TPTP Problem File: GEO473+1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : GEO473+1 : TPTP v9.0.0. Released v7.0.0.
% Domain : Mathematics
% Problem : Flyspeck project step
% Version : Especial.
% English :
% Refs : [Hal10] Hales (2010), A Revision of the Proof of the Kepler
% : [Urb16] Urban (2016), Email to Geoff Sutcliffe
% Source : [Urb16]
% Names :
% Status : Theorem
% Rating : 0.85 v9.0.0, 0.86 v8.2.0, 0.92 v8.1.0, 0.89 v7.5.0, 0.91 v7.4.0, 0.93 v7.3.0, 0.97 v7.1.0, 0.96 v7.0.0
% Syntax : Number of formulae : 3493 (1285 unt; 0 def)
% Number of atoms : 9966 (3785 equ)
% Maximal formula atoms : 25 ( 2 avg)
% Number of connectives : 6879 ( 406 ~; 214 |;2235 &)
% (1273 <=>;2751 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 6 avg)
% Maximal term depth : 28 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 372 ( 372 usr; 361 con; 0-2 aty)
% Number of variables : 14537 (13473 !;1064 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments :
%------------------------------------------------------------------------------
include('Axioms/GEO010+0.ax').
%------------------------------------------------------------------------------
fof(aFORALLu_1,axiom,
( ! [I0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))) )
=> p(s(bool,i(s(fun(num,bool),p0),s(num,I0)))) )
<=> p(s(bool,i(s(fun(num,bool),p0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))) ) ).
fof(aFORALLu_2,axiom,
! [P0] :
( ! [I0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) )
=> p(s(bool,i(s(fun(num,bool),P0),s(num,I0)))) )
<=> ( p(s(bool,i(s(fun(num,bool),P0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))
& p(s(bool,i(s(fun(num,bool),P0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) ) ) ).
fof(aFORALLu_3,axiom,
! [P0] :
( ! [I0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) )
=> p(s(bool,i(s(fun(num,bool),P0),s(num,I0)))) )
<=> ( p(s(bool,i(s(fun(num,bool),P0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))
& p(s(bool,i(s(fun(num,bool),P0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))
& p(s(bool,i(s(fun(num,bool),P0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) ) ) ).
fof(aSUMu_1,axiom,
s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(fun(num,real),f))) = s(real,i(s(fun(num,real),f),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) ).
fof(aSUMu_2,axiom,
! [T0] : s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(fun(num,real),T0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),T0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,i(s(fun(num,real),T0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) ).
fof(aHypermapo_THREE,axiom,
s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(num,i(s(fun(num,num),suc),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) ).
fof(aSUMu_3,axiom,
! [T0] : s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(fun(num,real),T0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),T0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),T0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(num,real),T0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))) ).
fof(avectoru_add,axiom,
! [N,U_0] :
( ! [X,Y,I0] : s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),i(s(fun(cart(real,N),fun(cart(real,N),fun(num,real))),U_0),s(cart(real,N),X))),s(cart(real,N),Y))),s(num,I0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),Y))),s(num,I0)))))
=> ! [X,Y] : s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),X))),s(cart(real,N),Y))) = s(cart(real,N),i(s(fun(fun(num,real),cart(real,N)),lambda),s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),i(s(fun(cart(real,N),fun(cart(real,N),fun(num,real))),U_0),s(cart(real,N),X))),s(cart(real,N),Y))))) ) ).
fof(avectoru_sub,axiom,
! [N,U_0] :
( ! [X,Y,I0] : s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),i(s(fun(cart(real,N),fun(cart(real,N),fun(num,real))),U_0),s(cart(real,N),X))),s(cart(real,N),Y))),s(num,I0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),Y))),s(num,I0)))))
=> ! [X,Y] : s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),X))),s(cart(real,N),Y))) = s(cart(real,N),i(s(fun(fun(num,real),cart(real,N)),lambda),s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),i(s(fun(cart(real,N),fun(cart(real,N),fun(num,real))),U_0),s(cart(real,N),X))),s(cart(real,N),Y))))) ) ).
fof(avectoru_neg,axiom,
! [N,U_0] :
( ! [X,I0] : s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),U_0),s(cart(real,N),X))),s(num,I0))) = s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0)))))
=> ! [X] : s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),vectoru_neg),s(cart(real,N),X))) = s(cart(real,N),i(s(fun(fun(num,real),cart(real,N)),lambda),s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),U_0),s(cart(real,N),X))))) ) ).
fof(avectoru_mul,axiom,
! [N,U_0] :
( ! [C0,X,I0] : s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),i(s(fun(real,fun(cart(real,N),fun(num,real))),U_0),s(real,C0))),s(cart(real,N),X))),s(num,I0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,C0))),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0)))))
=> ! [C0,X] : s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,C0))),s(cart(real,N),X))) = s(cart(real,N),i(s(fun(fun(num,real),cart(real,N)),lambda),s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),i(s(fun(real,fun(cart(real,N),fun(num,real))),U_0),s(real,C0))),s(cart(real,N),X))))) ) ).
fof(avec,axiom,
! [N,U_0] :
( ! [N0,I0] : s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),U_0),s(num,N0))),s(num,I0))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0)))
=> ! [N0] : s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,N0))) = s(cart(real,N),i(s(fun(fun(num,real),cart(real,N)),lambda),s(fun(num,real),i(s(fun(num,fun(num,real)),U_0),s(num,N0))))) ) ).
fof(adot,axiom,
! [N,U_0] :
( ! [X,Y,I0] : s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),i(s(fun(cart(real,N),fun(cart(real,N),fun(num,real))),U_0),s(cart(real,N),X))),s(cart(real,N),Y))),s(num,I0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),Y))),s(num,I0)))))
=> ! [X,Y] : s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),X))),s(cart(real,N),Y))) = s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))),s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),i(s(fun(cart(real,N),fun(cart(real,N),fun(num,real))),U_0),s(cart(real,N),X))),s(cart(real,N),Y))))) ) ).
fof(aDOTu_1,axiom,
s(real,i(s(fun(cart(real,n10),real),i(s(fun(cart(real,n10),fun(cart(real,n10),real)),dot),s(cart(real,n10),x))),s(cart(real,n10),y))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),i(s(fun(cart(real,n10),fun(num,real)),d_),s(cart(real,n10),x))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,n10),fun(num,real)),d_),s(cart(real,n10),y))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) ).
fof(aDOTu_2,axiom,
s(real,i(s(fun(cart(real,n20),real),i(s(fun(cart(real,n20),fun(cart(real,n20),real)),dot),s(cart(real,n20),x))),s(cart(real,n20),y))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),i(s(fun(cart(real,n20),fun(num,real)),d_),s(cart(real,n20),x))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,n20),fun(num,real)),d_),s(cart(real,n20),y))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),i(s(fun(cart(real,n20),fun(num,real)),d_),s(cart(real,n20),x))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,n20),fun(num,real)),d_),s(cart(real,n20),y))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))) ).
fof(aDOTu_3,axiom,
s(real,i(s(fun(cart(real,n3),real),i(s(fun(cart(real,n3),fun(cart(real,n3),real)),dot),s(cart(real,n3),x))),s(cart(real,n3),y))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),i(s(fun(cart(real,n3),fun(num,real)),d_),s(cart(real,n3),x))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,n3),fun(num,real)),d_),s(cart(real,n3),y))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),i(s(fun(cart(real,n3),fun(num,real)),d_),s(cart(real,n3),x))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,n3),fun(num,real)),d_),s(cart(real,n3),y))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),i(s(fun(cart(real,n3),fun(num,real)),d_),s(cart(real,n3),x))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,n3),fun(num,real)),d_),s(cart(real,n3),y))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))))) ).
fof(aVECu_COMPONENT,axiom,
! [N,K0,I0] : s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,K0))))),s(num,I0))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,K0))) ).
fof(aVECTORu_ADDu_COMPONENT,axiom,
! [N,X,Y,I0] : s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),X))),s(cart(real,N),Y))))),s(num,I0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),Y))),s(num,I0))))) ).
fof(aVECTORu_SUBu_COMPONENT,axiom,
! [N,X,Y,I0] : s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),X))),s(cart(real,N),Y))))),s(num,I0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),Y))),s(num,I0))))) ).
fof(aVECTORu_NEGu_COMPONENT,axiom,
! [N,X,I0] : s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),vectoru_neg),s(cart(real,N),X))))),s(num,I0))) = s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))))) ).
fof(aVECTORu_MULu_COMPONENT,axiom,
! [N,C0,X,I0] : s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,C0))),s(cart(real,N),X))))),s(num,I0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,C0))),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))))) ).
fof(aCONDu_COMPONENT,axiom,
! [Q99503,Q99508] : s(Q99503,i(s(fun(num,Q99503),i(s(fun(cart(Q99503,Q99508),fun(num,Q99503)),d_),s(cart(Q99503,Q99508),i(s(fun(cart(Q99503,Q99508),cart(Q99503,Q99508)),i(s(fun(cart(Q99503,Q99508),fun(cart(Q99503,Q99508),cart(Q99503,Q99508))),i(s(fun(bool,fun(cart(Q99503,Q99508),fun(cart(Q99503,Q99508),cart(Q99503,Q99508)))),cond),s(bool,b0))),s(cart(Q99503,Q99508),x))),s(cart(Q99503,Q99508),y))))),s(num,i0))) = s(Q99503,i(s(fun(Q99503,Q99503),i(s(fun(Q99503,fun(Q99503,Q99503)),i(s(fun(bool,fun(Q99503,fun(Q99503,Q99503))),cond),s(bool,b0))),s(Q99503,i(s(fun(num,Q99503),i(s(fun(cart(Q99503,Q99508),fun(num,Q99503)),d_),s(cart(Q99503,Q99508),x))),s(num,i0))))),s(Q99503,i(s(fun(num,Q99503),i(s(fun(cart(Q99503,Q99508),fun(num,Q99503)),d_),s(cart(Q99503,Q99508),y))),s(num,i0))))) ).
fof(aVECTORu_ADDu_SYM,axiom,
! [N,X,Y] : s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),X))),s(cart(real,N),Y))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),Y))),s(cart(real,N),X))) ).
fof(aVECTORu_ADDu_LID,axiom,
! [Q99561,X] : s(cart(real,Q99561),i(s(fun(cart(real,Q99561),cart(real,Q99561)),i(s(fun(cart(real,Q99561),fun(cart(real,Q99561),cart(real,Q99561))),vectoru_add),s(cart(real,Q99561),i(s(fun(num,cart(real,Q99561)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(real,Q99561),X))) = s(cart(real,Q99561),X) ).
fof(aVECTORu_ADDu_RID,axiom,
! [Q99576,X] : s(cart(real,Q99576),i(s(fun(cart(real,Q99576),cart(real,Q99576)),i(s(fun(cart(real,Q99576),fun(cart(real,Q99576),cart(real,Q99576))),vectoru_add),s(cart(real,Q99576),X))),s(cart(real,Q99576),i(s(fun(num,cart(real,Q99576)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(cart(real,Q99576),X) ).
fof(aVECTORu_SUBu_REFL,axiom,
! [Q99591,X] : s(cart(real,Q99591),i(s(fun(cart(real,Q99591),cart(real,Q99591)),i(s(fun(cart(real,Q99591),fun(cart(real,Q99591),cart(real,Q99591))),vectoru_sub),s(cart(real,Q99591),X))),s(cart(real,Q99591),X))) = s(cart(real,Q99591),i(s(fun(num,cart(real,Q99591)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ).
fof(aVECTORu_ADDu_LINV,axiom,
! [Q99609,X] : s(cart(real,Q99609),i(s(fun(cart(real,Q99609),cart(real,Q99609)),i(s(fun(cart(real,Q99609),fun(cart(real,Q99609),cart(real,Q99609))),vectoru_add),s(cart(real,Q99609),i(s(fun(cart(real,Q99609),cart(real,Q99609)),vectoru_neg),s(cart(real,Q99609),X))))),s(cart(real,Q99609),X))) = s(cart(real,Q99609),i(s(fun(num,cart(real,Q99609)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ).
fof(aVECTORu_ADDu_RINV,axiom,
! [Q99628,X] : s(cart(real,Q99628),i(s(fun(cart(real,Q99628),cart(real,Q99628)),i(s(fun(cart(real,Q99628),fun(cart(real,Q99628),cart(real,Q99628))),vectoru_add),s(cart(real,Q99628),X))),s(cart(real,Q99628),i(s(fun(cart(real,Q99628),cart(real,Q99628)),vectoru_neg),s(cart(real,Q99628),X))))) = s(cart(real,Q99628),i(s(fun(num,cart(real,Q99628)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ).
fof(aVECTORu_SUBu_RADD,axiom,
! [N,X,Y] : s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),X))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),X))),s(cart(real,N),Y))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),vectoru_neg),s(cart(real,N),Y))) ).
fof(aVECTORu_NEGu_SUB,axiom,
! [N,X,Y] : s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),vectoru_neg),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),X))),s(cart(real,N),Y))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),Y))),s(cart(real,N),X))) ).
fof(aVECTORu_SUBu_EQ,axiom,
! [Q99705,X,Y] :
( s(cart(real,Q99705),i(s(fun(cart(real,Q99705),cart(real,Q99705)),i(s(fun(cart(real,Q99705),fun(cart(real,Q99705),cart(real,Q99705))),vectoru_sub),s(cart(real,Q99705),X))),s(cart(real,Q99705),Y))) = s(cart(real,Q99705),i(s(fun(num,cart(real,Q99705)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
<=> s(cart(real,Q99705),X) = s(cart(real,Q99705),Y) ) ).
fof(aVECTORu_MULu_ASSOC,axiom,
! [Q99731,A5,B0,X] : s(cart(real,Q99731),i(s(fun(cart(real,Q99731),cart(real,Q99731)),i(s(fun(real,fun(cart(real,Q99731),cart(real,Q99731))),r_),s(real,A5))),s(cart(real,Q99731),i(s(fun(cart(real,Q99731),cart(real,Q99731)),i(s(fun(real,fun(cart(real,Q99731),cart(real,Q99731))),r_),s(real,B0))),s(cart(real,Q99731),X))))) = s(cart(real,Q99731),i(s(fun(cart(real,Q99731),cart(real,Q99731)),i(s(fun(real,fun(cart(real,Q99731),cart(real,Q99731))),r_),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,A5))),s(real,B0))))),s(cart(real,Q99731),X))) ).
fof(aVECTORu_MULu_LID,axiom,
! [Q99745,X] : s(cart(real,Q99745),i(s(fun(cart(real,Q99745),cart(real,Q99745)),i(s(fun(real,fun(cart(real,Q99745),cart(real,Q99745))),r_),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(cart(real,Q99745),X))) = s(cart(real,Q99745),X) ).
fof(aVECTORu_MULu_LZERO,axiom,
! [Q99762,X] : s(cart(real,Q99762),i(s(fun(cart(real,Q99762),cart(real,Q99762)),i(s(fun(real,fun(cart(real,Q99762),cart(real,Q99762))),r_),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(real,Q99762),X))) = s(cart(real,Q99762),i(s(fun(num,cart(real,Q99762)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ).
fof(aVECTORu_SUBu_ADD,axiom,
! [N] : s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),x))),s(cart(real,N),y))))),s(cart(real,N),y))) = s(cart(real,N),x) ).
fof(aVECTORu_SUBu_ADD2,axiom,
! [N] : s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),y))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),x))),s(cart(real,N),y))))) = s(cart(real,N),x) ).
fof(aVECTORu_ADDu_LDISTRIB,axiom,
! [Q99811] : s(cart(real,Q99811),i(s(fun(cart(real,Q99811),cart(real,Q99811)),i(s(fun(real,fun(cart(real,Q99811),cart(real,Q99811))),r_),s(real,c))),s(cart(real,Q99811),i(s(fun(cart(real,Q99811),cart(real,Q99811)),i(s(fun(cart(real,Q99811),fun(cart(real,Q99811),cart(real,Q99811))),vectoru_add),s(cart(real,Q99811),x))),s(cart(real,Q99811),y))))) = s(cart(real,Q99811),i(s(fun(cart(real,Q99811),cart(real,Q99811)),i(s(fun(cart(real,Q99811),fun(cart(real,Q99811),cart(real,Q99811))),vectoru_add),s(cart(real,Q99811),i(s(fun(cart(real,Q99811),cart(real,Q99811)),i(s(fun(real,fun(cart(real,Q99811),cart(real,Q99811))),r_),s(real,c))),s(cart(real,Q99811),x))))),s(cart(real,Q99811),i(s(fun(cart(real,Q99811),cart(real,Q99811)),i(s(fun(real,fun(cart(real,Q99811),cart(real,Q99811))),r_),s(real,c))),s(cart(real,Q99811),y))))) ).
fof(aVECTORu_SUBu_LDISTRIB,axiom,
! [Q99834] : s(cart(real,Q99834),i(s(fun(cart(real,Q99834),cart(real,Q99834)),i(s(fun(real,fun(cart(real,Q99834),cart(real,Q99834))),r_),s(real,c))),s(cart(real,Q99834),i(s(fun(cart(real,Q99834),cart(real,Q99834)),i(s(fun(cart(real,Q99834),fun(cart(real,Q99834),cart(real,Q99834))),vectoru_sub),s(cart(real,Q99834),x))),s(cart(real,Q99834),y))))) = s(cart(real,Q99834),i(s(fun(cart(real,Q99834),cart(real,Q99834)),i(s(fun(cart(real,Q99834),fun(cart(real,Q99834),cart(real,Q99834))),vectoru_sub),s(cart(real,Q99834),i(s(fun(cart(real,Q99834),cart(real,Q99834)),i(s(fun(real,fun(cart(real,Q99834),cart(real,Q99834))),r_),s(real,c))),s(cart(real,Q99834),x))))),s(cart(real,Q99834),i(s(fun(cart(real,Q99834),cart(real,Q99834)),i(s(fun(real,fun(cart(real,Q99834),cart(real,Q99834))),r_),s(real,c))),s(cart(real,Q99834),y))))) ).
fof(aVECTORu_ADDu_RDISTRIB,axiom,
! [Q99856] : s(cart(real,Q99856),i(s(fun(cart(real,Q99856),cart(real,Q99856)),i(s(fun(real,fun(cart(real,Q99856),cart(real,Q99856))),r_),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,a0))),s(real,b0))))),s(cart(real,Q99856),x))) = s(cart(real,Q99856),i(s(fun(cart(real,Q99856),cart(real,Q99856)),i(s(fun(cart(real,Q99856),fun(cart(real,Q99856),cart(real,Q99856))),vectoru_add),s(cart(real,Q99856),i(s(fun(cart(real,Q99856),cart(real,Q99856)),i(s(fun(real,fun(cart(real,Q99856),cart(real,Q99856))),r_),s(real,a0))),s(cart(real,Q99856),x))))),s(cart(real,Q99856),i(s(fun(cart(real,Q99856),cart(real,Q99856)),i(s(fun(real,fun(cart(real,Q99856),cart(real,Q99856))),r_),s(real,b0))),s(cart(real,Q99856),x))))) ).
fof(aVECTORu_SUBu_RDISTRIB,axiom,
! [Q99877] : s(cart(real,Q99877),i(s(fun(cart(real,Q99877),cart(real,Q99877)),i(s(fun(real,fun(cart(real,Q99877),cart(real,Q99877))),r_),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,a0))),s(real,b0))))),s(cart(real,Q99877),x))) = s(cart(real,Q99877),i(s(fun(cart(real,Q99877),cart(real,Q99877)),i(s(fun(cart(real,Q99877),fun(cart(real,Q99877),cart(real,Q99877))),vectoru_sub),s(cart(real,Q99877),i(s(fun(cart(real,Q99877),cart(real,Q99877)),i(s(fun(real,fun(cart(real,Q99877),cart(real,Q99877))),r_),s(real,a0))),s(cart(real,Q99877),x))))),s(cart(real,Q99877),i(s(fun(cart(real,Q99877),cart(real,Q99877)),i(s(fun(real,fun(cart(real,Q99877),cart(real,Q99877))),r_),s(real,b0))),s(cart(real,Q99877),x))))) ).
fof(aVECTORu_ADDu_SUB,axiom,
! [N] : s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),x))),s(cart(real,N),y))))),s(cart(real,N),x))) = s(cart(real,N),y) ).
fof(aVECTORu_EQu_ADDR,axiom,
! [Q99907] :
( s(cart(real,Q99907),i(s(fun(cart(real,Q99907),cart(real,Q99907)),i(s(fun(cart(real,Q99907),fun(cart(real,Q99907),cart(real,Q99907))),vectoru_add),s(cart(real,Q99907),x))),s(cart(real,Q99907),y))) = s(cart(real,Q99907),x)
<=> s(cart(real,Q99907),y) = s(cart(real,Q99907),i(s(fun(num,cart(real,Q99907)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ).
fof(aVECTORu_SUB,axiom,
! [N] : s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),x))),s(cart(real,N),y))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),x))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),vectoru_neg),s(cart(real,N),y))))) ).
fof(aVECTORu_SUBu_RZERO,axiom,
! [Q99936] : s(cart(real,Q99936),i(s(fun(cart(real,Q99936),cart(real,Q99936)),i(s(fun(cart(real,Q99936),fun(cart(real,Q99936),cart(real,Q99936))),vectoru_sub),s(cart(real,Q99936),x))),s(cart(real,Q99936),i(s(fun(num,cart(real,Q99936)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(cart(real,Q99936),x) ).
fof(aVECTORu_MULu_RZERO,axiom,
! [Q99948] : s(cart(real,Q99948),i(s(fun(cart(real,Q99948),cart(real,Q99948)),i(s(fun(real,fun(cart(real,Q99948),cart(real,Q99948))),r_),s(real,c))),s(cart(real,Q99948),i(s(fun(num,cart(real,Q99948)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(cart(real,Q99948),i(s(fun(num,cart(real,Q99948)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ).
fof(aVECTORu_NEGu_MINUS1,axiom,
! [Q99962] : s(cart(real,Q99962),i(s(fun(cart(real,Q99962),cart(real,Q99962)),vectoru_neg),s(cart(real,Q99962),x))) = s(cart(real,Q99962),i(s(fun(cart(real,Q99962),cart(real,Q99962)),i(s(fun(real,fun(cart(real,Q99962),cart(real,Q99962))),r_),s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(cart(real,Q99962),x))) ).
fof(aVECTORu_ADDu_ASSOC,axiom,
! [N] : s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),x))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),y))),s(cart(real,N),z))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),x))),s(cart(real,N),y))))),s(cart(real,N),z))) ).
fof(aVECTORu_SUBu_LZERO,axiom,
! [Q100000] : s(cart(real,Q100000),i(s(fun(cart(real,Q100000),cart(real,Q100000)),i(s(fun(cart(real,Q100000),fun(cart(real,Q100000),cart(real,Q100000))),vectoru_sub),s(cart(real,Q100000),i(s(fun(num,cart(real,Q100000)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(real,Q100000),x))) = s(cart(real,Q100000),i(s(fun(cart(real,Q100000),cart(real,Q100000)),vectoru_neg),s(cart(real,Q100000),x))) ).
fof(aVECTORu_NEGu_NEG,axiom,
! [N] : s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),vectoru_neg),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),vectoru_neg),s(cart(real,N),x))))) = s(cart(real,N),x) ).
fof(aVECTORu_MULu_LNEG,axiom,
! [Q100029] : s(cart(real,Q100029),i(s(fun(cart(real,Q100029),cart(real,Q100029)),i(s(fun(real,fun(cart(real,Q100029),cart(real,Q100029))),r_),s(real,i(s(fun(real,real),realu_neg),s(real,c))))),s(cart(real,Q100029),x))) = s(cart(real,Q100029),i(s(fun(cart(real,Q100029),cart(real,Q100029)),vectoru_neg),s(cart(real,Q100029),i(s(fun(cart(real,Q100029),cart(real,Q100029)),i(s(fun(real,fun(cart(real,Q100029),cart(real,Q100029))),r_),s(real,c))),s(cart(real,Q100029),x))))) ).
fof(aVECTORu_MULu_RNEG,axiom,
! [Q100046] : s(cart(real,Q100046),i(s(fun(cart(real,Q100046),cart(real,Q100046)),i(s(fun(real,fun(cart(real,Q100046),cart(real,Q100046))),r_),s(real,c))),s(cart(real,Q100046),i(s(fun(cart(real,Q100046),cart(real,Q100046)),vectoru_neg),s(cart(real,Q100046),x))))) = s(cart(real,Q100046),i(s(fun(cart(real,Q100046),cart(real,Q100046)),vectoru_neg),s(cart(real,Q100046),i(s(fun(cart(real,Q100046),cart(real,Q100046)),i(s(fun(real,fun(cart(real,Q100046),cart(real,Q100046))),r_),s(real,c))),s(cart(real,Q100046),x))))) ).
fof(aVECTORu_NEGu_0,axiom,
! [Q100059] : s(cart(real,Q100059),i(s(fun(cart(real,Q100059),cart(real,Q100059)),vectoru_neg),s(cart(real,Q100059),i(s(fun(num,cart(real,Q100059)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(cart(real,Q100059),i(s(fun(num,cart(real,Q100059)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ).
fof(aVECTORu_NEGu_EQu_0,axiom,
! [Q100076] :
( s(cart(real,Q100076),i(s(fun(cart(real,Q100076),cart(real,Q100076)),vectoru_neg),s(cart(real,Q100076),x))) = s(cart(real,Q100076),i(s(fun(num,cart(real,Q100076)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
<=> s(cart(real,Q100076),x) = s(cart(real,Q100076),i(s(fun(num,cart(real,Q100076)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ).
fof(aVECTORu_ADDu_ACu_conjunct2,axiom,
! [N] : s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),m))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),n))),s(cart(real,N),p1))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),n))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),m))),s(cart(real,N),p1))))) ).
fof(aVECTORu_ADDu_ACu_conjunct1,axiom,
! [N] : s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),m))),s(cart(real,N),n))))),s(cart(real,N),p1))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),m))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),n))),s(cart(real,N),p1))))) ).
fof(aVECTORu_ADDu_ACu_conjunct0,axiom,
! [N] : s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),m))),s(cart(real,N),n))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),n))),s(cart(real,N),m))) ).
fof(aVECu_EQ,axiom,
! [Q100159,M0,N0] :
( s(cart(real,Q100159),i(s(fun(num,cart(real,Q100159)),vec),s(num,M0))) = s(cart(real,Q100159),i(s(fun(num,cart(real,Q100159)),vec),s(num,N0)))
<=> s(num,M0) = s(num,N0) ) ).
fof(aEUCLIDEANu_SPACEu_INFINITE,axiom,
! [N] : p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),infinite),s(fun(cart(real,N),bool),univ)))) ).
fof(aDOTu_SYM,axiom,
! [Q100205,X,Y] : s(real,i(s(fun(cart(real,Q100205),real),i(s(fun(cart(real,Q100205),fun(cart(real,Q100205),real)),dot),s(cart(real,Q100205),X))),s(cart(real,Q100205),Y))) = s(real,i(s(fun(cart(real,Q100205),real),i(s(fun(cart(real,Q100205),fun(cart(real,Q100205),real)),dot),s(cart(real,Q100205),Y))),s(cart(real,Q100205),X))) ).
fof(aDOTu_LADD,axiom,
! [Q100240,X,Y,Z0] : s(real,i(s(fun(cart(real,Q100240),real),i(s(fun(cart(real,Q100240),fun(cart(real,Q100240),real)),dot),s(cart(real,Q100240),i(s(fun(cart(real,Q100240),cart(real,Q100240)),i(s(fun(cart(real,Q100240),fun(cart(real,Q100240),cart(real,Q100240))),vectoru_add),s(cart(real,Q100240),X))),s(cart(real,Q100240),Y))))),s(cart(real,Q100240),Z0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(cart(real,Q100240),real),i(s(fun(cart(real,Q100240),fun(cart(real,Q100240),real)),dot),s(cart(real,Q100240),X))),s(cart(real,Q100240),Z0))))),s(real,i(s(fun(cart(real,Q100240),real),i(s(fun(cart(real,Q100240),fun(cart(real,Q100240),real)),dot),s(cart(real,Q100240),Y))),s(cart(real,Q100240),Z0))))) ).
