SET007 Axioms: SET007+469.ax
%------------------------------------------------------------------------------
% File : SET007+469 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : On the Trivial Many Sorted Algebras and Many Sorted Congruences
% 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_9 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 51 ( 1 unt; 0 def)
% Number of atoms : 433 ( 21 equ)
% Maximal formula atoms : 18 ( 8 avg)
% Number of connectives : 443 ( 61 ~; 0 |; 188 &)
% ( 3 <=>; 191 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 10 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 42 ( 41 usr; 0 prp; 1-4 aty)
% Number of functors : 54 ( 54 usr; 3 con; 0-6 aty)
% Number of variables : 218 ( 206 !; 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_9,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ? [C] :
( m1_subset_1(C,k6_closure2(A,B))
& v1_relat_1(C)
& v1_funct_1(C)
& v1_pre_circ(C,A) ) ) ).
fof(rc2_msualg_9,axiom,
! [A,B] :
( ( v2_relat_1(B)
& m1_pboole(B,A) )
=> ? [C] :
( m4_pboole(C,A,B)
& v1_relat_1(C)
& v2_relat_1(C)
& v1_funct_1(C)
& v1_pre_circ(C,A) ) ) ).
fof(cc1_msualg_9,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_subset_1(C,u1_msualg_1(A)) )
=> ! [D] :
( m1_subset_1(D,k3_msualg_1(A,C,B))
=> ( v1_relat_1(D)
& v1_funct_1(D)
& v1_finseq_1(D) ) ) ) ).
fof(cc2_msualg_9,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& m1_subset_1(C,u1_struct_0(A))
& m2_pralg_2(D,B,A) )
=> ! [E] :
( m1_subset_1(E,k1_funct_1(k11_pralg_2(B,A,D),C))
=> ( v1_relat_1(E)
& v1_funct_1(E) ) ) ) ).
fof(fc1_msualg_9,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(fc2_msualg_9,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)) )
=> ( v4_msualg_1(k11_msafree(A,B),A)
& v5_msualg_1(k11_msafree(A,B),A)
& v2_msafree(k11_msafree(A,B),A) ) ) ).
fof(fc3_msualg_9,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)
& v5_msualg_1(C,A)
& l3_msualg_1(C,A) )
=> ( v4_msualg_1(k9_pralg_2(A,B,C),A)
& v5_msualg_1(k9_pralg_2(A,B,C),A) ) ) ).
fof(fc4_msualg_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ( v1_relat_1(u4_msualg_1(A,k8_msafree2(A)))
& v2_relat_1(u4_msualg_1(A,k8_msafree2(A)))
& ~ v3_relat_1(u4_msualg_1(A,k8_msafree2(A)))
& v1_funct_1(u4_msualg_1(A,k8_msafree2(A)))
& v1_pre_circ(u4_msualg_1(A,k8_msafree2(A)),u1_struct_0(A)) ) ) ).
fof(fc5_msualg_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ( v4_msualg_1(k8_msafree2(A),A)
& v5_msualg_1(k8_msafree2(A),A)
& v4_msafree2(k8_msafree2(A),A) ) ) ).
fof(t1_msualg_9,axiom,
! [A,B,C,D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( ( r2_hidden(A,k1_relat_1(D))
& r2_hidden(k1_funct_1(D,A),k2_zfmisc_1(B,C)) )
=> k1_funct_1(D,A) = k4_tarski(k1_funct_1(k15_mcart_1(D),A),k1_funct_1(k16_mcart_1(D),A)) ) ) ).
fof(t2_msualg_9,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,k1_tarski(B))
& m2_relset_1(C,A,k1_tarski(B)) )
=> k2_relat_1(C) = k1_tarski(B) ) ) ).
fof(t3_msualg_9,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ? [B] :
( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,A)
& m2_relset_1(B,k5_numbers,A)
& k2_relat_1(B) = A ) ) ).
fof(t4_msualg_9,axiom,
! [A] : r1_tarski(k8_eqrel_1(A,k1_eqrel_1(A)),k1_tarski(A)) ).
fof(t5_msualg_9,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> k8_eqrel_1(A,k1_eqrel_1(A)) = k1_tarski(A) ) ).
fof(t6_msualg_9,axiom,
! [A,B] :
? [C] :
( m1_pboole(C,A)
& r6_pboole(A,k1_pzfmisc1(A,C),k2_pre_circ(A,k1_tarski(B))) ) ).
