SET007 Axioms: SET007+419.ax
%------------------------------------------------------------------------------
% File : SET007+419 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Terms Over Many Sorted 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 : msaterm [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 80 ( 0 unt; 0 def)
% Number of atoms : 853 ( 79 equ)
% Maximal formula atoms : 30 ( 10 avg)
% Number of connectives : 957 ( 184 ~; 4 |; 382 &)
% ( 9 <=>; 378 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 13 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 38 ( 37 usr; 0 prp; 1-6 aty)
% Number of functors : 56 ( 56 usr; 11 con; 0-5 aty)
% Number of variables : 401 ( 393 !; 8 ?)
% 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_msaterm,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v2_relat_1(B)
& m1_pboole(B,A)
& m1_subset_1(C,A) )
=> ~ v1_xboole_0(k1_funct_1(B,C)) ) ).
fof(fc2_msaterm,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_xboole_0(k1_msaterm(A,B))
& v3_trees_3(k1_msaterm(A,B)) ) ) ).
fof(cc1_msaterm,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)) )
=> ! [C] :
( m1_subset_1(C,k1_msaterm(A,B))
=> v1_finset_1(C) ) ) ).
fof(d1_msaterm,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_pboole(B,u1_struct_0(A))
=> k1_msaterm(A,B) = k4_dtconstr(k5_msafree(A,B)) ) ) ).
fof(d2_msaterm,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)) )
=> ! [C] :
( m1_struct_0(C,k5_msafree(A,B),k7_dtconstr(k5_msafree(A,B)))
=> ! [D] :
( m1_trees_4(D,k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
=> ( m1_msaterm(D,A,B,C)
<=> m2_dtconstr(D,k5_msafree(A,B),C) ) ) ) ) ) ).
fof(t1_msaterm,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)) )
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D)
& v1_finseq_1(D) )
=> ( ( r2_hidden(k4_trees_4(k4_tarski(C,u1_struct_0(A)),D),k1_msaterm(A,B))
& v6_trees_3(D) )
<=> m1_msaterm(D,A,B,k2_msaterm(A,B,C)) ) ) ) ) ) ).
fof(t2_msaterm,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)) )
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
=> ~ ( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k1_funct_1(B,D))
=> k1_funct_1(C,k1_xboole_0) != k4_tarski(E,D) ) )
& ~ r2_hidden(k1_funct_1(C,k1_xboole_0),k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A)))) ) ) ) ) ).
fof(t3_msaterm,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)) )
=> ! [C] :
( l3_msualg_1(C,A)
=> ! [D] :
( m1_dtconstr(D,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B)))
=> ~ ( ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
~ ( r2_hidden(F,k1_funct_1(u4_msualg_1(A,C),E))
& k1_funct_1(D,k1_xboole_0) = k4_tarski(F,E) ) )
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,k1_funct_1(B,E))
=> k1_funct_1(D,k1_xboole_0) != k4_tarski(F,E) ) )
& ~ r2_hidden(k1_funct_1(D,k1_xboole_0),k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A)))) ) ) ) ) ) ).
fof(t4_msaterm,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)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_funct_1(B,C))
=> m1_dtconstr(k1_trees_4(k4_tarski(D,C)),u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) ) ) ) ) ).
fof(t5_msaterm,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)) )
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k1_funct_1(B,D))
=> ( k1_funct_1(C,k1_xboole_0) = k4_tarski(E,D)
=> C = k1_trees_4(k4_tarski(E,D)) ) ) ) ) ) ) ).
fof(t6_msaterm,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)) )
=> ! [C] :
( l3_msualg_1(C,A)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( r2_hidden(E,k1_funct_1(u4_msualg_1(A,C),D))
=> m1_dtconstr(k1_trees_4(k4_tarski(E,D)),u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B))) ) ) ) ) ) ).
fof(t7_msaterm,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)) )
=> ! [C] :
( l3_msualg_1(C,A)
=> ! [D] :
( m1_dtconstr(D,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( ( r2_hidden(F,k1_funct_1(u4_msualg_1(A,C),E))
& k1_funct_1(D,k1_xboole_0) = k4_tarski(F,E) )
=> D = k1_trees_4(k4_tarski(F,E)) ) ) ) ) ) ) ).
fof(t8_msaterm,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)) )
=> ! [C] :
( l3_msualg_1(C,A)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k1_funct_1(B,D))
=> m1_dtconstr(k1_trees_4(k4_tarski(E,D)),u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B))) ) ) ) ) ) ).
fof(t9_msaterm,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)) )
=> ! [C] :
( l3_msualg_1(C,A)
=> ! [D] :
( m1_dtconstr(D,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,k1_funct_1(B,E))
=> ( k1_funct_1(D,k1_xboole_0) = k4_tarski(F,E)
=> D = k1_trees_4(k4_tarski(F,E)) ) ) ) ) ) ) ) ).