fof(aDOTu_RADD,axiom,
! [Q100273,X,Y,Z0] : s(real,i(s(fun(cart(real,Q100273),real),i(s(fun(cart(real,Q100273),fun(cart(real,Q100273),real)),dot),s(cart(real,Q100273),X))),s(cart(real,Q100273),i(s(fun(cart(real,Q100273),cart(real,Q100273)),i(s(fun(cart(real,Q100273),fun(cart(real,Q100273),cart(real,Q100273))),vectoru_add),s(cart(real,Q100273),Y))),s(cart(real,Q100273),Z0))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(cart(real,Q100273),real),i(s(fun(cart(real,Q100273),fun(cart(real,Q100273),real)),dot),s(cart(real,Q100273),X))),s(cart(real,Q100273),Y))))),s(real,i(s(fun(cart(real,Q100273),real),i(s(fun(cart(real,Q100273),fun(cart(real,Q100273),real)),dot),s(cart(real,Q100273),X))),s(cart(real,Q100273),Z0))))) ).
fof(aDOTu_LSUB,axiom,
! [Q100306,X,Y,Z0] : s(real,i(s(fun(cart(real,Q100306),real),i(s(fun(cart(real,Q100306),fun(cart(real,Q100306),real)),dot),s(cart(real,Q100306),i(s(fun(cart(real,Q100306),cart(real,Q100306)),i(s(fun(cart(real,Q100306),fun(cart(real,Q100306),cart(real,Q100306))),vectoru_sub),s(cart(real,Q100306),X))),s(cart(real,Q100306),Y))))),s(cart(real,Q100306),Z0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(cart(real,Q100306),real),i(s(fun(cart(real,Q100306),fun(cart(real,Q100306),real)),dot),s(cart(real,Q100306),X))),s(cart(real,Q100306),Z0))))),s(real,i(s(fun(cart(real,Q100306),real),i(s(fun(cart(real,Q100306),fun(cart(real,Q100306),real)),dot),s(cart(real,Q100306),Y))),s(cart(real,Q100306),Z0))))) ).
fof(aDOTu_RSUB,axiom,
! [Q100339,X,Y,Z0] : s(real,i(s(fun(cart(real,Q100339),real),i(s(fun(cart(real,Q100339),fun(cart(real,Q100339),real)),dot),s(cart(real,Q100339),X))),s(cart(real,Q100339),i(s(fun(cart(real,Q100339),cart(real,Q100339)),i(s(fun(cart(real,Q100339),fun(cart(real,Q100339),cart(real,Q100339))),vectoru_sub),s(cart(real,Q100339),Y))),s(cart(real,Q100339),Z0))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(cart(real,Q100339),real),i(s(fun(cart(real,Q100339),fun(cart(real,Q100339),real)),dot),s(cart(real,Q100339),X))),s(cart(real,Q100339),Y))))),s(real,i(s(fun(cart(real,Q100339),real),i(s(fun(cart(real,Q100339),fun(cart(real,Q100339),real)),dot),s(cart(real,Q100339),X))),s(cart(real,Q100339),Z0))))) ).
fof(aDOTu_LMUL,axiom,
! [Q100362,C0,X,Y] : s(real,i(s(fun(cart(real,Q100362),real),i(s(fun(cart(real,Q100362),fun(cart(real,Q100362),real)),dot),s(cart(real,Q100362),i(s(fun(cart(real,Q100362),cart(real,Q100362)),i(s(fun(real,fun(cart(real,Q100362),cart(real,Q100362))),r_),s(real,C0))),s(cart(real,Q100362),X))))),s(cart(real,Q100362),Y))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,C0))),s(real,i(s(fun(cart(real,Q100362),real),i(s(fun(cart(real,Q100362),fun(cart(real,Q100362),real)),dot),s(cart(real,Q100362),X))),s(cart(real,Q100362),Y))))) ).
fof(aDOTu_RMUL,axiom,
! [Q100390,C0,X,Y] : s(real,i(s(fun(cart(real,Q100390),real),i(s(fun(cart(real,Q100390),fun(cart(real,Q100390),real)),dot),s(cart(real,Q100390),X))),s(cart(real,Q100390),i(s(fun(cart(real,Q100390),cart(real,Q100390)),i(s(fun(real,fun(cart(real,Q100390),cart(real,Q100390))),r_),s(real,C0))),s(cart(real,Q100390),Y))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,C0))),s(real,i(s(fun(cart(real,Q100390),real),i(s(fun(cart(real,Q100390),fun(cart(real,Q100390),real)),dot),s(cart(real,Q100390),X))),s(cart(real,Q100390),Y))))) ).
fof(aDOTu_LNEG,axiom,
! [Q100419,X,Y] : s(real,i(s(fun(cart(real,Q100419),real),i(s(fun(cart(real,Q100419),fun(cart(real,Q100419),real)),dot),s(cart(real,Q100419),i(s(fun(cart(real,Q100419),cart(real,Q100419)),vectoru_neg),s(cart(real,Q100419),X))))),s(cart(real,Q100419),Y))) = s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(cart(real,Q100419),real),i(s(fun(cart(real,Q100419),fun(cart(real,Q100419),real)),dot),s(cart(real,Q100419),X))),s(cart(real,Q100419),Y))))) ).
fof(aDOTu_RNEG,axiom,
! [Q100443,X,Y] : s(real,i(s(fun(cart(real,Q100443),real),i(s(fun(cart(real,Q100443),fun(cart(real,Q100443),real)),dot),s(cart(real,Q100443),X))),s(cart(real,Q100443),i(s(fun(cart(real,Q100443),cart(real,Q100443)),vectoru_neg),s(cart(real,Q100443),Y))))) = s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(cart(real,Q100443),real),i(s(fun(cart(real,Q100443),fun(cart(real,Q100443),real)),dot),s(cart(real,Q100443),X))),s(cart(real,Q100443),Y))))) ).
fof(aDOTu_LZERO,axiom,
! [Q100457,X] : s(real,i(s(fun(cart(real,Q100457),real),i(s(fun(cart(real,Q100457),fun(cart(real,Q100457),real)),dot),s(cart(real,Q100457),i(s(fun(num,cart(real,Q100457)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(real,Q100457),X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ).
fof(aDOTu_RZERO,axiom,
! [Q100472,X] : s(real,i(s(fun(cart(real,Q100472),real),i(s(fun(cart(real,Q100472),fun(cart(real,Q100472),real)),dot),s(cart(real,Q100472),X))),s(cart(real,Q100472),i(s(fun(num,cart(real,Q100472)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ).
fof(aDOTu_POSu_LE,axiom,
! [Q100487,X] : p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(cart(real,Q100487),real),i(s(fun(cart(real,Q100487),fun(cart(real,Q100487),real)),dot),s(cart(real,Q100487),X))),s(cart(real,Q100487),X)))))) ).
fof(aDOTu_EQu_0,axiom,
! [N,X] :
( s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),X))),s(cart(real,N),X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
<=> s(cart(real,N),X) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ).
fof(aDOTu_POSu_LT,axiom,
! [Q100537,X] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(cart(real,Q100537),real),i(s(fun(cart(real,Q100537),fun(cart(real,Q100537),real)),dot),s(cart(real,Q100537),X))),s(cart(real,Q100537),X))))))
<=> s(cart(real,Q100537),X) != s(cart(real,Q100537),i(s(fun(num,cart(real,Q100537)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ).
fof(aFORALLu_DOTu_EQu_0u_conjunct0,axiom,
! [Q100563,Y] :
( ! [X] : s(real,i(s(fun(cart(real,Q100563),real),i(s(fun(cart(real,Q100563),fun(cart(real,Q100563),real)),dot),s(cart(real,Q100563),X))),s(cart(real,Q100563),Y))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
<=> s(cart(real,Q100563),Y) = s(cart(real,Q100563),i(s(fun(num,cart(real,Q100563)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ).
fof(aFORALLu_DOTu_EQu_0u_conjunct1,axiom,
! [Q100586,X] :
( ! [Y] : s(real,i(s(fun(cart(real,Q100586),real),i(s(fun(cart(real,Q100586),fun(cart(real,Q100586),real)),dot),s(cart(real,Q100586),X))),s(cart(real,Q100586),Y))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
<=> s(cart(real,Q100586),X) = s(cart(real,Q100586),i(s(fun(num,cart(real,Q100586)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ).
fof(avectoru_norm,axiom,
! [Q100593,X] : s(real,i(s(fun(cart(real,Q100593),real),vectoru_norm),s(cart(real,Q100593),X))) = s(real,i(s(fun(real,real),sqrt),s(real,i(s(fun(cart(real,Q100593),real),i(s(fun(cart(real,Q100593),fun(cart(real,Q100593),real)),dot),s(cart(real,Q100593),X))),s(cart(real,Q100593),X))))) ).
fof(aFORALLu_DIMINDEXu_1,axiom,
( ! [I0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(n10,bool),num),dimindex),s(fun(n10,bool),univ)))))) )
=> p(s(bool,i(s(fun(num,bool),p0),s(num,I0)))) )
<=> p(s(bool,i(s(fun(num,bool),p0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))) ) ).
fof(aVECTORu_ONE,axiom,
! [U_0] :
( ! [X,I0] : s(real,i(s(fun(num,real),i(s(fun(cart(real,n10),fun(num,real)),U_0),s(cart(real,n10),X))),s(num,I0))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,n10),fun(num,real)),d_),s(cart(real,n10),X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))
=> ! [X] : s(cart(real,n10),X) = s(cart(real,n10),i(s(fun(fun(num,real),cart(real,n10)),lambda),s(fun(num,real),i(s(fun(cart(real,n10),fun(num,real)),U_0),s(cart(real,n10),X))))) ) ).
fof(aFORALLu_REALu_ONE,axiom,
! [U_0] :
( ! [X,I0] : s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),U_0),s(real,X))),s(num,I0))) = s(real,X)
=> ( ! [X] : p(s(bool,i(s(fun(cart(real,n10),bool),p0),s(cart(real,n10),X))))
<=> ! [X] : p(s(bool,i(s(fun(cart(real,n10),bool),p0),s(cart(real,n10),i(s(fun(fun(num,real),cart(real,n10)),lambda),s(fun(num,real),i(s(fun(real,fun(num,real)),U_0),s(real,X)))))))) ) ) ).
fof(aNORMu_REAL,axiom,
! [X] : s(real,i(s(fun(cart(real,n10),real),vectoru_norm),s(cart(real,n10),X))) = s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(num,real),i(s(fun(cart(real,n10),fun(num,real)),d_),s(cart(real,n10),X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) ).
fof(adist,axiom,
! [Q100698,X,Y] : s(real,i(s(fun(prod(cart(real,Q100698),cart(real,Q100698)),real),distance),s(prod(cart(real,Q100698),cart(real,Q100698)),i(s(fun(cart(real,Q100698),prod(cart(real,Q100698),cart(real,Q100698))),i(s(fun(cart(real,Q100698),fun(cart(real,Q100698),prod(cart(real,Q100698),cart(real,Q100698)))),c_),s(cart(real,Q100698),X))),s(cart(real,Q100698),Y))))) = s(real,i(s(fun(cart(real,Q100698),real),vectoru_norm),s(cart(real,Q100698),i(s(fun(cart(real,Q100698),cart(real,Q100698)),i(s(fun(cart(real,Q100698),fun(cart(real,Q100698),cart(real,Q100698))),vectoru_sub),s(cart(real,Q100698),X))),s(cart(real,Q100698),Y))))) ).
fof(aDISTu_REAL,axiom,
! [X,Y] : s(real,i(s(fun(prod(cart(real,n10),cart(real,n10)),real),distance),s(prod(cart(real,n10),cart(real,n10)),i(s(fun(cart(real,n10),prod(cart(real,n10),cart(real,n10))),i(s(fun(cart(real,n10),fun(cart(real,n10),prod(cart(real,n10),cart(real,n10)))),c_),s(cart(real,n10),X))),s(cart(real,n10),Y))))) = s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),i(s(fun(cart(real,n10),fun(num,real)),d_),s(cart(real,n10),X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,n10),fun(num,real)),d_),s(cart(real,n10),Y))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) ).
fof(aCONNECTEDu_REALu_LEMMA,axiom,
! [N,F0,A5,B0,E1,E2] :
( ( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,A5))),s(real,B0))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),i(s(fun(real,cart(real,N)),F0),s(real,A5))))),s(fun(cart(real,N),bool),E1))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),i(s(fun(real,cart(real,N)),F0),s(real,B0))))),s(fun(cart(real,N),bool),E2))))
& ! [E0,X] :
( ( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,A5))),s(real,X))))
& p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,B0))))
& p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,E0)))) )
=> ? [D0] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,D0))))
& ! [Y] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,Y))),s(real,X))))))),s(real,D0))))
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(prod(cart(real,N),cart(real,N)),real),distance),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),i(s(fun(real,cart(real,N)),F0),s(real,Y))))),s(cart(real,N),i(s(fun(real,cart(real,N)),F0),s(real,X))))))))),s(real,E0)))) ) ) )
& ! [Y] :
( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),Y))),s(fun(cart(real,N),bool),E1))))
=> ? [E0] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,E0))))
& ! [YI_] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(prod(cart(real,N),cart(real,N)),real),distance),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),YI_))),s(cart(real,N),Y))))))),s(real,E0))))
=> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),YI_))),s(fun(cart(real,N),bool),E1)))) ) ) )
& ! [Y] :
( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),Y))),s(fun(cart(real,N),bool),E2))))
=> ? [E0] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,E0))))
& ! [YI_] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(prod(cart(real,N),cart(real,N)),real),distance),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),YI_))),s(cart(real,N),Y))))))),s(real,E0))))
=> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),YI_))),s(fun(cart(real,N),bool),E2)))) ) ) )
& ~ ? [X] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,A5))),s(real,X))))
& p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,B0))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),i(s(fun(real,cart(real,N)),F0),s(real,X))))),s(fun(cart(real,N),bool),E1))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),i(s(fun(real,cart(real,N)),F0),s(real,X))))),s(fun(cart(real,N),bool),E2)))) ) )
=> ? [X] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,A5))),s(real,X))))
& p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,B0))))
& ~ p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),i(s(fun(real,cart(real,N)),F0),s(real,X))))),s(fun(cart(real,N),bool),E1))))
& ~ p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),i(s(fun(real,cart(real,N)),F0),s(real,X))))),s(fun(cart(real,N),bool),E2)))) ) ) ).
fof(aSQUAREu_BOUNDu_LEMMA,axiom,
! [X] : p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,X))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,X)))))))) ).
fof(aSQUAREu_CONTINUOUS,axiom,
! [X,E0] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,E0))))
=> ? [D0] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,D0))))
& ! [Y] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,Y))),s(real,X))))))),s(real,D0))))
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,Y))),s(real,Y))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,X))))))))),s(real,E0)))) ) ) ) ).
fof(aSQRTu_WORKS,axiom,
! [X] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X))))
=> ( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),sqrt),s(real,X))))))
& s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(real,real),sqrt),s(real,X))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(real,X) ) ) ).
fof(aSQRTu_POSu_LE,axiom,
! [X] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X))))
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),sqrt),s(real,X)))))) ) ).
fof(aSQRTu_POWu_2,axiom,
! [X] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X))))
=> s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(real,real),sqrt),s(real,X))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(real,X) ) ).
fof(aSQRTu_MUL,axiom,
! [X,Y] :
( ( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X))))
& p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) )
=> s(real,i(s(fun(real,real),sqrt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Y))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),sqrt),s(real,X))))),s(real,i(s(fun(real,real),sqrt),s(real,Y))))) ) ).
fof(aSQRTu_INV,axiom,
! [X] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X))))
=> s(real,i(s(fun(real,real),sqrt),s(real,i(s(fun(real,real),realu_inv),s(real,X))))) = s(real,i(s(fun(real,real),realu_inv),s(real,i(s(fun(real,real),sqrt),s(real,X))))) ) ).
fof(aSQRTu_DIV,axiom,
! [X,Y] :
( ( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X))))
& p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) )
=> s(real,i(s(fun(real,real),sqrt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,X))),s(real,Y))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,i(s(fun(real,real),sqrt),s(real,X))))),s(real,i(s(fun(real,real),sqrt),s(real,Y))))) ) ).
fof(aSQRTu_POW2,axiom,
! [X] :
( s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(real,real),sqrt),s(real,X))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(real,X)
<=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) ) ).
fof(aSQRTu_MONOu_LT,axiom,
! [X,Y] :
( ( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X))))
& p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y)))) )
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),sqrt),s(real,X))))),s(real,i(s(fun(real,real),sqrt),s(real,Y)))))) ) ).
fof(aSQRTu_MONOu_LE,axiom,
! [X,Y] :
( ( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X))))
& p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y)))) )
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),sqrt),s(real,X))))),s(real,i(s(fun(real,real),sqrt),s(real,Y)))))) ) ).
fof(aSQRTu_MONOu_LTu_EQ,axiom,
! [X,Y] :
( ( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X))))
& p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) )
=> s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),sqrt),s(real,X))))),s(real,i(s(fun(real,real),sqrt),s(real,Y))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y))) ) ).
fof(aSQRTu_MONOu_LEu_EQ,axiom,
! [X,Y] :
( ( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X))))
& p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) )
=> s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),sqrt),s(real,X))))),s(real,i(s(fun(real,real),sqrt),s(real,Y))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y))) ) ).
fof(aSQRTu_INJ,axiom,
! [X,Y] :
( ( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X))))
& p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) )
=> ( s(real,i(s(fun(real,real),sqrt),s(real,X))) = s(real,i(s(fun(real,real),sqrt),s(real,Y)))
<=> s(real,X) = s(real,Y) ) ) ).
fof(aSQRTu_LTu_0,axiom,
! [X] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X))))
=> s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),sqrt),s(real,X))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X))) ) ).
fof(aSQRTu_EQu_0,axiom,
! [X] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X))))
=> ( s(real,i(s(fun(real,real),sqrt),s(real,X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
<=> s(real,X) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ) ).
fof(aSQRTu_POSu_LT,axiom,
! [X] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X))))
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),sqrt),s(real,X)))))) ) ).
fof(aREALu_LEu_LSQRT,axiom,
! [X,Y] :
( ( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X))))
& p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y))))
& p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,Y))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))) )
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),sqrt),s(real,X))))),s(real,Y)))) ) ).
fof(aREALu_LEu_RSQRT,axiom,
! [X,Y] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,Y))))
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,i(s(fun(real,real),sqrt),s(real,Y)))))) ) ).
fof(aREALu_LTu_LSQRT,axiom,
! [X,Y] :
( ( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X))))
& p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y))))
& p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,Y))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))) )
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),sqrt),s(real,X))))),s(real,Y)))) ) ).
fof(aREALu_LTu_RSQRT,axiom,
! [X,Y] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,Y))))
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,i(s(fun(real,real),sqrt),s(real,Y)))))) ) ).
fof(aSQRTu_EVENu_POW2,axiom,
! [N0] :
( p(s(bool,i(s(fun(num,bool),even),s(num,N0))))
=> s(real,i(s(fun(real,real),sqrt),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(num,N0))))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) ) ).
fof(aREALu_DIVu_SQRT,axiom,
! [X] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X))))
=> s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,X))),s(real,i(s(fun(real,real),sqrt),s(real,X))))) = s(real,i(s(fun(real,real),sqrt),s(real,X))) ) ).
fof(aREALu_RSQRTu_LE,axiom,
! [X,Y] :
( ( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X))))
& p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y))))
& p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,i(s(fun(real,real),sqrt),s(real,Y)))))) )
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,Y)))) ) ).
fof(aREALu_LSQRTu_LE,axiom,
! [X,Y] :
( ( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X))))
& p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),sqrt),s(real,X))))),s(real,Y)))) )
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,Y))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))) ) ).
fof(aNORMu_0,axiom,
! [Q102146] : s(real,i(s(fun(cart(real,Q102146),real),vectoru_norm),s(cart(real,Q102146),i(s(fun(num,cart(real,Q102146)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ).
fof(aNORMu_POSu_LE,axiom,
! [Q102162,X] : p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(cart(real,Q102162),real),vectoru_norm),s(cart(real,Q102162),X)))))) ).
fof(aNORMu_NEG,axiom,
! [Q102180,X] : s(real,i(s(fun(cart(real,Q102180),real),vectoru_norm),s(cart(real,Q102180),i(s(fun(cart(real,Q102180),cart(real,Q102180)),vectoru_neg),s(cart(real,Q102180),X))))) = s(real,i(s(fun(cart(real,Q102180),real),vectoru_norm),s(cart(real,Q102180),X))) ).
fof(aNORMu_SUB,axiom,
! [Q102210,X,Y] : s(real,i(s(fun(cart(real,Q102210),real),vectoru_norm),s(cart(real,Q102210),i(s(fun(cart(real,Q102210),cart(real,Q102210)),i(s(fun(cart(real,Q102210),fun(cart(real,Q102210),cart(real,Q102210))),vectoru_sub),s(cart(real,Q102210),X))),s(cart(real,Q102210),Y))))) = s(real,i(s(fun(cart(real,Q102210),real),vectoru_norm),s(cart(real,Q102210),i(s(fun(cart(real,Q102210),cart(real,Q102210)),i(s(fun(cart(real,Q102210),fun(cart(real,Q102210),cart(real,Q102210))),vectoru_sub),s(cart(real,Q102210),Y))),s(cart(real,Q102210),X))))) ).
fof(aNORMu_MUL,axiom,
! [Q102231,A5,X] : s(real,i(s(fun(cart(real,Q102231),real),vectoru_norm),s(cart(real,Q102231),i(s(fun(cart(real,Q102231),cart(real,Q102231)),i(s(fun(real,fun(cart(real,Q102231),cart(real,Q102231))),r_),s(real,A5))),s(cart(real,Q102231),X))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),realu_abs),s(real,A5))))),s(real,i(s(fun(cart(real,Q102231),real),vectoru_norm),s(cart(real,Q102231),X))))) ).
fof(aNORMu_EQu_0u_DOT,axiom,
! [Q102254,X] :
( s(real,i(s(fun(cart(real,Q102254),real),vectoru_norm),s(cart(real,Q102254),X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
<=> s(real,i(s(fun(cart(real,Q102254),real),i(s(fun(cart(real,Q102254),fun(cart(real,Q102254),real)),dot),s(cart(real,Q102254),X))),s(cart(real,Q102254),X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ).
fof(aNORMu_EQu_0,axiom,
! [Q102285,X] :
( s(real,i(s(fun(cart(real,Q102285),real),vectoru_norm),s(cart(real,Q102285),X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
<=> s(cart(real,Q102285),X) = s(cart(real,Q102285),i(s(fun(num,cart(real,Q102285)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ).
fof(aNORMu_POSu_LT,axiom,
! [Q102307,X] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(cart(real,Q102307),real),vectoru_norm),s(cart(real,Q102307),X))))))
<=> s(cart(real,Q102307),X) != s(cart(real,Q102307),i(s(fun(num,cart(real,Q102307)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ).
fof(aNORMu_POWu_2,axiom,
! [Q102322,X] : s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,Q102322),real),vectoru_norm),s(cart(real,Q102322),X))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(real,i(s(fun(cart(real,Q102322),real),i(s(fun(cart(real,Q102322),fun(cart(real,Q102322),real)),dot),s(cart(real,Q102322),X))),s(cart(real,Q102322),X))) ).
fof(aNORMu_EQu_0u_IMP,axiom,
! [Q102346,X] :
( s(real,i(s(fun(cart(real,Q102346),real),vectoru_norm),s(cart(real,Q102346),X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
=> s(cart(real,Q102346),X) = s(cart(real,Q102346),i(s(fun(num,cart(real,Q102346)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ).
fof(aNORMu_LEu_0,axiom,
! [Q102367,X] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,Q102367),real),vectoru_norm),s(cart(real,Q102367),X))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))
<=> s(cart(real,Q102367),X) = s(cart(real,Q102367),i(s(fun(num,cart(real,Q102367)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ).
fof(aVECTORu_MULu_EQu_0,axiom,
! [Q102400,A5,X] :
( s(cart(real,Q102400),i(s(fun(cart(real,Q102400),cart(real,Q102400)),i(s(fun(real,fun(cart(real,Q102400),cart(real,Q102400))),r_),s(real,A5))),s(cart(real,Q102400),X))) = s(cart(real,Q102400),i(s(fun(num,cart(real,Q102400)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
<=> ( s(real,A5) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
| s(cart(real,Q102400),X) = s(cart(real,Q102400),i(s(fun(num,cart(real,Q102400)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ) ).
fof(aVECTORu_MULu_LCANCEL,axiom,
! [Q102424,A5,X,Y] :
( s(cart(real,Q102424),i(s(fun(cart(real,Q102424),cart(real,Q102424)),i(s(fun(real,fun(cart(real,Q102424),cart(real,Q102424))),r_),s(real,A5))),s(cart(real,Q102424),X))) = s(cart(real,Q102424),i(s(fun(cart(real,Q102424),cart(real,Q102424)),i(s(fun(real,fun(cart(real,Q102424),cart(real,Q102424))),r_),s(real,A5))),s(cart(real,Q102424),Y)))
<=> ( s(real,A5) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
| s(cart(real,Q102424),X) = s(cart(real,Q102424),Y) ) ) ).
fof(aVECTORu_MULu_RCANCEL,axiom,
! [Q102468,A5,B0,X] :
( s(cart(real,Q102468),i(s(fun(cart(real,Q102468),cart(real,Q102468)),i(s(fun(real,fun(cart(real,Q102468),cart(real,Q102468))),r_),s(real,A5))),s(cart(real,Q102468),X))) = s(cart(real,Q102468),i(s(fun(cart(real,Q102468),cart(real,Q102468)),i(s(fun(real,fun(cart(real,Q102468),cart(real,Q102468))),r_),s(real,B0))),s(cart(real,Q102468),X)))
<=> ( s(real,A5) = s(real,B0)
| s(cart(real,Q102468),X) = s(cart(real,Q102468),i(s(fun(num,cart(real,Q102468)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ) ).
fof(aVECTORu_MULu_LCANCELu_IMP,axiom,
! [Q102500,A5,X,Y] :
( ( s(real,A5) != s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
& s(cart(real,Q102500),i(s(fun(cart(real,Q102500),cart(real,Q102500)),i(s(fun(real,fun(cart(real,Q102500),cart(real,Q102500))),r_),s(real,A5))),s(cart(real,Q102500),X))) = s(cart(real,Q102500),i(s(fun(cart(real,Q102500),cart(real,Q102500)),i(s(fun(real,fun(cart(real,Q102500),cart(real,Q102500))),r_),s(real,A5))),s(cart(real,Q102500),Y))) )
=> s(cart(real,Q102500),X) = s(cart(real,Q102500),Y) ) ).
fof(aVECTORu_MULu_RCANCELu_IMP,axiom,
! [Q102535,A5,B0,X] :
( ( s(cart(real,Q102535),X) != s(cart(real,Q102535),i(s(fun(num,cart(real,Q102535)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
& s(cart(real,Q102535),i(s(fun(cart(real,Q102535),cart(real,Q102535)),i(s(fun(real,fun(cart(real,Q102535),cart(real,Q102535))),r_),s(real,A5))),s(cart(real,Q102535),X))) = s(cart(real,Q102535),i(s(fun(cart(real,Q102535),cart(real,Q102535)),i(s(fun(real,fun(cart(real,Q102535),cart(real,Q102535))),r_),s(real,B0))),s(cart(real,Q102535),X))) )
=> s(real,A5) = s(real,B0) ) ).
fof(aNORMu_CAUCHYu_SCHWARZ,axiom,
! [N,X,Y] : p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),X))),s(cart(real,N),Y))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),Y)))))))) ).
fof(aNORMu_CAUCHYu_SCHWARZu_ABS,axiom,
! [N,X,Y] : p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),X))),s(cart(real,N),Y))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),Y)))))))) ).