fof(t7_msualg_9,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ? [C] :
( v2_relat_1(C)
& m1_pboole(C,A)
& r2_pboole(A,B,C) ) ) ).
fof(t8_msualg_9,axiom,
! [A,B] :
( ( v2_relat_1(B)
& m1_pboole(B,A) )
=> ! [C] :
( ( v1_pre_circ(C,A)
& m4_pboole(C,A,B) )
=> ? [D] :
( v2_relat_1(D)
& v1_pre_circ(D,A)
& m4_pboole(D,A,B)
& r2_pboole(A,C,D) ) ) ) ).
fof(t9_msualg_9,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m3_pboole(D,A,B,k1_pzfmisc1(A,C))
=> ! [E] :
( m3_pboole(E,A,B,k1_pzfmisc1(A,C))
=> r6_pboole(A,D,E) ) ) ) ) ).
fof(t10_msualg_9,axiom,
! [A,B] :
( ( v2_relat_1(B)
& m1_pboole(B,A) )
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m3_pboole(D,A,B,k1_pzfmisc1(A,C))
=> v2_msualg_3(D,A,B,k1_pzfmisc1(A,C)) ) ) ) ).
fof(t11_msualg_9,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,A) )
=> ! [D] :
( m3_pboole(D,A,k1_pzfmisc1(A,B),C)
=> v1_msualg_3(D) ) ) ) ).
fof(t12_msualg_9,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)) )
=> v1_msualg_3(k15_msafree(A,B)) ) ) ).
fof(t13_msualg_9,axiom,
! [A,B] :
( ( v2_relat_1(B)
& v1_pre_circ(B,A)
& m1_pboole(B,A) )
=> ? [C] :
( m3_pboole(C,A,k2_pre_circ(A,k5_numbers),B)
& v2_msualg_3(C,A,k2_pre_circ(A,k5_numbers),B) ) ) ).
fof(t14_msualg_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_pralg_2(C,k4_card_3(u4_msualg_1(A,B)))
=> ! [D] :
( m1_pralg_2(D,k4_card_3(u4_msualg_1(A,B)))
=> ( ! [E] : k1_funct_1(k3_pralg_3(u4_msualg_1(A,B),E),C) = k1_funct_1(k3_pralg_3(u4_msualg_1(A,B),E),D)
=> r6_pboole(k1_pralg_2(k4_card_3(u4_msualg_1(A,B))),C,D) ) ) ) ) ) ).
fof(t15_msualg_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m2_pralg_2(D,B,A)
=> ! [E] :
( m1_pralg_2(E,k4_card_3(k10_pralg_2(B,A,C,D)))
=> ! [F] :
( m1_pralg_2(F,k4_card_3(k10_pralg_2(B,A,C,D)))
=> ( ! [G] :
( m1_subset_1(G,B)
=> k1_funct_1(k3_pralg_3(k10_pralg_2(B,A,C,D),G),E) = k1_funct_1(k3_pralg_3(k10_pralg_2(B,A,C,D),G),F) )
=> r6_pboole(k1_pralg_2(k4_card_3(k10_pralg_2(B,A,C,D))),E,F) ) ) ) ) ) ) ) ).
fof(t16_msualg_9,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] :
( ( v5_msualg_1(D,A)
& m1_msualg_2(D,A,B) )
=> ! [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(A),u4_msualg_1(A,C),u4_msualg_1(A,B))
=> ( r6_pboole(u1_struct_0(A),E,F)
=> r1_msualg_3(A,C,B,F) ) ) ) ) ) ) ) ) ).
fof(t17_msualg_9,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))
=> ( r3_msualg_3(A,B,C,D)
=> r6_msualg_3(A,B,k7_msualg_3(A,B,C,D)) ) ) ) ) ) ).
fof(t18_msualg_9,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))
=> ( v2_msualg_3(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
=> ! [E] :
( m1_subset_1(E,u1_msualg_1(A))
=> ! [F] :
( m1_subset_1(F,k3_msualg_1(A,E,C))
=> ? [G] :
( m1_subset_1(G,k3_msualg_1(A,E,B))
& k6_msualg_3(A,B,C,E,D,G) = F ) ) ) ) ) ) ) ) ).
