SET007 Axioms: SET007+357.ax
%------------------------------------------------------------------------------
% File : SET007+357 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Algebra of Vector Functions
% 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 : vfunct_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 77 ( 7 unt; 0 def)
% Number of atoms : 1073 ( 64 equ)
% Maximal formula atoms : 25 ( 13 avg)
% Number of connectives : 1137 ( 141 ~; 0 |; 678 &)
% ( 11 <=>; 307 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 12 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 1 prp; 0-4 aty)
% Number of functors : 35 ( 35 usr; 3 con; 0-4 aty)
% Number of variables : 324 ( 323 !; 1 ?)
% 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(d1_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,A,u1_struct_0(B)) )
=> ( E = k1_vfunct_1(A,B,C,D)
<=> ( k4_relset_1(A,u1_struct_0(B),E) = k5_subset_1(A,k4_relset_1(A,u1_struct_0(B),C),k4_relset_1(A,u1_struct_0(B),D))
& ! [F] :
( m1_subset_1(F,A)
=> ( r2_hidden(F,k4_relset_1(A,u1_struct_0(B),E))
=> k4_finseq_4(A,u1_struct_0(B),E,F) = k4_rlvect_1(B,k4_finseq_4(A,u1_struct_0(B),C,F),k4_finseq_4(A,u1_struct_0(B),D,F)) ) ) ) ) ) ) ) ) ) ).
fof(d2_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,A,u1_struct_0(B)) )
=> ( E = k2_vfunct_1(A,B,C,D)
<=> ( k4_relset_1(A,u1_struct_0(B),E) = k5_subset_1(A,k4_relset_1(A,u1_struct_0(B),C),k4_relset_1(A,u1_struct_0(B),D))
& ! [F] :
( m1_subset_1(F,A)
=> ( r2_hidden(F,k4_relset_1(A,u1_struct_0(B),E))
=> k4_finseq_4(A,u1_struct_0(B),E,F) = k6_rlvect_1(B,k4_finseq_4(A,u1_struct_0(B),C,F),k4_finseq_4(A,u1_struct_0(B),D,F)) ) ) ) ) ) ) ) ) ) ).
fof(d3_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k1_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,A,u1_struct_0(B)) )
=> ( E = k3_vfunct_1(A,B,C,D)
<=> ( k4_relset_1(A,u1_struct_0(B),E) = k5_subset_1(A,k4_relset_1(A,k1_numbers,C),k4_relset_1(A,u1_struct_0(B),D))
& ! [F] :
( m1_subset_1(F,A)
=> ( r2_hidden(F,k4_relset_1(A,u1_struct_0(B),E))
=> k4_finseq_4(A,u1_struct_0(B),E,F) = k3_rlvect_1(B,k4_finseq_4(A,u1_struct_0(B),D,F),k2_seq_1(A,k1_numbers,C,F)) ) ) ) ) ) ) ) ) ) ).
fof(d4_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,A,u1_struct_0(B)) )
=> ( E = k4_vfunct_1(A,B,C,D)
<=> ( k4_relset_1(A,u1_struct_0(B),E) = k4_relset_1(A,u1_struct_0(B),C)
& ! [F] :
( m1_subset_1(F,A)
=> ( r2_hidden(F,k4_relset_1(A,u1_struct_0(B),E))
=> k4_finseq_4(A,u1_struct_0(B),E,F) = k3_rlvect_1(B,k4_finseq_4(A,u1_struct_0(B),C,F),D) ) ) ) ) ) ) ) ) ) ).
fof(d5_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k1_numbers) )
=> ( D = k5_vfunct_1(A,B,C)
<=> ( k4_relset_1(A,k1_numbers,D) = k4_relset_1(A,u1_struct_0(B),C)
& ! [E] :
( m1_subset_1(E,A)
=> ( r2_hidden(E,k4_relset_1(A,k1_numbers,D))
=> k2_seq_1(A,k1_numbers,D,E) = k1_normsp_1(B,k4_finseq_4(A,u1_struct_0(B),C,E)) ) ) ) ) ) ) ) ) ).