fof(aREALu_ABSu_NORM,axiom,
! [Q102710,X] : s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(cart(real,Q102710),real),vectoru_norm),s(cart(real,Q102710),X))))) = s(real,i(s(fun(cart(real,Q102710),real),vectoru_norm),s(cart(real,Q102710),X))) ).
fof(aNORMu_CAUCHYu_SCHWARZu_DIV,axiom,
! [N,X,Y] : p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),X))),s(cart(real,N),Y))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),Y))))))))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) ).
fof(aNORMu_TRIANGLE,axiom,
! [Q102822,X,Y] : p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,Q102822),real),vectoru_norm),s(cart(real,Q102822),i(s(fun(cart(real,Q102822),cart(real,Q102822)),i(s(fun(cart(real,Q102822),fun(cart(real,Q102822),cart(real,Q102822))),vectoru_add),s(cart(real,Q102822),X))),s(cart(real,Q102822),Y))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(cart(real,Q102822),real),vectoru_norm),s(cart(real,Q102822),X))))),s(real,i(s(fun(cart(real,Q102822),real),vectoru_norm),s(cart(real,Q102822),Y)))))))) ).
fof(aNORMu_TRIANGLEu_SUB,axiom,
! [N,X,Y] : p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),Y))))),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),X))),s(cart(real,N),Y)))))))))) ).
fof(aNORMu_TRIANGLEu_LE,axiom,
! [Q102893,X,Y] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(cart(real,Q102893),real),vectoru_norm),s(cart(real,Q102893),X))))),s(real,i(s(fun(cart(real,Q102893),real),vectoru_norm),s(cart(real,Q102893),Y))))))),s(real,e0))))
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,Q102893),real),vectoru_norm),s(cart(real,Q102893),i(s(fun(cart(real,Q102893),cart(real,Q102893)),i(s(fun(cart(real,Q102893),fun(cart(real,Q102893),cart(real,Q102893))),vectoru_add),s(cart(real,Q102893),X))),s(cart(real,Q102893),Y))))))),s(real,e0)))) ) ).
fof(aNORMu_TRIANGLEu_LT,axiom,
! [Q102930,X,Y] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(cart(real,Q102930),real),vectoru_norm),s(cart(real,Q102930),X))))),s(real,i(s(fun(cart(real,Q102930),real),vectoru_norm),s(cart(real,Q102930),Y))))))),s(real,e0))))
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(cart(real,Q102930),real),vectoru_norm),s(cart(real,Q102930),i(s(fun(cart(real,Q102930),cart(real,Q102930)),i(s(fun(cart(real,Q102930),fun(cart(real,Q102930),cart(real,Q102930))),vectoru_add),s(cart(real,Q102930),X))),s(cart(real,Q102930),Y))))))),s(real,e0)))) ) ).
fof(aCOMPONENTu_LEu_NORM,axiom,
! [N,X,I0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) )
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))))))),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X)))))) ) ).
fof(aNORMu_BOUNDu_COMPONENTu_LE,axiom,
! [N,X,E0] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(real,E0))))
=> ! [I0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) )
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))))))),s(real,E0)))) ) ) ).
fof(aNORMu_BOUNDu_COMPONENTu_LT,axiom,
! [N,X,E0] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(real,E0))))
=> ! [I0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) )
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))))))),s(real,E0)))) ) ) ).
fof(aNORMu_LEu_L1,axiom,
! [N,U_0] :
( ! [X,I0] : s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),U_0),s(cart(real,N),X))),s(num,I0))) = s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0)))))
=> ! [X] : p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))),s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),U_0),s(cart(real,N),X)))))))) ) ).
fof(aREALu_ABSu_SUBu_NORM,axiom,
! [Q103229] : p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(cart(real,Q103229),real),vectoru_norm),s(cart(real,Q103229),x))))),s(real,i(s(fun(cart(real,Q103229),real),vectoru_norm),s(cart(real,Q103229),y))))))))),s(real,i(s(fun(cart(real,Q103229),real),vectoru_norm),s(cart(real,Q103229),i(s(fun(cart(real,Q103229),cart(real,Q103229)),i(s(fun(cart(real,Q103229),fun(cart(real,Q103229),cart(real,Q103229))),vectoru_sub),s(cart(real,Q103229),x))),s(cart(real,Q103229),y)))))))) ).
fof(aNORMu_LE,axiom,
! [Q103249,Q103251,X,Y] : s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,Q103249),real),vectoru_norm),s(cart(real,Q103249),X))))),s(real,i(s(fun(cart(real,Q103251),real),vectoru_norm),s(cart(real,Q103251),Y))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,Q103249),real),i(s(fun(cart(real,Q103249),fun(cart(real,Q103249),real)),dot),s(cart(real,Q103249),X))),s(cart(real,Q103249),X))))),s(real,i(s(fun(cart(real,Q103251),real),i(s(fun(cart(real,Q103251),fun(cart(real,Q103251),real)),dot),s(cart(real,Q103251),Y))),s(cart(real,Q103251),Y))))) ).
fof(aNORMu_LT,axiom,
! [Q103280,Q103282,X,Y] : s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(cart(real,Q103280),real),vectoru_norm),s(cart(real,Q103280),X))))),s(real,i(s(fun(cart(real,Q103282),real),vectoru_norm),s(cart(real,Q103282),Y))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(cart(real,Q103280),real),i(s(fun(cart(real,Q103280),fun(cart(real,Q103280),real)),dot),s(cart(real,Q103280),X))),s(cart(real,Q103280),X))))),s(real,i(s(fun(cart(real,Q103282),real),i(s(fun(cart(real,Q103282),fun(cart(real,Q103282),real)),dot),s(cart(real,Q103282),Y))),s(cart(real,Q103282),Y))))) ).
fof(aNORMu_EQ,axiom,
! [Q103311,Q103313,X,Y] :
( s(real,i(s(fun(cart(real,Q103311),real),vectoru_norm),s(cart(real,Q103311),X))) = s(real,i(s(fun(cart(real,Q103313),real),vectoru_norm),s(cart(real,Q103313),Y)))
<=> s(real,i(s(fun(cart(real,Q103311),real),i(s(fun(cart(real,Q103311),fun(cart(real,Q103311),real)),dot),s(cart(real,Q103311),X))),s(cart(real,Q103311),X))) = s(real,i(s(fun(cart(real,Q103313),real),i(s(fun(cart(real,Q103313),fun(cart(real,Q103313),real)),dot),s(cart(real,Q103313),Y))),s(cart(real,Q103313),Y))) ) ).
fof(aNORMu_EQu_1,axiom,
! [Q103338,X] :
( s(real,i(s(fun(cart(real,Q103338),real),vectoru_norm),s(cart(real,Q103338),X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))
<=> s(real,i(s(fun(cart(real,Q103338),real),i(s(fun(cart(real,Q103338),fun(cart(real,Q103338),real)),dot),s(cart(real,Q103338),X))),s(cart(real,Q103338),X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) ) ).
fof(aNORMu_LEu_COMPONENTWISE,axiom,
! [N,X,Y] :
( ! [I0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) )
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))))))),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),Y))),s(num,I0)))))))) )
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),Y)))))) ) ).
fof(aDOTu_SQUAREu_NORM,axiom,
! [Q103415,X] : s(real,i(s(fun(cart(real,Q103415),real),i(s(fun(cart(real,Q103415),fun(cart(real,Q103415),real)),dot),s(cart(real,Q103415),X))),s(cart(real,Q103415),X))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,Q103415),real),vectoru_norm),s(cart(real,Q103415),X))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) ).
fof(aNORMu_EQu_SQUARE,axiom,
! [N,X] :
( s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))) = s(real,a0)
<=> ( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,a0))))
& s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),X))),s(cart(real,N),X))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,a0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) ) ) ).
fof(aNORMu_LEu_SQUARE,axiom,
! [N,X] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(real,a0))))
<=> ( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,a0))))
& p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),X))),s(cart(real,N),X))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,a0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))) ) ) ).
fof(aNORMu_GEu_SQUARE,axiom,
! [N,X] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_ge),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(real,a0))))
<=> ( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,a0))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))
| p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_ge),s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),X))),s(cart(real,N),X))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,a0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))) ) ) ).
fof(aNORMu_LTu_SQUARE,axiom,
! [N,X] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(real,a0))))
<=> ( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,a0))))
& p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),X))),s(cart(real,N),X))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,a0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))) ) ) ).
fof(aNORMu_GTu_SQUARE,axiom,
! [N,X] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_gt),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(real,a0))))
<=> ( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,a0))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))
| p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_gt),s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),X))),s(cart(real,N),X))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,a0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))) ) ) ).
fof(aNORMu_LTu_SQUAREu_ALT,axiom,
! [N,X] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(real,a0))))
<=> ( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,a0))))
& p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),X))),s(cart(real,N),X))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,a0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))) ) ) ).
fof(aDOTu_NORM,axiom,
! [Q104506,X,Y] : s(real,i(s(fun(cart(real,Q104506),real),i(s(fun(cart(real,Q104506),fun(cart(real,Q104506),real)),dot),s(cart(real,Q104506),X))),s(cart(real,Q104506),Y))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,Q104506),real),vectoru_norm),s(cart(real,Q104506),i(s(fun(cart(real,Q104506),cart(real,Q104506)),i(s(fun(cart(real,Q104506),fun(cart(real,Q104506),cart(real,Q104506))),vectoru_add),s(cart(real,Q104506),X))),s(cart(real,Q104506),Y))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,Q104506),real),vectoru_norm),s(cart(real,Q104506),X))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,Q104506),real),vectoru_norm),s(cart(real,Q104506),Y))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) ).
fof(aDOTu_NORMu_NEG,axiom,
! [Q104559,X,Y] : s(real,i(s(fun(cart(real,Q104559),real),i(s(fun(cart(real,Q104559),fun(cart(real,Q104559),real)),dot),s(cart(real,Q104559),X))),s(cart(real,Q104559),Y))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,Q104559),real),vectoru_norm),s(cart(real,Q104559),X))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,Q104559),real),vectoru_norm),s(cart(real,Q104559),Y))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,Q104559),real),vectoru_norm),s(cart(real,Q104559),i(s(fun(cart(real,Q104559),cart(real,Q104559)),i(s(fun(cart(real,Q104559),fun(cart(real,Q104559),cart(real,Q104559))),vectoru_sub),s(cart(real,Q104559),X))),s(cart(real,Q104559),Y))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) ).
fof(aDOTu_NORMu_SUB,axiom,
! [Q104610,X,Y] : s(real,i(s(fun(cart(real,Q104610),real),i(s(fun(cart(real,Q104610),fun(cart(real,Q104610),real)),dot),s(cart(real,Q104610),X))),s(cart(real,Q104610),Y))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,Q104610),real),vectoru_norm),s(cart(real,Q104610),X))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,Q104610),real),vectoru_norm),s(cart(real,Q104610),Y))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,Q104610),real),vectoru_norm),s(cart(real,Q104610),i(s(fun(cart(real,Q104610),cart(real,Q104610)),i(s(fun(cart(real,Q104610),fun(cart(real,Q104610),cart(real,Q104610))),vectoru_sub),s(cart(real,Q104610),X))),s(cart(real,Q104610),Y))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) ).
fof(aVECTORu_EQ,axiom,
! [Q104636,X,Y] :
( s(cart(real,Q104636),X) = s(cart(real,Q104636),Y)
<=> ( s(real,i(s(fun(cart(real,Q104636),real),i(s(fun(cart(real,Q104636),fun(cart(real,Q104636),real)),dot),s(cart(real,Q104636),X))),s(cart(real,Q104636),X))) = s(real,i(s(fun(cart(real,Q104636),real),i(s(fun(cart(real,Q104636),fun(cart(real,Q104636),real)),dot),s(cart(real,Q104636),X))),s(cart(real,Q104636),Y)))
& s(real,i(s(fun(cart(real,Q104636),real),i(s(fun(cart(real,Q104636),fun(cart(real,Q104636),real)),dot),s(cart(real,Q104636),Y))),s(cart(real,Q104636),Y))) = s(real,i(s(fun(cart(real,Q104636),real),i(s(fun(cart(real,Q104636),fun(cart(real,Q104636),real)),dot),s(cart(real,Q104636),X))),s(cart(real,Q104636),X))) ) ) ).
fof(aDISTu_REFL,axiom,
! [Q104658,X] : s(real,i(s(fun(prod(cart(real,Q104658),cart(real,Q104658)),real),distance),s(prod(cart(real,Q104658),cart(real,Q104658)),i(s(fun(cart(real,Q104658),prod(cart(real,Q104658),cart(real,Q104658))),i(s(fun(cart(real,Q104658),fun(cart(real,Q104658),prod(cart(real,Q104658),cart(real,Q104658)))),c_),s(cart(real,Q104658),X))),s(cart(real,Q104658),X))))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ).
fof(aDISTu_SYM,axiom,
! [Q104680,X,Y] : s(real,i(s(fun(prod(cart(real,Q104680),cart(real,Q104680)),real),distance),s(prod(cart(real,Q104680),cart(real,Q104680)),i(s(fun(cart(real,Q104680),prod(cart(real,Q104680),cart(real,Q104680))),i(s(fun(cart(real,Q104680),fun(cart(real,Q104680),prod(cart(real,Q104680),cart(real,Q104680)))),c_),s(cart(real,Q104680),X))),s(cart(real,Q104680),Y))))) = s(real,i(s(fun(prod(cart(real,Q104680),cart(real,Q104680)),real),distance),s(prod(cart(real,Q104680),cart(real,Q104680)),i(s(fun(cart(real,Q104680),prod(cart(real,Q104680),cart(real,Q104680))),i(s(fun(cart(real,Q104680),fun(cart(real,Q104680),prod(cart(real,Q104680),cart(real,Q104680)))),c_),s(cart(real,Q104680),Y))),s(cart(real,Q104680),X))))) ).
fof(aDISTu_POSu_LE,axiom,
! [Q104710,X,Y] : p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(prod(cart(real,Q104710),cart(real,Q104710)),real),distance),s(prod(cart(real,Q104710),cart(real,Q104710)),i(s(fun(cart(real,Q104710),prod(cart(real,Q104710),cart(real,Q104710))),i(s(fun(cart(real,Q104710),fun(cart(real,Q104710),prod(cart(real,Q104710),cart(real,Q104710)))),c_),s(cart(real,Q104710),X))),s(cart(real,Q104710),Y)))))))) ).
fof(aDISTu_TRIANGLE,axiom,
! [N,X,Y,Z0] : p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(prod(cart(real,N),cart(real,N)),real),distance),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),X))),s(cart(real,N),Z0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(prod(cart(real,N),cart(real,N)),real),distance),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),X))),s(cart(real,N),Y))))))),s(real,i(s(fun(prod(cart(real,N),cart(real,N)),real),distance),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),Y))),s(cart(real,N),Z0)))))))))) ).
fof(aDISTu_TRIANGLEu_ALT,axiom,
! [Q104777,X,Y,Z0] : p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(prod(cart(real,Q104777),cart(real,Q104777)),real),distance),s(prod(cart(real,Q104777),cart(real,Q104777)),i(s(fun(cart(real,Q104777),prod(cart(real,Q104777),cart(real,Q104777))),i(s(fun(cart(real,Q104777),fun(cart(real,Q104777),prod(cart(real,Q104777),cart(real,Q104777)))),c_),s(cart(real,Q104777),Y))),s(cart(real,Q104777),Z0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(prod(cart(real,Q104777),cart(real,Q104777)),real),distance),s(prod(cart(real,Q104777),cart(real,Q104777)),i(s(fun(cart(real,Q104777),prod(cart(real,Q104777),cart(real,Q104777))),i(s(fun(cart(real,Q104777),fun(cart(real,Q104777),prod(cart(real,Q104777),cart(real,Q104777)))),c_),s(cart(real,Q104777),X))),s(cart(real,Q104777),Y))))))),s(real,i(s(fun(prod(cart(real,Q104777),cart(real,Q104777)),real),distance),s(prod(cart(real,Q104777),cart(real,Q104777)),i(s(fun(cart(real,Q104777),prod(cart(real,Q104777),cart(real,Q104777))),i(s(fun(cart(real,Q104777),fun(cart(real,Q104777),prod(cart(real,Q104777),cart(real,Q104777)))),c_),s(cart(real,Q104777),X))),s(cart(real,Q104777),Z0)))))))))) ).
fof(aDISTu_EQu_0,axiom,
! [Q104818,X,Y] :
( s(real,i(s(fun(prod(cart(real,Q104818),cart(real,Q104818)),real),distance),s(prod(cart(real,Q104818),cart(real,Q104818)),i(s(fun(cart(real,Q104818),prod(cart(real,Q104818),cart(real,Q104818))),i(s(fun(cart(real,Q104818),fun(cart(real,Q104818),prod(cart(real,Q104818),cart(real,Q104818)))),c_),s(cart(real,Q104818),X))),s(cart(real,Q104818),Y))))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
<=> s(cart(real,Q104818),X) = s(cart(real,Q104818),Y) ) ).
fof(aDISTu_POSu_LT,axiom,
! [Q104851,X,Y] :
( s(cart(real,Q104851),X) != s(cart(real,Q104851),Y)
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(prod(cart(real,Q104851),cart(real,Q104851)),real),distance),s(prod(cart(real,Q104851),cart(real,Q104851)),i(s(fun(cart(real,Q104851),prod(cart(real,Q104851),cart(real,Q104851))),i(s(fun(cart(real,Q104851),fun(cart(real,Q104851),prod(cart(real,Q104851),cart(real,Q104851)))),c_),s(cart(real,Q104851),X))),s(cart(real,Q104851),Y)))))))) ) ).
fof(aDISTu_NZ,axiom,
! [Q104879,X,Y] :
( s(cart(real,Q104879),X) != s(cart(real,Q104879),Y)
<=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(prod(cart(real,Q104879),cart(real,Q104879)),real),distance),s(prod(cart(real,Q104879),cart(real,Q104879)),i(s(fun(cart(real,Q104879),prod(cart(real,Q104879),cart(real,Q104879))),i(s(fun(cart(real,Q104879),fun(cart(real,Q104879),prod(cart(real,Q104879),cart(real,Q104879)))),c_),s(cart(real,Q104879),X))),s(cart(real,Q104879),Y)))))))) ) ).
fof(aDISTu_TRIANGLEu_LE,axiom,
! [Q104912,X,Y,Z0,E0] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(prod(cart(real,Q104912),cart(real,Q104912)),real),distance),s(prod(cart(real,Q104912),cart(real,Q104912)),i(s(fun(cart(real,Q104912),prod(cart(real,Q104912),cart(real,Q104912))),i(s(fun(cart(real,Q104912),fun(cart(real,Q104912),prod(cart(real,Q104912),cart(real,Q104912)))),c_),s(cart(real,Q104912),X))),s(cart(real,Q104912),Z0))))))),s(real,i(s(fun(prod(cart(real,Q104912),cart(real,Q104912)),real),distance),s(prod(cart(real,Q104912),cart(real,Q104912)),i(s(fun(cart(real,Q104912),prod(cart(real,Q104912),cart(real,Q104912))),i(s(fun(cart(real,Q104912),fun(cart(real,Q104912),prod(cart(real,Q104912),cart(real,Q104912)))),c_),s(cart(real,Q104912),Y))),s(cart(real,Q104912),Z0))))))))),s(real,E0))))
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(prod(cart(real,Q104912),cart(real,Q104912)),real),distance),s(prod(cart(real,Q104912),cart(real,Q104912)),i(s(fun(cart(real,Q104912),prod(cart(real,Q104912),cart(real,Q104912))),i(s(fun(cart(real,Q104912),fun(cart(real,Q104912),prod(cart(real,Q104912),cart(real,Q104912)))),c_),s(cart(real,Q104912),X))),s(cart(real,Q104912),Y))))))),s(real,E0)))) ) ).
fof(aDISTu_TRIANGLEu_LT,axiom,
! [Q104964,X,Y,Z0,E0] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(prod(cart(real,Q104964),cart(real,Q104964)),real),distance),s(prod(cart(real,Q104964),cart(real,Q104964)),i(s(fun(cart(real,Q104964),prod(cart(real,Q104964),cart(real,Q104964))),i(s(fun(cart(real,Q104964),fun(cart(real,Q104964),prod(cart(real,Q104964),cart(real,Q104964)))),c_),s(cart(real,Q104964),X))),s(cart(real,Q104964),Z0))))))),s(real,i(s(fun(prod(cart(real,Q104964),cart(real,Q104964)),real),distance),s(prod(cart(real,Q104964),cart(real,Q104964)),i(s(fun(cart(real,Q104964),prod(cart(real,Q104964),cart(real,Q104964))),i(s(fun(cart(real,Q104964),fun(cart(real,Q104964),prod(cart(real,Q104964),cart(real,Q104964)))),c_),s(cart(real,Q104964),Y))),s(cart(real,Q104964),Z0))))))))),s(real,E0))))
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(prod(cart(real,Q104964),cart(real,Q104964)),real),distance),s(prod(cart(real,Q104964),cart(real,Q104964)),i(s(fun(cart(real,Q104964),prod(cart(real,Q104964),cart(real,Q104964))),i(s(fun(cart(real,Q104964),fun(cart(real,Q104964),prod(cart(real,Q104964),cart(real,Q104964)))),c_),s(cart(real,Q104964),X))),s(cart(real,Q104964),Y))))))),s(real,E0)))) ) ).
fof(aDISTu_TRIANGLEu_HALFu_L,axiom,
! [Q105011,X1,X2,Y] :
( ( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(prod(cart(real,Q105011),cart(real,Q105011)),real),distance),s(prod(cart(real,Q105011),cart(real,Q105011)),i(s(fun(cart(real,Q105011),prod(cart(real,Q105011),cart(real,Q105011))),i(s(fun(cart(real,Q105011),fun(cart(real,Q105011),prod(cart(real,Q105011),cart(real,Q105011)))),c_),s(cart(real,Q105011),X1))),s(cart(real,Q105011),Y))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,e0))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))))
& p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(prod(cart(real,Q105011),cart(real,Q105011)),real),distance),s(prod(cart(real,Q105011),cart(real,Q105011)),i(s(fun(cart(real,Q105011),prod(cart(real,Q105011),cart(real,Q105011))),i(s(fun(cart(real,Q105011),fun(cart(real,Q105011),prod(cart(real,Q105011),cart(real,Q105011)))),c_),s(cart(real,Q105011),X2))),s(cart(real,Q105011),Y))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,e0))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))))) )
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(prod(cart(real,Q105011),cart(real,Q105011)),real),distance),s(prod(cart(real,Q105011),cart(real,Q105011)),i(s(fun(cart(real,Q105011),prod(cart(real,Q105011),cart(real,Q105011))),i(s(fun(cart(real,Q105011),fun(cart(real,Q105011),prod(cart(real,Q105011),cart(real,Q105011)))),c_),s(cart(real,Q105011),X1))),s(cart(real,Q105011),X2))))))),s(real,e0)))) ) ).
fof(aDISTu_TRIANGLEu_HALFu_R,axiom,
! [Q105069,X1,X2,Y] :
( ( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(prod(cart(real,Q105069),cart(real,Q105069)),real),distance),s(prod(cart(real,Q105069),cart(real,Q105069)),i(s(fun(cart(real,Q105069),prod(cart(real,Q105069),cart(real,Q105069))),i(s(fun(cart(real,Q105069),fun(cart(real,Q105069),prod(cart(real,Q105069),cart(real,Q105069)))),c_),s(cart(real,Q105069),Y))),s(cart(real,Q105069),X1))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,e0))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))))
& p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(prod(cart(real,Q105069),cart(real,Q105069)),real),distance),s(prod(cart(real,Q105069),cart(real,Q105069)),i(s(fun(cart(real,Q105069),prod(cart(real,Q105069),cart(real,Q105069))),i(s(fun(cart(real,Q105069),fun(cart(real,Q105069),prod(cart(real,Q105069),cart(real,Q105069)))),c_),s(cart(real,Q105069),Y))),s(cart(real,Q105069),X2))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,e0))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))))) )
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(prod(cart(real,Q105069),cart(real,Q105069)),real),distance),s(prod(cart(real,Q105069),cart(real,Q105069)),i(s(fun(cart(real,Q105069),prod(cart(real,Q105069),cart(real,Q105069))),i(s(fun(cart(real,Q105069),fun(cart(real,Q105069),prod(cart(real,Q105069),cart(real,Q105069)))),c_),s(cart(real,Q105069),X1))),s(cart(real,Q105069),X2))))))),s(real,e0)))) ) ).
fof(aDISTu_TRIANGLEu_ADD,axiom,
! [Q105155,X,XI_,Y,YI_] : p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(prod(cart(real,Q105155),cart(real,Q105155)),real),distance),s(prod(cart(real,Q105155),cart(real,Q105155)),i(s(fun(cart(real,Q105155),prod(cart(real,Q105155),cart(real,Q105155))),i(s(fun(cart(real,Q105155),fun(cart(real,Q105155),prod(cart(real,Q105155),cart(real,Q105155)))),c_),s(cart(real,Q105155),i(s(fun(cart(real,Q105155),cart(real,Q105155)),i(s(fun(cart(real,Q105155),fun(cart(real,Q105155),cart(real,Q105155))),vectoru_add),s(cart(real,Q105155),X))),s(cart(real,Q105155),Y))))),s(cart(real,Q105155),i(s(fun(cart(real,Q105155),cart(real,Q105155)),i(s(fun(cart(real,Q105155),fun(cart(real,Q105155),cart(real,Q105155))),vectoru_add),s(cart(real,Q105155),XI_))),s(cart(real,Q105155),YI_))))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(prod(cart(real,Q105155),cart(real,Q105155)),real),distance),s(prod(cart(real,Q105155),cart(real,Q105155)),i(s(fun(cart(real,Q105155),prod(cart(real,Q105155),cart(real,Q105155))),i(s(fun(cart(real,Q105155),fun(cart(real,Q105155),prod(cart(real,Q105155),cart(real,Q105155)))),c_),s(cart(real,Q105155),X))),s(cart(real,Q105155),XI_))))))),s(real,i(s(fun(prod(cart(real,Q105155),cart(real,Q105155)),real),distance),s(prod(cart(real,Q105155),cart(real,Q105155)),i(s(fun(cart(real,Q105155),prod(cart(real,Q105155),cart(real,Q105155))),i(s(fun(cart(real,Q105155),fun(cart(real,Q105155),prod(cart(real,Q105155),cart(real,Q105155)))),c_),s(cart(real,Q105155),Y))),s(cart(real,Q105155),YI_)))))))))) ).
fof(aDISTu_MUL,axiom,
! [Q105190,X,Y,C0] : s(real,i(s(fun(prod(cart(real,Q105190),cart(real,Q105190)),real),distance),s(prod(cart(real,Q105190),cart(real,Q105190)),i(s(fun(cart(real,Q105190),prod(cart(real,Q105190),cart(real,Q105190))),i(s(fun(cart(real,Q105190),fun(cart(real,Q105190),prod(cart(real,Q105190),cart(real,Q105190)))),c_),s(cart(real,Q105190),i(s(fun(cart(real,Q105190),cart(real,Q105190)),i(s(fun(real,fun(cart(real,Q105190),cart(real,Q105190))),r_),s(real,C0))),s(cart(real,Q105190),X))))),s(cart(real,Q105190),i(s(fun(cart(real,Q105190),cart(real,Q105190)),i(s(fun(real,fun(cart(real,Q105190),cart(real,Q105190))),r_),s(real,C0))),s(cart(real,Q105190),Y))))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),realu_abs),s(real,C0))))),s(real,i(s(fun(prod(cart(real,Q105190),cart(real,Q105190)),real),distance),s(prod(cart(real,Q105190),cart(real,Q105190)),i(s(fun(cart(real,Q105190),prod(cart(real,Q105190),cart(real,Q105190))),i(s(fun(cart(real,Q105190),fun(cart(real,Q105190),prod(cart(real,Q105190),cart(real,Q105190)))),c_),s(cart(real,Q105190),X))),s(cart(real,Q105190),Y))))))) ).
