SET007 Axioms: SET007+422.ax
%------------------------------------------------------------------------------
% File : SET007+422 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The Correspondence Between Homomorphisms of Universal Algebra
% 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 : msuhom_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 34 ( 0 unt; 0 def)
% Number of atoms : 378 ( 18 equ)
% Maximal formula atoms : 24 ( 11 avg)
% Number of connectives : 401 ( 57 ~; 0 |; 232 &)
% ( 2 <=>; 110 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 9 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 38 ( 37 usr; 0 prp; 1-4 aty)
% Number of functors : 40 ( 40 usr; 4 con; 0-6 aty)
% Number of variables : 103 ( 103 !; 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(t1_msuhom_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( r1_tarski(k2_relat_1(A),C)
=> k5_relat_1(A,k7_relat_1(B,C)) = k5_relat_1(A,B) ) ) ) ).
fof(t2_msuhom_1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> r1_tarski(k3_finseq_2(B),k3_finseq_2(A)) ) ).
fof(t3_msuhom_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( v1_funcop_1(A)
=> v1_funcop_1(k7_relat_1(A,B)) ) ) ).
fof(t4_msuhom_1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ! [C] :
( m1_pboole(C,A)
=> k6_pboole(B,k3_pre_circ(A,C,B)) = k7_relat_1(k6_pboole(A,C),k3_finseq_2(B)) ) ) ).
fof(d1_msuhom_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ( r1_msuhom_1(A,B)
<=> ( r1_tarski(u1_struct_0(A),u1_struct_0(B))
& r1_tarski(u1_msualg_1(A),u1_msualg_1(B))
& k2_partfun1(u1_msualg_1(B),k3_finseq_2(u1_struct_0(B)),u2_msualg_1(B),u1_msualg_1(A)) = u2_msualg_1(A)
& k2_partfun1(u1_msualg_1(B),u1_struct_0(B),u3_msualg_1(B),u1_msualg_1(A)) = u3_msualg_1(A) ) ) ) ) ).
fof(t5_msuhom_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_msualg_1(C) )
=> ( ( r1_msuhom_1(A,B)
& r1_msuhom_1(B,C) )
=> r1_msuhom_1(A,C) ) ) ) ) ).
fof(t6_msuhom_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_msualg_1(B)
& l1_msualg_1(B) )
=> ( ( r1_msuhom_1(A,B)
& r1_msuhom_1(B,A) )
=> A = B ) ) ) ).
fof(t7_msuhom_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( m1_subset_1(D,B)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,E)
& r1_xreal_0(E,A) )
=> k1_funct_1(k3_cqc_lang(D,C),k4_finseq_4(k5_numbers,B,k1_msuhom_1(B,A,D),E)) = C ) ) ) ) ) ) ).
fof(t8_msuhom_1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ! [E] :
( m3_pboole(E,A,C,D)
=> ! [F] :
( m1_pboole(F,B)
=> ! [G] :
( m1_pboole(G,B)
=> ( ( r6_pboole(B,F,k3_pre_circ(A,C,B))
& r6_pboole(B,G,k3_pre_circ(A,D,B)) )
=> m3_pboole(k3_pre_circ(A,E,B),B,F,G) ) ) ) ) ) ) ) ).
fof(d2_msuhom_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_msualg_1(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_msualg_1(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v4_msualg_1(C,B)
& v5_msualg_1(C,B)
& l3_msualg_1(C,B) )
=> ( r1_msuhom_1(A,B)
=> ! [D] :
( ( v4_msualg_1(D,A)
& v5_msualg_1(D,A)
& l3_msualg_1(D,A) )
=> ( D = k2_msuhom_1(A,B,C)
<=> ( u4_msualg_1(A,D) = k7_relat_1(u4_msualg_1(B,C),u1_struct_0(A))
& u5_msualg_1(A,D) = k7_relat_1(u5_msualg_1(B,C),u1_msualg_1(A)) ) ) ) ) ) ) ) ).