fof(d6_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,u1_struct_0(B)) )
=> ( D = k6_vfunct_1(A,B,C)
<=> ( k4_relset_1(A,u1_struct_0(B),D) = k4_relset_1(A,u1_struct_0(B),C)
& ! [E] :
( m1_subset_1(E,A)
=> ( r2_hidden(E,k4_relset_1(A,u1_struct_0(B),D))
=> k4_finseq_4(A,u1_struct_0(B),D,E) = k5_rlvect_1(B,k4_finseq_4(A,u1_struct_0(B),C,E)) ) ) ) ) ) ) ) ) ).
fof(t1_vfunct_1,axiom,
$true ).
fof(t2_vfunct_1,axiom,
$true ).
fof(t3_vfunct_1,axiom,
$true ).
fof(t4_vfunct_1,axiom,
$true ).
fof(t5_vfunct_1,axiom,
$true ).
fof(t6_vfunct_1,axiom,
$true ).
fof(t7_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k1_numbers) )
=> k6_subset_1(A,k4_relset_1(A,u1_struct_0(B),k3_vfunct_1(A,B,D,C)),k11_relset_1(A,u1_struct_0(B),k3_vfunct_1(A,B,D,C),k1_struct_0(B,k1_rlvect_1(B)))) = k5_subset_1(A,k6_subset_1(A,k4_relset_1(A,k1_numbers,D),k11_relset_1(A,k1_numbers,D,k1_tarski(np__0))),k6_subset_1(A,k4_relset_1(A,u1_struct_0(B),C),k11_relset_1(A,u1_struct_0(B),C,k1_struct_0(B,k1_rlvect_1(B))))) ) ) ) ) ).
fof(t8_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ( k11_relset_1(A,k1_numbers,k5_vfunct_1(A,B,C),k1_tarski(np__0)) = k11_relset_1(A,u1_struct_0(B),C,k1_struct_0(B,k1_rlvect_1(B)))
& k11_relset_1(A,u1_struct_0(B),k6_vfunct_1(A,B,C),k1_struct_0(B,k1_rlvect_1(B))) = k11_relset_1(A,u1_struct_0(B),C,k1_struct_0(B,k1_rlvect_1(B))) ) ) ) ) ).
fof(t9_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( D != np__0
=> k11_relset_1(A,u1_struct_0(B),k4_vfunct_1(A,B,C,D),k1_struct_0(B,k1_rlvect_1(B))) = k11_relset_1(A,u1_struct_0(B),C,k1_struct_0(B,k1_rlvect_1(B))) ) ) ) ) ) ).
fof(t10_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,u1_struct_0(B)) )
=> k1_vfunct_1(A,B,C,D) = k1_vfunct_1(A,B,D,C) ) ) ) ) ).
fof(t11_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,A,u1_struct_0(B)) )
=> k1_vfunct_1(A,B,k1_vfunct_1(A,B,C,D),E) = k1_vfunct_1(A,B,C,k1_vfunct_1(A,B,D,E)) ) ) ) ) ) ).
fof(t12_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k1_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k1_numbers) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,A,u1_struct_0(B)) )
=> k3_vfunct_1(A,B,k8_seq_1(A,k1_numbers,C,D),E) = k3_vfunct_1(A,B,C,k3_vfunct_1(A,B,D,E)) ) ) ) ) ) ).
fof(t13_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k1_numbers) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,A,k1_numbers) )
=> k3_vfunct_1(A,B,k6_seq_1(A,k1_numbers,D,E),C) = k1_vfunct_1(A,B,k3_vfunct_1(A,B,D,C),k3_vfunct_1(A,B,E,C)) ) ) ) ) ) ).