fof(aDISTu_TRIANGLEu_ADDu_HALF,axiom,
! [N,X,XI_,Y,YI_] :
( ( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(prod(cart(real,N),cart(real,N)),real),distance),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),X))),s(cart(real,N),XI_))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,e0))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))))
& p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(prod(cart(real,N),cart(real,N)),real),distance),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),Y))),s(cart(real,N),YI_))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,e0))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))))) )
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(prod(cart(real,N),cart(real,N)),real),distance),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),X))),s(cart(real,N),Y))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),XI_))),s(cart(real,N),YI_))))))))),s(real,e0)))) ) ).
fof(aDISTu_LEu_0,axiom,
! [Q105293,X,Y] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(prod(cart(real,Q105293),cart(real,Q105293)),real),distance),s(prod(cart(real,Q105293),cart(real,Q105293)),i(s(fun(cart(real,Q105293),prod(cart(real,Q105293),cart(real,Q105293))),i(s(fun(cart(real,Q105293),fun(cart(real,Q105293),prod(cart(real,Q105293),cart(real,Q105293)))),c_),s(cart(real,Q105293),X))),s(cart(real,Q105293),Y))))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))
<=> s(cart(real,Q105293),X) = s(cart(real,Q105293),Y) ) ).
fof(aDISTu_EQ,axiom,
! [Q105328,Q105334,W,X,Y,Z0] :
( s(real,i(s(fun(prod(cart(real,Q105328),cart(real,Q105328)),real),distance),s(prod(cart(real,Q105328),cart(real,Q105328)),i(s(fun(cart(real,Q105328),prod(cart(real,Q105328),cart(real,Q105328))),i(s(fun(cart(real,Q105328),fun(cart(real,Q105328),prod(cart(real,Q105328),cart(real,Q105328)))),c_),s(cart(real,Q105328),W))),s(cart(real,Q105328),X))))) = s(real,i(s(fun(prod(cart(real,Q105334),cart(real,Q105334)),real),distance),s(prod(cart(real,Q105334),cart(real,Q105334)),i(s(fun(cart(real,Q105334),prod(cart(real,Q105334),cart(real,Q105334))),i(s(fun(cart(real,Q105334),fun(cart(real,Q105334),prod(cart(real,Q105334),cart(real,Q105334)))),c_),s(cart(real,Q105334),Y))),s(cart(real,Q105334),Z0)))))
<=> s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(prod(cart(real,Q105328),cart(real,Q105328)),real),distance),s(prod(cart(real,Q105328),cart(real,Q105328)),i(s(fun(cart(real,Q105328),prod(cart(real,Q105328),cart(real,Q105328))),i(s(fun(cart(real,Q105328),fun(cart(real,Q105328),prod(cart(real,Q105328),cart(real,Q105328)))),c_),s(cart(real,Q105328),W))),s(cart(real,Q105328),X))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(prod(cart(real,Q105334),cart(real,Q105334)),real),distance),s(prod(cart(real,Q105334),cart(real,Q105334)),i(s(fun(cart(real,Q105334),prod(cart(real,Q105334),cart(real,Q105334))),i(s(fun(cart(real,Q105334),fun(cart(real,Q105334),prod(cart(real,Q105334),cart(real,Q105334)))),c_),s(cart(real,Q105334),Y))),s(cart(real,Q105334),Z0))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) ) ).
fof(aDISTu_0,axiom,
! [Q105385,X] :
( s(real,i(s(fun(prod(cart(real,Q105385),cart(real,Q105385)),real),distance),s(prod(cart(real,Q105385),cart(real,Q105385)),i(s(fun(cart(real,Q105385),prod(cart(real,Q105385),cart(real,Q105385))),i(s(fun(cart(real,Q105385),fun(cart(real,Q105385),prod(cart(real,Q105385),cart(real,Q105385)))),c_),s(cart(real,Q105385),X))),s(cart(real,Q105385),i(s(fun(num,cart(real,Q105385)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))) = s(real,i(s(fun(cart(real,Q105385),real),vectoru_norm),s(cart(real,Q105385),X)))
& s(real,i(s(fun(prod(cart(real,Q105385),cart(real,Q105385)),real),distance),s(prod(cart(real,Q105385),cart(real,Q105385)),i(s(fun(cart(real,Q105385),prod(cart(real,Q105385),cart(real,Q105385))),i(s(fun(cart(real,Q105385),fun(cart(real,Q105385),prod(cart(real,Q105385),cart(real,Q105385)))),c_),s(cart(real,Q105385),i(s(fun(num,cart(real,Q105385)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(real,Q105385),X))))) = s(real,i(s(fun(cart(real,Q105385),real),vectoru_norm),s(cart(real,Q105385),X))) ) ).
fof(aNEUTRALu_VECTORu_ADD,axiom,
! [N] : s(cart(real,N),i(s(fun(fun(cart(real,N),fun(cart(real,N),cart(real,N))),cart(real,N)),neutral),s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add))) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ).
fof(aMONOIDALu_VECTORu_ADD,axiom,
! [N] : p(s(bool,i(s(fun(fun(cart(real,N),fun(cart(real,N),cart(real,N))),bool),monoidal),s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add)))) ).
fof(avsum,axiom,
! [A,N,U_1] :
( ! [F0,I0,X] : s(real,i(s(fun(A,real),i(s(fun(num,fun(A,real)),i(s(fun(fun(A,cart(real,N)),fun(num,fun(A,real))),U_1),s(fun(A,cart(real,N)),F0))),s(num,I0))),s(A,X))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(A,cart(real,N)),F0),s(A,X))))),s(num,I0)))
=> ! [U_0] :
( ! [S0,F0,I0] : s(real,i(s(fun(num,real),i(s(fun(fun(A,cart(real,N)),fun(num,real)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),fun(num,real))),U_0),s(fun(A,bool),S0))),s(fun(A,cart(real,N)),F0))),s(num,I0))) = s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),i(s(fun(num,fun(A,real)),i(s(fun(fun(A,cart(real,N)),fun(num,fun(A,real))),U_1),s(fun(A,cart(real,N)),F0))),s(num,I0)))))
=> ! [S0,F0] : s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,N)),F0))) = s(cart(real,N),i(s(fun(fun(num,real),cart(real,N)),lambda),s(fun(num,real),i(s(fun(fun(A,cart(real,N)),fun(num,real)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),fun(num,real))),U_0),s(fun(A,bool),S0))),s(fun(A,cart(real,N)),F0))))) ) ) ).
fof(aVSUMu_CLAUSESu_conjunct0,axiom,
! [Q105493,Q105495,F0] : s(cart(real,Q105495),i(s(fun(fun(Q105493,cart(real,Q105495)),cart(real,Q105495)),i(s(fun(fun(Q105493,bool),fun(fun(Q105493,cart(real,Q105495)),cart(real,Q105495))),vsum),s(fun(Q105493,bool),empty))),s(fun(Q105493,cart(real,Q105495)),F0))) = s(cart(real,Q105495),i(s(fun(num,cart(real,Q105495)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ).
fof(aVSUMu_CLAUSESu_conjunct1,axiom,
! [Q105536,Q105541,X,F0,S0] :
( p(s(bool,i(s(fun(fun(Q105536,bool),bool),finite),s(fun(Q105536,bool),S0))))
=> s(cart(real,Q105541),i(s(fun(fun(Q105536,cart(real,Q105541)),cart(real,Q105541)),i(s(fun(fun(Q105536,bool),fun(fun(Q105536,cart(real,Q105541)),cart(real,Q105541))),vsum),s(fun(Q105536,bool),i(s(fun(fun(Q105536,bool),fun(Q105536,bool)),i(s(fun(Q105536,fun(fun(Q105536,bool),fun(Q105536,bool))),insert),s(Q105536,X))),s(fun(Q105536,bool),S0))))),s(fun(Q105536,cart(real,Q105541)),F0))) = s(cart(real,Q105541),i(s(fun(cart(real,Q105541),cart(real,Q105541)),i(s(fun(cart(real,Q105541),fun(cart(real,Q105541),cart(real,Q105541))),i(s(fun(bool,fun(cart(real,Q105541),fun(cart(real,Q105541),cart(real,Q105541)))),cond),s(bool,i(s(fun(fun(Q105536,bool),bool),i(s(fun(Q105536,fun(fun(Q105536,bool),bool)),in),s(Q105536,X))),s(fun(Q105536,bool),S0))))),s(cart(real,Q105541),i(s(fun(fun(Q105536,cart(real,Q105541)),cart(real,Q105541)),i(s(fun(fun(Q105536,bool),fun(fun(Q105536,cart(real,Q105541)),cart(real,Q105541))),vsum),s(fun(Q105536,bool),S0))),s(fun(Q105536,cart(real,Q105541)),F0))))),s(cart(real,Q105541),i(s(fun(cart(real,Q105541),cart(real,Q105541)),i(s(fun(cart(real,Q105541),fun(cart(real,Q105541),cart(real,Q105541))),vectoru_add),s(cart(real,Q105541),i(s(fun(Q105536,cart(real,Q105541)),F0),s(Q105536,X))))),s(cart(real,Q105541),i(s(fun(fun(Q105536,cart(real,Q105541)),cart(real,Q105541)),i(s(fun(fun(Q105536,bool),fun(fun(Q105536,cart(real,Q105541)),cart(real,Q105541))),vsum),s(fun(Q105536,bool),S0))),s(fun(Q105536,cart(real,Q105541)),F0))))))) ) ).
fof(aVSUM,axiom,
! [Q105555,Q105569,F0,S0] :
( p(s(bool,i(s(fun(fun(Q105555,bool),bool),finite),s(fun(Q105555,bool),S0))))
=> s(cart(real,Q105569),i(s(fun(fun(Q105555,cart(real,Q105569)),cart(real,Q105569)),i(s(fun(fun(Q105555,bool),fun(fun(Q105555,cart(real,Q105569)),cart(real,Q105569))),vsum),s(fun(Q105555,bool),S0))),s(fun(Q105555,cart(real,Q105569)),F0))) = s(cart(real,Q105569),i(s(fun(fun(Q105555,cart(real,Q105569)),cart(real,Q105569)),i(s(fun(fun(Q105555,bool),fun(fun(Q105555,cart(real,Q105569)),cart(real,Q105569))),i(s(fun(fun(cart(real,Q105569),fun(cart(real,Q105569),cart(real,Q105569))),fun(fun(Q105555,bool),fun(fun(Q105555,cart(real,Q105569)),cart(real,Q105569)))),iterate),s(fun(cart(real,Q105569),fun(cart(real,Q105569),cart(real,Q105569))),vectoru_add))),s(fun(Q105555,bool),S0))),s(fun(Q105555,cart(real,Q105569)),F0))) ) ).
fof(aVSUMu_EQu_0,axiom,
! [A,Q105605,F0,S0] :
( ! [X] :
( p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))
=> s(cart(real,Q105605),i(s(fun(A,cart(real,Q105605)),F0),s(A,X))) = s(cart(real,Q105605),i(s(fun(num,cart(real,Q105605)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) )
=> s(cart(real,Q105605),i(s(fun(fun(A,cart(real,Q105605)),cart(real,Q105605)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,Q105605)),cart(real,Q105605))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,Q105605)),F0))) = s(cart(real,Q105605),i(s(fun(num,cart(real,Q105605)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ).
fof(aVSUMu_0,axiom,
! [Q105615,Q105619,U_0] :
( ! [X] : s(cart(real,Q105619),i(s(fun(Q105615,cart(real,Q105619)),U_0),s(Q105615,X))) = s(cart(real,Q105619),i(s(fun(num,cart(real,Q105619)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
=> s(cart(real,Q105619),i(s(fun(fun(Q105615,cart(real,Q105619)),cart(real,Q105619)),i(s(fun(fun(Q105615,bool),fun(fun(Q105615,cart(real,Q105619)),cart(real,Q105619))),vsum),s(fun(Q105615,bool),s0))),s(fun(Q105615,cart(real,Q105619)),U_0))) = s(cart(real,Q105619),i(s(fun(num,cart(real,Q105619)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ).
fof(aVSUMu_LMUL,axiom,
! [Q105645,Q105652,U_0] :
( ! [C0,F0,X] : s(cart(real,Q105652),i(s(fun(Q105645,cart(real,Q105652)),i(s(fun(fun(Q105645,cart(real,Q105652)),fun(Q105645,cart(real,Q105652))),i(s(fun(real,fun(fun(Q105645,cart(real,Q105652)),fun(Q105645,cart(real,Q105652)))),U_0),s(real,C0))),s(fun(Q105645,cart(real,Q105652)),F0))),s(Q105645,X))) = s(cart(real,Q105652),i(s(fun(cart(real,Q105652),cart(real,Q105652)),i(s(fun(real,fun(cart(real,Q105652),cart(real,Q105652))),r_),s(real,C0))),s(cart(real,Q105652),i(s(fun(Q105645,cart(real,Q105652)),F0),s(Q105645,X)))))
=> ! [F0,C0,S0] : s(cart(real,Q105652),i(s(fun(fun(Q105645,cart(real,Q105652)),cart(real,Q105652)),i(s(fun(fun(Q105645,bool),fun(fun(Q105645,cart(real,Q105652)),cart(real,Q105652))),vsum),s(fun(Q105645,bool),S0))),s(fun(Q105645,cart(real,Q105652)),i(s(fun(fun(Q105645,cart(real,Q105652)),fun(Q105645,cart(real,Q105652))),i(s(fun(real,fun(fun(Q105645,cart(real,Q105652)),fun(Q105645,cart(real,Q105652)))),U_0),s(real,C0))),s(fun(Q105645,cart(real,Q105652)),F0))))) = s(cart(real,Q105652),i(s(fun(cart(real,Q105652),cart(real,Q105652)),i(s(fun(real,fun(cart(real,Q105652),cart(real,Q105652))),r_),s(real,C0))),s(cart(real,Q105652),i(s(fun(fun(Q105645,cart(real,Q105652)),cart(real,Q105652)),i(s(fun(fun(Q105645,bool),fun(fun(Q105645,cart(real,Q105652)),cart(real,Q105652))),vsum),s(fun(Q105645,bool),S0))),s(fun(Q105645,cart(real,Q105652)),F0))))) ) ).
fof(aVSUMu_RMUL,axiom,
! [Q105678,Q105681,U_0] :
( ! [C0,V,X] : s(cart(real,Q105681),i(s(fun(Q105678,cart(real,Q105681)),i(s(fun(cart(real,Q105681),fun(Q105678,cart(real,Q105681))),i(s(fun(fun(Q105678,real),fun(cart(real,Q105681),fun(Q105678,cart(real,Q105681)))),U_0),s(fun(Q105678,real),C0))),s(cart(real,Q105681),V))),s(Q105678,X))) = s(cart(real,Q105681),i(s(fun(cart(real,Q105681),cart(real,Q105681)),i(s(fun(real,fun(cart(real,Q105681),cart(real,Q105681))),r_),s(real,i(s(fun(Q105678,real),C0),s(Q105678,X))))),s(cart(real,Q105681),V)))
=> ! [C0,S0,V] : s(cart(real,Q105681),i(s(fun(fun(Q105678,cart(real,Q105681)),cart(real,Q105681)),i(s(fun(fun(Q105678,bool),fun(fun(Q105678,cart(real,Q105681)),cart(real,Q105681))),vsum),s(fun(Q105678,bool),S0))),s(fun(Q105678,cart(real,Q105681)),i(s(fun(cart(real,Q105681),fun(Q105678,cart(real,Q105681))),i(s(fun(fun(Q105678,real),fun(cart(real,Q105681),fun(Q105678,cart(real,Q105681)))),U_0),s(fun(Q105678,real),C0))),s(cart(real,Q105681),V))))) = s(cart(real,Q105681),i(s(fun(cart(real,Q105681),cart(real,Q105681)),i(s(fun(real,fun(cart(real,Q105681),cart(real,Q105681))),r_),s(real,i(s(fun(fun(Q105678,real),real),i(s(fun(fun(Q105678,bool),fun(fun(Q105678,real),real)),sum),s(fun(Q105678,bool),S0))),s(fun(Q105678,real),C0))))),s(cart(real,Q105681),V))) ) ).
fof(aVSUMu_ADD,axiom,
! [Q105715,Q105728,U_0] :
( ! [F0,G0,X] : s(cart(real,Q105728),i(s(fun(Q105715,cart(real,Q105728)),i(s(fun(fun(Q105715,cart(real,Q105728)),fun(Q105715,cart(real,Q105728))),i(s(fun(fun(Q105715,cart(real,Q105728)),fun(fun(Q105715,cart(real,Q105728)),fun(Q105715,cart(real,Q105728)))),U_0),s(fun(Q105715,cart(real,Q105728)),F0))),s(fun(Q105715,cart(real,Q105728)),G0))),s(Q105715,X))) = s(cart(real,Q105728),i(s(fun(cart(real,Q105728),cart(real,Q105728)),i(s(fun(cart(real,Q105728),fun(cart(real,Q105728),cart(real,Q105728))),vectoru_add),s(cart(real,Q105728),i(s(fun(Q105715,cart(real,Q105728)),F0),s(Q105715,X))))),s(cart(real,Q105728),i(s(fun(Q105715,cart(real,Q105728)),G0),s(Q105715,X)))))
=> ! [F0,G0,S0] :
( p(s(bool,i(s(fun(fun(Q105715,bool),bool),finite),s(fun(Q105715,bool),S0))))
=> s(cart(real,Q105728),i(s(fun(fun(Q105715,cart(real,Q105728)),cart(real,Q105728)),i(s(fun(fun(Q105715,bool),fun(fun(Q105715,cart(real,Q105728)),cart(real,Q105728))),vsum),s(fun(Q105715,bool),S0))),s(fun(Q105715,cart(real,Q105728)),i(s(fun(fun(Q105715,cart(real,Q105728)),fun(Q105715,cart(real,Q105728))),i(s(fun(fun(Q105715,cart(real,Q105728)),fun(fun(Q105715,cart(real,Q105728)),fun(Q105715,cart(real,Q105728)))),U_0),s(fun(Q105715,cart(real,Q105728)),F0))),s(fun(Q105715,cart(real,Q105728)),G0))))) = s(cart(real,Q105728),i(s(fun(cart(real,Q105728),cart(real,Q105728)),i(s(fun(cart(real,Q105728),fun(cart(real,Q105728),cart(real,Q105728))),vectoru_add),s(cart(real,Q105728),i(s(fun(fun(Q105715,cart(real,Q105728)),cart(real,Q105728)),i(s(fun(fun(Q105715,bool),fun(fun(Q105715,cart(real,Q105728)),cart(real,Q105728))),vsum),s(fun(Q105715,bool),S0))),s(fun(Q105715,cart(real,Q105728)),F0))))),s(cart(real,Q105728),i(s(fun(fun(Q105715,cart(real,Q105728)),cart(real,Q105728)),i(s(fun(fun(Q105715,bool),fun(fun(Q105715,cart(real,Q105728)),cart(real,Q105728))),vsum),s(fun(Q105715,bool),S0))),s(fun(Q105715,cart(real,Q105728)),G0))))) ) ) ).
fof(aVSUMu_SUB,axiom,
! [Q105761,Q105774,U_0] :
( ! [F0,G0,X] : s(cart(real,Q105774),i(s(fun(Q105761,cart(real,Q105774)),i(s(fun(fun(Q105761,cart(real,Q105774)),fun(Q105761,cart(real,Q105774))),i(s(fun(fun(Q105761,cart(real,Q105774)),fun(fun(Q105761,cart(real,Q105774)),fun(Q105761,cart(real,Q105774)))),U_0),s(fun(Q105761,cart(real,Q105774)),F0))),s(fun(Q105761,cart(real,Q105774)),G0))),s(Q105761,X))) = s(cart(real,Q105774),i(s(fun(cart(real,Q105774),cart(real,Q105774)),i(s(fun(cart(real,Q105774),fun(cart(real,Q105774),cart(real,Q105774))),vectoru_sub),s(cart(real,Q105774),i(s(fun(Q105761,cart(real,Q105774)),F0),s(Q105761,X))))),s(cart(real,Q105774),i(s(fun(Q105761,cart(real,Q105774)),G0),s(Q105761,X)))))
=> ! [F0,G0,S0] :
( p(s(bool,i(s(fun(fun(Q105761,bool),bool),finite),s(fun(Q105761,bool),S0))))
=> s(cart(real,Q105774),i(s(fun(fun(Q105761,cart(real,Q105774)),cart(real,Q105774)),i(s(fun(fun(Q105761,bool),fun(fun(Q105761,cart(real,Q105774)),cart(real,Q105774))),vsum),s(fun(Q105761,bool),S0))),s(fun(Q105761,cart(real,Q105774)),i(s(fun(fun(Q105761,cart(real,Q105774)),fun(Q105761,cart(real,Q105774))),i(s(fun(fun(Q105761,cart(real,Q105774)),fun(fun(Q105761,cart(real,Q105774)),fun(Q105761,cart(real,Q105774)))),U_0),s(fun(Q105761,cart(real,Q105774)),F0))),s(fun(Q105761,cart(real,Q105774)),G0))))) = s(cart(real,Q105774),i(s(fun(cart(real,Q105774),cart(real,Q105774)),i(s(fun(cart(real,Q105774),fun(cart(real,Q105774),cart(real,Q105774))),vectoru_sub),s(cart(real,Q105774),i(s(fun(fun(Q105761,cart(real,Q105774)),cart(real,Q105774)),i(s(fun(fun(Q105761,bool),fun(fun(Q105761,cart(real,Q105774)),cart(real,Q105774))),vsum),s(fun(Q105761,bool),S0))),s(fun(Q105761,cart(real,Q105774)),F0))))),s(cart(real,Q105774),i(s(fun(fun(Q105761,cart(real,Q105774)),cart(real,Q105774)),i(s(fun(fun(Q105761,bool),fun(fun(Q105761,cart(real,Q105774)),cart(real,Q105774))),vsum),s(fun(Q105761,bool),S0))),s(fun(Q105761,cart(real,Q105774)),G0))))) ) ) ).
fof(aVSUMu_CONST,axiom,
! [Q105798,Q105801,U_0] :
( ! [C0,N0] : s(cart(real,Q105801),i(s(fun(Q105798,cart(real,Q105801)),i(s(fun(cart(real,Q105801),fun(Q105798,cart(real,Q105801))),U_0),s(cart(real,Q105801),C0))),s(Q105798,N0))) = s(cart(real,Q105801),C0)
=> ! [C0,S0] :
( p(s(bool,i(s(fun(fun(Q105798,bool),bool),finite),s(fun(Q105798,bool),S0))))
=> s(cart(real,Q105801),i(s(fun(fun(Q105798,cart(real,Q105801)),cart(real,Q105801)),i(s(fun(fun(Q105798,bool),fun(fun(Q105798,cart(real,Q105801)),cart(real,Q105801))),vsum),s(fun(Q105798,bool),S0))),s(fun(Q105798,cart(real,Q105801)),i(s(fun(cart(real,Q105801),fun(Q105798,cart(real,Q105801))),U_0),s(cart(real,Q105801),C0))))) = s(cart(real,Q105801),i(s(fun(cart(real,Q105801),cart(real,Q105801)),i(s(fun(real,fun(cart(real,Q105801),cart(real,Q105801))),r_),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(fun(Q105798,bool),num),card),s(fun(Q105798,bool),S0))))))),s(cart(real,Q105801),C0))) ) ) ).
fof(aVSUMu_COMPONENT,axiom,
! [A,N,U_0] :
( ! [F0,I0,X] : s(real,i(s(fun(A,real),i(s(fun(num,fun(A,real)),i(s(fun(fun(A,cart(real,N)),fun(num,fun(A,real))),U_0),s(fun(A,cart(real,N)),F0))),s(num,I0))),s(A,X))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(A,cart(real,N)),F0),s(A,X))))),s(num,I0)))
=> ! [S0,F0,I0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) )
=> s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,N)),F0))))),s(num,I0))) = s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),i(s(fun(num,fun(A,real)),i(s(fun(fun(A,cart(real,N)),fun(num,fun(A,real))),U_0),s(fun(A,cart(real,N)),F0))),s(num,I0))))) ) ) ).
fof(aVSUMu_IMAGE,axiom,
! [Q105914,Q105918,Q105892,F0,G0,S0] :
( ( p(s(bool,i(s(fun(fun(Q105918,bool),bool),finite),s(fun(Q105918,bool),S0))))
& ! [X,Y] :
( ( p(s(bool,i(s(fun(fun(Q105918,bool),bool),i(s(fun(Q105918,fun(fun(Q105918,bool),bool)),in),s(Q105918,X))),s(fun(Q105918,bool),S0))))
& p(s(bool,i(s(fun(fun(Q105918,bool),bool),i(s(fun(Q105918,fun(fun(Q105918,bool),bool)),in),s(Q105918,Y))),s(fun(Q105918,bool),S0))))
& s(Q105892,i(s(fun(Q105918,Q105892),F0),s(Q105918,X))) = s(Q105892,i(s(fun(Q105918,Q105892),F0),s(Q105918,Y))) )
=> s(Q105918,X) = s(Q105918,Y) ) )
=> s(cart(real,Q105914),i(s(fun(fun(Q105892,cart(real,Q105914)),cart(real,Q105914)),i(s(fun(fun(Q105892,bool),fun(fun(Q105892,cart(real,Q105914)),cart(real,Q105914))),vsum),s(fun(Q105892,bool),i(s(fun(fun(Q105918,bool),fun(Q105892,bool)),i(s(fun(fun(Q105918,Q105892),fun(fun(Q105918,bool),fun(Q105892,bool))),image),s(fun(Q105918,Q105892),F0))),s(fun(Q105918,bool),S0))))),s(fun(Q105892,cart(real,Q105914)),G0))) = s(cart(real,Q105914),i(s(fun(fun(Q105918,cart(real,Q105914)),cart(real,Q105914)),i(s(fun(fun(Q105918,bool),fun(fun(Q105918,cart(real,Q105914)),cart(real,Q105914))),vsum),s(fun(Q105918,bool),S0))),s(fun(Q105918,cart(real,Q105914)),i(s(fun(fun(Q105918,Q105892),fun(Q105918,cart(real,Q105914))),i(s(fun(fun(Q105892,cart(real,Q105914)),fun(fun(Q105918,Q105892),fun(Q105918,cart(real,Q105914)))),o),s(fun(Q105892,cart(real,Q105914)),G0))),s(fun(Q105918,Q105892),F0))))) ) ).
fof(aVSUMu_UNION,axiom,
! [Q105942,Q105967,F0,S0,T0] :
( ( p(s(bool,i(s(fun(fun(Q105942,bool),bool),finite),s(fun(Q105942,bool),S0))))
& p(s(bool,i(s(fun(fun(Q105942,bool),bool),finite),s(fun(Q105942,bool),T0))))
& p(s(bool,i(s(fun(fun(Q105942,bool),bool),i(s(fun(fun(Q105942,bool),fun(fun(Q105942,bool),bool)),disjoint),s(fun(Q105942,bool),S0))),s(fun(Q105942,bool),T0)))) )
=> s(cart(real,Q105967),i(s(fun(fun(Q105942,cart(real,Q105967)),cart(real,Q105967)),i(s(fun(fun(Q105942,bool),fun(fun(Q105942,cart(real,Q105967)),cart(real,Q105967))),vsum),s(fun(Q105942,bool),i(s(fun(fun(Q105942,bool),fun(Q105942,bool)),i(s(fun(fun(Q105942,bool),fun(fun(Q105942,bool),fun(Q105942,bool))),union),s(fun(Q105942,bool),S0))),s(fun(Q105942,bool),T0))))),s(fun(Q105942,cart(real,Q105967)),F0))) = s(cart(real,Q105967),i(s(fun(cart(real,Q105967),cart(real,Q105967)),i(s(fun(cart(real,Q105967),fun(cart(real,Q105967),cart(real,Q105967))),vectoru_add),s(cart(real,Q105967),i(s(fun(fun(Q105942,cart(real,Q105967)),cart(real,Q105967)),i(s(fun(fun(Q105942,bool),fun(fun(Q105942,cart(real,Q105967)),cart(real,Q105967))),vsum),s(fun(Q105942,bool),S0))),s(fun(Q105942,cart(real,Q105967)),F0))))),s(cart(real,Q105967),i(s(fun(fun(Q105942,cart(real,Q105967)),cart(real,Q105967)),i(s(fun(fun(Q105942,bool),fun(fun(Q105942,cart(real,Q105967)),cart(real,Q105967))),vsum),s(fun(Q105942,bool),T0))),s(fun(Q105942,cart(real,Q105967)),F0))))) ) ).