fof(t19_msualg_9,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_msualg_1(A))
=> ! [D] :
( m1_subset_1(D,k3_msualg_1(A,C,B))
=> r2_hidden(k8_funct_2(k3_msualg_1(A,C,B),k4_msualg_1(A,C,B),k5_msualg_1(A,C,B),D),k1_funct_1(u4_msualg_1(A,B),k2_msualg_1(A,C))) ) ) ) ) ).
fof(t20_msualg_9,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] :
( ( v5_msualg_1(D,A)
& l3_msualg_1(D,A) )
=> ! [E] :
( m3_pboole(E,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,D))
=> ( ( r2_msualg_3(A,B,C,E)
& r1_msualg_3(A,B,D,F) )
=> ! [G] :
( m3_pboole(G,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
=> ( r6_pboole(u1_struct_0(A),k3_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),u4_msualg_1(A,D),E,G),F)
=> r1_msualg_3(A,C,D,G) ) ) ) ) ) ) ) ) ) ).
fof(d1_msualg_9,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,A) )
=> ! [D] :
( ( v2_relat_1(D)
& m1_pboole(D,A) )
=> ! [E] :
( m3_pboole(E,A,B,k11_pboole(A,C,D))
=> ! [F] :
( m3_pboole(F,A,B,C)
=> ( F = k1_msualg_9(A,B,C,D,E)
<=> ! [G] :
( r2_hidden(G,A)
=> k1_funct_1(F,G) = k15_mcart_1(k1_funct_1(E,G)) ) ) ) ) ) ) ) ).
fof(d2_msualg_9,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,A) )
=> ! [D] :
( ( v2_relat_1(D)
& m1_pboole(D,A) )
=> ! [E] :
( m3_pboole(E,A,B,k11_pboole(A,C,D))
=> ! [F] :
( m3_pboole(F,A,B,D)
=> ( F = k2_msualg_9(A,B,C,D,E)
<=> ! [G] :
( r2_hidden(G,A)
=> k1_funct_1(F,G) = k16_mcart_1(k1_funct_1(E,G)) ) ) ) ) ) ) ) ).
fof(t21_msualg_9,axiom,
! [A,B,C] :
( m1_pboole(C,A)
=> ! [D] :
( m3_pboole(D,A,C,k11_pboole(A,k2_pre_circ(A,k1_tarski(B)),k2_pre_circ(A,k1_tarski(B))))
=> r6_pboole(A,k1_msualg_9(A,C,k2_pre_circ(A,k1_tarski(B)),k2_pre_circ(A,k1_tarski(B)),D),k2_msualg_9(A,C,k2_pre_circ(A,k1_tarski(B)),k2_pre_circ(A,k1_tarski(B)),D)) ) ) ).
fof(t22_msualg_9,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,A) )
=> ! [D] :
( ( v2_relat_1(D)
& m1_pboole(D,A) )
=> ! [E] :
( m3_pboole(E,A,B,k11_pboole(A,C,D))
=> ( v2_msualg_3(E,A,B,k11_pboole(A,C,D))
=> v2_msualg_3(k1_msualg_9(A,B,C,D,E),A,B,C) ) ) ) ) ) ).
fof(t23_msualg_9,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,A) )
=> ! [D] :
( ( v2_relat_1(D)
& m1_pboole(D,A) )
=> ! [E] :
( m3_pboole(E,A,B,k11_pboole(A,C,D))
=> ( v2_msualg_3(E,A,B,k11_pboole(A,C,D))
=> v2_msualg_3(k2_msualg_9(A,B,C,D,E),A,B,D) ) ) ) ) ) ).
fof(t24_msualg_9,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( ( v2_relat_1(D)
& m1_pboole(D,A) )
=> ! [E] :
( ( v2_relat_1(E)
& m1_pboole(E,A) )
=> ! [F] :
( m3_pboole(F,A,B,k11_pboole(A,D,E))
=> ( r1_pboole(A,C,k1_mssubfam(A,F))
=> ! [G] :
( r2_hidden(G,A)
=> k1_funct_1(k1_closure1(A,F,C),G) = k4_tarski(k1_funct_1(k1_closure1(A,k1_msualg_9(A,B,D,E,F),C),G),k1_funct_1(k1_closure1(A,k2_msualg_9(A,B,D,E,F),C),G)) ) ) ) ) ) ) ) ).