fof(t10_msaterm,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)) )
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
=> ! [D] :
( m1_subset_1(D,u1_msualg_1(A))
=> ~ ( k1_funct_1(C,k1_xboole_0) = k4_tarski(D,u1_struct_0(A))
& ! [E] :
( m1_msaterm(E,A,B,k2_msaterm(A,B,D))
=> C != k4_trees_4(k4_tarski(D,u1_struct_0(A)),E) ) ) ) ) ) ) ).
fof(d3_msaterm,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] :
( ( v2_relat_1(C)
& m1_pboole(C,u1_struct_0(A)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k1_funct_1(u4_msualg_1(A,B),D))
=> k4_msaterm(A,B,C,D,E) = k1_trees_4(k4_tarski(E,D)) ) ) ) ) ) ).
fof(d4_msaterm,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,u1_struct_0(A)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k1_funct_1(C,D))
=> k5_msaterm(A,B,C,D,E) = k1_trees_4(k4_tarski(E,D)) ) ) ) ) ) ).
fof(t11_msaterm,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)) )
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
=> ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& r2_hidden(C,k7_msafree(A,B,D)) ) ) ) ) ).
fof(t12_msaterm,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)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_tarski(k7_msafree(A,B,C),k1_msaterm(A,B)) ) ) ) ).
fof(t13_msaterm,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)) )
=> k1_msaterm(A,B) = k3_card_3(k8_msafree(A,B)) ) ) ).
fof(d5_msaterm,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)) )
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( D = k7_msaterm(A,B,C)
<=> r2_hidden(C,k7_msafree(A,B,D)) ) ) ) ) ) ).
fof(t14_msaterm,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)) )
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k1_funct_1(B,D))
=> ( C = k1_trees_4(k4_tarski(E,D))
=> k7_msaterm(A,B,C) = D ) ) ) ) ) ) ).
fof(t15_msaterm,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)) )
=> ! [C] :
( l3_msualg_1(C,A)
=> ! [D] :
( m1_dtconstr(D,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( ( r2_hidden(F,k1_funct_1(u4_msualg_1(A,C),E))
& D = k1_trees_4(k4_tarski(F,E)) )
=> k7_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B),D) = E ) ) ) ) ) ) ).
fof(t16_msaterm,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)) )
=> ! [C] :
( l3_msualg_1(C,A)
=> ! [D] :
( m1_dtconstr(D,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,k1_funct_1(B,E))
=> ( D = k1_trees_4(k4_tarski(F,E))
=> k7_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B),D) = E ) ) ) ) ) ) ) ).
fof(t17_msaterm,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)) )
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
=> ! [D] :
( m1_subset_1(D,u1_msualg_1(A))
=> ( k1_funct_1(C,k1_xboole_0) = k4_tarski(D,u1_struct_0(A))
=> k7_msaterm(A,B,C) = k2_msualg_1(A,D) ) ) ) ) ) ).
fof(t18_msaterm,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)) )
=> ! [C] :
( ( v5_msualg_1(C,A)
& l3_msualg_1(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k1_funct_1(u4_msualg_1(A,C),D))
=> k7_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B),k4_msaterm(A,C,B,D,E)) = D ) ) ) ) ) ).
fof(t19_msaterm,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)) )
=> ! [C] :
( l3_msualg_1(C,A)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k1_funct_1(B,D))
=> k7_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B),k5_msaterm(A,C,B,D,E)) = D ) ) ) ) ) ).
fof(t20_msaterm,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)) )
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ! [D] :
( m1_msaterm(D,A,B,k2_msaterm(A,B,C))
=> k7_msaterm(A,B,k6_msaterm(A,B,k2_msaterm(A,B,C),D)) = k2_msualg_1(A,C) ) ) ) ) ).
fof(t21_msaterm,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)) )
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ! [D] :
( m1_trees_4(D,k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
=> ( m1_msaterm(D,A,B,k2_msaterm(A,B,C))
<=> r1_lang1(k5_msafree(A,B),k2_msaterm(A,B,C),k1_dtconstr(u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),D)) ) ) ) ) ) ).
fof(t22_msaterm,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)) )
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ! [D] :
( m1_msaterm(D,A,B,k2_msaterm(A,B,C))
=> ( k3_finseq_1(D) = k3_finseq_1(k1_msualg_1(A,C))
& k4_finseq_1(D) = k4_finseq_1(k1_msualg_1(A,C))
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(E,k4_finseq_1(D))
=> m1_dtconstr(k1_funct_1(D,E),u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) ) ) ) ) ) ) ) ).
fof(t23_msaterm,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)) )
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ! [D] :
( m1_msaterm(D,A,B,k2_msaterm(A,B,C))
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(E,k4_finseq_1(D))
=> ! [F] :
( m1_dtconstr(F,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
=> ( F = k1_funct_1(D,E)
=> ( F = k4_finseq_4(k5_numbers,k1_msaterm(A,B),D,E)
& k7_msaterm(A,B,F) = k1_funct_1(k1_msualg_1(A,C),E)
& k7_msaterm(A,B,F) = k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,C),E) ) ) ) ) ) ) ) ) ) ).