fof(aVSUMu_DIFF,axiom,
! [Q105987,Q106012,F0,S0,T0] :
( ( p(s(bool,i(s(fun(fun(Q105987,bool),bool),finite),s(fun(Q105987,bool),S0))))
& p(s(bool,i(s(fun(fun(Q105987,bool),bool),i(s(fun(fun(Q105987,bool),fun(fun(Q105987,bool),bool)),subset),s(fun(Q105987,bool),T0))),s(fun(Q105987,bool),S0)))) )
=> s(cart(real,Q106012),i(s(fun(fun(Q105987,cart(real,Q106012)),cart(real,Q106012)),i(s(fun(fun(Q105987,bool),fun(fun(Q105987,cart(real,Q106012)),cart(real,Q106012))),vsum),s(fun(Q105987,bool),i(s(fun(fun(Q105987,bool),fun(Q105987,bool)),i(s(fun(fun(Q105987,bool),fun(fun(Q105987,bool),fun(Q105987,bool))),diff),s(fun(Q105987,bool),S0))),s(fun(Q105987,bool),T0))))),s(fun(Q105987,cart(real,Q106012)),F0))) = s(cart(real,Q106012),i(s(fun(cart(real,Q106012),cart(real,Q106012)),i(s(fun(cart(real,Q106012),fun(cart(real,Q106012),cart(real,Q106012))),vectoru_sub),s(cart(real,Q106012),i(s(fun(fun(Q105987,cart(real,Q106012)),cart(real,Q106012)),i(s(fun(fun(Q105987,bool),fun(fun(Q105987,cart(real,Q106012)),cart(real,Q106012))),vsum),s(fun(Q105987,bool),S0))),s(fun(Q105987,cart(real,Q106012)),F0))))),s(cart(real,Q106012),i(s(fun(fun(Q105987,cart(real,Q106012)),cart(real,Q106012)),i(s(fun(fun(Q105987,bool),fun(fun(Q105987,cart(real,Q106012)),cart(real,Q106012))),vsum),s(fun(Q105987,bool),T0))),s(fun(Q105987,cart(real,Q106012)),F0))))) ) ).
fof(aVSUMu_DELETE,axiom,
! [Q106054,Q106053,F0,S0,A5] :
( ( p(s(bool,i(s(fun(fun(Q106053,bool),bool),finite),s(fun(Q106053,bool),S0))))
& p(s(bool,i(s(fun(fun(Q106053,bool),bool),i(s(fun(Q106053,fun(fun(Q106053,bool),bool)),in),s(Q106053,A5))),s(fun(Q106053,bool),S0)))) )
=> s(cart(real,Q106054),i(s(fun(fun(Q106053,cart(real,Q106054)),cart(real,Q106054)),i(s(fun(fun(Q106053,bool),fun(fun(Q106053,cart(real,Q106054)),cart(real,Q106054))),vsum),s(fun(Q106053,bool),i(s(fun(Q106053,fun(Q106053,bool)),i(s(fun(fun(Q106053,bool),fun(Q106053,fun(Q106053,bool))),delete),s(fun(Q106053,bool),S0))),s(Q106053,A5))))),s(fun(Q106053,cart(real,Q106054)),F0))) = s(cart(real,Q106054),i(s(fun(cart(real,Q106054),cart(real,Q106054)),i(s(fun(cart(real,Q106054),fun(cart(real,Q106054),cart(real,Q106054))),vectoru_sub),s(cart(real,Q106054),i(s(fun(fun(Q106053,cart(real,Q106054)),cart(real,Q106054)),i(s(fun(fun(Q106053,bool),fun(fun(Q106053,cart(real,Q106054)),cart(real,Q106054))),vsum),s(fun(Q106053,bool),S0))),s(fun(Q106053,cart(real,Q106054)),F0))))),s(cart(real,Q106054),i(s(fun(Q106053,cart(real,Q106054)),F0),s(Q106053,A5))))) ) ).
fof(aVSUMu_INCLu_EXCL,axiom,
! [A,N,S0,T0,F0] :
( ( p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0))))
& p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),T0)))) )
=> s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,N)),F0))))),s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),T0))),s(fun(A,cart(real,N)),F0))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),S0))),s(fun(A,bool),T0))))),s(fun(A,cart(real,N)),F0))))),s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),S0))),s(fun(A,bool),T0))))),s(fun(A,cart(real,N)),F0))))) ) ).
fof(aVSUMu_NEG,axiom,
! [Q106132,Q106140,U_0] :
( ! [F0,X] : s(cart(real,Q106140),i(s(fun(Q106132,cart(real,Q106140)),i(s(fun(fun(Q106132,cart(real,Q106140)),fun(Q106132,cart(real,Q106140))),U_0),s(fun(Q106132,cart(real,Q106140)),F0))),s(Q106132,X))) = s(cart(real,Q106140),i(s(fun(cart(real,Q106140),cart(real,Q106140)),vectoru_neg),s(cart(real,Q106140),i(s(fun(Q106132,cart(real,Q106140)),F0),s(Q106132,X)))))
=> ! [F0,S0] : s(cart(real,Q106140),i(s(fun(fun(Q106132,cart(real,Q106140)),cart(real,Q106140)),i(s(fun(fun(Q106132,bool),fun(fun(Q106132,cart(real,Q106140)),cart(real,Q106140))),vsum),s(fun(Q106132,bool),S0))),s(fun(Q106132,cart(real,Q106140)),i(s(fun(fun(Q106132,cart(real,Q106140)),fun(Q106132,cart(real,Q106140))),U_0),s(fun(Q106132,cart(real,Q106140)),F0))))) = s(cart(real,Q106140),i(s(fun(cart(real,Q106140),cart(real,Q106140)),vectoru_neg),s(cart(real,Q106140),i(s(fun(fun(Q106132,cart(real,Q106140)),cart(real,Q106140)),i(s(fun(fun(Q106132,bool),fun(fun(Q106132,cart(real,Q106140)),cart(real,Q106140))),vsum),s(fun(Q106132,bool),S0))),s(fun(Q106132,cart(real,Q106140)),F0))))) ) ).
fof(aVSUMu_EQ,axiom,
! [Q106171,Q106182,F0,G0,S0] :
( ! [X] :
( p(s(bool,i(s(fun(fun(Q106171,bool),bool),i(s(fun(Q106171,fun(fun(Q106171,bool),bool)),in),s(Q106171,X))),s(fun(Q106171,bool),S0))))
=> s(cart(real,Q106182),i(s(fun(Q106171,cart(real,Q106182)),F0),s(Q106171,X))) = s(cart(real,Q106182),i(s(fun(Q106171,cart(real,Q106182)),G0),s(Q106171,X))) )
=> s(cart(real,Q106182),i(s(fun(fun(Q106171,cart(real,Q106182)),cart(real,Q106182)),i(s(fun(fun(Q106171,bool),fun(fun(Q106171,cart(real,Q106182)),cart(real,Q106182))),vsum),s(fun(Q106171,bool),S0))),s(fun(Q106171,cart(real,Q106182)),F0))) = s(cart(real,Q106182),i(s(fun(fun(Q106171,cart(real,Q106182)),cart(real,Q106182)),i(s(fun(fun(Q106171,bool),fun(fun(Q106171,cart(real,Q106182)),cart(real,Q106182))),vsum),s(fun(Q106171,bool),S0))),s(fun(Q106171,cart(real,Q106182)),G0))) ) ).
fof(aVSUMu_SUPERSET,axiom,
! [A,N,F0,U,V] :
( ( p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),U))),s(fun(A,bool),V))))
& ! [X] :
( ( p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),V))))
& ~ p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),U)))) )
=> s(cart(real,N),i(s(fun(A,cart(real,N)),F0),s(A,X))) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) )
=> s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),V))),s(fun(A,cart(real,N)),F0))) = s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),U))),s(fun(A,cart(real,N)),F0))) ) ).
fof(aVSUMu_EQu_SUPERSET,axiom,
! [A,Q106306,F0,S0,T0] :
( ( p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),T0))))
& p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),T0))),s(fun(A,bool),S0))))
& ! [X] :
( p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T0))))
=> s(cart(real,Q106306),i(s(fun(A,cart(real,Q106306)),F0),s(A,X))) = s(cart(real,Q106306),i(s(fun(A,cart(real,Q106306)),g),s(A,X))) )
& ! [X] :
( ( p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))
& ~ p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T0)))) )
=> s(cart(real,Q106306),i(s(fun(A,cart(real,Q106306)),F0),s(A,X))) = s(cart(real,Q106306),i(s(fun(num,cart(real,Q106306)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) )
=> s(cart(real,Q106306),i(s(fun(fun(A,cart(real,Q106306)),cart(real,Q106306)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,Q106306)),cart(real,Q106306))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,Q106306)),F0))) = s(cart(real,Q106306),i(s(fun(fun(A,cart(real,Q106306)),cart(real,Q106306)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,Q106306)),cart(real,Q106306))),vsum),s(fun(A,bool),T0))),s(fun(A,cart(real,Q106306)),g))) ) ).
fof(aVSUMu_UNIONu_RZERO,axiom,
! [A,N,F0,U,V] :
( ( p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),U))))
& ! [X] :
( ( p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),V))))
& ~ p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),U)))) )
=> s(cart(real,N),i(s(fun(A,cart(real,N)),F0),s(A,X))) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) )
=> s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),U))),s(fun(A,bool),V))))),s(fun(A,cart(real,N)),F0))) = s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),U))),s(fun(A,cart(real,N)),F0))) ) ).
fof(aVSUMu_UNIONu_LZERO,axiom,
! [A,N,F0,U,V] :
( ( p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),V))))
& ! [X] :
( ( p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),U))))
& ~ p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),V)))) )
=> s(cart(real,N),i(s(fun(A,cart(real,N)),F0),s(A,X))) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) )
=> s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),U))),s(fun(A,bool),V))))),s(fun(A,cart(real,N)),F0))) = s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),V))),s(fun(A,cart(real,N)),F0))) ) ).
fof(aVSUMu_RESTRICT,axiom,
! [Q106444,Q106450,U_0] :
( ! [S0,F0,X] : s(cart(real,Q106450),i(s(fun(Q106444,cart(real,Q106450)),i(s(fun(fun(Q106444,cart(real,Q106450)),fun(Q106444,cart(real,Q106450))),i(s(fun(fun(Q106444,bool),fun(fun(Q106444,cart(real,Q106450)),fun(Q106444,cart(real,Q106450)))),U_0),s(fun(Q106444,bool),S0))),s(fun(Q106444,cart(real,Q106450)),F0))),s(Q106444,X))) = s(cart(real,Q106450),i(s(fun(cart(real,Q106450),cart(real,Q106450)),i(s(fun(cart(real,Q106450),fun(cart(real,Q106450),cart(real,Q106450))),i(s(fun(bool,fun(cart(real,Q106450),fun(cart(real,Q106450),cart(real,Q106450)))),cond),s(bool,i(s(fun(fun(Q106444,bool),bool),i(s(fun(Q106444,fun(fun(Q106444,bool),bool)),in),s(Q106444,X))),s(fun(Q106444,bool),S0))))),s(cart(real,Q106450),i(s(fun(Q106444,cart(real,Q106450)),F0),s(Q106444,X))))),s(cart(real,Q106450),i(s(fun(num,cart(real,Q106450)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))
=> ! [F0,S0] :
( p(s(bool,i(s(fun(fun(Q106444,bool),bool),finite),s(fun(Q106444,bool),S0))))
=> s(cart(real,Q106450),i(s(fun(fun(Q106444,cart(real,Q106450)),cart(real,Q106450)),i(s(fun(fun(Q106444,bool),fun(fun(Q106444,cart(real,Q106450)),cart(real,Q106450))),vsum),s(fun(Q106444,bool),S0))),s(fun(Q106444,cart(real,Q106450)),i(s(fun(fun(Q106444,cart(real,Q106450)),fun(Q106444,cart(real,Q106450))),i(s(fun(fun(Q106444,bool),fun(fun(Q106444,cart(real,Q106450)),fun(Q106444,cart(real,Q106450)))),U_0),s(fun(Q106444,bool),S0))),s(fun(Q106444,cart(real,Q106450)),F0))))) = s(cart(real,Q106450),i(s(fun(fun(Q106444,cart(real,Q106450)),cart(real,Q106450)),i(s(fun(fun(Q106444,bool),fun(fun(Q106444,cart(real,Q106450)),cart(real,Q106450))),vsum),s(fun(Q106444,bool),S0))),s(fun(Q106444,cart(real,Q106450)),F0))) ) ) ).
fof(aVSUMu_RESTRICTu_SET,axiom,
! [Q106500,Q106502,U_1] :
( ! [P0,F0,X] : s(cart(real,Q106502),i(s(fun(Q106500,cart(real,Q106502)),i(s(fun(fun(Q106500,cart(real,Q106502)),fun(Q106500,cart(real,Q106502))),i(s(fun(fun(Q106500,bool),fun(fun(Q106500,cart(real,Q106502)),fun(Q106500,cart(real,Q106502)))),U_1),s(fun(Q106500,bool),P0))),s(fun(Q106500,cart(real,Q106502)),F0))),s(Q106500,X))) = s(cart(real,Q106502),i(s(fun(cart(real,Q106502),cart(real,Q106502)),i(s(fun(cart(real,Q106502),fun(cart(real,Q106502),cart(real,Q106502))),i(s(fun(bool,fun(cart(real,Q106502),fun(cart(real,Q106502),cart(real,Q106502)))),cond),s(bool,i(s(fun(Q106500,bool),P0),s(Q106500,X))))),s(cart(real,Q106502),i(s(fun(Q106500,cart(real,Q106502)),F0),s(Q106500,X))))),s(cart(real,Q106502),i(s(fun(num,cart(real,Q106502)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))
=> ! [U_0] :
( ! [S0,P0,GENR_PVARR_278] :
( p(s(bool,i(s(fun(Q106500,bool),i(s(fun(fun(Q106500,bool),fun(Q106500,bool)),i(s(fun(fun(Q106500,bool),fun(fun(Q106500,bool),fun(Q106500,bool))),U_0),s(fun(Q106500,bool),S0))),s(fun(Q106500,bool),P0))),s(Q106500,GENR_PVARR_278))))
<=> ? [X,V] :
( ( p(s(bool,V))
<=> ( p(s(bool,i(s(fun(fun(Q106500,bool),bool),i(s(fun(Q106500,fun(fun(Q106500,bool),bool)),in),s(Q106500,X))),s(fun(Q106500,bool),S0))))
& p(s(bool,i(s(fun(Q106500,bool),P0),s(Q106500,X)))) ) )
& p(s(bool,i(s(fun(Q106500,bool),i(s(fun(bool,fun(Q106500,bool)),i(s(fun(Q106500,fun(bool,fun(Q106500,bool))),setspec),s(Q106500,GENR_PVARR_278))),s(bool,V))),s(Q106500,X)))) ) )
=> ! [P0,S0,F0] : s(cart(real,Q106502),i(s(fun(fun(Q106500,cart(real,Q106502)),cart(real,Q106502)),i(s(fun(fun(Q106500,bool),fun(fun(Q106500,cart(real,Q106502)),cart(real,Q106502))),vsum),s(fun(Q106500,bool),i(s(fun(fun(Q106500,bool),fun(Q106500,bool)),gspec),s(fun(Q106500,bool),i(s(fun(fun(Q106500,bool),fun(Q106500,bool)),i(s(fun(fun(Q106500,bool),fun(fun(Q106500,bool),fun(Q106500,bool))),U_0),s(fun(Q106500,bool),S0))),s(fun(Q106500,bool),P0))))))),s(fun(Q106500,cart(real,Q106502)),F0))) = s(cart(real,Q106502),i(s(fun(fun(Q106500,cart(real,Q106502)),cart(real,Q106502)),i(s(fun(fun(Q106500,bool),fun(fun(Q106500,cart(real,Q106502)),cart(real,Q106502))),vsum),s(fun(Q106500,bool),S0))),s(fun(Q106500,cart(real,Q106502)),i(s(fun(fun(Q106500,cart(real,Q106502)),fun(Q106500,cart(real,Q106502))),i(s(fun(fun(Q106500,bool),fun(fun(Q106500,cart(real,Q106502)),fun(Q106500,cart(real,Q106502)))),U_1),s(fun(Q106500,bool),P0))),s(fun(Q106500,cart(real,Q106502)),F0))))) ) ) ).
fof(aVSUMu_CASES,axiom,
! [A,N,U_2] :
( ! [P0,X] :
( p(s(bool,i(s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),U_2),s(fun(A,bool),P0))),s(A,X))))
<=> ~ p(s(bool,i(s(fun(A,bool),P0),s(A,X)))) )
=> ! [U_1] :
( ! [S0,P0,GENR_PVARR_279] :
( p(s(bool,i(s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),U_1),s(fun(A,bool),S0))),s(fun(A,bool),P0))),s(A,GENR_PVARR_279))))
<=> ? [X,V] :
( ( p(s(bool,V))
<=> ( p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))
& p(s(bool,i(s(fun(A,bool),P0),s(A,X)))) ) )
& p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_279))),s(bool,V))),s(A,X)))) ) )
=> ! [U_0] :
( ! [P0,F0,G0,X] : s(cart(real,N),i(s(fun(A,cart(real,N)),i(s(fun(fun(A,cart(real,N)),fun(A,cart(real,N))),i(s(fun(fun(A,cart(real,N)),fun(fun(A,cart(real,N)),fun(A,cart(real,N)))),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),fun(fun(A,cart(real,N)),fun(A,cart(real,N))))),U_0),s(fun(A,bool),P0))),s(fun(A,cart(real,N)),F0))),s(fun(A,cart(real,N)),G0))),s(A,X))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),i(s(fun(bool,fun(cart(real,N),fun(cart(real,N),cart(real,N)))),cond),s(bool,i(s(fun(A,bool),P0),s(A,X))))),s(cart(real,N),i(s(fun(A,cart(real,N)),F0),s(A,X))))),s(cart(real,N),i(s(fun(A,cart(real,N)),G0),s(A,X)))))
=> ! [S0,P0,F0,G0] :
( p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0))))
=> s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,N)),i(s(fun(fun(A,cart(real,N)),fun(A,cart(real,N))),i(s(fun(fun(A,cart(real,N)),fun(fun(A,cart(real,N)),fun(A,cart(real,N)))),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),fun(fun(A,cart(real,N)),fun(A,cart(real,N))))),U_0),s(fun(A,bool),P0))),s(fun(A,cart(real,N)),F0))),s(fun(A,cart(real,N)),G0))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),U_1),s(fun(A,bool),S0))),s(fun(A,bool),P0))))))),s(fun(A,cart(real,N)),F0))))),s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),U_1),s(fun(A,bool),S0))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),U_2),s(fun(A,bool),P0))))))))),s(fun(A,cart(real,N)),G0))))) ) ) ) ) ).
fof(aVSUMu_SING,axiom,
! [Q106605,Q106610,F0,X] : s(cart(real,Q106605),i(s(fun(fun(Q106610,cart(real,Q106605)),cart(real,Q106605)),i(s(fun(fun(Q106610,bool),fun(fun(Q106610,cart(real,Q106605)),cart(real,Q106605))),vsum),s(fun(Q106610,bool),i(s(fun(fun(Q106610,bool),fun(Q106610,bool)),i(s(fun(Q106610,fun(fun(Q106610,bool),fun(Q106610,bool))),insert),s(Q106610,X))),s(fun(Q106610,bool),empty))))),s(fun(Q106610,cart(real,Q106605)),F0))) = s(cart(real,Q106605),i(s(fun(Q106610,cart(real,Q106605)),F0),s(Q106610,X))) ).
fof(aVSUMu_NORM,axiom,
! [Q106640,Q106632,U_0] :
( ! [F0,X] : s(real,i(s(fun(Q106640,real),i(s(fun(fun(Q106640,cart(real,Q106632)),fun(Q106640,real)),U_0),s(fun(Q106640,cart(real,Q106632)),F0))),s(Q106640,X))) = s(real,i(s(fun(cart(real,Q106632),real),vectoru_norm),s(cart(real,Q106632),i(s(fun(Q106640,cart(real,Q106632)),F0),s(Q106640,X)))))
=> ! [F0,S0] :
( p(s(bool,i(s(fun(fun(Q106640,bool),bool),finite),s(fun(Q106640,bool),S0))))
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,Q106632),real),vectoru_norm),s(cart(real,Q106632),i(s(fun(fun(Q106640,cart(real,Q106632)),cart(real,Q106632)),i(s(fun(fun(Q106640,bool),fun(fun(Q106640,cart(real,Q106632)),cart(real,Q106632))),vsum),s(fun(Q106640,bool),S0))),s(fun(Q106640,cart(real,Q106632)),F0))))))),s(real,i(s(fun(fun(Q106640,real),real),i(s(fun(fun(Q106640,bool),fun(fun(Q106640,real),real)),sum),s(fun(Q106640,bool),S0))),s(fun(Q106640,real),i(s(fun(fun(Q106640,cart(real,Q106632)),fun(Q106640,real)),U_0),s(fun(Q106640,cart(real,Q106632)),F0)))))))) ) ) ).
fof(aVSUMu_NORMu_LE,axiom,
! [N,A,S0,F0,G0] :
( ( p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0))))
& ! [X] :
( p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(A,cart(real,N)),F0),s(A,X))))))),s(real,i(s(fun(A,real),G0),s(A,X)))))) ) )
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,N)),F0))))))),s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),G0)))))) ) ).
fof(aVSUMu_NORMu_TRIANGLE,axiom,
! [Q106736,Q106745,U_0] :
( ! [F0,A5] : s(real,i(s(fun(Q106736,real),i(s(fun(fun(Q106736,cart(real,Q106745)),fun(Q106736,real)),U_0),s(fun(Q106736,cart(real,Q106745)),F0))),s(Q106736,A5))) = s(real,i(s(fun(cart(real,Q106745),real),vectoru_norm),s(cart(real,Q106745),i(s(fun(Q106736,cart(real,Q106745)),F0),s(Q106736,A5)))))
=> ! [S0,F0,B0] :
( ( p(s(bool,i(s(fun(fun(Q106736,bool),bool),finite),s(fun(Q106736,bool),S0))))
& p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(fun(Q106736,real),real),i(s(fun(fun(Q106736,bool),fun(fun(Q106736,real),real)),sum),s(fun(Q106736,bool),S0))),s(fun(Q106736,real),i(s(fun(fun(Q106736,cart(real,Q106745)),fun(Q106736,real)),U_0),s(fun(Q106736,cart(real,Q106745)),F0))))))),s(real,B0)))) )
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,Q106745),real),vectoru_norm),s(cart(real,Q106745),i(s(fun(fun(Q106736,cart(real,Q106745)),cart(real,Q106745)),i(s(fun(fun(Q106736,bool),fun(fun(Q106736,cart(real,Q106745)),cart(real,Q106745))),vsum),s(fun(Q106736,bool),S0))),s(fun(Q106736,cart(real,Q106745)),F0))))))),s(real,B0)))) ) ) ).
fof(aVSUMu_NORMu_BOUND,axiom,
! [Q106792,A,S0,F0,B0] :
( ( p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0))))
& ! [X] :
( p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,Q106792),real),vectoru_norm),s(cart(real,Q106792),i(s(fun(A,cart(real,Q106792)),F0),s(A,X))))))),s(real,B0)))) ) )
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,Q106792),real),vectoru_norm),s(cart(real,Q106792),i(s(fun(fun(A,cart(real,Q106792)),cart(real,Q106792)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,Q106792)),cart(real,Q106792))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,Q106792)),F0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0))))))),s(real,B0)))))) ) ).
fof(aVSUMu_CLAUSESu_NUMSEGu_conjunct0,axiom,
! [Q106879,M0] :
? [V] :
( ( p(s(bool,V))
<=> s(num,M0) = s(num,i(s(fun(num,num),numeral),s(num,u_0))) )
& s(cart(real,Q106879),i(s(fun(fun(num,cart(real,Q106879)),cart(real,Q106879)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q106879)),cart(real,Q106879))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(num,cart(real,Q106879)),f))) = s(cart(real,Q106879),i(s(fun(cart(real,Q106879),cart(real,Q106879)),i(s(fun(cart(real,Q106879),fun(cart(real,Q106879),cart(real,Q106879))),i(s(fun(bool,fun(cart(real,Q106879),fun(cart(real,Q106879),cart(real,Q106879)))),cond),s(bool,V))),s(cart(real,Q106879),i(s(fun(num,cart(real,Q106879)),f),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(real,Q106879),i(s(fun(num,cart(real,Q106879)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) ) ).
fof(aVSUMu_CLAUSESu_NUMSEGu_conjunct1,axiom,
! [Q106879,M0,N0] : s(cart(real,Q106879),i(s(fun(fun(num,cart(real,Q106879)),cart(real,Q106879)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q106879)),cart(real,Q106879))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,i(s(fun(num,num),suc),s(num,N0))))))),s(fun(num,cart(real,Q106879)),f))) = s(cart(real,Q106879),i(s(fun(cart(real,Q106879),cart(real,Q106879)),i(s(fun(cart(real,Q106879),fun(cart(real,Q106879),cart(real,Q106879))),i(s(fun(bool,fun(cart(real,Q106879),fun(cart(real,Q106879),cart(real,Q106879)))),cond),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,i(s(fun(num,num),suc),s(num,N0))))))),s(cart(real,Q106879),i(s(fun(cart(real,Q106879),cart(real,Q106879)),i(s(fun(cart(real,Q106879),fun(cart(real,Q106879),cart(real,Q106879))),vectoru_add),s(cart(real,Q106879),i(s(fun(fun(num,cart(real,Q106879)),cart(real,Q106879)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q106879)),cart(real,Q106879))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q106879)),f))))),s(cart(real,Q106879),i(s(fun(num,cart(real,Q106879)),f),s(num,i(s(fun(num,num),suc),s(num,N0))))))))),s(cart(real,Q106879),i(s(fun(fun(num,cart(real,Q106879)),cart(real,Q106879)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q106879)),cart(real,Q106879))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q106879)),f))))) ).
fof(aVSUMu_CLAUSESu_RIGHT,axiom,
! [N,F0,M0,N0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) )
=> s(cart(real,N),i(s(fun(fun(num,cart(real,N)),cart(real,N)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,N)),cart(real,N))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,N)),F0))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(fun(num,cart(real,N)),cart(real,N)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,N)),cart(real,N))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(fun(num,cart(real,N)),F0))))),s(cart(real,N),i(s(fun(num,cart(real,N)),F0),s(num,N0))))) ) ).
fof(aVSUMu_CMULu_NUMSEG,axiom,
! [Q106968,U_0] :
( ! [C0,F0,X] : s(cart(real,Q106968),i(s(fun(num,cart(real,Q106968)),i(s(fun(fun(num,cart(real,Q106968)),fun(num,cart(real,Q106968))),i(s(fun(real,fun(fun(num,cart(real,Q106968)),fun(num,cart(real,Q106968)))),U_0),s(real,C0))),s(fun(num,cart(real,Q106968)),F0))),s(num,X))) = s(cart(real,Q106968),i(s(fun(cart(real,Q106968),cart(real,Q106968)),i(s(fun(real,fun(cart(real,Q106968),cart(real,Q106968))),r_),s(real,C0))),s(cart(real,Q106968),i(s(fun(num,cart(real,Q106968)),F0),s(num,X)))))
=> ! [F0,C0,M0,N0] : s(cart(real,Q106968),i(s(fun(fun(num,cart(real,Q106968)),cart(real,Q106968)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q106968)),cart(real,Q106968))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q106968)),i(s(fun(fun(num,cart(real,Q106968)),fun(num,cart(real,Q106968))),i(s(fun(real,fun(fun(num,cart(real,Q106968)),fun(num,cart(real,Q106968)))),U_0),s(real,C0))),s(fun(num,cart(real,Q106968)),F0))))) = s(cart(real,Q106968),i(s(fun(cart(real,Q106968),cart(real,Q106968)),i(s(fun(real,fun(cart(real,Q106968),cart(real,Q106968))),r_),s(real,C0))),s(cart(real,Q106968),i(s(fun(fun(num,cart(real,Q106968)),cart(real,Q106968)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q106968)),cart(real,Q106968))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q106968)),F0))))) ) ).
