SET007 Axioms: SET007+739.ax
%------------------------------------------------------------------------------
% File : SET007+739 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Free Order 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 : osafree [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 135 ( 1 unt; 0 def)
% Number of atoms : 1675 ( 108 equ)
% Maximal formula atoms : 34 ( 12 avg)
% Number of connectives : 1827 ( 287 ~; 1 |;1059 &)
% ( 52 <=>; 428 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 12 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 66 ( 64 usr; 1 prp; 0-4 aty)
% Number of functors : 99 ( 99 usr; 3 con; 0-5 aty)
% Number of variables : 525 ( 494 !; 31 ?)
% 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_osafree,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& m1_pboole(B,u1_struct_0(A)) )
=> ( ~ v3_struct_0(k2_osafree(A,B))
& v1_lang1(k2_osafree(A,B)) ) ) ).
fof(fc2_osafree,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ( ~ v3_struct_0(k2_osafree(A,B))
& v1_lang1(k2_osafree(A,B))
& v1_dtconstr(k2_osafree(A,B))
& v2_dtconstr(k2_osafree(A,B))
& v3_dtconstr(k2_osafree(A,B)) ) ) ).
fof(fc3_osafree,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( ~ v1_xboole_0(k4_osafree(A,B,C))
& v3_trees_3(k4_osafree(A,B,C)) ) ) ).
fof(fc4_osafree,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ( v1_relat_1(k5_osafree(A,B))
& v2_relat_1(k5_osafree(A,B))
& ~ v3_relat_1(k5_osafree(A,B))
& v1_funct_1(k5_osafree(A,B))
& v11_osalg_1(k5_osafree(A,B),A) ) ) ).
fof(fc5_osafree,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ( v4_msualg_1(k8_osafree(A,B),A)
& v5_msualg_1(k8_osafree(A,B),A)
& v12_osalg_1(k8_osafree(A,B),A) ) ) ).
fof(fc6_osafree,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A))
& m1_subset_1(C,u1_msualg_1(A)) )
=> ~ v1_xboole_0(k3_msualg_1(A,C,k8_osafree(A,B))) ) ).
fof(rc1_osafree,axiom,
? [A] :
( l3_osalg_1(A)
& ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A)
& v10_osalg_1(A)
& v2_osalg_4(A) ) ).
fof(fc7_osafree,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ( v1_relat_1(k20_osafree(A,B))
& v1_funct_1(k20_osafree(A,B))
& v1_msualg_4(k20_osafree(A,B))
& v3_msualg_4(k20_osafree(A,B),A,k8_osafree(A,B))
& v4_msualg_4(k20_osafree(A,B),A,k8_osafree(A,B))
& v3_osalg_4(k20_osafree(A,B),A,k8_osafree(A,B)) ) ) ).
fof(fc8_osafree,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ~ v1_xboole_0(k21_osafree(A,B,C)) ) ).
fof(fc9_osafree,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ~ v1_xboole_0(k23_osafree(A,B,C)) ) ).
fof(fc10_osafree,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ( v1_relat_1(k24_osafree(A,B))
& v2_relat_1(k24_osafree(A,B))
& ~ v3_relat_1(k24_osafree(A,B))
& v1_funct_1(k24_osafree(A,B)) ) ) ).
fof(rc2_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ? [B] :
( l3_msualg_1(B,A)
& v4_msualg_1(B,A)
& v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& v13_osalg_1(B,A)
& v2_osafree(B,A) ) ) ).
fof(d1_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
=> ( m1_osafree(C,A,B)
<=> ! [D] :
( m2_osalg_2(D,A,B)
=> ( r6_pboole(u1_struct_0(A),D,k2_osalg_2(A,C))
=> r6_pboole(u1_struct_0(A),u4_msualg_1(A,k10_osalg_2(A,B,D)),u4_msualg_1(A,B)) ) ) ) ) ) ) ).
fof(t1_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v4_msualg_1(B,A)
& v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
=> ( m1_osafree(C,A,B)
<=> ! [D] :
( m2_osalg_2(D,A,B)
=> ( r6_pboole(u1_struct_0(A),D,k2_osalg_2(A,C))
=> k10_osalg_2(A,B,D) = B ) ) ) ) ) ) ).
fof(d2_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& v13_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_osafree(C,A,B)
=> ( v1_osafree(C,A,B)
<=> ! [D] :
( ( v5_msualg_1(D,A)
& v12_osalg_1(D,A)
& v13_osalg_1(D,A)
& l3_msualg_1(D,A) )
=> ! [E] :
( m3_pboole(E,u1_struct_0(A),C,u4_msualg_1(A,D))
=> ? [F] :
( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,D))
& r1_msualg_3(A,B,D,F)
& v1_osalg_3(F,A)
& r6_pboole(u1_struct_0(A),k1_msafree(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,D),C,F),E) ) ) ) ) ) ) ) ).
fof(d3_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& v13_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ( v2_osafree(B,A)
<=> ? [C] :
( m1_osafree(C,A,B)
& v1_osafree(C,A,B) ) ) ) ) ).
fof(d4_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( m1_pboole(B,u1_struct_0(A))
=> ! [C] :
( m2_relset_1(C,k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B))),k3_finseq_2(k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B)))))
=> ( C = k1_osafree(A,B)
<=> ! [D] :
( m1_subset_1(D,k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B))))
=> ! [E] :
( m2_finseq_2(E,k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B))),k3_finseq_2(k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B)))))
=> ( r2_hidden(k4_tarski(D,E),C)
<=> ( r2_hidden(D,k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))))
& ! [F] :
( m1_subset_1(F,u1_msualg_1(A))
=> ( k4_tarski(F,u1_struct_0(A)) = D
=> ( k3_finseq_1(E) = k3_finseq_1(k1_msualg_1(A,F))
& ! [G] :
( r2_hidden(G,k4_finseq_1(E))
=> ( ( r2_hidden(k1_funct_1(E,G),k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))))
=> ! [H] :
( m1_subset_1(H,u1_msualg_1(A))
=> ( k4_tarski(H,u1_struct_0(A)) = k1_funct_1(E,G)
=> r3_orders_2(A,k1_osalg_1(A,H),k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,F),G)) ) ) )
& ~ ( r2_hidden(k1_funct_1(E,G),k3_card_3(k3_msafree(u1_struct_0(A),B)))
& ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ~ ( r3_orders_2(A,H,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,F),G))
& r2_hidden(k1_funct_1(E,G),k2_msafree(u1_struct_0(A),B,H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t2_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( m1_pboole(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ! [D] :
( m2_finseq_2(D,k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B))),k3_finseq_2(k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B)))))
=> ( r2_hidden(k4_tarski(k4_tarski(C,u1_struct_0(A)),D),k1_osafree(A,B))
<=> ( k3_finseq_1(D) = k3_finseq_1(k1_msualg_1(A,C))
& ! [E] :
( r2_hidden(E,k4_finseq_1(D))
=> ( ( r2_hidden(k1_funct_1(D,E),k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))))
=> ! [F] :
( m1_subset_1(F,u1_msualg_1(A))
=> ( k4_tarski(F,u1_struct_0(A)) = k1_funct_1(D,E)
=> r3_orders_2(A,k1_osalg_1(A,F),k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,C),E)) ) ) )
& ~ ( r2_hidden(k1_funct_1(D,E),k3_card_3(k3_msafree(u1_struct_0(A),B)))
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( r3_orders_2(A,F,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,C),E))
& r2_hidden(k1_funct_1(D,E),k2_msafree(u1_struct_0(A),B,F)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d5_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( m1_pboole(B,u1_struct_0(A))
=> k2_osafree(A,B) = g1_lang1(k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B))),k1_osafree(A,B)) ) ) ).