fof(t24_msaterm,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)) )
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D)
& v1_finseq_1(D) )
=> ~ ( ( k3_finseq_1(D) = k3_finseq_1(k1_msualg_1(A,C))
| k4_finseq_1(D) = k4_finseq_1(k1_msualg_1(A,C)) )
& ( ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(E,k4_finseq_1(D))
& ! [F] :
( m1_dtconstr(F,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
=> ~ ( F = k1_funct_1(D,E)
& k7_msaterm(A,B,F) = k1_funct_1(k1_msualg_1(A,C),E) ) ) ) )
| ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(E,k4_finseq_1(D))
& ! [F] :
( m1_dtconstr(F,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
=> ~ ( F = k1_funct_1(D,E)
& k7_msaterm(A,B,F) = k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,C),E) ) ) ) ) )
& ~ m1_msaterm(D,A,B,k2_msaterm(A,B,C)) ) ) ) ) ) ).
fof(t25_msaterm,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)) )
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ! [D] :
( m1_trees_4(D,k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
=> ~ ( ( k3_finseq_1(D) = k3_finseq_1(k1_msualg_1(A,C))
| k4_finseq_1(D) = k4_finseq_1(k1_msualg_1(A,C)) )
& ( ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(E,k4_finseq_1(D))
=> ! [F] :
( m1_dtconstr(F,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
=> ( F = k1_funct_1(D,E)
=> k7_msaterm(A,B,F) = k1_funct_1(k1_msualg_1(A,C),E) ) ) ) )
| ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(E,k4_finseq_1(D))
=> ! [F] :
( m1_dtconstr(F,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
=> ( F = k1_funct_1(D,E)
=> k7_msaterm(A,B,F) = k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,C),E) ) ) ) ) )
& ~ m1_msaterm(D,A,B,k2_msaterm(A,B,C)) ) ) ) ) ) ).
fof(t26_msaterm,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)) )
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,u1_struct_0(A)) )
=> ( r2_pboole(u1_struct_0(A),B,C)
=> ! [D] :
( m1_dtconstr(D,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
=> m1_dtconstr(D,u1_struct_0(k5_msafree(A,C)),k5_trees_3(u1_struct_0(k5_msafree(A,C))),k1_msaterm(A,C)) ) ) ) ) ) ).
fof(t27_msaterm,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,u1_struct_0(A)) )
=> ! [D] :
( m1_dtconstr(D,u1_struct_0(k5_msafree(A,C)),k5_trees_3(u1_struct_0(k5_msafree(A,C))),k1_msaterm(A,C))
=> m1_dtconstr(D,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))) ) ) ) ) ).
fof(d6_msaterm,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)) )
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
=> ( m2_msaterm(C,A,B)
<=> r2_hidden(k1_funct_1(C,k1_xboole_0),k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A)))) ) ) ) ) ).
fof(d7_msaterm,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)) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(k1_msaterm(A,B))) )
=> ( m3_msaterm(C,A,B)
<=> ? [D] :
( m2_msaterm(D,A,B)
& r2_hidden(D,C) ) ) ) ) ) ).
fof(t28_msaterm,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)) )
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
=> ( ~ v1_trees_9(C)
=> m2_msaterm(C,A,B) ) ) ) ) ).
fof(t29_msaterm,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)) )
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B))
=> ! [D] :
( m1_trees_1(D,k1_relat_1(C))
=> m1_dtconstr(k7_trees_2(u1_struct_0(k5_msafree(A,B)),C,D),u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) ) ) ) ) ).
fof(d8_msaterm,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,u1_struct_0(A)) )
=> ( m4_msaterm(C,A,B)
<=> r5_pboole(u1_struct_0(A),C,u4_msualg_1(A,B)) ) ) ) ) ).
fof(t30_msaterm,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m4_msaterm(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( r2_hidden(E,k1_funct_1(u4_msualg_1(A,B),D))
=> ! [F] :
( m1_subset_1(F,k1_funct_1(C,D))
=> E != F ) ) ) ) ) ) ).