fof(t9_msuhom_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_msualg_1(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v4_msualg_1(B,A)
& v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> B = k2_msuhom_1(A,A,B) ) ) ).
fof(t10_msuhom_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_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ( r1_unialg_2(A,B)
=> k7_msualg_1(A) = k7_msualg_1(B) ) ) ) ).
fof(d3_msuhom_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_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( k7_msualg_1(A) = k7_msualg_1(B)
=> k3_msuhom_1(A,B,C) = k2_pre_circ(k1_tarski(np__0),C) ) ) ) ) ).
fof(t11_msuhom_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_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( r1_unialg_2(A,B)
=> ! [D] :
( m1_subset_1(D,u1_msualg_1(k7_msualg_1(A)))
=> k1_msualg_3(u1_struct_0(k7_msualg_1(A)),u4_msualg_1(k7_msualg_1(A),k10_msualg_1(A)),u4_msualg_1(k7_msualg_1(A),k2_msuhom_1(k7_msualg_1(A),k7_msualg_1(B),k10_msualg_1(B))),k3_msuhom_1(A,B,C),k2_msualg_1(k7_msualg_1(A),D)) = C ) ) ) ) ) ).
fof(t12_msuhom_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(k7_msualg_1(A)))
=> k5_msualg_1(k7_msualg_1(A),B,k10_msualg_1(A)) = k1_funct_1(u1_unialg_1(A),B) ) ) ).
fof(t13_msuhom_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(k7_msualg_1(A)))
=> m2_unialg_2(k5_msualg_1(k7_msualg_1(A),B,k10_msualg_1(A)),u1_struct_0(A),k1_unialg_2(A)) ) ) ).
fof(t14_msuhom_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(k7_msualg_1(A)))
=> ! [C] :
( m1_subset_1(C,k3_msualg_1(k7_msualg_1(A),B,k10_msualg_1(A)))
=> m2_finseq_1(C,u1_struct_0(A)) ) ) ) ).
fof(t15_msuhom_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_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( r1_unialg_2(A,B)
=> ! [D] :
( m1_subset_1(D,u1_msualg_1(k7_msualg_1(A)))
=> ! [E] :
( m1_subset_1(E,k3_msualg_1(k7_msualg_1(A),D,k10_msualg_1(A)))
=> k6_msualg_3(k7_msualg_1(A),k10_msualg_1(A),k2_msuhom_1(k7_msualg_1(A),k7_msualg_1(B),k10_msualg_1(B)),D,k3_msuhom_1(A,B,C),E) = k5_relat_1(E,C) ) ) ) ) ) ) ).
fof(t16_msuhom_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_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( r1_alg_1(A,B,C)
=> r1_msualg_3(k7_msualg_1(A),k10_msualg_1(A),k2_msuhom_1(k7_msualg_1(A),k7_msualg_1(B),k10_msualg_1(B)),k3_msuhom_1(A,B,C)) ) ) ) ) ).
fof(t17_msuhom_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_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( r1_unialg_2(A,B)
=> m1_pboole(k3_msuhom_1(A,B,C),k1_tarski(np__0)) ) ) ) ) ).
fof(t18_msuhom_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_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( r3_alg_1(A,B,C)
=> r2_msualg_3(k7_msualg_1(A),k10_msualg_1(A),k2_msuhom_1(k7_msualg_1(A),k7_msualg_1(B),k10_msualg_1(B)),k3_msuhom_1(A,B,C)) ) ) ) ) ).
fof(t19_msuhom_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_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( r2_alg_1(A,B,C)
=> r3_msualg_3(k7_msualg_1(A),k10_msualg_1(A),k2_msuhom_1(k7_msualg_1(A),k7_msualg_1(B),k10_msualg_1(B)),k3_msuhom_1(A,B,C)) ) ) ) ) ).