fof(t3_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ( k6_lang1(k2_osafree(A,B)) = k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A)))
& k5_lang1(k2_osafree(A,B)) = k3_card_3(k3_msafree(u1_struct_0(A),B)) ) ) ) ).
fof(t4_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( r2_hidden(C,k6_dtconstr(k2_osafree(A,B)))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& ? [E] :
( r2_hidden(E,k1_funct_1(B,D))
& C = k4_tarski(E,D) ) ) ) ) ) ).
fof(d6_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> k3_osafree(A,B,C) = k4_tarski(C,u1_struct_0(A)) ) ) ) ).
fof(d8_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( ( v11_osalg_1(C,A)
& m1_pboole(C,u1_struct_0(A)) )
=> ( C = k5_osafree(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k1_funct_1(C,D) = k4_osafree(A,B,D) ) ) ) ) ) ).
fof(t5_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ! [D] :
( r2_hidden(D,k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k5_osafree(A,B))),C))
=> m1_trees_4(D,k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B))) ) ) ) ) ).
fof(t6_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_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(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> ( r2_hidden(D,k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k5_osafree(A,B))),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))
=> r2_hidden(k1_funct_1(D,E),k4_osafree(A,B,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,C),E))) ) ) ) ) ) ) ) ) ).
fof(t7_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_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(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> ( r1_lang1(k2_osafree(A,B),k3_osafree(A,B,C),k1_dtconstr(u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),D))
<=> r2_hidden(D,k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k5_osafree(A,B))),C)) ) ) ) ) ) ).
fof(t8_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> k3_tarski(k2_relat_1(k5_osafree(A,B))) = k4_dtconstr(k2_osafree(A,B)) ) ) ).
fof(d9_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_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_funct_1(D)
& v1_funct_2(D,k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k5_osafree(A,B))),C),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k5_osafree(A,B)),C))
& m2_relset_1(D,k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k5_osafree(A,B))),C),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k5_osafree(A,B)),C)) )
=> ( D = k6_osafree(A,B,C)
<=> ! [E] :
( m1_trees_4(E,k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> ( r1_lang1(k2_osafree(A,B),k3_osafree(A,B,C),k1_dtconstr(u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),E))
=> k1_funct_1(D,E) = k12_trees_4(u1_struct_0(k2_osafree(A,B)),k3_osafree(A,B,C),E) ) ) ) ) ) ) ) ).
fof(d10_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m3_pboole(C,u1_msualg_1(A),k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k5_osafree(A,B))),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k5_osafree(A,B)))
=> ( C = k7_osafree(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_msualg_1(A))
=> k5_msualg_4(A,k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k5_osafree(A,B))),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k5_osafree(A,B)),C,D) = k6_osafree(A,B,D) ) ) ) ) ) ).
fof(d11_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> k8_osafree(A,B) = g3_msualg_1(A,k5_osafree(A,B),k7_osafree(A,B)) ) ) ).
fof(t10_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_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,u1_struct_0(A))
=> ! [E] :
( r2_hidden(E,k1_funct_1(B,C))
=> ( m1_dtconstr(k1_trees_4(k4_tarski(E,C)),u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
& ! [F] : k4_tarski(F,u1_struct_0(A)) != k1_funct_1(k1_trees_4(k4_tarski(E,C)),k1_xboole_0)
& ( r2_hidden(k1_trees_4(k4_tarski(E,C)),k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),D))
=> r3_orders_2(A,C,D) )
& ( r3_orders_2(A,C,D)
=> r2_hidden(k1_trees_4(k4_tarski(E,C)),k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),D)) ) ) ) ) ) ) ) ).
fof(t11_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(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] :
( m2_dtconstr(E,k2_osafree(A,B),k9_osafree(A,B,D))
& C = k9_dtconstr(k2_osafree(A,B),k9_osafree(A,B,D),E)
& r1_lang1(k2_osafree(A,B),k9_osafree(A,B,D),k1_dtconstr(u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),E))
& r2_hidden(E,k3_msualg_1(A,D,k8_osafree(A,B)))
& C = k1_funct_1(k5_msualg_1(A,D,k8_osafree(A,B)),E) )
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] : C != k1_trees_4(k4_tarski(F,E)) )
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r2_hidden(C,k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),E))
<=> r3_orders_2(A,k1_osalg_1(A,D),E) ) ) ) ) ) ) ) ) ).
fof(t12_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_osafree(A,B)))
=> ! [D] :
( m1_trees_4(D,k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> ( r1_lang1(k2_osafree(A,B),C,k1_dtconstr(u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),D))
=> ( r2_hidden(C,k7_dtconstr(k2_osafree(A,B)))
& r2_hidden(k12_trees_4(u1_struct_0(k2_osafree(A,B)),C,D),k4_dtconstr(k2_osafree(A,B)))
& ? [E] :
( m1_subset_1(E,u1_msualg_1(A))
& C = k4_tarski(E,u1_struct_0(A))
& r2_hidden(D,k3_msualg_1(A,E,k8_osafree(A,B)))
& k12_trees_4(u1_struct_0(k2_osafree(A,B)),C,D) = k1_funct_1(k5_msualg_1(A,E,k8_osafree(A,B)),D)
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( r2_hidden(k12_trees_4(u1_struct_0(k2_osafree(A,B)),C,D),k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),F))
<=> r3_orders_2(A,k1_osalg_1(A,E),F) ) ) ) ) ) ) ) ) ) ).