fof(d9_msaterm,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] :
( ( v2_relat_1(C)
& m1_pboole(C,u1_struct_0(A)) )
=> ! [D] :
( m1_dtconstr(D,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))
=> ! [E] :
( m3_pboole(E,u1_struct_0(A),C,u4_msualg_1(A,B))
=> ! [F] :
( ( v1_relat_1(F)
& v1_funct_1(F)
& v1_finset_1(F)
& v3_trees_2(F) )
=> ( r1_msaterm(A,B,C,D,E,F)
<=> ( k1_relat_1(F) = k1_relat_1(D)
& ! [G] :
( m1_trees_1(G,k1_relat_1(F))
=> ( ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,k1_funct_1(C,H))
=> ( k1_funct_1(D,G) = k4_tarski(I,H)
=> k1_funct_1(F,G) = k8_funct_2(k1_funct_1(C,H),k1_funct_1(u4_msualg_1(A,B),H),k1_msualg_3(u1_struct_0(A),C,u4_msualg_1(A,B),E,H),I) ) ) )
& ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,k1_funct_1(u4_msualg_1(A,B),H))
=> ( k1_funct_1(D,G) = k4_tarski(I,H)
=> k1_funct_1(F,G) = I ) ) )
& ! [H] :
( m1_subset_1(H,u1_msualg_1(A))
=> ( k1_funct_1(D,G) = k4_tarski(H,u1_struct_0(A))
=> k1_funct_1(F,G) = k1_funct_1(k5_msualg_1(A,H,B),k2_trees_9(F,G)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t31_msaterm,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] :
( m4_msaterm(C,A,B)
=> ! [D] :
( m1_dtconstr(D,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))
=> ! [E] :
( m3_pboole(E,u1_struct_0(A),C,u4_msualg_1(A,B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,k1_funct_1(u4_msualg_1(A,B),F))
=> ( D = k1_trees_4(k4_tarski(G,F))
=> r1_msaterm(A,B,C,D,E,k2_trees_4(k1_funct_1(u4_msualg_1(A,B),F),G)) ) ) ) ) ) ) ) ) ).
fof(t32_msaterm,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] :
( m4_msaterm(C,A,B)
=> ! [D] :
( m1_dtconstr(D,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))
=> ! [E] :
( m3_pboole(E,u1_struct_0(A),C,u4_msualg_1(A,B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,k1_funct_1(C,F))
=> ( D = k1_trees_4(k4_tarski(G,F))
=> r1_msaterm(A,B,C,D,E,k2_trees_4(k1_funct_1(u4_msualg_1(A,B),F),k8_funct_2(k1_funct_1(C,F),k1_funct_1(u4_msualg_1(A,B),F),k1_msualg_3(u1_struct_0(A),C,u4_msualg_1(A,B),E,F),G))) ) ) ) ) ) ) ) ) ).
fof(t33_msaterm,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] :
( m4_msaterm(C,A,B)
=> ! [D] :
( m3_pboole(D,u1_struct_0(A),C,u4_msualg_1(A,B))
=> ! [E] :
( m1_subset_1(E,u1_msualg_1(A))
=> ! [F] :
( m1_msaterm(F,A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),k2_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),E))
=> ! [G] :
( ( v1_relat_1(G)
& v1_funct_1(G)
& v1_finseq_1(G)
& v6_trees_3(G) )
=> ~ ( k3_finseq_1(G) = k3_finseq_1(F)
& ! [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
=> ! [I] :
( m1_dtconstr(I,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))
=> ~ ( r2_hidden(H,k4_finseq_1(F))
& I = k1_funct_1(F,H)
& ! [J] :
( ( v1_relat_1(J)
& v1_funct_1(J)
& v1_finset_1(J)
& v3_trees_2(J) )
=> ~ ( J = k1_funct_1(G,H)
& r1_msaterm(A,B,C,I,D,J) ) ) ) ) )
& ! [H] :
( ( v1_relat_1(H)
& v1_funct_1(H)
& v1_finset_1(H)
& v3_trees_2(H) )
=> ~ ( H = k4_trees_4(k1_funct_1(k5_msualg_1(A,E,B),k16_trees_3(G)),G)
& r1_msaterm(A,B,C,k6_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),k2_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),E),F),D,H) ) ) ) ) ) ) ) ) ) ) ).
fof(t34_msaterm,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] :
( m4_msaterm(C,A,B)
=> ! [D] :
( m3_pboole(D,u1_struct_0(A),C,u4_msualg_1(A,B))
=> ! [E] :
( m1_dtconstr(E,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))
=> ! [F] :
( ( v1_relat_1(F)
& v1_funct_1(F)
& v1_finset_1(F)
& v3_trees_2(F) )
=> ( r1_msaterm(A,B,C,E,D,F)
=> ! [G] :
( m1_trees_1(G,k1_relat_1(E))
=> ! [H] :
( m1_trees_1(H,k1_relat_1(F))
=> ( H = G
=> r1_msaterm(A,B,C,k8_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),E,G),D,k5_trees_2(F,H)) ) ) ) ) ) ) ) ) ) ) ).