fof(t14_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,A,k1_numbers) )
=> k3_vfunct_1(A,B,E,k1_vfunct_1(A,B,C,D)) = k1_vfunct_1(A,B,k3_vfunct_1(A,B,E,C),k3_vfunct_1(A,B,E,D)) ) ) ) ) ) ).
fof(t15_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,A,k1_numbers) )
=> k4_vfunct_1(A,B,k3_vfunct_1(A,B,E,C),D) = k3_vfunct_1(A,B,k13_seq_1(A,k1_numbers,E,D),C) ) ) ) ) ) ).
fof(t16_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,A,k1_numbers) )
=> k4_vfunct_1(A,B,k3_vfunct_1(A,B,E,C),D) = k3_vfunct_1(A,B,E,k4_vfunct_1(A,B,C,D)) ) ) ) ) ) ).
fof(t17_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k1_numbers) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,A,k1_numbers) )
=> k3_vfunct_1(A,B,k7_seq_1(A,k1_numbers,D,E),C) = k2_vfunct_1(A,B,k3_vfunct_1(A,B,D,C),k3_vfunct_1(A,B,E,C)) ) ) ) ) ) ).
fof(t18_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,A,k1_numbers) )
=> k2_vfunct_1(A,B,k3_vfunct_1(A,B,E,C),k3_vfunct_1(A,B,E,D)) = k3_vfunct_1(A,B,E,k2_vfunct_1(A,B,C,D)) ) ) ) ) ) ).
fof(t19_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,u1_struct_0(B)) )
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> k4_vfunct_1(A,B,k1_vfunct_1(A,B,C,D),E) = k1_vfunct_1(A,B,k4_vfunct_1(A,B,C,E),k4_vfunct_1(A,B,D,E)) ) ) ) ) ) ).
fof(t20_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> k4_vfunct_1(A,B,C,k4_real_1(D,E)) = k4_vfunct_1(A,B,k4_vfunct_1(A,B,C,E),D) ) ) ) ) ) ).
fof(t21_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,u1_struct_0(B)) )
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> k4_vfunct_1(A,B,k2_vfunct_1(A,B,C,D),E) = k2_vfunct_1(A,B,k4_vfunct_1(A,B,C,E),k4_vfunct_1(A,B,D,E)) ) ) ) ) ) ).
fof(t22_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,u1_struct_0(B)) )
=> k2_vfunct_1(A,B,C,D) = k4_vfunct_1(A,B,k2_vfunct_1(A,B,D,C),k1_real_1(np__1)) ) ) ) ) ).
fof(t23_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,A,u1_struct_0(B)) )
=> k2_vfunct_1(A,B,C,k1_vfunct_1(A,B,D,E)) = k2_vfunct_1(A,B,k2_vfunct_1(A,B,C,D),E) ) ) ) ) ) ).
fof(t24_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> k4_vfunct_1(A,B,C,np__1) = C ) ) ) ).
fof(t25_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,A,u1_struct_0(B)) )
=> k2_vfunct_1(A,B,C,k2_vfunct_1(A,B,D,E)) = k1_vfunct_1(A,B,k2_vfunct_1(A,B,C,D),E) ) ) ) ) ) ).
fof(t26_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,A,u1_struct_0(B)) )
=> k1_vfunct_1(A,B,C,k2_vfunct_1(A,B,D,E)) = k2_vfunct_1(A,B,k1_vfunct_1(A,B,C,D),E) ) ) ) ) ) ).
fof(t27_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k1_numbers) )
=> k5_vfunct_1(A,B,k3_vfunct_1(A,B,D,C)) = k8_seq_1(A,k1_numbers,k21_seq_1(A,k1_numbers,D),k5_vfunct_1(A,B,C)) ) ) ) ) ).
fof(t28_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> k5_vfunct_1(A,B,k4_vfunct_1(A,B,C,D)) = k13_seq_1(A,k1_numbers,k5_vfunct_1(A,B,C),k18_complex1(D)) ) ) ) ) ).