fof(aVSUMu_EQu_NUMSEG,axiom,
! [Q107021,F0,G0,M0,N0] :
( ! [X] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,X))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,X))),s(num,N0)))) )
=> s(cart(real,Q107021),i(s(fun(num,cart(real,Q107021)),F0),s(num,X))) = s(cart(real,Q107021),i(s(fun(num,cart(real,Q107021)),G0),s(num,X))) )
=> s(cart(real,Q107021),i(s(fun(fun(num,cart(real,Q107021)),cart(real,Q107021)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q107021)),cart(real,Q107021))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q107021)),F0))) = s(cart(real,Q107021),i(s(fun(fun(num,cart(real,Q107021)),cart(real,Q107021)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q107021)),cart(real,Q107021))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q107021)),G0))) ) ).
fof(aVSUMu_IMAGEu_GEN,axiom,
! [B,A,Q107061,U_1] :
( ! [S0,F0,Y,GENR_PVARR_281] :
( p(s(bool,i(s(fun(A,bool),i(s(fun(B,fun(A,bool)),i(s(fun(fun(A,B),fun(B,fun(A,bool))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(B,fun(A,bool)))),U_1),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(B,Y))),s(A,GENR_PVARR_281))))
<=> ? [X,V] :
( ( p(s(bool,V))
<=> ( p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))
& s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,Y) ) )
& p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_281))),s(bool,V))),s(A,X)))) ) )
=> ! [U_0] :
( ! [S0,F0,G0,Y] : s(cart(real,Q107061),i(s(fun(B,cart(real,Q107061)),i(s(fun(fun(A,cart(real,Q107061)),fun(B,cart(real,Q107061))),i(s(fun(fun(A,B),fun(fun(A,cart(real,Q107061)),fun(B,cart(real,Q107061)))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(fun(A,cart(real,Q107061)),fun(B,cart(real,Q107061))))),U_0),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(fun(A,cart(real,Q107061)),G0))),s(B,Y))) = s(cart(real,Q107061),i(s(fun(fun(A,cart(real,Q107061)),cart(real,Q107061)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,Q107061)),cart(real,Q107061))),vsum),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(B,fun(A,bool)),i(s(fun(fun(A,B),fun(B,fun(A,bool))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(B,fun(A,bool)))),U_1),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(B,Y))))))),s(fun(A,cart(real,Q107061)),G0)))
=> ! [F0,G0,S0] :
( p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0))))
=> s(cart(real,Q107061),i(s(fun(fun(A,cart(real,Q107061)),cart(real,Q107061)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,Q107061)),cart(real,Q107061))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,Q107061)),G0))) = s(cart(real,Q107061),i(s(fun(fun(B,cart(real,Q107061)),cart(real,Q107061)),i(s(fun(fun(B,bool),fun(fun(B,cart(real,Q107061)),cart(real,Q107061))),vsum),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0))))),s(fun(B,cart(real,Q107061)),i(s(fun(fun(A,cart(real,Q107061)),fun(B,cart(real,Q107061))),i(s(fun(fun(A,B),fun(fun(A,cart(real,Q107061)),fun(B,cart(real,Q107061)))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(fun(A,cart(real,Q107061)),fun(B,cart(real,Q107061))))),U_0),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(fun(A,cart(real,Q107061)),G0))))) ) ) ) ).
fof(aVSUMu_GROUP,axiom,
! [B,A,Q107150,U_1] :
( ! [S0,F0,Y,GENR_PVARR_282] :
( p(s(bool,i(s(fun(A,bool),i(s(fun(B,fun(A,bool)),i(s(fun(fun(A,B),fun(B,fun(A,bool))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(B,fun(A,bool)))),U_1),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(B,Y))),s(A,GENR_PVARR_282))))
<=> ? [X,V] :
( ( p(s(bool,V))
<=> ( p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))
& s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,Y) ) )
& p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_282))),s(bool,V))),s(A,X)))) ) )
=> ! [U_0] :
( ! [S0,F0,G0,Y] : s(cart(real,Q107150),i(s(fun(B,cart(real,Q107150)),i(s(fun(fun(A,cart(real,Q107150)),fun(B,cart(real,Q107150))),i(s(fun(fun(A,B),fun(fun(A,cart(real,Q107150)),fun(B,cart(real,Q107150)))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(fun(A,cart(real,Q107150)),fun(B,cart(real,Q107150))))),U_0),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(fun(A,cart(real,Q107150)),G0))),s(B,Y))) = s(cart(real,Q107150),i(s(fun(fun(A,cart(real,Q107150)),cart(real,Q107150)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,Q107150)),cart(real,Q107150))),vsum),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(B,fun(A,bool)),i(s(fun(fun(A,B),fun(B,fun(A,bool))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(B,fun(A,bool)))),U_1),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(B,Y))))))),s(fun(A,cart(real,Q107150)),G0)))
=> ! [F0,G0,S0,T0] :
( ( p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0))))
& p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(B,bool),fun(fun(B,bool),bool)),subset),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0))))),s(fun(B,bool),T0)))) )
=> s(cart(real,Q107150),i(s(fun(fun(B,cart(real,Q107150)),cart(real,Q107150)),i(s(fun(fun(B,bool),fun(fun(B,cart(real,Q107150)),cart(real,Q107150))),vsum),s(fun(B,bool),T0))),s(fun(B,cart(real,Q107150)),i(s(fun(fun(A,cart(real,Q107150)),fun(B,cart(real,Q107150))),i(s(fun(fun(A,B),fun(fun(A,cart(real,Q107150)),fun(B,cart(real,Q107150)))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(fun(A,cart(real,Q107150)),fun(B,cart(real,Q107150))))),U_0),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(fun(A,cart(real,Q107150)),G0))))) = s(cart(real,Q107150),i(s(fun(fun(A,cart(real,Q107150)),cart(real,Q107150)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,Q107150)),cart(real,Q107150))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,Q107150)),G0))) ) ) ) ).
fof(aVSUMu_VMUL,axiom,
! [Q107186,Q107185,U_0] :
( ! [F0,V,X] : s(cart(real,Q107185),i(s(fun(Q107186,cart(real,Q107185)),i(s(fun(cart(real,Q107185),fun(Q107186,cart(real,Q107185))),i(s(fun(fun(Q107186,real),fun(cart(real,Q107185),fun(Q107186,cart(real,Q107185)))),U_0),s(fun(Q107186,real),F0))),s(cart(real,Q107185),V))),s(Q107186,X))) = s(cart(real,Q107185),i(s(fun(cart(real,Q107185),cart(real,Q107185)),i(s(fun(real,fun(cart(real,Q107185),cart(real,Q107185))),r_),s(real,i(s(fun(Q107186,real),F0),s(Q107186,X))))),s(cart(real,Q107185),V)))
=> ! [F0,V,S0] :
( p(s(bool,i(s(fun(fun(Q107186,bool),bool),finite),s(fun(Q107186,bool),S0))))
=> s(cart(real,Q107185),i(s(fun(cart(real,Q107185),cart(real,Q107185)),i(s(fun(real,fun(cart(real,Q107185),cart(real,Q107185))),r_),s(real,i(s(fun(fun(Q107186,real),real),i(s(fun(fun(Q107186,bool),fun(fun(Q107186,real),real)),sum),s(fun(Q107186,bool),S0))),s(fun(Q107186,real),F0))))),s(cart(real,Q107185),V))) = s(cart(real,Q107185),i(s(fun(fun(Q107186,cart(real,Q107185)),cart(real,Q107185)),i(s(fun(fun(Q107186,bool),fun(fun(Q107186,cart(real,Q107185)),cart(real,Q107185))),vsum),s(fun(Q107186,bool),S0))),s(fun(Q107186,cart(real,Q107185)),i(s(fun(cart(real,Q107185),fun(Q107186,cart(real,Q107185))),i(s(fun(fun(Q107186,real),fun(cart(real,Q107185),fun(Q107186,cart(real,Q107185)))),U_0),s(fun(Q107186,real),F0))),s(cart(real,Q107185),V))))) ) ) ).
fof(aVSUMu_DELTA,axiom,
! [Q107219,Q107222,U_0] :
( ! [A5,X] :
? [V] :
( ( p(s(bool,V))
<=> s(Q107219,X) = s(Q107219,A5) )
& s(cart(real,Q107222),i(s(fun(Q107219,cart(real,Q107222)),i(s(fun(Q107219,fun(Q107219,cart(real,Q107222))),U_0),s(Q107219,A5))),s(Q107219,X))) = s(cart(real,Q107222),i(s(fun(cart(real,Q107222),cart(real,Q107222)),i(s(fun(cart(real,Q107222),fun(cart(real,Q107222),cart(real,Q107222))),i(s(fun(bool,fun(cart(real,Q107222),fun(cart(real,Q107222),cart(real,Q107222)))),cond),s(bool,V))),s(cart(real,Q107222),b0))),s(cart(real,Q107222),i(s(fun(num,cart(real,Q107222)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) )
=> ! [S0,A5] : s(cart(real,Q107222),i(s(fun(fun(Q107219,cart(real,Q107222)),cart(real,Q107222)),i(s(fun(fun(Q107219,bool),fun(fun(Q107219,cart(real,Q107222)),cart(real,Q107222))),vsum),s(fun(Q107219,bool),S0))),s(fun(Q107219,cart(real,Q107222)),i(s(fun(Q107219,fun(Q107219,cart(real,Q107222))),U_0),s(Q107219,A5))))) = s(cart(real,Q107222),i(s(fun(cart(real,Q107222),cart(real,Q107222)),i(s(fun(cart(real,Q107222),fun(cart(real,Q107222),cart(real,Q107222))),i(s(fun(bool,fun(cart(real,Q107222),fun(cart(real,Q107222),cart(real,Q107222)))),cond),s(bool,i(s(fun(fun(Q107219,bool),bool),i(s(fun(Q107219,fun(fun(Q107219,bool),bool)),in),s(Q107219,A5))),s(fun(Q107219,bool),S0))))),s(cart(real,Q107222),b0))),s(cart(real,Q107222),i(s(fun(num,cart(real,Q107222)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) ) ).
fof(aVSUMu_ADDu_NUMSEG,axiom,
! [Q107272,U_0] :
( ! [F0,G0,I0] : s(cart(real,Q107272),i(s(fun(num,cart(real,Q107272)),i(s(fun(fun(num,cart(real,Q107272)),fun(num,cart(real,Q107272))),i(s(fun(fun(num,cart(real,Q107272)),fun(fun(num,cart(real,Q107272)),fun(num,cart(real,Q107272)))),U_0),s(fun(num,cart(real,Q107272)),F0))),s(fun(num,cart(real,Q107272)),G0))),s(num,I0))) = s(cart(real,Q107272),i(s(fun(cart(real,Q107272),cart(real,Q107272)),i(s(fun(cart(real,Q107272),fun(cart(real,Q107272),cart(real,Q107272))),vectoru_add),s(cart(real,Q107272),i(s(fun(num,cart(real,Q107272)),F0),s(num,I0))))),s(cart(real,Q107272),i(s(fun(num,cart(real,Q107272)),G0),s(num,I0)))))
=> ! [F0,G0,M0,N0] : s(cart(real,Q107272),i(s(fun(fun(num,cart(real,Q107272)),cart(real,Q107272)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q107272)),cart(real,Q107272))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q107272)),i(s(fun(fun(num,cart(real,Q107272)),fun(num,cart(real,Q107272))),i(s(fun(fun(num,cart(real,Q107272)),fun(fun(num,cart(real,Q107272)),fun(num,cart(real,Q107272)))),U_0),s(fun(num,cart(real,Q107272)),F0))),s(fun(num,cart(real,Q107272)),G0))))) = s(cart(real,Q107272),i(s(fun(cart(real,Q107272),cart(real,Q107272)),i(s(fun(cart(real,Q107272),fun(cart(real,Q107272),cart(real,Q107272))),vectoru_add),s(cart(real,Q107272),i(s(fun(fun(num,cart(real,Q107272)),cart(real,Q107272)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q107272)),cart(real,Q107272))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q107272)),F0))))),s(cart(real,Q107272),i(s(fun(fun(num,cart(real,Q107272)),cart(real,Q107272)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q107272)),cart(real,Q107272))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q107272)),G0))))) ) ).
fof(aVSUMu_SUBu_NUMSEG,axiom,
! [Q107324,U_0] :
( ! [F0,G0,I0] : s(cart(real,Q107324),i(s(fun(num,cart(real,Q107324)),i(s(fun(fun(num,cart(real,Q107324)),fun(num,cart(real,Q107324))),i(s(fun(fun(num,cart(real,Q107324)),fun(fun(num,cart(real,Q107324)),fun(num,cart(real,Q107324)))),U_0),s(fun(num,cart(real,Q107324)),F0))),s(fun(num,cart(real,Q107324)),G0))),s(num,I0))) = s(cart(real,Q107324),i(s(fun(cart(real,Q107324),cart(real,Q107324)),i(s(fun(cart(real,Q107324),fun(cart(real,Q107324),cart(real,Q107324))),vectoru_sub),s(cart(real,Q107324),i(s(fun(num,cart(real,Q107324)),F0),s(num,I0))))),s(cart(real,Q107324),i(s(fun(num,cart(real,Q107324)),G0),s(num,I0)))))
=> ! [F0,G0,M0,N0] : s(cart(real,Q107324),i(s(fun(fun(num,cart(real,Q107324)),cart(real,Q107324)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q107324)),cart(real,Q107324))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q107324)),i(s(fun(fun(num,cart(real,Q107324)),fun(num,cart(real,Q107324))),i(s(fun(fun(num,cart(real,Q107324)),fun(fun(num,cart(real,Q107324)),fun(num,cart(real,Q107324)))),U_0),s(fun(num,cart(real,Q107324)),F0))),s(fun(num,cart(real,Q107324)),G0))))) = s(cart(real,Q107324),i(s(fun(cart(real,Q107324),cart(real,Q107324)),i(s(fun(cart(real,Q107324),fun(cart(real,Q107324),cart(real,Q107324))),vectoru_sub),s(cart(real,Q107324),i(s(fun(fun(num,cart(real,Q107324)),cart(real,Q107324)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q107324)),cart(real,Q107324))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q107324)),F0))))),s(cart(real,Q107324),i(s(fun(fun(num,cart(real,Q107324)),cart(real,Q107324)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q107324)),cart(real,Q107324))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q107324)),G0))))) ) ).
fof(aVSUMu_ADDu_SPLIT,axiom,
! [Q107387,F0,M0,N0,P0] :
( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))
=> s(cart(real,Q107387),i(s(fun(fun(num,cart(real,Q107387)),cart(real,Q107387)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q107387)),cart(real,Q107387))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,P0))))))),s(fun(num,cart(real,Q107387)),F0))) = s(cart(real,Q107387),i(s(fun(cart(real,Q107387),cart(real,Q107387)),i(s(fun(cart(real,Q107387),fun(cart(real,Q107387),cart(real,Q107387))),vectoru_add),s(cart(real,Q107387),i(s(fun(fun(num,cart(real,Q107387)),cart(real,Q107387)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q107387)),cart(real,Q107387))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q107387)),F0))))),s(cart(real,Q107387),i(s(fun(fun(num,cart(real,Q107387)),cart(real,Q107387)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q107387)),cart(real,Q107387))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,P0))))))),s(fun(num,cart(real,Q107387)),F0))))) ) ).
fof(aVSUMu_VSUMu_PRODUCT,axiom,
! [A,B,Q107444,U_2] :
( ! [X,F0] :
( p(s(bool,i(s(fun(fun(prod(A,B),cart(real,Q107444)),bool),i(s(fun(fun(A,fun(B,cart(real,Q107444))),fun(fun(prod(A,B),cart(real,Q107444)),bool)),U_2),s(fun(A,fun(B,cart(real,Q107444))),X))),s(fun(prod(A,B),cart(real,Q107444)),F0))))
<=> ! [I0,J0] : p(s(bool,i(s(fun(cart(real,Q107444),bool),i(s(fun(cart(real,Q107444),fun(cart(real,Q107444),bool)),geq),s(cart(real,Q107444),i(s(fun(prod(A,B),cart(real,Q107444)),F0),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,I0))),s(B,J0))))))),s(cart(real,Q107444),i(s(fun(B,cart(real,Q107444)),i(s(fun(A,fun(B,cart(real,Q107444))),X),s(A,I0))),s(B,J0)))))) )
=> ! [U_1] :
( ! [S0,T0,GENR_PVARR_283] :
( p(s(bool,i(s(fun(prod(A,B),bool),i(s(fun(fun(A,fun(B,bool)),fun(prod(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(A,fun(B,bool)),fun(prod(A,B),bool))),U_1),s(fun(A,bool),S0))),s(fun(A,fun(B,bool)),T0))),s(prod(A,B),GENR_PVARR_283))))
<=> ? [I0,J0,V] :
( ( p(s(bool,V))
<=> ( p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,I0))),s(fun(A,bool),S0))))
& p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,J0))),s(fun(B,bool),i(s(fun(A,fun(B,bool)),T0),s(A,I0)))))) ) )
& p(s(bool,i(s(fun(prod(A,B),bool),i(s(fun(bool,fun(prod(A,B),bool)),i(s(fun(prod(A,B),fun(bool,fun(prod(A,B),bool))),setspec),s(prod(A,B),GENR_PVARR_283))),s(bool,V))),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,I0))),s(B,J0)))))) ) )
=> ! [U_0] :
( ! [T0,X,I0] : s(cart(real,Q107444),i(s(fun(A,cart(real,Q107444)),i(s(fun(fun(A,fun(B,cart(real,Q107444))),fun(A,cart(real,Q107444))),i(s(fun(fun(A,fun(B,bool)),fun(fun(A,fun(B,cart(real,Q107444))),fun(A,cart(real,Q107444)))),U_0),s(fun(A,fun(B,bool)),T0))),s(fun(A,fun(B,cart(real,Q107444))),X))),s(A,I0))) = s(cart(real,Q107444),i(s(fun(fun(B,cart(real,Q107444)),cart(real,Q107444)),i(s(fun(fun(B,bool),fun(fun(B,cart(real,Q107444)),cart(real,Q107444))),vsum),s(fun(B,bool),i(s(fun(A,fun(B,bool)),T0),s(A,I0))))),s(fun(B,cart(real,Q107444)),i(s(fun(A,fun(B,cart(real,Q107444))),X),s(A,I0)))))
=> ! [S0,T0,X] :
( ( p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0))))
& ! [I0] :
( p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,I0))),s(fun(A,bool),S0))))
=> p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),i(s(fun(A,fun(B,bool)),T0),s(A,I0)))))) ) )
=> s(cart(real,Q107444),i(s(fun(fun(A,cart(real,Q107444)),cart(real,Q107444)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,Q107444)),cart(real,Q107444))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,Q107444)),i(s(fun(fun(A,fun(B,cart(real,Q107444))),fun(A,cart(real,Q107444))),i(s(fun(fun(A,fun(B,bool)),fun(fun(A,fun(B,cart(real,Q107444))),fun(A,cart(real,Q107444)))),U_0),s(fun(A,fun(B,bool)),T0))),s(fun(A,fun(B,cart(real,Q107444))),X))))) = s(cart(real,Q107444),i(s(fun(fun(prod(A,B),cart(real,Q107444)),cart(real,Q107444)),i(s(fun(fun(prod(A,B),bool),fun(fun(prod(A,B),cart(real,Q107444)),cart(real,Q107444))),vsum),s(fun(prod(A,B),bool),i(s(fun(fun(prod(A,B),bool),fun(prod(A,B),bool)),gspec),s(fun(prod(A,B),bool),i(s(fun(fun(A,fun(B,bool)),fun(prod(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(A,fun(B,bool)),fun(prod(A,B),bool))),U_1),s(fun(A,bool),S0))),s(fun(A,fun(B,bool)),T0))))))),s(fun(prod(A,B),cart(real,Q107444)),i(s(fun(fun(fun(prod(A,B),cart(real,Q107444)),bool),fun(prod(A,B),cart(real,Q107444))),gabs),s(fun(fun(prod(A,B),cart(real,Q107444)),bool),i(s(fun(fun(A,fun(B,cart(real,Q107444))),fun(fun(prod(A,B),cart(real,Q107444)),bool)),U_2),s(fun(A,fun(B,cart(real,Q107444))),X))))))) ) ) ) ) ).
fof(aVSUMu_IMAGEu_NONZERO,axiom,
! [N,A,B,D0,I0,S0] :
( ( p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0))))
& ! [X,Y] :
( ( p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))
& p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),S0))))
& s(A,X) != s(A,Y)
& s(B,i(s(fun(A,B),I0),s(A,X))) = s(B,i(s(fun(A,B),I0),s(A,Y))) )
=> s(cart(real,N),i(s(fun(B,cart(real,N)),D0),s(B,i(s(fun(A,B),I0),s(A,X))))) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) )
=> s(cart(real,N),i(s(fun(fun(B,cart(real,N)),cart(real,N)),i(s(fun(fun(B,bool),fun(fun(B,cart(real,N)),cart(real,N))),vsum),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),I0))),s(fun(A,bool),S0))))),s(fun(B,cart(real,N)),D0))) = s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,N)),i(s(fun(fun(A,B),fun(A,cart(real,N))),i(s(fun(fun(B,cart(real,N)),fun(fun(A,B),fun(A,cart(real,N)))),o),s(fun(B,cart(real,N)),D0))),s(fun(A,B),I0))))) ) ).
fof(aVSUMu_UNIONu_NONZERO,axiom,
! [Q107636,Q107660,F0,S0,T0] :
( ( p(s(bool,i(s(fun(fun(Q107636,bool),bool),finite),s(fun(Q107636,bool),S0))))
& p(s(bool,i(s(fun(fun(Q107636,bool),bool),finite),s(fun(Q107636,bool),T0))))
& ! [X] :
( p(s(bool,i(s(fun(fun(Q107636,bool),bool),i(s(fun(Q107636,fun(fun(Q107636,bool),bool)),in),s(Q107636,X))),s(fun(Q107636,bool),i(s(fun(fun(Q107636,bool),fun(Q107636,bool)),i(s(fun(fun(Q107636,bool),fun(fun(Q107636,bool),fun(Q107636,bool))),inter),s(fun(Q107636,bool),S0))),s(fun(Q107636,bool),T0))))))
=> s(cart(real,Q107660),i(s(fun(Q107636,cart(real,Q107660)),F0),s(Q107636,X))) = s(cart(real,Q107660),i(s(fun(num,cart(real,Q107660)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) )
=> s(cart(real,Q107660),i(s(fun(fun(Q107636,cart(real,Q107660)),cart(real,Q107660)),i(s(fun(fun(Q107636,bool),fun(fun(Q107636,cart(real,Q107660)),cart(real,Q107660))),vsum),s(fun(Q107636,bool),i(s(fun(fun(Q107636,bool),fun(Q107636,bool)),i(s(fun(fun(Q107636,bool),fun(fun(Q107636,bool),fun(Q107636,bool))),union),s(fun(Q107636,bool),S0))),s(fun(Q107636,bool),T0))))),s(fun(Q107636,cart(real,Q107660)),F0))) = s(cart(real,Q107660),i(s(fun(cart(real,Q107660),cart(real,Q107660)),i(s(fun(cart(real,Q107660),fun(cart(real,Q107660),cart(real,Q107660))),vectoru_add),s(cart(real,Q107660),i(s(fun(fun(Q107636,cart(real,Q107660)),cart(real,Q107660)),i(s(fun(fun(Q107636,bool),fun(fun(Q107636,cart(real,Q107660)),cart(real,Q107660))),vsum),s(fun(Q107636,bool),S0))),s(fun(Q107636,cart(real,Q107660)),F0))))),s(cart(real,Q107660),i(s(fun(fun(Q107636,cart(real,Q107660)),cart(real,Q107660)),i(s(fun(fun(Q107636,bool),fun(fun(Q107636,cart(real,Q107660)),cart(real,Q107660))),vsum),s(fun(Q107636,bool),T0))),s(fun(Q107636,cart(real,Q107660)),F0))))) ) ).
fof(aVSUMu_UNIONSu_NONZERO,axiom,
! [A,Q107754,U_0] :
( ! [F0,T0] : s(cart(real,Q107754),i(s(fun(fun(A,bool),cart(real,Q107754)),i(s(fun(fun(A,cart(real,Q107754)),fun(fun(A,bool),cart(real,Q107754))),U_0),s(fun(A,cart(real,Q107754)),F0))),s(fun(A,bool),T0))) = s(cart(real,Q107754),i(s(fun(fun(A,cart(real,Q107754)),cart(real,Q107754)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,Q107754)),cart(real,Q107754))),vsum),s(fun(A,bool),T0))),s(fun(A,cart(real,Q107754)),F0)))
=> ! [F0,S0] :
( ( p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),finite),s(fun(fun(A,bool),bool),S0))))
& ! [T0] :
( p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),i(s(fun(fun(A,bool),fun(fun(fun(A,bool),bool),bool)),in),s(fun(A,bool),T0))),s(fun(fun(A,bool),bool),S0))))
=> p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),T0)))) )
& ! [T1,T2,X] :
( ( p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),i(s(fun(fun(A,bool),fun(fun(fun(A,bool),bool),bool)),in),s(fun(A,bool),T1))),s(fun(fun(A,bool),bool),S0))))
& p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),i(s(fun(fun(A,bool),fun(fun(fun(A,bool),bool),bool)),in),s(fun(A,bool),T2))),s(fun(fun(A,bool),bool),S0))))
& s(fun(A,bool),T1) != s(fun(A,bool),T2)
& p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T1))))
& p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T2)))) )
=> s(cart(real,Q107754),i(s(fun(A,cart(real,Q107754)),F0),s(A,X))) = s(cart(real,Q107754),i(s(fun(num,cart(real,Q107754)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) )
=> s(cart(real,Q107754),i(s(fun(fun(A,cart(real,Q107754)),cart(real,Q107754)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,Q107754)),cart(real,Q107754))),vsum),s(fun(A,bool),i(s(fun(fun(fun(A,bool),bool),fun(A,bool)),unions),s(fun(fun(A,bool),bool),S0))))),s(fun(A,cart(real,Q107754)),F0))) = s(cart(real,Q107754),i(s(fun(fun(fun(A,bool),cart(real,Q107754)),cart(real,Q107754)),i(s(fun(fun(fun(A,bool),bool),fun(fun(fun(A,bool),cart(real,Q107754)),cart(real,Q107754))),vsum),s(fun(fun(A,bool),bool),S0))),s(fun(fun(A,bool),cart(real,Q107754)),i(s(fun(fun(A,cart(real,Q107754)),fun(fun(A,bool),cart(real,Q107754))),U_0),s(fun(A,cart(real,Q107754)),F0))))) ) ) ).
fof(aVSUMu_CLAUSESu_LEFT,axiom,
! [Q107795,F0,M0,N0] :
( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0))))
=> s(cart(real,Q107795),i(s(fun(fun(num,cart(real,Q107795)),cart(real,Q107795)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q107795)),cart(real,Q107795))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q107795)),F0))) = s(cart(real,Q107795),i(s(fun(cart(real,Q107795),cart(real,Q107795)),i(s(fun(cart(real,Q107795),fun(cart(real,Q107795),cart(real,Q107795))),vectoru_add),s(cart(real,Q107795),i(s(fun(num,cart(real,Q107795)),F0),s(num,M0))))),s(cart(real,Q107795),i(s(fun(fun(num,cart(real,Q107795)),cart(real,Q107795)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q107795)),cart(real,Q107795))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,N0))))),s(fun(num,cart(real,Q107795)),F0))))) ) ).