fof(t25_msualg_9,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] :
( m3_pboole(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k8_msafree2(A)))
=> ! [D] :
( m1_subset_1(D,u1_msualg_1(A))
=> ! [E] :
( m1_subset_1(E,k3_msualg_1(A,D,B))
=> ( k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k8_msafree2(A)),C,k2_msualg_1(A,D)),k8_funct_2(k3_msualg_1(A,D,B),k4_msualg_1(A,D,B),k5_msualg_1(A,D,B),E)) = np__0
& k8_funct_2(k3_msualg_1(A,D,k8_msafree2(A)),k4_msualg_1(A,D,k8_msafree2(A)),k5_msualg_1(A,D,k8_msafree2(A)),k6_msualg_3(A,B,k8_msafree2(A),D,C,E)) = np__0 ) ) ) ) ) ) ).
fof(t26_msualg_9,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] :
( m3_pboole(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k8_msafree2(A)))
=> r2_msualg_3(A,B,k8_msafree2(A),C) ) ) ) ).
fof(t27_msualg_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ( ? [C] :
( m1_pboole(C,u1_struct_0(A))
& r6_pboole(u1_struct_0(A),u4_msualg_1(A,B),k1_pzfmisc1(u1_struct_0(A),C)) )
=> r6_msualg_3(A,B,k8_msafree2(A)) ) ) ) ).
fof(t28_msualg_9,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)
& v4_msualg_4(C,A,B)
& m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> m4_pboole(C,u1_struct_0(A),k11_pboole(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))) ) ) ) ).
fof(t29_msualg_9,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,k1_zfmisc_1(u1_struct_0(k6_msualg_5(A,B))))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k1_closure2(u1_struct_0(A),k11_pboole(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)))))
=> ( C = D
=> ( v3_msualg_4(k6_mssubfam(u1_struct_0(A),k11_pboole(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)),k5_closure2(u1_struct_0(A),k11_pboole(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)),D)),A,B)
& v4_msualg_4(k6_mssubfam(u1_struct_0(A),k11_pboole(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)),k5_closure2(u1_struct_0(A),k11_pboole(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)),D)),A,B)
& m1_msualg_4(k6_mssubfam(u1_struct_0(A),k11_pboole(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)),k5_closure2(u1_struct_0(A),k11_pboole(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)),D)),u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) ) ) ) ) ).
fof(t30_msualg_9,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)
& v4_msualg_4(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),C,k11_pboole(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)))
=> r6_pboole(u1_struct_0(A),u4_msualg_1(A,k14_msualg_4(A,B,C)),k1_pzfmisc1(u1_struct_0(A),u4_msualg_1(A,B))) ) ) ) ) ).
fof(t31_msualg_9,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)
=> r6_pboole(u1_struct_0(A),k3_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k14_msualg_4(A,B,k18_msualg_4(A,B,C,D))),u4_msualg_1(A,C),k16_msualg_4(A,B,k18_msualg_4(A,B,C,D)),k20_msualg_4(A,B,C,D)),D) ) ) ) ) ) ).
fof(t32_msualg_9,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)
& v4_msualg_4(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,k14_msualg_4(A,B,C)),D))
=> ? [F] :
( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,B),D))
& E = k3_msualg_4(A,B,C,D,F) ) ) ) ) ) ) ).
fof(t33_msualg_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( 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)) )
=> ! [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)
=> ! [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),k2_msualg_4(A,B,C,E))
=> ( r1_tarski(k3_msualg_4(A,B,C,E,F),k3_msualg_4(A,B,D,E,G))
& ( v5_msualg_1(B,A)
=> r1_tarski(k3_msualg_4(A,B,C,E,G),k3_msualg_4(A,B,D,E,F)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t34_msualg_9,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)
& v4_msualg_4(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))
=> ( k8_funct_2(k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,k14_msualg_4(A,B,C)),D),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k14_msualg_4(A,B,C)),k16_msualg_4(A,B,C),D),E) = k8_funct_2(k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,k14_msualg_4(A,B,C)),D),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k14_msualg_4(A,B,C)),k16_msualg_4(A,B,C),D),F)
<=> r2_hidden(k4_tarski(E,F),k2_msualg_4(A,B,C,D)) ) ) ) ) ) ) ) ).