fof(t29_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> k6_vfunct_1(A,B,C) = k4_vfunct_1(A,B,C,k1_real_1(np__1)) ) ) ) ).
fof(t30_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> k6_vfunct_1(A,B,k6_vfunct_1(A,B,C)) = C ) ) ) ).
fof(t31_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,u1_struct_0(B)) )
=> k2_vfunct_1(A,B,C,D) = k1_vfunct_1(A,B,C,k6_vfunct_1(A,B,D)) ) ) ) ) ).
fof(t32_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,u1_struct_0(B)) )
=> k2_vfunct_1(A,B,C,k6_vfunct_1(A,B,D)) = k1_vfunct_1(A,B,C,D) ) ) ) ) ).
fof(t33_vfunct_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,B,u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,B,u1_struct_0(C)) )
=> ( k2_partfun1(B,u1_struct_0(C),k1_vfunct_1(B,C,D,E),A) = k1_vfunct_1(B,C,k2_partfun1(B,u1_struct_0(C),D,A),k2_partfun1(B,u1_struct_0(C),E,A))
& k2_partfun1(B,u1_struct_0(C),k1_vfunct_1(B,C,D,E),A) = k1_vfunct_1(B,C,k2_partfun1(B,u1_struct_0(C),D,A),E)
& k2_partfun1(B,u1_struct_0(C),k1_vfunct_1(B,C,D,E),A) = k1_vfunct_1(B,C,D,k2_partfun1(B,u1_struct_0(C),E,A)) ) ) ) ) ) ).
fof(t34_vfunct_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,B,u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,B,k1_numbers) )
=> ( k2_partfun1(B,u1_struct_0(C),k3_vfunct_1(B,C,E,D),A) = k3_vfunct_1(B,C,k2_partfun1(B,k1_numbers,E,A),k2_partfun1(B,u1_struct_0(C),D,A))
& k2_partfun1(B,u1_struct_0(C),k3_vfunct_1(B,C,E,D),A) = k3_vfunct_1(B,C,k2_partfun1(B,k1_numbers,E,A),D)
& k2_partfun1(B,u1_struct_0(C),k3_vfunct_1(B,C,E,D),A) = k3_vfunct_1(B,C,E,k2_partfun1(B,u1_struct_0(C),D,A)) ) ) ) ) ) ).
fof(t35_vfunct_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,B,u1_struct_0(C)) )
=> ( k2_partfun1(B,u1_struct_0(C),k6_vfunct_1(B,C,D),A) = k6_vfunct_1(B,C,k2_partfun1(B,u1_struct_0(C),D,A))
& k2_partfun1(B,k1_numbers,k5_vfunct_1(B,C,D),A) = k5_vfunct_1(B,C,k2_partfun1(B,u1_struct_0(C),D,A)) ) ) ) ) ).
fof(t36_vfunct_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,B,u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,B,u1_struct_0(C)) )
=> ( k2_partfun1(B,u1_struct_0(C),k2_vfunct_1(B,C,D,E),A) = k2_vfunct_1(B,C,k2_partfun1(B,u1_struct_0(C),D,A),k2_partfun1(B,u1_struct_0(C),E,A))
& k2_partfun1(B,u1_struct_0(C),k2_vfunct_1(B,C,D,E),A) = k2_vfunct_1(B,C,k2_partfun1(B,u1_struct_0(C),D,A),E)
& k2_partfun1(B,u1_struct_0(C),k2_vfunct_1(B,C,D,E),A) = k2_vfunct_1(B,C,D,k2_partfun1(B,u1_struct_0(C),E,A)) ) ) ) ) ) ).
fof(t37_vfunct_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,B,u1_struct_0(C)) )
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> k2_partfun1(B,u1_struct_0(C),k4_vfunct_1(B,C,D,E),A) = k4_vfunct_1(B,C,k2_partfun1(B,u1_struct_0(C),D,A),E) ) ) ) ) ).