fof(aVSUMu_DIFFS,axiom,
! [Q107857,U_0] :
( ! [K0] : s(cart(real,Q107857),i(s(fun(num,cart(real,Q107857)),U_0),s(num,K0))) = s(cart(real,Q107857),i(s(fun(cart(real,Q107857),cart(real,Q107857)),i(s(fun(cart(real,Q107857),fun(cart(real,Q107857),cart(real,Q107857))),vectoru_sub),s(cart(real,Q107857),i(s(fun(num,cart(real,Q107857)),f),s(num,K0))))),s(cart(real,Q107857),i(s(fun(num,cart(real,Q107857)),f),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,K0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))
=> ! [M0,N0] : s(cart(real,Q107857),i(s(fun(fun(num,cart(real,Q107857)),cart(real,Q107857)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q107857)),cart(real,Q107857))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q107857)),U_0))) = s(cart(real,Q107857),i(s(fun(cart(real,Q107857),cart(real,Q107857)),i(s(fun(cart(real,Q107857),fun(cart(real,Q107857),cart(real,Q107857))),i(s(fun(bool,fun(cart(real,Q107857),fun(cart(real,Q107857),cart(real,Q107857)))),cond),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0))))),s(cart(real,Q107857),i(s(fun(cart(real,Q107857),cart(real,Q107857)),i(s(fun(cart(real,Q107857),fun(cart(real,Q107857),cart(real,Q107857))),vectoru_sub),s(cart(real,Q107857),i(s(fun(num,cart(real,Q107857)),f),s(num,M0))))),s(cart(real,Q107857),i(s(fun(num,cart(real,Q107857)),f),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))),s(cart(real,Q107857),i(s(fun(num,cart(real,Q107857)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) ) ).
fof(aVSUMu_DIFFSu_ALT,axiom,
! [Q107910,U_0] :
( ! [K0] : s(cart(real,Q107910),i(s(fun(num,cart(real,Q107910)),U_0),s(num,K0))) = s(cart(real,Q107910),i(s(fun(cart(real,Q107910),cart(real,Q107910)),i(s(fun(cart(real,Q107910),fun(cart(real,Q107910),cart(real,Q107910))),vectoru_sub),s(cart(real,Q107910),i(s(fun(num,cart(real,Q107910)),f),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,K0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(cart(real,Q107910),i(s(fun(num,cart(real,Q107910)),f),s(num,K0)))))
=> ! [M0,N0] : s(cart(real,Q107910),i(s(fun(fun(num,cart(real,Q107910)),cart(real,Q107910)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q107910)),cart(real,Q107910))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q107910)),U_0))) = s(cart(real,Q107910),i(s(fun(cart(real,Q107910),cart(real,Q107910)),i(s(fun(cart(real,Q107910),fun(cart(real,Q107910),cart(real,Q107910))),i(s(fun(bool,fun(cart(real,Q107910),fun(cart(real,Q107910),cart(real,Q107910)))),cond),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0))))),s(cart(real,Q107910),i(s(fun(cart(real,Q107910),cart(real,Q107910)),i(s(fun(cart(real,Q107910),fun(cart(real,Q107910),cart(real,Q107910))),vectoru_sub),s(cart(real,Q107910),i(s(fun(num,cart(real,Q107910)),f),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(cart(real,Q107910),i(s(fun(num,cart(real,Q107910)),f),s(num,M0))))))),s(cart(real,Q107910),i(s(fun(num,cart(real,Q107910)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) ) ).
fof(aVSUMu_DELETEu_CASES,axiom,
! [A,Q107975,X,F0,S0] :
( p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0))))
=> s(cart(real,Q107975),i(s(fun(fun(A,cart(real,Q107975)),cart(real,Q107975)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,Q107975)),cart(real,Q107975))),vsum),s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),S0))),s(A,X))))),s(fun(A,cart(real,Q107975)),F0))) = s(cart(real,Q107975),i(s(fun(cart(real,Q107975),cart(real,Q107975)),i(s(fun(cart(real,Q107975),fun(cart(real,Q107975),cart(real,Q107975))),i(s(fun(bool,fun(cart(real,Q107975),fun(cart(real,Q107975),cart(real,Q107975)))),cond),s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))),s(cart(real,Q107975),i(s(fun(cart(real,Q107975),cart(real,Q107975)),i(s(fun(cart(real,Q107975),fun(cart(real,Q107975),cart(real,Q107975))),vectoru_sub),s(cart(real,Q107975),i(s(fun(fun(A,cart(real,Q107975)),cart(real,Q107975)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,Q107975)),cart(real,Q107975))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,Q107975)),F0))))),s(cart(real,Q107975),i(s(fun(A,cart(real,Q107975)),F0),s(A,X))))))),s(cart(real,Q107975),i(s(fun(fun(A,cart(real,Q107975)),cart(real,Q107975)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,Q107975)),cart(real,Q107975))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,Q107975)),F0))))) ) ).
fof(aVSUMu_EQu_GENERAL,axiom,
! [A,B,N,S0,T0,F0,G0,H0] :
( ( ! [Y] :
( p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,Y))),s(fun(B,bool),T0))))
=> ( ? [X] :
( p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))
& s(B,i(s(fun(A,B),H0),s(A,X))) = s(B,Y) )
& ! [X,XI_] :
( ( p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))
& s(B,i(s(fun(A,B),H0),s(A,X))) = s(B,Y)
& p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,XI_))),s(fun(A,bool),S0))))
& s(B,i(s(fun(A,B),H0),s(A,XI_))) = s(B,Y) )
=> s(A,X) = s(A,XI_) ) ) )
& ! [X] :
( p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))
=> ( p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,i(s(fun(A,B),H0),s(A,X))))),s(fun(B,bool),T0))))
& s(cart(real,N),i(s(fun(B,cart(real,N)),G0),s(B,i(s(fun(A,B),H0),s(A,X))))) = s(cart(real,N),i(s(fun(A,cart(real,N)),F0),s(A,X))) ) ) )
=> s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,N)),F0))) = s(cart(real,N),i(s(fun(fun(B,cart(real,N)),cart(real,N)),i(s(fun(fun(B,bool),fun(fun(B,cart(real,N)),cart(real,N))),vsum),s(fun(B,bool),T0))),s(fun(B,cart(real,N)),G0))) ) ).
fof(aVSUMu_EQu_GENERALu_INVERSES,axiom,
! [A,B,N,S0,T0,F0,G0,H0,K0] :
( ( ! [Y] :
( p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,Y))),s(fun(B,bool),T0))))
=> ( p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,i(s(fun(B,A),K0),s(B,Y))))),s(fun(A,bool),S0))))
& s(B,i(s(fun(A,B),H0),s(A,i(s(fun(B,A),K0),s(B,Y))))) = s(B,Y) ) )
& ! [X] :
( p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))
=> ( p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,i(s(fun(A,B),H0),s(A,X))))),s(fun(B,bool),T0))))
& s(A,i(s(fun(B,A),K0),s(B,i(s(fun(A,B),H0),s(A,X))))) = s(A,X)
& s(cart(real,N),i(s(fun(B,cart(real,N)),G0),s(B,i(s(fun(A,B),H0),s(A,X))))) = s(cart(real,N),i(s(fun(A,cart(real,N)),F0),s(A,X))) ) ) )
=> s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,N)),F0))) = s(cart(real,N),i(s(fun(fun(B,cart(real,N)),cart(real,N)),i(s(fun(fun(B,bool),fun(fun(B,cart(real,N)),cart(real,N))),vsum),s(fun(B,bool),T0))),s(fun(B,cart(real,N)),G0))) ) ).
fof(aVSUMu_NORMu_ALLSUBSETSu_BOUND,axiom,
! [A,N,U_0] :
( ! [F0,X] : s(real,i(s(fun(A,real),i(s(fun(fun(A,cart(real,N)),fun(A,real)),U_0),s(fun(A,cart(real,N)),F0))),s(A,X))) = s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(A,cart(real,N)),F0),s(A,X)))))
=> ! [F0,P0,E0] :
( ( p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),P0))))
& ! [Q0] :
( p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),Q0))),s(fun(A,bool),P0))))
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),Q0))),s(fun(A,cart(real,N)),F0))))))),s(real,E0)))) ) )
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),P0))),s(fun(A,real),i(s(fun(fun(A,cart(real,N)),fun(A,real)),U_0),s(fun(A,cart(real,N)),F0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))),s(real,E0)))))))) ) ) ).
fof(aDOTu_LSUM,axiom,
! [Q108537,Q108528,U_0] :
( ! [F0,Y,X] : s(real,i(s(fun(Q108537,real),i(s(fun(cart(real,Q108528),fun(Q108537,real)),i(s(fun(fun(Q108537,cart(real,Q108528)),fun(cart(real,Q108528),fun(Q108537,real))),U_0),s(fun(Q108537,cart(real,Q108528)),F0))),s(cart(real,Q108528),Y))),s(Q108537,X))) = s(real,i(s(fun(cart(real,Q108528),real),i(s(fun(cart(real,Q108528),fun(cart(real,Q108528),real)),dot),s(cart(real,Q108528),i(s(fun(Q108537,cart(real,Q108528)),F0),s(Q108537,X))))),s(cart(real,Q108528),Y)))
=> ! [S0,F0,Y] :
( p(s(bool,i(s(fun(fun(Q108537,bool),bool),finite),s(fun(Q108537,bool),S0))))
=> s(real,i(s(fun(cart(real,Q108528),real),i(s(fun(cart(real,Q108528),fun(cart(real,Q108528),real)),dot),s(cart(real,Q108528),i(s(fun(fun(Q108537,cart(real,Q108528)),cart(real,Q108528)),i(s(fun(fun(Q108537,bool),fun(fun(Q108537,cart(real,Q108528)),cart(real,Q108528))),vsum),s(fun(Q108537,bool),S0))),s(fun(Q108537,cart(real,Q108528)),F0))))),s(cart(real,Q108528),Y))) = s(real,i(s(fun(fun(Q108537,real),real),i(s(fun(fun(Q108537,bool),fun(fun(Q108537,real),real)),sum),s(fun(Q108537,bool),S0))),s(fun(Q108537,real),i(s(fun(cart(real,Q108528),fun(Q108537,real)),i(s(fun(fun(Q108537,cart(real,Q108528)),fun(cart(real,Q108528),fun(Q108537,real))),U_0),s(fun(Q108537,cart(real,Q108528)),F0))),s(cart(real,Q108528),Y))))) ) ) ).
fof(aDOTu_RSUM,axiom,
! [Q108573,Q108564,U_0] :
( ! [X,F0,Y] : s(real,i(s(fun(Q108573,real),i(s(fun(fun(Q108573,cart(real,Q108564)),fun(Q108573,real)),i(s(fun(cart(real,Q108564),fun(fun(Q108573,cart(real,Q108564)),fun(Q108573,real))),U_0),s(cart(real,Q108564),X))),s(fun(Q108573,cart(real,Q108564)),F0))),s(Q108573,Y))) = s(real,i(s(fun(cart(real,Q108564),real),i(s(fun(cart(real,Q108564),fun(cart(real,Q108564),real)),dot),s(cart(real,Q108564),X))),s(cart(real,Q108564),i(s(fun(Q108573,cart(real,Q108564)),F0),s(Q108573,Y)))))
=> ! [S0,F0,X] :
( p(s(bool,i(s(fun(fun(Q108573,bool),bool),finite),s(fun(Q108573,bool),S0))))
=> s(real,i(s(fun(cart(real,Q108564),real),i(s(fun(cart(real,Q108564),fun(cart(real,Q108564),real)),dot),s(cart(real,Q108564),X))),s(cart(real,Q108564),i(s(fun(fun(Q108573,cart(real,Q108564)),cart(real,Q108564)),i(s(fun(fun(Q108573,bool),fun(fun(Q108573,cart(real,Q108564)),cart(real,Q108564))),vsum),s(fun(Q108573,bool),S0))),s(fun(Q108573,cart(real,Q108564)),F0))))) = s(real,i(s(fun(fun(Q108573,real),real),i(s(fun(fun(Q108573,bool),fun(fun(Q108573,real),real)),sum),s(fun(Q108573,bool),S0))),s(fun(Q108573,real),i(s(fun(fun(Q108573,cart(real,Q108564)),fun(Q108573,real)),i(s(fun(cart(real,Q108564),fun(fun(Q108573,cart(real,Q108564)),fun(Q108573,real))),U_0),s(cart(real,Q108564),X))),s(fun(Q108573,cart(real,Q108564)),F0))))) ) ) ).
fof(aVSUMu_OFFSET,axiom,
! [Q108605,U_0] :
( ! [F0,P0,I0] : s(cart(real,Q108605),i(s(fun(num,cart(real,Q108605)),i(s(fun(num,fun(num,cart(real,Q108605))),i(s(fun(fun(num,cart(real,Q108605)),fun(num,fun(num,cart(real,Q108605)))),U_0),s(fun(num,cart(real,Q108605)),F0))),s(num,P0))),s(num,I0))) = s(cart(real,Q108605),i(s(fun(num,cart(real,Q108605)),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,I0))),s(num,P0)))))
=> ! [F0,M0,P0] : s(cart(real,Q108605),i(s(fun(fun(num,cart(real,Q108605)),cart(real,Q108605)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q108605)),cart(real,Q108605))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,P0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,n))),s(num,P0))))))),s(fun(num,cart(real,Q108605)),F0))) = s(cart(real,Q108605),i(s(fun(fun(num,cart(real,Q108605)),cart(real,Q108605)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q108605)),cart(real,Q108605))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,n))))),s(fun(num,cart(real,Q108605)),i(s(fun(num,fun(num,cart(real,Q108605))),i(s(fun(fun(num,cart(real,Q108605)),fun(num,fun(num,cart(real,Q108605)))),U_0),s(fun(num,cart(real,Q108605)),F0))),s(num,P0))))) ) ).
fof(aVSUMu_OFFSETu_0,axiom,
! [Q108650,U_0] :
( ! [F0,M0,I0] : s(cart(real,Q108650),i(s(fun(num,cart(real,Q108650)),i(s(fun(num,fun(num,cart(real,Q108650))),i(s(fun(fun(num,cart(real,Q108650)),fun(num,fun(num,cart(real,Q108650)))),U_0),s(fun(num,cart(real,Q108650)),F0))),s(num,M0))),s(num,I0))) = s(cart(real,Q108650),i(s(fun(num,cart(real,Q108650)),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,I0))),s(num,M0)))))
=> ! [F0,M0,N0] :
( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0))))
=> s(cart(real,Q108650),i(s(fun(fun(num,cart(real,Q108650)),cart(real,Q108650)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q108650)),cart(real,Q108650))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q108650)),F0))) = s(cart(real,Q108650),i(s(fun(fun(num,cart(real,Q108650)),cart(real,Q108650)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q108650)),cart(real,Q108650))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,N0))),s(num,M0))))))),s(fun(num,cart(real,Q108650)),i(s(fun(num,fun(num,cart(real,Q108650))),i(s(fun(fun(num,cart(real,Q108650)),fun(num,fun(num,cart(real,Q108650)))),U_0),s(fun(num,cart(real,Q108650)),F0))),s(num,M0))))) ) ) ).
fof(aVSUMu_TRIVu_NUMSEG,axiom,
! [Q108694,F0,M0,N0] :
( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,N0))),s(num,M0))))
=> s(cart(real,Q108694),i(s(fun(fun(num,cart(real,Q108694)),cart(real,Q108694)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q108694)),cart(real,Q108694))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q108694)),F0))) = s(cart(real,Q108694),i(s(fun(num,cart(real,Q108694)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ).
fof(aVSUMu_CONSTu_NUMSEG,axiom,
! [Q108721,U_0] :
( ! [C0,N0] : s(cart(real,Q108721),i(s(fun(num,cart(real,Q108721)),i(s(fun(cart(real,Q108721),fun(num,cart(real,Q108721))),U_0),s(cart(real,Q108721),C0))),s(num,N0))) = s(cart(real,Q108721),C0)
=> ! [C0,M0,N0] : s(cart(real,Q108721),i(s(fun(fun(num,cart(real,Q108721)),cart(real,Q108721)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q108721)),cart(real,Q108721))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q108721)),i(s(fun(cart(real,Q108721),fun(num,cart(real,Q108721))),U_0),s(cart(real,Q108721),C0))))) = s(cart(real,Q108721),i(s(fun(cart(real,Q108721),cart(real,Q108721)),i(s(fun(real,fun(cart(real,Q108721),cart(real,Q108721))),r_),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,M0))))))),s(cart(real,Q108721),C0))) ) ).
fof(aVSUMu_SUC,axiom,
! [Q108775,F0,M0,N0] : s(cart(real,Q108775),i(s(fun(fun(num,cart(real,Q108775)),cart(real,Q108775)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q108775)),cart(real,Q108775))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),suc),s(num,N0))))),s(num,i(s(fun(num,num),suc),s(num,M0))))))),s(fun(num,cart(real,Q108775)),F0))) = s(cart(real,Q108775),i(s(fun(fun(num,cart(real,Q108775)),cart(real,Q108775)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q108775)),cart(real,Q108775))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,N0))),s(num,M0))))),s(fun(num,cart(real,Q108775)),i(s(fun(fun(num,num),fun(num,cart(real,Q108775))),i(s(fun(fun(num,cart(real,Q108775)),fun(fun(num,num),fun(num,cart(real,Q108775)))),o),s(fun(num,cart(real,Q108775)),F0))),s(fun(num,num),suc))))) ).
fof(aVSUMu_BIJECTION,axiom,
! [N,A,F0,P0,S0] :
( ( ! [X] :
( p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))
=> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,i(s(fun(A,A),P0),s(A,X))))),s(fun(A,bool),S0)))) )
& ! [Y] :
( p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),S0))))
=> ( ? [X] :
( p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))
& s(A,i(s(fun(A,A),P0),s(A,X))) = s(A,Y) )
& ! [X,XI_] :
( ( p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))
& s(A,i(s(fun(A,A),P0),s(A,X))) = s(A,Y)
& p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,XI_))),s(fun(A,bool),S0))))
& s(A,i(s(fun(A,A),P0),s(A,XI_))) = s(A,Y) )
=> s(A,X) = s(A,XI_) ) ) ) )
=> s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,N)),F0))) = s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,N)),i(s(fun(fun(A,A),fun(A,cart(real,N))),i(s(fun(fun(A,cart(real,N)),fun(fun(A,A),fun(A,cart(real,N)))),o),s(fun(A,cart(real,N)),F0))),s(fun(A,A),P0))))) ) ).
fof(aVSUMu_PARTIALu_SUC,axiom,
! [N,U_1] :
( ! [F0,G0,K0] : s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,N))),i(s(fun(fun(num,real),fun(fun(num,cart(real,N)),fun(num,cart(real,N)))),U_1),s(fun(num,real),F0))),s(fun(num,cart(real,N)),G0))),s(num,K0))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,K0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(num,real),F0),s(num,K0))))))),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,K0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))
=> ! [U_0] :
( ! [F0,G0,K0] : s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,N))),i(s(fun(fun(num,real),fun(fun(num,cart(real,N)),fun(num,cart(real,N)))),U_0),s(fun(num,real),F0))),s(fun(num,cart(real,N)),G0))),s(num,K0))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(num,real),F0),s(num,K0))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,K0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,K0)))))))
=> ! [F0,G0,M0,N0] : s(cart(real,N),i(s(fun(fun(num,cart(real,N)),cart(real,N)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,N)),cart(real,N))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,N)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,N))),i(s(fun(fun(num,real),fun(fun(num,cart(real,N)),fun(num,cart(real,N)))),U_0),s(fun(num,real),F0))),s(fun(num,cart(real,N)),G0))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),i(s(fun(bool,fun(cart(real,N),fun(cart(real,N),cart(real,N)))),cond),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(num,real),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(num,real),F0),s(num,M0))))),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,M0))))))))),s(cart(real,N),i(s(fun(fun(num,cart(real,N)),cart(real,N)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,N)),cart(real,N))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,N)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,N))),i(s(fun(fun(num,real),fun(fun(num,cart(real,N)),fun(num,cart(real,N)))),U_1),s(fun(num,real),F0))),s(fun(num,cart(real,N)),G0))))))))),s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) ) ) ).
fof(aVSUMu_PARTIALu_PRE,axiom,
! [N,U_1] :
( ! [F0,G0,K0] : s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,N))),i(s(fun(fun(num,real),fun(fun(num,cart(real,N)),fun(num,cart(real,N)))),U_1),s(fun(num,real),F0))),s(fun(num,cart(real,N)),G0))),s(num,K0))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,K0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(num,real),F0),s(num,K0))))))),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,K0)))))
=> ! [U_0] :
( ! [F0,G0,K0] : s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,N))),i(s(fun(fun(num,real),fun(fun(num,cart(real,N)),fun(num,cart(real,N)))),U_0),s(fun(num,real),F0))),s(fun(num,cart(real,N)),G0))),s(num,K0))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(num,real),F0),s(num,K0))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,K0))))),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,K0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))))
=> ! [F0,G0,M0,N0] : s(cart(real,N),i(s(fun(fun(num,cart(real,N)),cart(real,N)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,N)),cart(real,N))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,N)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,N))),i(s(fun(fun(num,real),fun(fun(num,cart(real,N)),fun(num,cart(real,N)))),U_0),s(fun(num,real),F0))),s(fun(num,cart(real,N)),G0))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),i(s(fun(bool,fun(cart(real,N),fun(cart(real,N),cart(real,N)))),cond),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(num,real),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,N0))))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(num,real),F0),s(num,M0))))),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,M0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))))),s(cart(real,N),i(s(fun(fun(num,cart(real,N)),cart(real,N)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,N)),cart(real,N))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,N)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,N))),i(s(fun(fun(num,real),fun(fun(num,cart(real,N)),fun(num,cart(real,N)))),U_1),s(fun(num,real),F0))),s(fun(num,cart(real,N)),G0))))))))),s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) ) ) ).
fof(aVSUMu_COMBINEu_L,axiom,
! [Q109147,F0,M0,N0,P0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,P0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) )
=> s(cart(real,Q109147),i(s(fun(cart(real,Q109147),cart(real,Q109147)),i(s(fun(cart(real,Q109147),fun(cart(real,Q109147),cart(real,Q109147))),vectoru_add),s(cart(real,Q109147),i(s(fun(fun(num,cart(real,Q109147)),cart(real,Q109147)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q109147)),cart(real,Q109147))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(fun(num,cart(real,Q109147)),F0))))),s(cart(real,Q109147),i(s(fun(fun(num,cart(real,Q109147)),cart(real,Q109147)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q109147)),cart(real,Q109147))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,N0))),s(num,P0))))),s(fun(num,cart(real,Q109147)),F0))))) = s(cart(real,Q109147),i(s(fun(fun(num,cart(real,Q109147)),cart(real,Q109147)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q109147)),cart(real,Q109147))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,P0))))),s(fun(num,cart(real,Q109147)),F0))) ) ).
fof(aVSUMu_COMBINEu_R,axiom,
! [Q109210,F0,M0,N0,P0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,P0)))) )
=> s(cart(real,Q109210),i(s(fun(cart(real,Q109210),cart(real,Q109210)),i(s(fun(cart(real,Q109210),fun(cart(real,Q109210),cart(real,Q109210))),vectoru_add),s(cart(real,Q109210),i(s(fun(fun(num,cart(real,Q109210)),cart(real,Q109210)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q109210)),cart(real,Q109210))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q109210)),F0))))),s(cart(real,Q109210),i(s(fun(fun(num,cart(real,Q109210)),cart(real,Q109210)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q109210)),cart(real,Q109210))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,P0))))),s(fun(num,cart(real,Q109210)),F0))))) = s(cart(real,Q109210),i(s(fun(fun(num,cart(real,Q109210)),cart(real,Q109210)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q109210)),cart(real,Q109210))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,P0))))),s(fun(num,cart(real,Q109210)),F0))) ) ).
fof(aVSUMu_INJECTION,axiom,
! [Q109287,Q109292,F0,P0,S0] :
( ( p(s(bool,i(s(fun(fun(Q109287,bool),bool),finite),s(fun(Q109287,bool),S0))))
& ! [X] :
( p(s(bool,i(s(fun(fun(Q109287,bool),bool),i(s(fun(Q109287,fun(fun(Q109287,bool),bool)),in),s(Q109287,X))),s(fun(Q109287,bool),S0))))
=> p(s(bool,i(s(fun(fun(Q109287,bool),bool),i(s(fun(Q109287,fun(fun(Q109287,bool),bool)),in),s(Q109287,i(s(fun(Q109287,Q109287),P0),s(Q109287,X))))),s(fun(Q109287,bool),S0)))) )
& ! [X,Y] :
( ( p(s(bool,i(s(fun(fun(Q109287,bool),bool),i(s(fun(Q109287,fun(fun(Q109287,bool),bool)),in),s(Q109287,X))),s(fun(Q109287,bool),S0))))
& p(s(bool,i(s(fun(fun(Q109287,bool),bool),i(s(fun(Q109287,fun(fun(Q109287,bool),bool)),in),s(Q109287,Y))),s(fun(Q109287,bool),S0))))
& s(Q109287,i(s(fun(Q109287,Q109287),P0),s(Q109287,X))) = s(Q109287,i(s(fun(Q109287,Q109287),P0),s(Q109287,Y))) )
=> s(Q109287,X) = s(Q109287,Y) ) )
=> s(cart(real,Q109292),i(s(fun(fun(Q109287,cart(real,Q109292)),cart(real,Q109292)),i(s(fun(fun(Q109287,bool),fun(fun(Q109287,cart(real,Q109292)),cart(real,Q109292))),vsum),s(fun(Q109287,bool),S0))),s(fun(Q109287,cart(real,Q109292)),i(s(fun(fun(Q109287,Q109287),fun(Q109287,cart(real,Q109292))),i(s(fun(fun(Q109287,cart(real,Q109292)),fun(fun(Q109287,Q109287),fun(Q109287,cart(real,Q109292)))),o),s(fun(Q109287,cart(real,Q109292)),F0))),s(fun(Q109287,Q109287),P0))))) = s(cart(real,Q109292),i(s(fun(fun(Q109287,cart(real,Q109292)),cart(real,Q109292)),i(s(fun(fun(Q109287,bool),fun(fun(Q109287,cart(real,Q109292)),cart(real,Q109292))),vsum),s(fun(Q109287,bool),S0))),s(fun(Q109287,cart(real,Q109292)),F0))) ) ).