fof(t13_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_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(D,k3_msualg_1(A,C,k8_osafree(A,B)))
<=> ( m1_trees_4(D,k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
& r1_lang1(k2_osafree(A,B),k9_osafree(A,B,C),k16_trees_3(D)) ) ) ) ) ) ) ).
fof(t14_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& r2_hidden(C,k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),D))
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r2_hidden(C,k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),E))
=> r3_orders_2(A,D,E) ) ) ) ) ) ) ).
fof(d12_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( D = k10_osafree(A,B,C)
<=> ( r2_hidden(C,k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),D))
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r2_hidden(C,k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),E))
=> r3_orders_2(A,D,E) ) ) ) ) ) ) ) ) ).
fof(t15_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,k3_card_3(u4_msualg_1(A,k8_osafree(A,B))))
<=> m1_dtconstr(C,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B))) ) ) ) ).
fof(t16_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( r2_hidden(D,k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),C))
=> m1_dtconstr(D,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B))) ) ) ) ) ).
fof(t17_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( r2_hidden(D,k1_funct_1(B,C))
=> ! [E] :
( m1_dtconstr(E,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> ( E = k1_trees_4(k4_tarski(D,C))
=> k10_osafree(A,B,E) = C ) ) ) ) ) ) ).
fof(t18_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_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_subset_1(D,k3_msualg_1(A,C,k8_osafree(A,B)))
=> ! [E] :
( m1_dtconstr(E,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> ( E = k8_funct_2(k3_msualg_1(A,C,k8_osafree(A,B)),k4_msualg_1(A,C,k8_osafree(A,B)),k5_msualg_1(A,C,k8_osafree(A,B)),D)
=> k10_osafree(A,B,E) = k1_osalg_1(A,C) ) ) ) ) ) ) ).
fof(d13_osafree,axiom,
$true ).
fof(d14_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_trees_4(C,k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> ! [D] :
( m2_finseq_2(D,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
=> ( D = k11_osafree(A,B,C)
<=> ( k4_finseq_1(D) = k4_finseq_1(C)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(E,k4_finseq_1(C))
& ! [F] :
( m1_dtconstr(F,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> ~ ( F = k1_funct_1(C,E)
& k1_funct_1(D,E) = k10_osafree(A,B,F) ) ) ) ) ) ) ) ) ) ) ).
fof(t19_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_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(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> ( r2_osalg_1(A,k11_osafree(A,B,D),k1_msualg_1(A,C))
<=> r2_hidden(D,k3_msualg_1(A,C,k8_osafree(A,B))) ) ) ) ) ) ).
fof(d15_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A)
& v10_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_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(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> ( r1_lang1(k2_osafree(A,B),k9_osafree(A,B,k3_osalg_1(A,C,k11_osafree(A,B,D))),k1_dtconstr(u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),D))
=> k12_osafree(A,B,C,D) = k12_trees_4(u1_struct_0(k2_osafree(A,B)),k9_osafree(A,B,k3_osalg_1(A,C,k11_osafree(A,B,D))),D) ) ) ) ) ) ).
fof(d16_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_osafree(A,B)))
=> ( ? [D] :
( v1_relat_1(D)
& v1_funct_1(D)
& v1_finseq_1(D)
& r1_lang1(k2_osafree(A,B),C,D) )
=> ! [D] :
( m1_subset_1(D,u1_msualg_1(A))
=> ( D = k13_osafree(A,B,C)
<=> k4_tarski(D,u1_struct_0(A)) = C ) ) ) ) ) ) ).
fof(d17_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_osafree(A,B)))
=> ( r2_hidden(C,k6_dtconstr(k2_osafree(A,B)))
=> k14_osafree(A,B,C) = k2_trees_4(u1_struct_0(k2_osafree(A,B)),C) ) ) ) ) ).
fof(d18_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( ( v3_msualg_4(C,A,k8_osafree(A,B))
& v4_msualg_4(C,A,k8_osafree(A,B))
& v3_osalg_4(C,A,k8_osafree(A,B))
& m1_osalg_4(C,A,k8_osafree(A,B)) )
=> ( C = k15_osafree(A,B)
<=> ! [D] :
( ( v3_msualg_4(D,A,k8_osafree(A,B))
& v4_msualg_4(D,A,k8_osafree(A,B))
& v3_osalg_4(D,A,k8_osafree(A,B))
& m1_osalg_4(D,A,k8_osafree(A,B)) )
=> r2_pboole(u1_struct_0(A),C,D) ) ) ) ) ) ).
fof(d19_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> k16_osafree(A,B) = k16_osalg_4(A,k8_osafree(A,B),k15_osafree(A,B)) ) ) ).
fof(d22_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A))))
& m2_relset_1(C,k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A)))) )
=> ( C = k19_osafree(A,B)
<=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(k2_osafree(A,B)))
=> ( r2_hidden(D,k6_dtconstr(k2_osafree(A,B)))
=> k1_funct_1(C,k2_trees_4(u1_struct_0(k2_osafree(A,B)),D)) = k17_osafree(A,B,D) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(k2_osafree(A,B)))
=> ! [E] :
( m1_trees_4(E,k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> ( r1_lang1(k2_osafree(A,B),D,k1_dtconstr(u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),E))
=> k1_funct_1(C,k12_trees_4(u1_struct_0(k2_osafree(A,B)),D,E)) = k18_osafree(A,B,D,k15_lang1(k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A))),E,C)) ) ) ) ) ) ) ) ) ).
fof(t20_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(C,k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),D))
<=> r2_hidden(k4_tarski(C,D),k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A))),k19_osafree(A,B),C)) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_dtconstr(E,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> ( r2_hidden(k4_tarski(E,D),k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A))),k19_osafree(A,B),C))
=> r2_hidden(k4_tarski(C,D),k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A))),k19_osafree(A,B),E)) ) ) ) ) ) ) ) ).
fof(t21_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ? [E] :
( m1_dtconstr(E,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
& r2_hidden(k4_tarski(E,D),k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A))),k19_osafree(A,B),C)) )
=> r2_hidden(k4_tarski(C,D),k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A))),k19_osafree(A,B),C)) ) ) ) ) ) ).