fof(t38_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,u1_struct_0(B)) )
=> ( ( ( v1_partfun1(C,A,u1_struct_0(B))
& v1_partfun1(D,A,u1_struct_0(B)) )
=> v1_partfun1(k1_vfunct_1(A,B,C,D),A,u1_struct_0(B)) )
& ( v1_partfun1(k1_vfunct_1(A,B,C,D),A,u1_struct_0(B))
=> ( v1_partfun1(C,A,u1_struct_0(B))
& v1_partfun1(D,A,u1_struct_0(B)) ) )
& ( ( v1_partfun1(C,A,u1_struct_0(B))
& v1_partfun1(D,A,u1_struct_0(B)) )
=> v1_partfun1(k2_vfunct_1(A,B,C,D),A,u1_struct_0(B)) )
& ( v1_partfun1(k2_vfunct_1(A,B,C,D),A,u1_struct_0(B))
=> ( v1_partfun1(C,A,u1_struct_0(B))
& v1_partfun1(D,A,u1_struct_0(B)) ) ) ) ) ) ) ) ).
fof(t39_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k1_numbers) )
=> ( ( v1_partfun1(D,A,k1_numbers)
& v1_partfun1(C,A,u1_struct_0(B)) )
<=> v1_partfun1(k3_vfunct_1(A,B,D,C),A,u1_struct_0(B)) ) ) ) ) ) ).
fof(t40_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( v1_partfun1(C,A,u1_struct_0(B))
<=> v1_partfun1(k4_vfunct_1(A,B,C,D),A,u1_struct_0(B)) ) ) ) ) ) ).
fof(t41_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ( v1_partfun1(C,A,u1_struct_0(B))
<=> v1_partfun1(k6_vfunct_1(A,B,C),A,u1_struct_0(B)) ) ) ) ) ).
fof(t42_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ( v1_partfun1(C,A,u1_struct_0(B))
<=> v1_partfun1(k5_vfunct_1(A,B,C),A,k1_numbers) ) ) ) ) ).
fof(t43_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,A,u1_struct_0(C)) )
=> ( ( v1_partfun1(D,A,u1_struct_0(C))
& v1_partfun1(E,A,u1_struct_0(C)) )
=> ( k4_finseq_4(A,u1_struct_0(C),k1_vfunct_1(A,C,D,E),B) = k4_rlvect_1(C,k4_finseq_4(A,u1_struct_0(C),D,B),k4_finseq_4(A,u1_struct_0(C),E,B))
& k4_finseq_4(A,u1_struct_0(C),k2_vfunct_1(A,C,D,E),B) = k6_rlvect_1(C,k4_finseq_4(A,u1_struct_0(C),D,B),k4_finseq_4(A,u1_struct_0(C),E,B)) ) ) ) ) ) ) ) ).
fof(t44_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,A,k1_numbers) )
=> ( ( v1_partfun1(E,A,k1_numbers)
& v1_partfun1(D,A,u1_struct_0(C)) )
=> k4_finseq_4(A,u1_struct_0(C),k3_vfunct_1(A,C,E,D),B) = k3_rlvect_1(C,k4_finseq_4(A,u1_struct_0(C),D,B),k2_seq_1(A,k1_numbers,E,B)) ) ) ) ) ) ) ).
fof(t45_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,u1_struct_0(C)) )
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( v1_partfun1(D,A,u1_struct_0(C))
=> k4_finseq_4(A,u1_struct_0(C),k4_vfunct_1(A,C,D,E),B) = k3_rlvect_1(C,k4_finseq_4(A,u1_struct_0(C),D,B),E) ) ) ) ) ) ) ).