fof(t35_msaterm,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] :
( m4_msaterm(C,A,B)
=> ! [D] :
( m3_pboole(D,u1_struct_0(A),C,u4_msualg_1(A,B))
=> ! [E] :
( m1_subset_1(E,u1_msualg_1(A))
=> ! [F] :
( m1_msaterm(F,A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),k2_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),E))
=> ! [G] :
( ( v1_relat_1(G)
& v1_funct_1(G)
& v1_finset_1(G)
& v3_trees_2(G) )
=> ~ ( r1_msaterm(A,B,C,k6_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),k2_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),E),F),D,G)
& ! [H] :
( ( v1_relat_1(H)
& v1_funct_1(H)
& v1_finseq_1(H)
& v6_trees_3(H) )
=> ~ ( k3_finseq_1(H) = k3_finseq_1(F)
& G = k4_trees_4(k1_funct_1(k5_msualg_1(A,E,B),k16_trees_3(H)),H)
& ! [I] :
( m2_subset_1(I,k1_numbers,k5_numbers)
=> ! [J] :
( m1_dtconstr(J,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))
=> ~ ( r2_hidden(I,k4_finseq_1(F))
& J = k1_funct_1(F,I)
& ! [K] :
( ( v1_relat_1(K)
& v1_funct_1(K)
& v1_finset_1(K)
& v3_trees_2(K) )
=> ~ ( K = k1_funct_1(H,I)
& r1_msaterm(A,B,C,J,D,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t36_msaterm,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] :
( m4_msaterm(C,A,B)
=> ! [D] :
( m1_dtconstr(D,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))
=> ! [E] :
( m3_pboole(E,u1_struct_0(A),C,u4_msualg_1(A,B))
=> ? [F] :
( v1_relat_1(F)
& v1_funct_1(F)
& v1_finset_1(F)
& v3_trees_2(F)
& r1_msaterm(A,B,C,D,E,F) ) ) ) ) ) ) ).
fof(t37_msaterm,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] :
( m4_msaterm(C,A,B)
=> ! [D] :
( m1_dtconstr(D,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))
=> ! [E] :
( m3_pboole(E,u1_struct_0(A),C,u4_msualg_1(A,B))
=> ! [F] :
( ( v1_relat_1(F)
& v1_funct_1(F)
& v1_finset_1(F)
& v3_trees_2(F) )
=> ! [G] :
( ( v1_relat_1(G)
& v1_funct_1(G)
& v1_finset_1(G)
& v3_trees_2(G) )
=> ( ( r1_msaterm(A,B,C,D,E,F)
& r1_msaterm(A,B,C,D,E,G) )
=> F = G ) ) ) ) ) ) ) ) ).
fof(t38_msaterm,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] :
( m4_msaterm(C,A,B)
=> ! [D] :
( m1_dtconstr(D,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))
=> ! [E] :
( m3_pboole(E,u1_struct_0(A),C,u4_msualg_1(A,B))
=> ! [F] :
( ( v1_relat_1(F)
& v1_funct_1(F)
& v1_finset_1(F)
& v3_trees_2(F) )
=> ( r1_msaterm(A,B,C,D,E,F)
=> r2_hidden(k1_funct_1(F,k1_xboole_0),k1_funct_1(u4_msualg_1(A,B),k7_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),D))) ) ) ) ) ) ) ) ).
fof(d10_msaterm,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] :
( m4_msaterm(C,A,B)
=> ! [D] :
( m1_dtconstr(D,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))
=> ! [E] :
( m3_pboole(E,u1_struct_0(A),C,u4_msualg_1(A,B))
=> ! [F] :
( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,B),k7_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),D)))
=> ( F = k9_msaterm(A,B,C,D,E)
<=> ? [G] :
( v1_relat_1(G)
& v1_funct_1(G)
& v1_finset_1(G)
& v3_trees_2(G)
& r1_msaterm(A,B,C,D,E,G)
& F = k1_funct_1(G,k1_xboole_0) ) ) ) ) ) ) ) ) ).
fof(t39_msaterm,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] :
( m4_msaterm(C,A,B)
=> ! [D] :
( m3_pboole(D,u1_struct_0(A),C,u4_msualg_1(A,B))
=> ! [E] :
( m1_dtconstr(E,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))
=> ! [F] :
( ( v1_relat_1(F)
& v1_funct_1(F)
& v1_finset_1(F)
& v3_trees_2(F) )
=> ( r1_msaterm(A,B,C,E,D,F)
=> k9_msaterm(A,B,C,E,D) = k1_funct_1(F,k1_xboole_0) ) ) ) ) ) ) ) ).
fof(t40_msaterm,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] :
( m4_msaterm(C,A,B)
=> ! [D] :
( m3_pboole(D,u1_struct_0(A),C,u4_msualg_1(A,B))
=> ! [E] :
( m1_dtconstr(E,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))
=> ! [F] :
( ( v1_relat_1(F)
& v1_funct_1(F)
& v1_finset_1(F)
& v3_trees_2(F) )
=> ( r1_msaterm(A,B,C,E,D,F)
=> ! [G] :
( m1_trees_1(G,k1_relat_1(E))
=> k1_funct_1(F,G) = k9_msaterm(A,B,C,k8_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),E,G),D) ) ) ) ) ) ) ) ) ).
fof(t41_msaterm,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] :
( m4_msaterm(C,A,B)
=> ! [D] :
( m3_pboole(D,u1_struct_0(A),C,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))
=> k9_msaterm(A,B,C,k4_msaterm(A,B,C,E,F),D) = F ) ) ) ) ) ) ).