fof(t22_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> ! [D] :
( m1_dtconstr(D,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( ( r3_orders_2(A,E,F)
& r2_hidden(C,k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),E))
& r2_hidden(D,k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),E)) )
=> ( r2_hidden(k4_tarski(D,E),k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A))),k19_osafree(A,B),C))
<=> r2_hidden(k4_tarski(D,F),k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A))),k19_osafree(A,B),C)) ) ) ) ) ) ) ) ) ).
fof(t23_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> ! [D] :
( m1_dtconstr(D,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> ! [E] :
( m1_dtconstr(E,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( ( r2_hidden(k4_tarski(D,F),k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A))),k19_osafree(A,B),C))
& r2_hidden(k4_tarski(E,F),k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A))),k19_osafree(A,B),D)) )
=> r2_hidden(k4_tarski(C,F),k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A))),k19_osafree(A,B),E)) ) ) ) ) ) ) ) ).
fof(t24_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C,D,E] :
( r2_hidden(k4_tarski(C,E),k1_funct_1(k19_osafree(A,B),D))
=> ( r2_hidden(C,k4_dtconstr(k2_osafree(A,B)))
& r2_hidden(D,k4_dtconstr(k2_osafree(A,B)))
& r2_hidden(E,u1_struct_0(A)) ) ) ) ) ).
fof(t25_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m2_subset_1(C,k1_zfmisc_1(u1_struct_0(A)),k2_osalg_4(A))
=> ! [D,E] :
( r2_hidden(k4_tarski(D,E),k5_osalg_4(A,k8_osafree(A,B),k20_osafree(A,B),C))
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(A))
& r2_hidden(F,C)
& r2_hidden(k4_tarski(D,F),k1_funct_1(k19_osafree(A,B),E)) ) ) ) ) ) ).
fof(t26_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_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(u4_msualg_1(A,k8_osafree(A,B)),C))
=> k8_osalg_4(A,k8_osafree(A,B),k20_osafree(A,B),C,D) = k1_funct_5(k1_funct_1(k19_osafree(A,B),D)) ) ) ) ) ).
fof(t27_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,k8_osafree(A,B)))
=> ( r6_pboole(u1_struct_0(A),C,k20_osafree(A,B))
<=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( r2_hidden(F,k1_funct_1(B,D))
=> ( ( r3_orders_2(A,D,E)
=> r2_hidden(k4_tarski(k1_trees_4(k4_tarski(F,D)),k1_trees_4(k4_tarski(F,D))),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,k8_osafree(A,B)),C,E)) )
& ! [G] :
( ( r2_hidden(k4_tarski(k1_trees_4(k4_tarski(F,D)),G),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,k8_osafree(A,B)),C,E))
| r2_hidden(k4_tarski(G,k1_trees_4(k4_tarski(F,D))),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,k8_osafree(A,B)),C,E)) )
=> ( r3_orders_2(A,D,E)
& G = k1_trees_4(k4_tarski(F,D)) ) ) ) ) ) )
& ! [D] :
( m1_subset_1(D,u1_msualg_1(A))
=> ! [E] :
( m1_subset_1(E,u1_msualg_1(A))
=> ! [F] :
( m1_subset_1(F,k3_msualg_1(A,D,k8_osafree(A,B)))
=> ! [G] :
( m1_subset_1(G,k3_msualg_1(A,E,k8_osafree(A,B)))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ( r2_hidden(k4_tarski(k8_funct_2(k3_msualg_1(A,D,k8_osafree(A,B)),k4_msualg_1(A,D,k8_osafree(A,B)),k5_msualg_1(A,D,k8_osafree(A,B)),F),k8_funct_2(k3_msualg_1(A,E,k8_osafree(A,B)),k4_msualg_1(A,E,k8_osafree(A,B)),k5_msualg_1(A,E,k8_osafree(A,B)),G)),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,k8_osafree(A,B)),C,H))
<=> ( r1_osalg_1(A,D,E)
& k3_finseq_1(k1_msualg_1(A,D)) = k3_finseq_1(k1_msualg_1(A,E))
& r3_orders_2(A,k1_osalg_1(A,D),H)
& r3_orders_2(A,k1_osalg_1(A,E),H)
& ? [I] :
( m2_finseq_2(I,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
& k4_finseq_1(I) = k4_finseq_1(F)
& ! [J] :
( m2_subset_1(J,k1_numbers,k5_numbers)
=> ( r2_hidden(J,k4_finseq_1(I))
=> r2_hidden(k4_tarski(k1_funct_1(F,J),k1_funct_1(G,J)),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,k8_osafree(A,B)),C,k4_finseq_4(k5_numbers,u1_struct_0(A),I,J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t28_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> v3_osalg_4(k20_osafree(A,B),A,k8_osafree(A,B)) ) ) ).
fof(d24_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_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_zfmisc_1(k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),C)))
=> ( D = k21_osafree(A,B,C)
<=> ! [E] :
( r2_hidden(E,D)
<=> ? [F] :
( r2_hidden(F,k1_funct_1(B,C))
& E = k1_trees_4(k4_tarski(F,C)) ) ) ) ) ) ) ) ).
fof(d25_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)))
=> ( C = k22_osafree(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k1_funct_1(C,D) = k21_osafree(A,B,D) ) ) ) ) ) ).
fof(t30_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> v2_relat_1(k22_osafree(A,B)) ) ) ).
fof(d26_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_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_zfmisc_1(k1_funct_1(u4_msualg_1(A,k16_osafree(A,B)),C)))
=> ( D = k23_osafree(A,B,C)
<=> ! [E] :
( r2_hidden(E,D)
<=> ? [F] :
( r2_hidden(F,k1_funct_1(B,C))
& E = k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,k16_osalg_4(A,k8_osafree(A,B),k15_osafree(A,B))),k18_osalg_4(A,k8_osafree(A,B),k15_osafree(A,B)),C),k1_trees_4(k4_tarski(F,C))) ) ) ) ) ) ) ) ).
fof(d27_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_osafree(C,A,k16_osafree(A,B))
=> ( C = k24_osafree(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k1_funct_1(C,D) = k23_osafree(A,B,D) ) ) ) ) ) ).
fof(t32_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> v2_relat_1(k24_osafree(A,B)) ) ) ).
