_6,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v5_msualg_1(B,A)
& l3_msualg_1(B,A)
& m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(A)) )
=> ! [E] :
( m2_msualg_6(E,A,B,C,D)
=> ( v1_funct_1(E)
& v1_funct_2(E,k1_funct_1(u4_msualg_1(A,B),C),k1_funct_1(u4_msualg_1(A,B),D))
& m2_relset_1(E,k1_funct_1(u4_msualg_1(A,B),C),k1_funct_1(u4_msualg_1(A,B),D)) ) ) ) ).
fof(existence_m2_msualg_6,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v5_msualg_1(B,A)
& l3_msualg_1(B,A)
& m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(A)) )
=> ? [E] : m2_msualg_6(E,A,B,C,D) ) ).
fof(dt_k1_msualg_6,axiom,
! [A,B,C,D] :
( ( m1_pboole(B,A)
& m3_pboole(C,A,B,B)
& m3_pboole(D,A,B,B) )
=> m3_pboole(k1_msualg_6(A,B,C,D),A,B,B) ) ).
fof(redefinition_k1_msualg_6,axiom,
! [A,B,C,D] :
( ( m1_pboole(B,A)
& m3_pboole(C,A,B,B)
& m3_pboole(D,A,B,B) )
=> k1_msualg_6(A,B,C,D) = k13_pboole(C,D) ) ).
fof(dt_k2_msualg_6,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& l3_msualg_1(B,A)
& m1_msualg_6(C,A,B)
& m1_msualg_6(D,A,B) )
=> m1_msualg_6(k2_msualg_6(A,B,C,D),A,B) ) ).
fof(redefinition_k2_msualg_6,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& l3_msualg_1(B,A)
& m1_msualg_6(C,A,B)
& m1_msualg_6(D,A,B) )
=> k2_msualg_6(A,B,C,D) = k13_pboole(C,D) ) ).
fof(dt_k3_msualg_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> m2_relset_1(k3_msualg_6(A),u1_struct_0(A),u1_struct_0(A)) ) ).
fof(dt_k4_msualg_6,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& m1_subset_1(B,u1_msualg_1(A))
& m1_subset_1(C,k5_numbers)
& l3_msualg_1(D,A)
& v1_relat_1(E)
& v1_funct_1(E) )
=> ( v1_relat_1(k4_msualg_6(A,B,C,D,E))
& v1_funct_1(k4_msualg_6(A,B,C,D,E)) ) ) ).
fof(dt_k5_msualg_6,axiom,
! [A,B] :
( m1_pboole(B,A)
=> m1_msualg_4(k5_msualg_6(A,B),A,B,B) ) ).
fof(dt_k6_msualg_6,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v5_msualg_1(B,A)
& l3_msualg_1(B,A)
& m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ( v3_msualg_6(k6_msualg_6(A,B,C),A,B)
& m1_msualg_4(k6_msualg_6(A,B,C),u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) ).
fof(dt_k7_msualg_6,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v5_msualg_1(B,A)
& l3_msualg_1(B,A)
& m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ( v4_msualg_6(k7_msualg_6(A,B,C),A,B)
& m1_msualg_4(k7_msualg_6(A,B,C),u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) ).
fof(dt_k8_msualg_6,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v5_msualg_1(B,A)
& l3_msualg_1(B,A)
& m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ( v3_msualg_6(k8_msualg_6(A,B,C),A,B)
& v4_msualg_6(k8_msualg_6(A,B,C),A,B)
& m1_msualg_4(k8_msualg_6(A,B,C),u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) ).
fof(dt_k9_msualg_6,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v5_msualg_1(B,A)
& l3_msualg_1(B,A)
& m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ( v3_msualg_4(k9_msualg_6(A,B,C),A,B)
& m1_msualg_4(k9_msualg_6(A,B,C),u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) ).
fof(dt_k10_msualg_6,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v5_msualg_1(B,A)
& l3_msualg_1(B,A)
& m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ( v3_msualg_4(k10_msualg_6(A,B,C),A,B)
& v3_msualg_6(k10_msualg_6(A,B,C),A,B)
& v4_msualg_6(k10_msualg_6(A,B,C),A,B)
& m1_msualg_4(k10_msualg_6(A,B,C),u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) ).
%------------------------------------------------------------------------------