fof(t42_msaterm,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] :
( m4_msaterm(C,A,B)
=> ! [D] :
( m3_pboole(D,u1_struct_0(A),C,u4_msualg_1(A,B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,k1_funct_1(C,E))
=> k9_msaterm(A,B,C,k5_msaterm(A,B,C,E,F),D) = k8_funct_2(k1_funct_1(C,E),k1_funct_1(u4_msualg_1(A,B),E),k1_msualg_3(u1_struct_0(A),C,u4_msualg_1(A,B),D,E),F) ) ) ) ) ) ) ).
fof(t43_msaterm,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] :
( m4_msaterm(C,A,B)
=> ! [D] :
( m3_pboole(D,u1_struct_0(A),C,u4_msualg_1(A,B))
=> ! [E] :
( m1_subset_1(E,u1_msualg_1(A))
=> ! [F] :
( m1_msaterm(F,A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),k2_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),E))
=> ! [G] :
( ( v1_relat_1(G)
& v1_funct_1(G)
& v1_finseq_1(G) )
=> ( ( k3_finseq_1(G) = k3_finseq_1(F)
& ! [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
=> ( r2_hidden(H,k4_finseq_1(F))
=> ! [I] :
( m1_dtconstr(I,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))
=> ( I = k1_funct_1(F,H)
=> k1_funct_1(G,H) = k9_msaterm(A,B,C,I,D) ) ) ) ) )
=> k9_msaterm(A,B,C,k6_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),k2_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),E),F),D) = k1_funct_1(k5_msualg_1(A,E,B),G) ) ) ) ) ) ) ) ) ).
fof(s1_msaterm,axiom,
( ( ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s1_msaterm))
=> ! [B] :
( m1_subset_1(B,k1_funct_1(f2_s1_msaterm,A))
=> p1_s1_msaterm(k1_trees_4(k4_tarski(B,A))) ) )
& ! [A] :
( m1_subset_1(A,u1_msualg_1(f1_s1_msaterm))
=> ! [B] :
( m1_msaterm(B,f1_s1_msaterm,f2_s1_msaterm,k2_msaterm(f1_s1_msaterm,f2_s1_msaterm,A))
=> ( ! [C] :
( m1_dtconstr(C,u1_struct_0(k5_msafree(f1_s1_msaterm,f2_s1_msaterm)),k5_trees_3(u1_struct_0(k5_msafree(f1_s1_msaterm,f2_s1_msaterm))),k1_msaterm(f1_s1_msaterm,f2_s1_msaterm))
=> ( r2_hidden(C,k2_relat_1(B))
=> p1_s1_msaterm(C) ) )
=> p1_s1_msaterm(k4_trees_4(k4_tarski(A,u1_struct_0(f1_s1_msaterm)),B)) ) ) ) )
=> ! [A] :
( m1_dtconstr(A,u1_struct_0(k5_msafree(f1_s1_msaterm,f2_s1_msaterm)),k5_trees_3(u1_struct_0(k5_msafree(f1_s1_msaterm,f2_s1_msaterm))),k1_msaterm(f1_s1_msaterm,f2_s1_msaterm))
=> p1_s1_msaterm(A) ) ) ).
fof(s2_msaterm,axiom,
( ( ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s2_msaterm))
=> ! [B] :
( m1_subset_1(B,k1_funct_1(u4_msualg_1(f1_s2_msaterm,f2_s2_msaterm),A))
=> p1_s2_msaterm(k1_trees_4(k4_tarski(B,A))) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s2_msaterm))
=> ! [B] :
( m1_subset_1(B,k1_funct_1(f3_s2_msaterm,A))
=> p1_s2_msaterm(k1_trees_4(k4_tarski(B,A))) ) )
& ! [A] :
( m1_subset_1(A,u1_msualg_1(f1_s2_msaterm))
=> ! [B] :
( m1_msaterm(B,f1_s2_msaterm,k2_pboole(u1_struct_0(f1_s2_msaterm),u4_msualg_1(f1_s2_msaterm,f2_s2_msaterm),f3_s2_msaterm),k2_msaterm(f1_s2_msaterm,k2_pboole(u1_struct_0(f1_s2_msaterm),u4_msualg_1(f1_s2_msaterm,f2_s2_msaterm),f3_s2_msaterm),A))
=> ( ! [C] :