fof(d28_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( ( v3_msualg_4(C,A,k8_osafree(A,B))
& v4_msualg_4(C,A,k8_osafree(A,B))
& m1_osalg_4(C,A,k8_osafree(A,B)) )
=> ! [D] :
( m1_dtconstr(D,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> ! [E] :
( m1_subset_1(E,k6_osalg_4(A,k8_osafree(A,B),C,k10_osafree(A,B,D)))
=> ( E = k25_osafree(A,B,C,D)
<=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),F))
=> ( D = G
=> E = k8_osalg_4(A,k8_osafree(A,B),C,F,G) ) ) ) ) ) ) ) ) ) ).
fof(t33_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( ( v3_msualg_4(C,A,k8_osafree(A,B))
& v4_msualg_4(C,A,k8_osafree(A,B))
& m1_osalg_4(C,A,k8_osafree(A,B)) )
=> ! [D] :
( m1_dtconstr(D,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> r2_hidden(D,k25_osafree(A,B,C,D)) ) ) ) ) ).
fof(t34_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_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_dtconstr(D,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> ! [E,F] :
( ( r2_hidden(E,k1_funct_1(B,C))
& D = k1_trees_4(k4_tarski(E,C)) )
=> ( r2_hidden(F,k25_osafree(A,B,k20_osafree(A,B),D))
<=> F = D ) ) ) ) ) ) ).
fof(t35_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( ( v3_msualg_4(C,A,k8_osafree(A,B))
& v4_msualg_4(C,A,k8_osafree(A,B))
& m1_osalg_4(C,A,k8_osafree(A,B)) )
=> ! [D] :
( m1_dtconstr(D,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> ! [E] :
( m1_dtconstr(E,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> ( r2_hidden(E,k25_osafree(A,B,C,D))
<=> k25_osafree(A,B,C,D) = k25_osafree(A,B,C,E) ) ) ) ) ) ) ).
fof(t36_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( ( v3_msualg_4(C,A,k8_osafree(A,B))
& v4_msualg_4(C,A,k8_osafree(A,B))
& m1_osalg_4(C,A,k8_osafree(A,B)) )
=> ! [D] :
( ( v3_msualg_4(D,A,k8_osafree(A,B))
& v4_msualg_4(D,A,k8_osafree(A,B))
& m1_osalg_4(D,A,k8_osafree(A,B)) )
=> ! [E] :
( m1_dtconstr(E,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> ( r2_pboole(u1_struct_0(A),C,D)
=> r1_tarski(k25_osafree(A,B,C,E),k25_osafree(A,B,D,E)) ) ) ) ) ) ) ).
fof(t37_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_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_dtconstr(D,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> ! [E,F] :
( ( r2_hidden(E,k1_funct_1(B,C))
& D = k1_trees_4(k4_tarski(E,C)) )
=> ( r2_hidden(F,k25_osafree(A,B,k15_osafree(A,B),D))
<=> F = D ) ) ) ) ) ) ).
fof(d29_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_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)) )
=> ! [D] :
( m3_pboole(D,u1_struct_0(A),k22_osafree(A,B),C)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k2_osafree(A,B)))
=> ( r2_hidden(E,k6_dtconstr(k2_osafree(A,B)))
=> ! [F] :
( m1_subset_1(F,k3_card_3(C))
=> ( F = k26_osafree(A,B,C,D,E)
<=> ! [G] :
( ( v1_relat_1(G)
& v1_funct_1(G) )
=> ( G = k1_funct_1(D,k2_mcart_1(E))
=> F = k1_funct_1(G,k2_trees_4(u1_struct_0(k2_osafree(A,B)),E)) ) ) ) ) ) ) ) ) ) ) ).
fof(t38_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( ( v5_msualg_1(C,A)
& v12_osalg_1(C,A)
& v13_osalg_1(C,A)
& l3_msualg_1(C,A) )
=> ! [D] :
( m3_pboole(D,u1_struct_0(A),k22_osafree(A,B),u4_msualg_1(A,C))
=> ? [E] :
( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,C))
& r1_msualg_3(A,k8_osafree(A,B),C,E)
& v1_osalg_3(E,A)
& r6_pboole(u1_struct_0(A),k1_msafree(u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,C),k22_osafree(A,B),E),D) ) ) ) ) ) ).
fof(d30_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k23_osafree(A,B,C),k21_osafree(A,B,C))
& m2_relset_1(D,k23_osafree(A,B,C),k21_osafree(A,B,C)) )
=> ( D = k27_osafree(A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(k2_osafree(A,B)))
=> ( r2_hidden(k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,k16_osalg_4(A,k8_osafree(A,B),k15_osafree(A,B))),k18_osalg_4(A,k8_osafree(A,B),k15_osafree(A,B)),C),k2_trees_4(u1_struct_0(k2_osafree(A,B)),E)),k23_osafree(A,B,C))
=> k1_funct_1(D,k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,k16_osalg_4(A,k8_osafree(A,B),k15_osafree(A,B))),k18_osalg_4(A,k8_osafree(A,B),k15_osafree(A,B)),C),k2_trees_4(u1_struct_0(k2_osafree(A,B)),E))) = k2_trees_4(u1_struct_0(k2_osafree(A,B)),E) ) ) ) ) ) ) ) ).
fof(d31_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m3_pboole(C,u1_struct_0(A),k24_osafree(A,B),k22_osafree(A,B))
=> ( C = k28_osafree(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k1_msualg_3(u1_struct_0(A),k24_osafree(A,B),k22_osafree(A,B),C,D) = k27_osafree(A,B,D) ) ) ) ) ) ).
fof(t39_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> v1_osafree(k24_osafree(A,B),A,k16_osafree(A,B)) ) ) ).
fof(t40_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> v2_osafree(k16_osafree(A,B),A) ) ) ).
fof(d32_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A)
& v10_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)))
& m2_relset_1(C,k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B))) )
=> ( C = k29_osafree(A,B)
<=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(k2_osafree(A,B)))
=> ( r2_hidden(D,k6_dtconstr(k2_osafree(A,B)))
=> k1_funct_1(C,k2_trees_4(u1_struct_0(k2_osafree(A,B)),D)) = k14_osafree(A,B,D) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(k2_osafree(A,B)))
=> ! [E] :
( m1_trees_4(E,k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> ( r1_lang1(k2_osafree(A,B),D,k1_dtconstr(u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),E))
=> k1_funct_1(C,k12_trees_4(u1_struct_0(k2_osafree(A,B)),D,E)) = k12_osafree(A,B,k13_osafree(A,B,D),k15_lang1(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),E,C)) ) ) ) ) ) ) ) ) ).