fof(t20_msuhom_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_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( r4_alg_1(A,B,C)
=> r4_msualg_3(k7_msualg_1(A),k10_msualg_1(A),k2_msuhom_1(k7_msualg_1(A),k7_msualg_1(B),k10_msualg_1(B)),k3_msuhom_1(A,B,C)) ) ) ) ) ).
fof(t21_msuhom_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_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( ( r1_unialg_2(A,B)
& r1_msualg_3(k7_msualg_1(A),k10_msualg_1(A),k2_msuhom_1(k7_msualg_1(A),k7_msualg_1(B),k10_msualg_1(B)),k3_msuhom_1(A,B,C)) )
=> r1_alg_1(A,B,C) ) ) ) ) ).
fof(t22_msuhom_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_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( ( r1_unialg_2(A,B)
& r2_msualg_3(k7_msualg_1(A),k10_msualg_1(A),k2_msuhom_1(k7_msualg_1(A),k7_msualg_1(B),k10_msualg_1(B)),k3_msuhom_1(A,B,C)) )
=> r3_alg_1(A,B,C) ) ) ) ) ).
fof(t23_msuhom_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_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( ( r1_unialg_2(A,B)
& r3_msualg_3(k7_msualg_1(A),k10_msualg_1(A),k2_msuhom_1(k7_msualg_1(A),k7_msualg_1(B),k10_msualg_1(B)),k3_msuhom_1(A,B,C)) )
=> r2_alg_1(A,B,C) ) ) ) ) ).
fof(t24_msuhom_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_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( ( r1_unialg_2(A,B)
& r4_msualg_3(k7_msualg_1(A),k10_msualg_1(A),k2_msuhom_1(k7_msualg_1(A),k7_msualg_1(B),k10_msualg_1(B)),k3_msuhom_1(A,B,C)) )
=> r4_alg_1(A,B,C) ) ) ) ) ).
fof(t25_msuhom_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> r6_pboole(u1_struct_0(k7_msualg_1(A)),k3_msuhom_1(A,A,k6_partfun1(u1_struct_0(A))),k2_msualg_3(u1_struct_0(k7_msualg_1(A)),u4_msualg_1(k7_msualg_1(A),k10_msualg_1(A)))) ) ).
fof(t26_msuhom_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_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_unialg_1(C)
& v7_unialg_1(C)
& v8_unialg_1(C)
& l1_unialg_1(C) )
=> ( ( r1_unialg_2(A,B)
& r1_unialg_2(B,C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> k13_pboole(k3_msuhom_1(A,B,D),k3_msuhom_1(B,C,E)) = k3_msuhom_1(A,C,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E)) ) ) ) ) ) ) ).
fof(reflexivity_r1_msuhom_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A)
& ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> r1_msuhom_1(A,A) ) ).
fof(dt_k1_msuhom_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,A) )
=> m2_finseq_1(k1_msuhom_1(A,B,C),A) ) ).
fof(redefinition_k1_msuhom_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,A) )
=> k1_msuhom_1(A,B,C) = k2_finseq_2(B,C) ) ).
fof(dt_k2_msuhom_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v1_msualg_1(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& ~ v3_struct_0(B)
& v1_msualg_1(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B)
& v4_msualg_1(C,B)
& v5_msualg_1(C,B)
& l3_msualg_1(C,B) )
=> ( v4_msualg_1(k2_msuhom_1(A,B,C),A)
& v5_msualg_1(k2_msuhom_1(A,B,C),A)
& l3_msualg_1(k2_msuhom_1(A,B,C),A) ) ) ).
fof(dt_k3_msuhom_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A)
& ~ v3_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> m3_pboole(k3_msuhom_1(A,B,C),u1_struct_0(k7_msualg_1(A)),u4_msualg_1(k7_msualg_1(A),k10_msualg_1(A)),u4_msualg_1(k7_msualg_1(A),k2_msuhom_1(k7_msualg_1(A),k7_msualg_1(B),k10_msualg_1(B)))) ) ).
%------------------------------------------------------------------------------