( m1_dtconstr(C,u1_struct_0(k5_msafree(f1_s2_msaterm,k2_pboole(u1_struct_0(f1_s2_msaterm),u4_msualg_1(f1_s2_msaterm,f2_s2_msaterm),f3_s2_msaterm))),k5_trees_3(u1_struct_0(k5_msafree(f1_s2_msaterm,k2_pboole(u1_struct_0(f1_s2_msaterm),u4_msualg_1(f1_s2_msaterm,f2_s2_msaterm),f3_s2_msaterm)))),k1_msaterm(f1_s2_msaterm,k2_pboole(u1_struct_0(f1_s2_msaterm),u4_msualg_1(f1_s2_msaterm,f2_s2_msaterm),f3_s2_msaterm)))
=> ( r2_hidden(C,k2_relat_1(B))
=> p1_s2_msaterm(C) ) )
=> p1_s2_msaterm(k12_trees_4(u1_struct_0(k5_msafree(f1_s2_msaterm,k2_pboole(u1_struct_0(f1_s2_msaterm),u4_msualg_1(f1_s2_msaterm,f2_s2_msaterm),f3_s2_msaterm))),k2_msaterm(f1_s2_msaterm,k2_pboole(u1_struct_0(f1_s2_msaterm),u4_msualg_1(f1_s2_msaterm,f2_s2_msaterm),f3_s2_msaterm),A),B)) ) ) ) )
=> ! [A] :
( m1_dtconstr(A,u1_struct_0(k5_msafree(f1_s2_msaterm,k2_pboole(u1_struct_0(f1_s2_msaterm),u4_msualg_1(f1_s2_msaterm,f2_s2_msaterm),f3_s2_msaterm))),k5_trees_3(u1_struct_0(k5_msafree(f1_s2_msaterm,k2_pboole(u1_struct_0(f1_s2_msaterm),u4_msualg_1(f1_s2_msaterm,f2_s2_msaterm),f3_s2_msaterm)))),k1_msaterm(f1_s2_msaterm,k2_pboole(u1_struct_0(f1_s2_msaterm),u4_msualg_1(f1_s2_msaterm,f2_s2_msaterm),f3_s2_msaterm)))
=> p1_s2_msaterm(A) ) ) ).
fof(s3_msaterm,axiom,
( ( ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s3_msaterm))
=> ! [B] :
( m1_subset_1(B,k1_funct_1(u4_msualg_1(f1_s3_msaterm,f2_s3_msaterm),A))
=> p1_s3_msaterm(k4_msaterm(f1_s3_msaterm,f2_s3_msaterm,f3_s3_msaterm,A,B)) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s3_msaterm))
=> ! [B] :
( m1_subset_1(B,k1_funct_1(f3_s3_msaterm,A))
=> p1_s3_msaterm(k5_msaterm(f1_s3_msaterm,f2_s3_msaterm,f3_s3_msaterm,A,B)) ) )
& ! [A] :
( m1_subset_1(A,u1_msualg_1(f1_s3_msaterm))
=> ! [B] :
( m1_msaterm(B,f1_s3_msaterm,k2_pboole(u1_struct_0(f1_s3_msaterm),u4_msualg_1(f1_s3_msaterm,f2_s3_msaterm),f3_s3_msaterm),k2_msaterm(f1_s3_msaterm,k2_pboole(u1_struct_0(f1_s3_msaterm),u4_msualg_1(f1_s3_msaterm,f2_s3_msaterm),f3_s3_msaterm),A))
=> ( ! [C] :
( m1_dtconstr(C,u1_struct_0(k5_msafree(f1_s3_msaterm,k2_pboole(u1_struct_0(f1_s3_msaterm),u4_msualg_1(f1_s3_msaterm,f2_s3_msaterm),f3_s3_msaterm))),k5_trees_3(u1_struct_0(k5_msafree(f1_s3_msaterm,k2_pboole(u1_struct_0(f1_s3_msaterm),u4_msualg_1(f1_s3_msaterm,f2_s3_msaterm),f3_s3_msaterm)))),k1_msaterm(f1_s3_msaterm,k2_pboole(u1_struct_0(f1_s3_msaterm),u4_msualg_1(f1_s3_msaterm,f2_s3_msaterm),f3_s3_msaterm)))
=> ( r2_hidden(C,k2_relat_1(B))
=> p1_s3_msaterm(C) ) )
=> p1_s3_msaterm(k6_msaterm(f1_s3_msaterm,k2_pboole(u1_struct_0(f1_s3_msaterm),u4_msualg_1(f1_s3_msaterm,f2_s3_msaterm),f3_s3_msaterm),k2_msaterm(f1_s3_msaterm,k2_pboole(u1_struct_0(f1_s3_msaterm),u4_msualg_1(f1_s3_msaterm,f2_s3_msaterm),f3_s3_msaterm),A),B)) ) ) ) )
=> ! [A] :
( m1_dtconstr(A,u1_struct_0(k5_msafree(f1_s3_msaterm,k2_pboole(u1_struct_0(f1_s3_msaterm),u4_msualg_1(f1_s3_msaterm,f2_s3_msaterm),f3_s3_msaterm))),k5_trees_3(u1_struct_0(k5_msafree(f1_s3_msaterm,k2_pboole(u1_struct_0(f1_s3_msaterm),u4_msualg_1(f1_s3_msaterm,f2_s3_msaterm),f3_s3_msaterm)))),k1_msaterm(f1_s3_msaterm,k2_pboole(u1_struct_0(f1_s3_msaterm),u4_msualg_1(f1_s3_msaterm,f2_s3_msaterm),f3_s3_msaterm)))
=> p1_s3_msaterm(A) ) ) ).