fof(t41_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A)
& v10_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> ( r2_hidden(k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),k29_osafree(A,B),C),k25_osafree(A,B,k20_osafree(A,B),C))
& r3_orders_2(A,k10_osafree(A,B,k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),k29_osafree(A,B),C)),k10_osafree(A,B,C))
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( ( r2_hidden(E,k1_funct_1(B,D))
& C = k1_trees_4(k4_tarski(E,D)) )
=> k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),k29_osafree(A,B),C) = C ) )
& ! [D] :
( m1_subset_1(D,u1_msualg_1(A))
=> ! [E] :
( m1_trees_4(E,k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> ( ( r1_lang1(k2_osafree(A,B),k9_osafree(A,B,D),k1_dtconstr(u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),E))
& C = k12_trees_4(u1_struct_0(k2_osafree(A,B)),k9_osafree(A,B,D),E) )
=> ( r2_osalg_1(A,k11_osafree(A,B,k15_lang1(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),E,k29_osafree(A,B))),k1_msualg_1(A,D))
& r1_lang1(k2_osafree(A,B),k9_osafree(A,B,D),k16_trees_3(k15_lang1(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),E,k29_osafree(A,B))))
& r1_lang1(k2_osafree(A,B),k9_osafree(A,B,k3_osalg_1(A,D,k11_osafree(A,B,k15_lang1(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),E,k29_osafree(A,B))))),k16_trees_3(k15_lang1(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),E,k29_osafree(A,B))))
& k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),k29_osafree(A,B),C) = k4_trees_4(k9_osafree(A,B,k3_osalg_1(A,D,k11_osafree(A,B,k15_lang1(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),E,k29_osafree(A,B))))),k15_lang1(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),E,k29_osafree(A,B))) ) ) ) ) ) ) ) ) ).
fof(t42_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A)
& v10_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> ! [D] :
( m1_dtconstr(D,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> ( r2_hidden(D,k25_osafree(A,B,k20_osafree(A,B),C))
=> k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),k29_osafree(A,B),D) = k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),k29_osafree(A,B),C) ) ) ) ) ) ).
fof(t43_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A)
& v10_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> ! [D] :
( m1_dtconstr(D,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> ( r2_hidden(D,k25_osafree(A,B,k20_osafree(A,B),C))
<=> k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),k29_osafree(A,B),D) = k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),k29_osafree(A,B),C) ) ) ) ) ) ).
fof(t44_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A)
& v10_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),k29_osafree(A,B),k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),k29_osafree(A,B),C)) = k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),k29_osafree(A,B),C) ) ) ) ).
fof(t45_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A)
& v10_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( ( v3_msualg_4(C,A,k8_osafree(A,B))
& v3_osalg_4(C,A,k8_osafree(A,B))
& m1_osalg_4(C,A,k8_osafree(A,B)) )
=> ! [D] :
( m1_dtconstr(D,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> r2_hidden(k4_tarski(D,k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),k29_osafree(A,B),D)),k2_msualg_4(A,k8_osafree(A,B),C,k10_osafree(A,B,D))) ) ) ) ) ).
fof(t46_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A)
& v10_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( ( v3_msualg_4(C,A,k8_osafree(A,B))
& v3_osalg_4(C,A,k8_osafree(A,B))
& m1_osalg_4(C,A,k8_osafree(A,B)) )
=> r2_pboole(u1_struct_0(A),k20_osafree(A,B),C) ) ) ) ).
fof(t47_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A)
& v10_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> r6_pboole(u1_struct_0(A),k15_osafree(A,B),k20_osafree(A,B)) ) ) ).
fof(d33_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A)
& v10_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
=> ( m2_osafree(C,A,B)
<=> k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),k29_osafree(A,B),C) = C ) ) ) ) ).
fof(d34_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A)
& v10_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> k30_osafree(A,B) = k2_relat_1(k29_osafree(A,B)) ) ) ).
fof(t48_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A)
& v10_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m2_osafree(C,A,B)
<=> r2_hidden(C,k30_osafree(A,B)) ) ) ) ).
fof(dt_m1_osafree,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_osafree(C,A,B)
=> m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) ) ) ).
fof(existence_m1_osafree,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ? [C] : m1_osafree(C,A,B) ) ).
fof(dt_m2_osafree,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A)
& v10_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m2_osafree(C,A,B)
=> m1_dtconstr(C,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B))) ) ) ).
fof(existence_m2_osafree,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A)
& v10_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ? [C] : m2_osafree(C,A,B) ) ).
fof(dt_k1_osafree,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& m1_pboole(B,u1_struct_0(A)) )
=> m2_relset_1(k1_osafree(A,B),k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B))),k3_finseq_2(k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B))))) ) ).
fof(dt_k2_osafree,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& m1_pboole(B,u1_struct_0(A)) )
=> l1_lang1(k2_osafree(A,B)) ) ).
fof(dt_k3_osafree,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A))
& m1_subset_1(C,u1_msualg_1(A)) )
=> m1_subset_1(k3_osafree(A,B,C),u1_struct_0(k2_osafree(A,B))) ) ).
fof(dt_k4_osafree,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k4_osafree(A,B,C),k1_zfmisc_1(k4_dtconstr(k2_osafree(A,B)))) ) ).
fof(dt_k5_osafree,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ( v11_osalg_1(k5_osafree(A,B),A)
& m1_pboole(k5_osafree(A,B),u1_struct_0(A)) ) ) ).
fof(dt_k6_osafree,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A))
& m1_subset_1(C,u1_msualg_1(A)) )
=> ( v1_funct_1(k6_osafree(A,B,C))
& v1_funct_2(k6_osafree(A,B,C),k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k5_osafree(A,B))),C),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k5_osafree(A,B)),C))
& m2_relset_1(k6_osafree(A,B,C),k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k5_osafree(A,B))),C),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k5_osafree(A,B)),C)) ) ) ).
fof(dt_k7_osafree,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> m3_pboole(k7_osafree(A,B),u1_msualg_1(A),k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k5_osafree(A,B))),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k5_osafree(A,B))) ) ).
fof(dt_k8_osafree,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ( v12_osalg_1(k8_osafree(A,B),A)
& l3_msualg_1(k8_osafree(A,B),A) ) ) ).
fof(dt_k9_osafree,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A))
& m1_subset_1(C,u1_msualg_1(A)) )
=> m1_struct_0(k9_osafree(A,B,C),k2_osafree(A,B),k7_dtconstr(k2_osafree(A,B))) ) ).