fof(t46_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,u1_struct_0(C)) )
=> ( v1_partfun1(D,A,u1_struct_0(C))
=> ( k4_finseq_4(A,u1_struct_0(C),k6_vfunct_1(A,C,D),B) = k5_rlvect_1(C,k4_finseq_4(A,u1_struct_0(C),D,B))
& k2_seq_1(A,k1_numbers,k5_vfunct_1(A,C,D),B) = k1_normsp_1(C,k4_finseq_4(A,u1_struct_0(C),D,B)) ) ) ) ) ) ) ).
fof(d7_vfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ! [D] :
( r1_vfunct_1(A,B,C,D)
<=> ? [E] :
( m1_subset_1(E,k1_numbers)
& ! [F] :
( m1_subset_1(F,A)
=> ( r2_hidden(F,k3_xboole_0(D,k4_relset_1(A,u1_struct_0(B),C)))
=> r1_xreal_0(k1_normsp_1(B,k4_finseq_4(A,u1_struct_0(B),C,F)),E) ) ) ) ) ) ) ) ).
fof(t47_vfunct_1,axiom,
$true ).
fof(t48_vfunct_1,axiom,
! [A,B,C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( ~ v3_struct_0(D)
& v3_rlvect_1(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& v7_rlvect_1(D)
& v2_normsp_1(D)
& l1_normsp_1(D) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,C,u1_struct_0(D)) )
=> ( ( r1_tarski(A,B)
& r1_vfunct_1(C,D,E,B) )
=> r1_vfunct_1(C,D,E,A) ) ) ) ) ).
fof(t49_vfunct_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,B,u1_struct_0(C)) )
=> ( r1_xboole_0(A,k4_relset_1(B,u1_struct_0(C),D))
=> r1_vfunct_1(B,C,D,A) ) ) ) ) ).
fof(t50_vfunct_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,B,u1_struct_0(C)) )
=> r1_vfunct_1(B,C,k4_vfunct_1(B,C,D,np__0),A) ) ) ) ).
fof(t51_vfunct_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,B,u1_struct_0(C)) )
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( r1_vfunct_1(B,C,D,A)
=> r1_vfunct_1(B,C,k4_vfunct_1(B,C,D,E),A) ) ) ) ) ) ).
fof(t52_vfunct_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,B,u1_struct_0(C)) )
=> ( r1_vfunct_1(B,C,D,A)
=> ( r3_rfunct_1(k5_vfunct_1(B,C,D),A)
& r1_vfunct_1(B,C,k6_vfunct_1(B,C,D),A) ) ) ) ) ) ).
fof(t53_vfunct_1,axiom,
! [A,B,C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( ~ v3_struct_0(D)
& v3_rlvect_1(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& v7_rlvect_1(D)
& v2_normsp_1(D)
& l1_normsp_1(D) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,C,u1_struct_0(D)) )
=> ! [F] :
( ( v1_funct_1(F)
& m2_relset_1(F,C,u1_struct_0(D)) )
=> ( ( r1_vfunct_1(C,D,E,A)
& r1_vfunct_1(C,D,F,B) )
=> r1_vfunct_1(C,D,k1_vfunct_1(C,D,E,F),k3_xboole_0(A,B)) ) ) ) ) ) ).
fof(t54_vfunct_1,axiom,
! [A,B,C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( ~ v3_struct_0(D)
& v3_rlvect_1(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& v7_rlvect_1(D)
& v2_normsp_1(D)
& l1_normsp_1(D) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,C,u1_struct_0(D)) )
=> ! [F] :
( ( v1_funct_1(F)
& m2_relset_1(F,C,k1_numbers) )
=> ( ( r3_rfunct_1(F,A)
& r1_vfunct_1(C,D,E,B) )
=> r1_vfunct_1(C,D,k3_vfunct_1(C,D,F,E),k3_xboole_0(A,B)) ) ) ) ) ) ).