fof(t35_msualg_9,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)
& v4_msualg_4(C,A,B)
& 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)
& v4_msualg_4(D,A,B)
& m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ! [E] :
( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,k14_msualg_4(A,B,C)),u4_msualg_1(A,k14_msualg_4(A,B,D)))
=> ( ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,k1_funct_1(u4_msualg_1(A,k14_msualg_4(A,B,C)),F))
=> ! [H] :
( m1_subset_1(H,k1_funct_1(u4_msualg_1(A,B),F))
=> ( G = k3_msualg_4(A,B,C,F,H)
=> k8_funct_2(k1_funct_1(u4_msualg_1(A,k14_msualg_4(A,B,C)),F),k1_funct_1(u4_msualg_1(A,k14_msualg_4(A,B,D)),F),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,k14_msualg_4(A,B,C)),u4_msualg_1(A,k14_msualg_4(A,B,D)),E,F),G) = k3_msualg_4(A,B,D,F,H) ) ) ) )
=> r6_pboole(u1_struct_0(A),k3_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k14_msualg_4(A,B,C)),u4_msualg_1(A,k14_msualg_4(A,B,D)),k16_msualg_4(A,B,C),E),k16_msualg_4(A,B,D)) ) ) ) ) ) ) ).
fof(t36_msualg_9,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)
& v4_msualg_4(C,A,B)
& 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)
& v4_msualg_4(D,A,B)
& m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ! [E] :
( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,k14_msualg_4(A,B,C)),u4_msualg_1(A,k14_msualg_4(A,B,D)))
=> ( ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,k1_funct_1(u4_msualg_1(A,k14_msualg_4(A,B,C)),F))
=> ! [H] :
( m1_subset_1(H,k1_funct_1(u4_msualg_1(A,B),F))
=> ( G = k3_msualg_4(A,B,C,F,H)
=> k8_funct_2(k1_funct_1(u4_msualg_1(A,k14_msualg_4(A,B,C)),F),k1_funct_1(u4_msualg_1(A,k14_msualg_4(A,B,D)),F),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,k14_msualg_4(A,B,C)),u4_msualg_1(A,k14_msualg_4(A,B,D)),E,F),G) = k3_msualg_4(A,B,D,F,H) ) ) ) )
=> r2_msualg_3(A,k14_msualg_4(A,B,C),k14_msualg_4(A,B,D),E) ) ) ) ) ) ) ).
fof(t37_msualg_9,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] :
( ( v3_msualg_4(E,A,B)
& v4_msualg_4(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),E,k18_msualg_4(A,B,C,D))
& ! [F] :
( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,k14_msualg_4(A,B,E)),u4_msualg_1(A,C))
=> ~ ( r1_msualg_3(A,k14_msualg_4(A,B,E),C,F)
& r6_pboole(u1_struct_0(A),D,k3_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k14_msualg_4(A,B,E)),u4_msualg_1(A,C),k16_msualg_4(A,B,E),F)) ) ) ) ) ) ) ) ) ) ).
fof(s1_msualg_9,axiom,
( ! [A] :
( m1_subset_1(A,f1_s1_msualg_9)
=> ? [B] : p1_s1_msualg_9(A,B) )
=> ? [A] :
( m1_pboole(A,f1_s1_msualg_9)
& ! [B] :
( m1_subset_1(B,f1_s1_msualg_9)
=> p1_s1_msualg_9(B,k1_funct_1(A,B)) ) ) ) ).
fof(dt_k1_msualg_9,axiom,
! [A,B,C,D,E] :
( ( m1_pboole(B,A)
& v2_relat_1(C)
& m1_pboole(C,A)
& v2_relat_1(D)
& m1_pboole(D,A)
& m3_pboole(E,A,B,k11_pboole(A,C,D)) )
=> m3_pboole(k1_msualg_9(A,B,C,D,E),A,B,C) ) ).
fof(dt_k2_msualg_9,axiom,
! [A,B,C,D,E] :
( ( m1_pboole(B,A)
& v2_relat_1(C)
& m1_pboole(C,A)
& v2_relat_1(D)
& m1_pboole(D,A)
& m3_pboole(E,A,B,k11_pboole(A,C,D)) )
=> m3_pboole(k2_msualg_9(A,B,C,D,E),A,B,D) ) ).
%------------------------------------------------------------------------------