fof(redefinition_k9_osafree,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A))
& m1_subset_1(C,u1_msualg_1(A)) )
=> k9_osafree(A,B,C) = k3_osafree(A,B,C) ) ).
fof(dt_k10_osafree,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A))
& m1_subset_1(C,k4_dtconstr(k2_osafree(A,B))) )
=> m1_subset_1(k10_osafree(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k11_osafree,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A))
& m1_finseq_1(C,k4_dtconstr(k2_osafree(A,B))) )
=> m2_finseq_2(k11_osafree(A,B,C),u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) ) ).
fof(dt_k12_osafree,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A)
& v10_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A))
& m1_subset_1(C,u1_msualg_1(A))
& m1_finseq_1(D,k4_dtconstr(k2_osafree(A,B))) )
=> m1_dtconstr(k12_osafree(A,B,C,D),u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B))) ) ).
fof(dt_k13_osafree,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(k2_osafree(A,B))) )
=> m1_subset_1(k13_osafree(A,B,C),u1_msualg_1(A)) ) ).
fof(dt_k14_osafree,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(k2_osafree(A,B))) )
=> m1_dtconstr(k14_osafree(A,B,C),u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B))) ) ).
fof(dt_k15_osafree,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ( v3_msualg_4(k15_osafree(A,B),A,k8_osafree(A,B))
& v4_msualg_4(k15_osafree(A,B),A,k8_osafree(A,B))
& v3_osalg_4(k15_osafree(A,B),A,k8_osafree(A,B))
& m1_osalg_4(k15_osafree(A,B),A,k8_osafree(A,B)) ) ) ).
fof(dt_k16_osafree,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ( v4_msualg_1(k16_osafree(A,B),A)
& v5_msualg_1(k16_osafree(A,B),A)
& v12_osalg_1(k16_osafree(A,B),A)
& v13_osalg_1(k16_osafree(A,B),A)
& l3_msualg_1(k16_osafree(A,B),A) ) ) ).
fof(dt_k17_osafree,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(k2_osafree(A,B))) )
=> m1_subset_1(k17_osafree(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A)))) ) ).
fof(dt_k18_osafree,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(k2_osafree(A,B)))
& m1_finseq_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A)))) )
=> m1_subset_1(k18_osafree(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A)))) ) ).
fof(dt_k19_osafree,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ( v1_funct_1(k19_osafree(A,B))
& v1_funct_2(k19_osafree(A,B),k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A))))
& m2_relset_1(k19_osafree(A,B),k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A)))) ) ) ).
fof(dt_k20_osafree,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ( v3_msualg_4(k20_osafree(A,B),A,k8_osafree(A,B))
& m1_osalg_4(k20_osafree(A,B),A,k8_osafree(A,B)) ) ) ).
fof(dt_k21_osafree,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k21_osafree(A,B,C),k1_zfmisc_1(k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),C))) ) ).
fof(dt_k22_osafree,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> m4_pboole(k22_osafree(A,B),u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B))) ) ).
fof(dt_k23_osafree,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k23_osafree(A,B,C),k1_zfmisc_1(k1_funct_1(u4_msualg_1(A,k16_osafree(A,B)),C))) ) ).
fof(dt_k24_osafree,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> m1_osafree(k24_osafree(A,B),A,k16_osafree(A,B)) ) ).
fof(dt_k25_osafree,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A))
& v3_msualg_4(C,A,k8_osafree(A,B))
& v4_msualg_4(C,A,k8_osafree(A,B))
& m1_osalg_4(C,A,k8_osafree(A,B))
& m1_subset_1(D,k4_dtconstr(k2_osafree(A,B))) )
=> m1_subset_1(k25_osafree(A,B,C,D),k6_osalg_4(A,k8_osafree(A,B),C,k10_osafree(A,B,D))) ) ).
fof(dt_k26_osafree,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A))
& v2_relat_1(C)
& m1_pboole(C,u1_struct_0(A))
& m3_pboole(D,u1_struct_0(A),k22_osafree(A,B),C)
& m1_subset_1(E,u1_struct_0(k2_osafree(A,B))) )
=> m1_subset_1(k26_osafree(A,B,C,D,E),k3_card_3(C)) ) ).
fof(dt_k27_osafree,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( v1_funct_1(k27_osafree(A,B,C))
& v1_funct_2(k27_osafree(A,B,C),k23_osafree(A,B,C),k21_osafree(A,B,C))
& m2_relset_1(k27_osafree(A,B,C),k23_osafree(A,B,C),k21_osafree(A,B,C)) ) ) ).
fof(dt_k28_osafree,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> m3_pboole(k28_osafree(A,B),u1_struct_0(A),k24_osafree(A,B),k22_osafree(A,B)) ) ).
fof(dt_k29_osafree,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A)
& v10_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ( v1_funct_1(k29_osafree(A,B))
& v1_funct_2(k29_osafree(A,B),k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)))
& m2_relset_1(k29_osafree(A,B),k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B))) ) ) ).
fof(dt_k30_osafree,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A)
& v10_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> m1_subset_1(k30_osafree(A,B),k1_zfmisc_1(k4_dtconstr(k2_osafree(A,B)))) ) ).
fof(d7_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k4_osafree(A,B,C) = a_3_0_osafree(A,B,C) ) ) ) ).
fof(t9_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),C) = a_3_0_osafree(A,B,C) ) ) ) ).
fof(d20_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_osafree(A,B)))
=> k17_osafree(A,B,C) = a_3_1_osafree(A,B,C) ) ) ) ).
fof(d21_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_osafree(A,B)))
=> ! [D] :
( m2_finseq_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A))))
=> k18_osafree(A,B,C,D) = a_4_0_osafree(A,B,C,D) ) ) ) ) ).
fof(d23_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( ( v3_msualg_4(C,A,k8_osafree(A,B))
& m1_osalg_4(C,A,k8_osafree(A,B)) )
=> ( C = k20_osafree(A,B)
<=> ! [D] :
( r2_hidden(D,u1_struct_0(A))
=> k1_funct_1(C,D) = a_3_2_osafree(A,B,D) ) ) ) ) ) ).
fof(t29_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k21_osafree(A,B,C) = a_3_3_osafree(A,B,C) ) ) ) ).
fof(t31_osafree,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k23_osafree(A,B,C) = a_3_4_osafree(A,B,C) ) ) ) ).