fof(t55_vfunct_1,axiom,
! [A,B,C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( ~ v3_struct_0(D)
& v3_rlvect_1(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& v7_rlvect_1(D)
& v2_normsp_1(D)
& l1_normsp_1(D) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,C,u1_struct_0(D)) )
=> ! [F] :
( ( v1_funct_1(F)
& m2_relset_1(F,C,u1_struct_0(D)) )
=> ( ( r1_vfunct_1(C,D,E,A)
& r1_vfunct_1(C,D,F,B) )
=> r1_vfunct_1(C,D,k2_vfunct_1(C,D,E,F),k3_xboole_0(A,B)) ) ) ) ) ) ).
fof(t56_vfunct_1,axiom,
! [A,B,C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( ~ v3_struct_0(D)
& v3_rlvect_1(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& v7_rlvect_1(D)
& v2_normsp_1(D)
& l1_normsp_1(D) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,C,u1_struct_0(D)) )
=> ( ( r1_vfunct_1(C,D,E,A)
& r1_vfunct_1(C,D,E,B) )
=> r1_vfunct_1(C,D,E,k2_xboole_0(A,B)) ) ) ) ) ).
fof(t57_vfunct_1,axiom,
! [A,B,C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( ~ v3_struct_0(D)
& v3_rlvect_1(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& v7_rlvect_1(D)
& v2_normsp_1(D)
& l1_normsp_1(D) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,C,u1_struct_0(D)) )
=> ! [F] :
( ( v1_funct_1(F)
& m2_relset_1(F,C,u1_struct_0(D)) )
=> ( ( r1_partfun2(C,u1_struct_0(D),E,A)
& r1_partfun2(C,u1_struct_0(D),F,B) )
=> ( r1_partfun2(C,u1_struct_0(D),k1_vfunct_1(C,D,E,F),k3_xboole_0(A,B))
& r1_partfun2(C,u1_struct_0(D),k2_vfunct_1(C,D,E,F),k3_xboole_0(A,B)) ) ) ) ) ) ) ).
fof(t58_vfunct_1,axiom,
! [A,B,C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( ~ v3_struct_0(D)
& v3_rlvect_1(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& v7_rlvect_1(D)
& v2_normsp_1(D)
& l1_normsp_1(D) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,C,u1_struct_0(D)) )
=> ! [F] :
( ( v1_funct_1(F)
& m2_relset_1(F,C,k1_numbers) )
=> ( ( r1_partfun2(C,k1_numbers,F,A)
& r1_partfun2(C,u1_struct_0(D),E,B) )
=> r1_partfun2(C,u1_struct_0(D),k3_vfunct_1(C,D,F,E),k3_xboole_0(A,B)) ) ) ) ) ) ).
fof(t59_vfunct_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,B,u1_struct_0(C)) )
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( r1_partfun2(B,u1_struct_0(C),D,A)
=> r1_partfun2(B,u1_struct_0(C),k4_vfunct_1(B,C,D,E),A) ) ) ) ) ) ).
fof(t60_vfunct_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,B,u1_struct_0(C)) )
=> ( r1_partfun2(B,u1_struct_0(C),D,A)
=> ( r1_partfun2(B,k1_numbers,k5_vfunct_1(B,C,D),A)
& r1_partfun2(B,u1_struct_0(C),k6_vfunct_1(B,C,D),A) ) ) ) ) ) ).
fof(t61_vfunct_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,B,u1_struct_0(C)) )
=> ( r1_partfun2(B,u1_struct_0(C),D,A)
=> r1_vfunct_1(B,C,D,A) ) ) ) ) ).
fof(t62_vfunct_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,B,u1_struct_0(C)) )
=> ( r1_partfun2(B,u1_struct_0(C),D,A)
=> ( ! [E] :
( m1_subset_1(E,k1_numbers)
=> r1_vfunct_1(B,C,k4_vfunct_1(B,C,D,E),A) )
& r1_vfunct_1(B,C,k6_vfunct_1(B,C,D),A)
& r3_rfunct_1(k5_vfunct_1(B,C,D),A) ) ) ) ) ) ).