fof(dt_m1_msaterm,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A))
& m1_subset_1(C,k7_dtconstr(k5_msafree(A,B))) )
=> ! [D] :
( m1_msaterm(D,A,B,C)
=> m1_trees_4(D,k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) ) ) ).
fof(existence_m1_msaterm,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A))
& m1_subset_1(C,k7_dtconstr(k5_msafree(A,B))) )
=> ? [D] : m1_msaterm(D,A,B,C) ) ).
fof(dt_m2_msaterm,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)) )
=> ! [C] :
( m2_msaterm(C,A,B)
=> m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) ) ) ).
fof(existence_m2_msaterm,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)) )
=> ? [C] : m2_msaterm(C,A,B) ) ).
fof(dt_m3_msaterm,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)) )
=> ! [C] :
( m3_msaterm(C,A,B)
=> ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(k1_msaterm(A,B))) ) ) ) ).
fof(existence_m3_msaterm,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)) )
=> ? [C] : m3_msaterm(C,A,B) ) ).
fof(dt_m4_msaterm,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m4_msaterm(C,A,B)
=> ( v2_relat_1(C)
& m1_pboole(C,u1_struct_0(A)) ) ) ) ).
fof(existence_m4_msaterm,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& l3_msualg_1(B,A) )
=> ? [C] : m4_msaterm(C,A,B) ) ).
fof(dt_k1_msaterm,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& m1_pboole(B,u1_struct_0(A)) )
=> m1_subset_1(k1_msaterm(A,B),k1_zfmisc_1(k5_trees_3(u1_struct_0(k5_msafree(A,B))))) ) ).
fof(dt_k2_msaterm,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A))
& m1_subset_1(C,u1_msualg_1(A)) )
=> m1_struct_0(k2_msaterm(A,B,C),k5_msafree(A,B),k7_dtconstr(k5_msafree(A,B))) ) ).
fof(redefinition_k2_msaterm,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A))
& m1_subset_1(C,u1_msualg_1(A)) )
=> k2_msaterm(A,B,C) = k6_msafree(A,B,C) ) ).
fof(dt_k3_msaterm,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A))
& m1_subset_1(C,k1_msaterm(A,B))
& m1_subset_1(D,k1_relat_1(C)) )
=> m1_subset_1(k3_msaterm(A,B,C,D),u1_struct_0(k5_msafree(A,B))) ) ).
fof(redefinition_k3_msaterm,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A))
& m1_subset_1(C,k1_msaterm(A,B))
& m1_subset_1(D,k1_relat_1(C)) )
=> k3_msaterm(A,B,C,D) = k1_funct_1(C,D) ) ).
fof(dt_k4_msaterm,axiom,
! [A,B,C,D,E] :
( ( ~ 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_pboole(C,u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(A))
& m1_subset_1(E,k1_funct_1(u4_msualg_1(A,B),D)) )
=> m1_dtconstr(k4_msaterm(A,B,C,D,E),u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))) ) ).
fof(dt_k5_msaterm,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& l3_msualg_1(B,A)
& v2_relat_1(C)
& m1_pboole(C,u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(A))
& m1_subset_1(E,k1_funct_1(C,D)) )
=> m1_dtconstr(k5_msaterm(A,B,C,D,E),u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))) ) ).
fof(dt_k6_msaterm,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A))
& m1_subset_1(C,k7_dtconstr(k5_msafree(A,B)))
& m1_msaterm(D,A,B,C) )
=> m1_dtconstr(k6_msaterm(A,B,C,D),u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) ) ).
fof(redefinition_k6_msaterm,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A))
& m1_subset_1(C,k7_dtconstr(k5_msafree(A,B)))
& m1_msaterm(D,A,B,C) )
=> k6_msaterm(A,B,C,D) = k4_trees_4(C,D) ) ).
fof(dt_k7_msaterm,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A))
& m1_subset_1(C,k1_msaterm(A,B)) )
=> m1_subset_1(k7_msaterm(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k8_msaterm,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A))
& m1_subset_1(C,k1_msaterm(A,B))
& m1_subset_1(D,k1_relat_1(C)) )
=> m1_dtconstr(k8_msaterm(A,B,C,D),u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) ) ).
fof(redefinition_k8_msaterm,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A))
& m1_subset_1(C,k1_msaterm(A,B))
& m1_subset_1(D,k1_relat_1(C)) )
=> k8_msaterm(A,B,C,D) = k5_trees_2(C,D) ) ).
fof(dt_k9_msaterm,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v5_msualg_1(B,A)
& l3_msualg_1(B,A)
& m4_msaterm(C,A,B)
& m1_subset_1(D,k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))
& m3_pboole(E,u1_struct_0(A),C,u4_msualg_1(A,B)) )
=> m1_subset_1(k9_msaterm(A,B,C,D,E),k1_funct_1(u4_msualg_1(A,B),k7_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),D))) ) ).
%------------------------------------------------------------------------------