fof(fraenkel_a_3_0_osafree,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& v4_osalg_1(B)
& v5_osalg_1(B)
& l3_osalg_1(B)
& v2_relat_1(C)
& m1_pboole(C,u1_struct_0(B))
& m1_subset_1(D,u1_struct_0(B)) )
=> ( r2_hidden(A,a_3_0_osafree(B,C,D))
<=> ? [E] :
( m1_dtconstr(E,u1_struct_0(k2_osafree(B,C)),k5_trees_3(u1_struct_0(k2_osafree(B,C))),k4_dtconstr(k2_osafree(B,C)))
& A = E
& ~ ( ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
~ ( r3_orders_2(B,F,D)
& r2_hidden(G,k1_funct_1(C,F))
& E = k1_trees_4(k4_tarski(G,F)) ) )
& ! [F] :
( m1_subset_1(F,u1_msualg_1(B))
=> ~ ( k4_tarski(F,u1_struct_0(B)) = k1_funct_1(E,k1_xboole_0)
& r3_orders_2(B,k1_osalg_1(B,F),D) ) ) ) ) ) ) ).
fof(fraenkel_a_3_1_osafree,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& v4_osalg_1(B)
& v5_osalg_1(B)
& l3_osalg_1(B)
& v2_relat_1(C)
& m1_pboole(C,u1_struct_0(B))
& m1_subset_1(D,u1_struct_0(k2_osafree(B,C))) )
=> ( r2_hidden(A,a_3_1_osafree(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = k4_tarski(k2_trees_4(u1_struct_0(k2_osafree(B,C)),D),E)
& ? [F] :
( m1_subset_1(F,u1_struct_0(B))
& ? [G] :
( r2_hidden(G,k1_funct_1(C,F))
& D = k4_tarski(G,F)
& r3_orders_2(B,F,E) ) ) ) ) ) ).
fof(fraenkel_a_4_0_osafree,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& v4_osalg_1(B)
& v5_osalg_1(B)
& l3_osalg_1(B)
& v2_relat_1(C)
& m1_pboole(C,u1_struct_0(B))
& m1_subset_1(D,u1_struct_0(k2_osafree(B,C)))
& m2_finseq_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(B,C)),u1_struct_0(B)))) )
=> ( r2_hidden(A,a_4_0_osafree(B,C,D,E))
<=> ? [F,G,H] :
( m1_subset_1(F,u1_msualg_1(B))
& m1_subset_1(G,k3_msualg_1(B,F,k8_osafree(B,C)))
& m1_subset_1(H,u1_struct_0(B))
& A = k4_tarski(k8_funct_2(k3_msualg_1(B,F,k8_osafree(B,C)),k4_msualg_1(B,F,k8_osafree(B,C)),k5_msualg_1(B,F,k8_osafree(B,C)),G),H)
& ? [I] :
( m1_subset_1(I,u1_msualg_1(B))
& D = k4_tarski(I,u1_struct_0(B))
& r1_osalg_1(B,I,F)
& k3_finseq_1(k1_msualg_1(B,I)) = k3_finseq_1(k1_msualg_1(B,F))
& r3_orders_2(B,k1_osalg_1(B,I),H)
& r3_orders_2(B,k1_osalg_1(B,F),H) )
& ? [I] :
( m2_finseq_2(I,u1_struct_0(B),k3_finseq_2(u1_struct_0(B)))
& k4_finseq_1(I) = k4_finseq_1(E)
& ! [J] :
( m2_subset_1(J,k1_numbers,k5_numbers)
=> ( r2_hidden(J,k4_finseq_1(E))
=> r2_hidden(k4_tarski(k1_funct_1(G,J),k4_finseq_4(k5_numbers,u1_struct_0(B),I,J)),k1_funct_1(E,J)) ) ) ) ) ) ) ).
fof(fraenkel_a_3_2_osafree,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& v4_osalg_1(B)
& v5_osalg_1(B)
& v2_osalg_4(B)
& l3_osalg_1(B)
& v2_relat_1(C)
& m1_pboole(C,u1_struct_0(B)) )
=> ( r2_hidden(A,a_3_2_osafree(B,C,D))
<=> ? [E,F] :
( m1_dtconstr(E,u1_struct_0(k2_osafree(B,C)),k5_trees_3(u1_struct_0(k2_osafree(B,C))),k4_dtconstr(k2_osafree(B,C)))
& m1_dtconstr(F,u1_struct_0(k2_osafree(B,C)),k5_trees_3(u1_struct_0(k2_osafree(B,C))),k4_dtconstr(k2_osafree(B,C)))
& A = k4_tarski(E,F)
& r2_hidden(k4_tarski(E,D),k8_funct_2(k4_dtconstr(k2_osafree(B,C)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(B,C)),u1_struct_0(B))),k19_osafree(B,C),F)) ) ) ) ).
fof(fraenkel_a_3_3_osafree,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& v4_osalg_1(B)
& v5_osalg_1(B)
& v2_osalg_4(B)
& l3_osalg_1(B)
& v2_relat_1(C)
& m1_pboole(C,u1_struct_0(B))
& m1_subset_1(D,u1_struct_0(B)) )
=> ( r2_hidden(A,a_3_3_osafree(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(k2_osafree(B,C)))
& A = k2_trees_4(u1_struct_0(k2_osafree(B,C)),E)
& r2_hidden(E,k6_dtconstr(k2_osafree(B,C)))
& k2_mcart_1(E) = D ) ) ) ).
fof(fraenkel_a_3_4_osafree,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& v4_osalg_1(B)
& v5_osalg_1(B)
& v2_osalg_4(B)
& l3_osalg_1(B)
& v2_relat_1(C)
& m1_pboole(C,u1_struct_0(B))
& m1_subset_1(D,u1_struct_0(B)) )
=> ( r2_hidden(A,a_3_4_osafree(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(k2_osafree(B,C)))
& A = k1_funct_1(k1_msualg_3(u1_struct_0(B),u4_msualg_1(B,k8_osafree(B,C)),u4_msualg_1(B,k16_osalg_4(B,k8_osafree(B,C),k15_osafree(B,C))),k18_osalg_4(B,k8_osafree(B,C),k15_osafree(B,C)),D),k2_trees_4(u1_struct_0(k2_osafree(B,C)),E))
& r2_hidden(E,k6_dtconstr(k2_osafree(B,C)))
& k2_mcart_1(E) = D ) ) ) ).
%------------------------------------------------------------------------------