fof(t63_vfunct_1,axiom,
! [A,B,C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( ~ v3_struct_0(D)
& v3_rlvect_1(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& v7_rlvect_1(D)
& v2_normsp_1(D)
& l1_normsp_1(D) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,C,u1_struct_0(D)) )
=> ! [F] :
( ( v1_funct_1(F)
& m2_relset_1(F,C,u1_struct_0(D)) )
=> ( ( r1_vfunct_1(C,D,E,A)
& r1_partfun2(C,u1_struct_0(D),F,B) )
=> r1_vfunct_1(C,D,k1_vfunct_1(C,D,E,F),k3_xboole_0(A,B)) ) ) ) ) ) ).
fof(t64_vfunct_1,axiom,
! [A,B,C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( ~ v3_struct_0(D)
& v3_rlvect_1(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& v7_rlvect_1(D)
& v2_normsp_1(D)
& l1_normsp_1(D) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,C,u1_struct_0(D)) )
=> ! [F] :
( ( v1_funct_1(F)
& m2_relset_1(F,C,u1_struct_0(D)) )
=> ( ( r1_vfunct_1(C,D,E,A)
& r1_partfun2(C,u1_struct_0(D),F,B) )
=> ( r1_vfunct_1(C,D,k2_vfunct_1(C,D,E,F),k3_xboole_0(A,B))
& r1_vfunct_1(C,D,k2_vfunct_1(C,D,F,E),k3_xboole_0(A,B)) ) ) ) ) ) ) ).
fof(dt_k1_vfunct_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B)
& v1_funct_1(C)
& m1_relset_1(C,A,u1_struct_0(B))
& v1_funct_1(D)
& m1_relset_1(D,A,u1_struct_0(B)) )
=> ( v1_funct_1(k1_vfunct_1(A,B,C,D))
& m2_relset_1(k1_vfunct_1(A,B,C,D),A,u1_struct_0(B)) ) ) ).
fof(dt_k2_vfunct_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B)
& v1_funct_1(C)
& m1_relset_1(C,A,u1_struct_0(B))
& v1_funct_1(D)
& m1_relset_1(D,A,u1_struct_0(B)) )
=> ( v1_funct_1(k2_vfunct_1(A,B,C,D))
& m2_relset_1(k2_vfunct_1(A,B,C,D),A,u1_struct_0(B)) ) ) ).
fof(dt_k3_vfunct_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B)
& v1_funct_1(C)
& m1_relset_1(C,A,k1_numbers)
& v1_funct_1(D)
& m1_relset_1(D,A,u1_struct_0(B)) )
=> ( v1_funct_1(k3_vfunct_1(A,B,C,D))
& m2_relset_1(k3_vfunct_1(A,B,C,D),A,u1_struct_0(B)) ) ) ).
fof(dt_k4_vfunct_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B)
& v1_funct_1(C)
& m1_relset_1(C,A,u1_struct_0(B))
& m1_subset_1(D,k1_numbers) )
=> ( v1_funct_1(k4_vfunct_1(A,B,C,D))
& m2_relset_1(k4_vfunct_1(A,B,C,D),A,u1_struct_0(B)) ) ) ).
fof(dt_k5_vfunct_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B)
& v1_funct_1(C)
& m1_relset_1(C,A,u1_struct_0(B)) )
=> ( v1_funct_1(k5_vfunct_1(A,B,C))
& m2_relset_1(k5_vfunct_1(A,B,C),A,k1_numbers) ) ) ).
fof(dt_k6_vfunct_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B)
& v1_funct_1(C)
& m1_relset_1(C,A,u1_struct_0(B)) )
=> ( v1_funct_1(k6_vfunct_1(A,B,C))
& m2_relset_1(k6_vfunct_1(A,B,C),A,u1_struct_0(B)) ) ) ).
%------------------------------------------------------------------------------