fof(aVSUMu_SWAP,axiom,
! [Q109341,Q109340,Q109337,U_2] :
( ! [F0,J0,I0] : s(cart(real,Q109337),i(s(fun(Q109341,cart(real,Q109337)),i(s(fun(Q109340,fun(Q109341,cart(real,Q109337))),i(s(fun(fun(Q109341,fun(Q109340,cart(real,Q109337))),fun(Q109340,fun(Q109341,cart(real,Q109337)))),U_2),s(fun(Q109341,fun(Q109340,cart(real,Q109337))),F0))),s(Q109340,J0))),s(Q109341,I0))) = s(cart(real,Q109337),i(s(fun(Q109340,cart(real,Q109337)),i(s(fun(Q109341,fun(Q109340,cart(real,Q109337))),F0),s(Q109341,I0))),s(Q109340,J0)))
=> ! [U_1] :
( ! [S0,F0,J0] : s(cart(real,Q109337),i(s(fun(Q109340,cart(real,Q109337)),i(s(fun(fun(Q109341,fun(Q109340,cart(real,Q109337))),fun(Q109340,cart(real,Q109337))),i(s(fun(fun(Q109341,bool),fun(fun(Q109341,fun(Q109340,cart(real,Q109337))),fun(Q109340,cart(real,Q109337)))),U_1),s(fun(Q109341,bool),S0))),s(fun(Q109341,fun(Q109340,cart(real,Q109337))),F0))),s(Q109340,J0))) = s(cart(real,Q109337),i(s(fun(fun(Q109341,cart(real,Q109337)),cart(real,Q109337)),i(s(fun(fun(Q109341,bool),fun(fun(Q109341,cart(real,Q109337)),cart(real,Q109337))),vsum),s(fun(Q109341,bool),S0))),s(fun(Q109341,cart(real,Q109337)),i(s(fun(Q109340,fun(Q109341,cart(real,Q109337))),i(s(fun(fun(Q109341,fun(Q109340,cart(real,Q109337))),fun(Q109340,fun(Q109341,cart(real,Q109337)))),U_2),s(fun(Q109341,fun(Q109340,cart(real,Q109337))),F0))),s(Q109340,J0)))))
=> ! [U_0] :
( ! [T0,F0,I0] : s(cart(real,Q109337),i(s(fun(Q109341,cart(real,Q109337)),i(s(fun(fun(Q109341,fun(Q109340,cart(real,Q109337))),fun(Q109341,cart(real,Q109337))),i(s(fun(fun(Q109340,bool),fun(fun(Q109341,fun(Q109340,cart(real,Q109337))),fun(Q109341,cart(real,Q109337)))),U_0),s(fun(Q109340,bool),T0))),s(fun(Q109341,fun(Q109340,cart(real,Q109337))),F0))),s(Q109341,I0))) = s(cart(real,Q109337),i(s(fun(fun(Q109340,cart(real,Q109337)),cart(real,Q109337)),i(s(fun(fun(Q109340,bool),fun(fun(Q109340,cart(real,Q109337)),cart(real,Q109337))),vsum),s(fun(Q109340,bool),T0))),s(fun(Q109340,cart(real,Q109337)),i(s(fun(Q109341,fun(Q109340,cart(real,Q109337))),F0),s(Q109341,I0)))))
=> ! [F0,S0,T0] :
( ( p(s(bool,i(s(fun(fun(Q109341,bool),bool),finite),s(fun(Q109341,bool),S0))))
& p(s(bool,i(s(fun(fun(Q109340,bool),bool),finite),s(fun(Q109340,bool),T0)))) )
=> s(cart(real,Q109337),i(s(fun(fun(Q109341,cart(real,Q109337)),cart(real,Q109337)),i(s(fun(fun(Q109341,bool),fun(fun(Q109341,cart(real,Q109337)),cart(real,Q109337))),vsum),s(fun(Q109341,bool),S0))),s(fun(Q109341,cart(real,Q109337)),i(s(fun(fun(Q109341,fun(Q109340,cart(real,Q109337))),fun(Q109341,cart(real,Q109337))),i(s(fun(fun(Q109340,bool),fun(fun(Q109341,fun(Q109340,cart(real,Q109337))),fun(Q109341,cart(real,Q109337)))),U_0),s(fun(Q109340,bool),T0))),s(fun(Q109341,fun(Q109340,cart(real,Q109337))),F0))))) = s(cart(real,Q109337),i(s(fun(fun(Q109340,cart(real,Q109337)),cart(real,Q109337)),i(s(fun(fun(Q109340,bool),fun(fun(Q109340,cart(real,Q109337)),cart(real,Q109337))),vsum),s(fun(Q109340,bool),T0))),s(fun(Q109340,cart(real,Q109337)),i(s(fun(fun(Q109341,fun(Q109340,cart(real,Q109337))),fun(Q109340,cart(real,Q109337))),i(s(fun(fun(Q109341,bool),fun(fun(Q109341,fun(Q109340,cart(real,Q109337))),fun(Q109340,cart(real,Q109337)))),U_1),s(fun(Q109341,bool),S0))),s(fun(Q109341,fun(Q109340,cart(real,Q109337))),F0))))) ) ) ) ) ).
fof(aVSUMu_SWAPu_NUMSEG,axiom,
! [Q109392,U_2] :
( ! [F0,J0,I0] : s(cart(real,Q109392),i(s(fun(num,cart(real,Q109392)),i(s(fun(num,fun(num,cart(real,Q109392))),i(s(fun(fun(num,fun(num,cart(real,Q109392))),fun(num,fun(num,cart(real,Q109392)))),U_2),s(fun(num,fun(num,cart(real,Q109392))),F0))),s(num,J0))),s(num,I0))) = s(cart(real,Q109392),i(s(fun(num,cart(real,Q109392)),i(s(fun(num,fun(num,cart(real,Q109392))),F0),s(num,I0))),s(num,J0)))
=> ! [U_1] :
( ! [F0,J0] : s(fun(num,cart(real,Q109392)),i(s(fun(num,fun(num,cart(real,Q109392))),i(s(fun(fun(num,fun(num,cart(real,Q109392))),fun(num,fun(num,cart(real,Q109392)))),U_1),s(fun(num,fun(num,cart(real,Q109392))),F0))),s(num,J0))) = s(fun(num,cart(real,Q109392)),i(s(fun(num,fun(num,cart(real,Q109392))),i(s(fun(fun(num,fun(num,cart(real,Q109392))),fun(num,fun(num,cart(real,Q109392)))),U_2),s(fun(num,fun(num,cart(real,Q109392))),F0))),s(num,J0)))
=> ! [U_0] :
( ! [C0,D0,F0,I0] : s(cart(real,Q109392),i(s(fun(num,cart(real,Q109392)),i(s(fun(fun(num,fun(num,cart(real,Q109392))),fun(num,cart(real,Q109392))),i(s(fun(num,fun(fun(num,fun(num,cart(real,Q109392))),fun(num,cart(real,Q109392)))),i(s(fun(num,fun(num,fun(fun(num,fun(num,cart(real,Q109392))),fun(num,cart(real,Q109392))))),U_0),s(num,C0))),s(num,D0))),s(fun(num,fun(num,cart(real,Q109392))),F0))),s(num,I0))) = s(cart(real,Q109392),i(s(fun(fun(num,cart(real,Q109392)),cart(real,Q109392)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q109392)),cart(real,Q109392))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,C0))),s(num,D0))))),s(fun(num,cart(real,Q109392)),i(s(fun(num,fun(num,cart(real,Q109392))),F0),s(num,I0)))))
=> ! [A5,B0,C0,D0,F0] : s(cart(real,Q109392),i(s(fun(fun(num,cart(real,Q109392)),cart(real,Q109392)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q109392)),cart(real,Q109392))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,A5))),s(num,B0))))),s(fun(num,cart(real,Q109392)),i(s(fun(fun(num,fun(num,cart(real,Q109392))),fun(num,cart(real,Q109392))),i(s(fun(num,fun(fun(num,fun(num,cart(real,Q109392))),fun(num,cart(real,Q109392)))),i(s(fun(num,fun(num,fun(fun(num,fun(num,cart(real,Q109392))),fun(num,cart(real,Q109392))))),U_0),s(num,C0))),s(num,D0))),s(fun(num,fun(num,cart(real,Q109392))),F0))))) = s(cart(real,Q109392),i(s(fun(fun(num,cart(real,Q109392)),cart(real,Q109392)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q109392)),cart(real,Q109392))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,C0))),s(num,D0))))),s(fun(num,cart(real,Q109392)),i(s(fun(fun(num,fun(num,cart(real,Q109392))),fun(num,cart(real,Q109392))),i(s(fun(num,fun(fun(num,fun(num,cart(real,Q109392))),fun(num,cart(real,Q109392)))),i(s(fun(num,fun(num,fun(fun(num,fun(num,cart(real,Q109392))),fun(num,cart(real,Q109392))))),U_0),s(num,A5))),s(num,B0))),s(fun(num,fun(num,cart(real,Q109392))),i(s(fun(fun(num,fun(num,cart(real,Q109392))),fun(num,fun(num,cart(real,Q109392)))),U_1),s(fun(num,fun(num,cart(real,Q109392))),F0))))))) ) ) ) ).
fof(aVSUMu_ADDu_GEN,axiom,
! [Q109481,Q109494,U_1] :
( ! [F0,G0,X] : s(cart(real,Q109494),i(s(fun(Q109481,cart(real,Q109494)),i(s(fun(fun(Q109481,cart(real,Q109494)),fun(Q109481,cart(real,Q109494))),i(s(fun(fun(Q109481,cart(real,Q109494)),fun(fun(Q109481,cart(real,Q109494)),fun(Q109481,cart(real,Q109494)))),U_1),s(fun(Q109481,cart(real,Q109494)),F0))),s(fun(Q109481,cart(real,Q109494)),G0))),s(Q109481,X))) = s(cart(real,Q109494),i(s(fun(cart(real,Q109494),cart(real,Q109494)),i(s(fun(cart(real,Q109494),fun(cart(real,Q109494),cart(real,Q109494))),vectoru_add),s(cart(real,Q109494),i(s(fun(Q109481,cart(real,Q109494)),F0),s(Q109481,X))))),s(cart(real,Q109494),i(s(fun(Q109481,cart(real,Q109494)),G0),s(Q109481,X)))))
=> ! [U_0] :
( ! [S0,F0,GENR_PVARR_286] :
( p(s(bool,i(s(fun(Q109481,bool),i(s(fun(fun(Q109481,cart(real,Q109494)),fun(Q109481,bool)),i(s(fun(fun(Q109481,bool),fun(fun(Q109481,cart(real,Q109494)),fun(Q109481,bool))),U_0),s(fun(Q109481,bool),S0))),s(fun(Q109481,cart(real,Q109494)),F0))),s(Q109481,GENR_PVARR_286))))
<=> ? [X,V] :
( ( p(s(bool,V))
<=> ( p(s(bool,i(s(fun(fun(Q109481,bool),bool),i(s(fun(Q109481,fun(fun(Q109481,bool),bool)),in),s(Q109481,X))),s(fun(Q109481,bool),S0))))
& s(cart(real,Q109494),i(s(fun(Q109481,cart(real,Q109494)),F0),s(Q109481,X))) != s(cart(real,Q109494),i(s(fun(num,cart(real,Q109494)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) )
& p(s(bool,i(s(fun(Q109481,bool),i(s(fun(bool,fun(Q109481,bool)),i(s(fun(Q109481,fun(bool,fun(Q109481,bool))),setspec),s(Q109481,GENR_PVARR_286))),s(bool,V))),s(Q109481,X)))) ) )
=> ! [F0,G0,S0] :
( ( p(s(bool,i(s(fun(fun(Q109481,bool),bool),finite),s(fun(Q109481,bool),i(s(fun(fun(Q109481,bool),fun(Q109481,bool)),gspec),s(fun(Q109481,bool),i(s(fun(fun(Q109481,cart(real,Q109494)),fun(Q109481,bool)),i(s(fun(fun(Q109481,bool),fun(fun(Q109481,cart(real,Q109494)),fun(Q109481,bool))),U_0),s(fun(Q109481,bool),S0))),s(fun(Q109481,cart(real,Q109494)),F0))))))))
& p(s(bool,i(s(fun(fun(Q109481,bool),bool),finite),s(fun(Q109481,bool),i(s(fun(fun(Q109481,bool),fun(Q109481,bool)),gspec),s(fun(Q109481,bool),i(s(fun(fun(Q109481,cart(real,Q109494)),fun(Q109481,bool)),i(s(fun(fun(Q109481,bool),fun(fun(Q109481,cart(real,Q109494)),fun(Q109481,bool))),U_0),s(fun(Q109481,bool),S0))),s(fun(Q109481,cart(real,Q109494)),G0)))))))) )
=> s(cart(real,Q109494),i(s(fun(fun(Q109481,cart(real,Q109494)),cart(real,Q109494)),i(s(fun(fun(Q109481,bool),fun(fun(Q109481,cart(real,Q109494)),cart(real,Q109494))),vsum),s(fun(Q109481,bool),S0))),s(fun(Q109481,cart(real,Q109494)),i(s(fun(fun(Q109481,cart(real,Q109494)),fun(Q109481,cart(real,Q109494))),i(s(fun(fun(Q109481,cart(real,Q109494)),fun(fun(Q109481,cart(real,Q109494)),fun(Q109481,cart(real,Q109494)))),U_1),s(fun(Q109481,cart(real,Q109494)),F0))),s(fun(Q109481,cart(real,Q109494)),G0))))) = s(cart(real,Q109494),i(s(fun(cart(real,Q109494),cart(real,Q109494)),i(s(fun(cart(real,Q109494),fun(cart(real,Q109494),cart(real,Q109494))),vectoru_add),s(cart(real,Q109494),i(s(fun(fun(Q109481,cart(real,Q109494)),cart(real,Q109494)),i(s(fun(fun(Q109481,bool),fun(fun(Q109481,cart(real,Q109494)),cart(real,Q109494))),vsum),s(fun(Q109481,bool),S0))),s(fun(Q109481,cart(real,Q109494)),F0))))),s(cart(real,Q109494),i(s(fun(fun(Q109481,cart(real,Q109494)),cart(real,Q109494)),i(s(fun(fun(Q109481,bool),fun(fun(Q109481,cart(real,Q109494)),cart(real,Q109494))),vsum),s(fun(Q109481,bool),S0))),s(fun(Q109481,cart(real,Q109494)),G0))))) ) ) ) ).
fof(aVSUMu_CASESu_1,axiom,
! [Q109577,Q109575,U_0] :
( ! [A5,X] :
? [V] :
( ( p(s(bool,V))
<=> s(Q109575,X) = s(Q109575,A5) )
& s(cart(real,Q109577),i(s(fun(Q109575,cart(real,Q109577)),i(s(fun(Q109575,fun(Q109575,cart(real,Q109577))),U_0),s(Q109575,A5))),s(Q109575,X))) = s(cart(real,Q109577),i(s(fun(cart(real,Q109577),cart(real,Q109577)),i(s(fun(cart(real,Q109577),fun(cart(real,Q109577),cart(real,Q109577))),i(s(fun(bool,fun(cart(real,Q109577),fun(cart(real,Q109577),cart(real,Q109577)))),cond),s(bool,V))),s(cart(real,Q109577),y))),s(cart(real,Q109577),i(s(fun(Q109575,cart(real,Q109577)),f),s(Q109575,X))))) )
=> ! [S0,A5] :
( ( p(s(bool,i(s(fun(fun(Q109575,bool),bool),finite),s(fun(Q109575,bool),S0))))
& p(s(bool,i(s(fun(fun(Q109575,bool),bool),i(s(fun(Q109575,fun(fun(Q109575,bool),bool)),in),s(Q109575,A5))),s(fun(Q109575,bool),S0)))) )
=> s(cart(real,Q109577),i(s(fun(fun(Q109575,cart(real,Q109577)),cart(real,Q109577)),i(s(fun(fun(Q109575,bool),fun(fun(Q109575,cart(real,Q109577)),cart(real,Q109577))),vsum),s(fun(Q109575,bool),S0))),s(fun(Q109575,cart(real,Q109577)),i(s(fun(Q109575,fun(Q109575,cart(real,Q109577))),U_0),s(Q109575,A5))))) = s(cart(real,Q109577),i(s(fun(cart(real,Q109577),cart(real,Q109577)),i(s(fun(cart(real,Q109577),fun(cart(real,Q109577),cart(real,Q109577))),vectoru_add),s(cart(real,Q109577),i(s(fun(fun(Q109575,cart(real,Q109577)),cart(real,Q109577)),i(s(fun(fun(Q109575,bool),fun(fun(Q109575,cart(real,Q109577)),cart(real,Q109577))),vsum),s(fun(Q109575,bool),S0))),s(fun(Q109575,cart(real,Q109577)),f))))),s(cart(real,Q109577),i(s(fun(cart(real,Q109577),cart(real,Q109577)),i(s(fun(cart(real,Q109577),fun(cart(real,Q109577),cart(real,Q109577))),vectoru_sub),s(cart(real,Q109577),y))),s(cart(real,Q109577),i(s(fun(Q109575,cart(real,Q109577)),f),s(Q109575,A5))))))) ) ) ).
fof(aVSUMu_SINGu_NUMSEG,axiom,
! [Q109587] : s(cart(real,Q109587),i(s(fun(fun(num,cart(real,Q109587)),cart(real,Q109587)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q109587)),cart(real,Q109587))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,n))),s(num,n))))),s(fun(num,cart(real,Q109587)),f))) = s(cart(real,Q109587),i(s(fun(num,cart(real,Q109587)),f),s(num,n))) ).
fof(aVSUMu_1,axiom,
! [Q109598] : s(cart(real,Q109598),i(s(fun(fun(num,cart(real,Q109598)),cart(real,Q109598)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q109598)),cart(real,Q109598))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(fun(num,cart(real,Q109598)),f))) = s(cart(real,Q109598),i(s(fun(num,cart(real,Q109598)),f),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) ).
fof(aVSUMu_2,axiom,
! [Q109622,T0] : s(cart(real,Q109622),i(s(fun(fun(num,cart(real,Q109622)),cart(real,Q109622)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q109622)),cart(real,Q109622))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(fun(num,cart(real,Q109622)),T0))) = s(cart(real,Q109622),i(s(fun(cart(real,Q109622),cart(real,Q109622)),i(s(fun(cart(real,Q109622),fun(cart(real,Q109622),cart(real,Q109622))),vectoru_add),s(cart(real,Q109622),i(s(fun(num,cart(real,Q109622)),T0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(cart(real,Q109622),i(s(fun(num,cart(real,Q109622)),T0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) ).
fof(aVSUMu_3,axiom,
! [Q109650,T0] : s(cart(real,Q109650),i(s(fun(fun(num,cart(real,Q109650)),cart(real,Q109650)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q109650)),cart(real,Q109650))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(fun(num,cart(real,Q109650)),T0))) = s(cart(real,Q109650),i(s(fun(cart(real,Q109650),cart(real,Q109650)),i(s(fun(cart(real,Q109650),fun(cart(real,Q109650),cart(real,Q109650))),vectoru_add),s(cart(real,Q109650),i(s(fun(num,cart(real,Q109650)),T0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(cart(real,Q109650),i(s(fun(cart(real,Q109650),cart(real,Q109650)),i(s(fun(cart(real,Q109650),fun(cart(real,Q109650),cart(real,Q109650))),vectoru_add),s(cart(real,Q109650),i(s(fun(num,cart(real,Q109650)),T0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(cart(real,Q109650),i(s(fun(num,cart(real,Q109650)),T0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))) ).
fof(aVSUMu_PAIR,axiom,
! [N,U_0] :
( ! [F0,I0] : s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,N))),U_0),s(fun(num,cart(real,N)),F0))),s(num,I0))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(num,cart(real,N)),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,I0))))))),s(cart(real,N),i(s(fun(num,cart(real,N)),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,I0))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))
=> ! [F0,M0,N0] : s(cart(real,N),i(s(fun(fun(num,cart(real,N)),cart(real,N)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,N)),cart(real,N))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,M0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,N0))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(fun(num,cart(real,N)),F0))) = s(cart(real,N),i(s(fun(fun(num,cart(real,N)),cart(real,N)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,N)),cart(real,N))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,N)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,N))),U_0),s(fun(num,cart(real,N)),F0))))) ) ).
fof(aVSUMu_PAIRu_0,axiom,
! [N,U_0] :
( ! [F0,I0] : s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,N))),U_0),s(fun(num,cart(real,N)),F0))),s(num,I0))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(num,cart(real,N)),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,I0))))))),s(cart(real,N),i(s(fun(num,cart(real,N)),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,I0))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))
=> ! [F0,N0] : s(cart(real,N),i(s(fun(fun(num,cart(real,N)),cart(real,N)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,N)),cart(real,N))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,N0))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(fun(num,cart(real,N)),F0))) = s(cart(real,N),i(s(fun(fun(num,cart(real,N)),cart(real,N)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,N)),cart(real,N))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0))))),s(fun(num,cart(real,N)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,N))),U_0),s(fun(num,cart(real,N)),F0))))) ) ).
fof(abasis,axiom,
! [Q109978,U_0] :
( ! [K0,I0] :
? [V] :
( ( p(s(bool,V))
<=> s(num,I0) = s(num,K0) )
& s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),U_0),s(num,K0))),s(num,I0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,V))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) )
=> ! [K0] : s(cart(real,Q109978),i(s(fun(num,cart(real,Q109978)),basis),s(num,K0))) = s(cart(real,Q109978),i(s(fun(fun(num,real),cart(real,Q109978)),lambda),s(fun(num,real),i(s(fun(num,fun(num,real)),U_0),s(num,K0))))) ) ).
fof(aNORMu_BASIS,axiom,
! [N,K0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,K0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,K0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) )
=> s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,K0))))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) ) ).
fof(aNORMu_BASISu_1,axiom,
! [Q110060] : s(real,i(s(fun(cart(real,Q110060),real),vectoru_norm),s(cart(real,Q110060),i(s(fun(num,cart(real,Q110060)),basis),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) ).
fof(aVECTORu_CHOOSEu_SIZE,axiom,
! [N,C0] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,C0))))
=> ? [X] : s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))) = s(real,C0) ) ).
fof(aVECTORu_CHOOSEu_DIST,axiom,
! [N,X,E0] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,E0))))
=> ? [Y] : s(real,i(s(fun(prod(cart(real,N),cart(real,N)),real),distance),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),X))),s(cart(real,N),Y))))) = s(real,E0) ) ).
fof(aBASISu_INJ,axiom,
! [N,I0,J0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,J0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,J0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))
& s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,I0))) = s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,J0))) )
=> s(num,I0) = s(num,J0) ) ).
fof(aBASISu_NE,axiom,
! [N,I0,J0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,J0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,J0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))
& s(num,I0) != s(num,J0) )
=> s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,I0))) != s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,J0))) ) ).
fof(aBASISu_COMPONENT,axiom,
! [N,K0,I0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) )
=> ? [V] :
( ( p(s(bool,V))
<=> s(num,I0) = s(num,K0) )
& s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,K0))))),s(num,I0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,V))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) ) ) ).
fof(aBASISu_EXPANSION,axiom,
! [N,U_0] :
( ! [X,I0] : s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(real,N),fun(num,cart(real,N))),U_0),s(cart(real,N),X))),s(num,I0))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))))),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,I0)))))
=> ! [X] : s(cart(real,N),i(s(fun(fun(num,cart(real,N)),cart(real,N)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,N)),cart(real,N))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))),s(fun(num,cart(real,N)),i(s(fun(cart(real,N),fun(num,cart(real,N))),U_0),s(cart(real,N),X))))) = s(cart(real,N),X) ) ).
fof(aBASISu_EXPANSIONu_UNIQUE,axiom,
! [N,U_0] :
( ! [F0,I0] : s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(fun(num,real),fun(num,cart(real,N))),U_0),s(fun(num,real),F0))),s(num,I0))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(num,real),F0),s(num,I0))))),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,I0)))))
=> ! [F0,X] :
( s(cart(real,N),i(s(fun(fun(num,cart(real,N)),cart(real,N)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,N)),cart(real,N))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))),s(fun(num,cart(real,N)),i(s(fun(fun(num,real),fun(num,cart(real,N))),U_0),s(fun(num,real),F0))))) = s(cart(real,N),X)
<=> ! [I0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) )
=> s(real,i(s(fun(num,real),F0),s(num,I0))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))) ) ) ) ).
fof(aDOTu_BASIS,axiom,
! [N,X,I0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) )
=> ( s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,I0))))),s(cart(real,N),X))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0)))
& s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),X))),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,I0))))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))) ) ) ).
fof(aDOTu_BASISu_BASIS,axiom,
! [N,I0,J0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,J0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,J0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) )
=> ? [V] :
( ( p(s(bool,V))
<=> s(num,I0) = s(num,J0) )
& s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,I0))))),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,J0))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,V))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) ) ) ).
fof(aDOTu_BASISu_BASISu_UNEQUAL,axiom,
! [Q110508,I0,J0] :
( s(num,I0) != s(num,J0)
=> s(real,i(s(fun(cart(real,Q110508),real),i(s(fun(cart(real,Q110508),fun(cart(real,Q110508),real)),dot),s(cart(real,Q110508),i(s(fun(num,cart(real,Q110508)),basis),s(num,I0))))),s(cart(real,Q110508),i(s(fun(num,cart(real,Q110508)),basis),s(num,J0))))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ).
fof(aBASISu_EQu_0,axiom,
! [N,I0] :
( s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,I0))) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
<=> ~ p(s(bool,i(s(fun(fun(num,bool),bool),i(s(fun(num,fun(fun(num,bool),bool)),in),s(num,I0))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))))) ) ).
fof(aBASISu_NONZERO,axiom,
! [N,K0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,K0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,K0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) )
=> s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,K0))) != s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ).
fof(aVECTORu_EQu_LDOT,axiom,
! [Q110589,Y,Z0] :
( ! [X] : s(real,i(s(fun(cart(real,Q110589),real),i(s(fun(cart(real,Q110589),fun(cart(real,Q110589),real)),dot),s(cart(real,Q110589),X))),s(cart(real,Q110589),Y))) = s(real,i(s(fun(cart(real,Q110589),real),i(s(fun(cart(real,Q110589),fun(cart(real,Q110589),real)),dot),s(cart(real,Q110589),X))),s(cart(real,Q110589),Z0)))
<=> s(cart(real,Q110589),Y) = s(cart(real,Q110589),Z0) ) ).
fof(aVECTORu_EQu_RDOT,axiom,
! [Q110616,X,Y] :
( ! [Z0] : s(real,i(s(fun(cart(real,Q110616),real),i(s(fun(cart(real,Q110616),fun(cart(real,Q110616),real)),dot),s(cart(real,Q110616),X))),s(cart(real,Q110616),Z0))) = s(real,i(s(fun(cart(real,Q110616),real),i(s(fun(cart(real,Q110616),fun(cart(real,Q110616),real)),dot),s(cart(real,Q110616),Y))),s(cart(real,Q110616),Z0)))
<=> s(cart(real,Q110616),X) = s(cart(real,Q110616),Y) ) ).
fof(aorthogonal,axiom,
! [Q110633,X,Y] :
( p(s(bool,i(s(fun(cart(real,Q110633),bool),i(s(fun(cart(real,Q110633),fun(cart(real,Q110633),bool)),orthogonal),s(cart(real,Q110633),X))),s(cart(real,Q110633),Y))))
<=> s(real,i(s(fun(cart(real,Q110633),real),i(s(fun(cart(real,Q110633),fun(cart(real,Q110633),real)),dot),s(cart(real,Q110633),X))),s(cart(real,Q110633),Y))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ).
fof(aORTHOGONALu_0,axiom,
! [Q110652,X] :
( p(s(bool,i(s(fun(cart(real,Q110652),bool),i(s(fun(cart(real,Q110652),fun(cart(real,Q110652),bool)),orthogonal),s(cart(real,Q110652),i(s(fun(num,cart(real,Q110652)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(real,Q110652),X))))
& p(s(bool,i(s(fun(cart(real,Q110652),bool),i(s(fun(cart(real,Q110652),fun(cart(real,Q110652),bool)),orthogonal),s(cart(real,Q110652),X))),s(cart(real,Q110652),i(s(fun(num,cart(real,Q110652)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) ) ).
fof(aORTHOGONALu_REFL,axiom,
! [Q110667,X] :
( p(s(bool,i(s(fun(cart(real,Q110667),bool),i(s(fun(cart(real,Q110667),fun(cart(real,Q110667),bool)),orthogonal),s(cart(real,Q110667),X))),s(cart(real,Q110667),X))))
<=> s(cart(real,Q110667),X) = s(cart(real,Q110667),i(s(fun(num,cart(real,Q110667)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ).
fof(aORTHOGONALu_SYM,axiom,
! [Q110681,X,Y] : s(bool,i(s(fun(cart(real,Q110681),bool),i(s(fun(cart(real,Q110681),fun(cart(real,Q110681),bool)),orthogonal),s(cart(real,Q110681),X))),s(cart(real,Q110681),Y))) = s(bool,i(s(fun(cart(real,Q110681),bool),i(s(fun(cart(real,Q110681),fun(cart(real,Q110681),bool)),orthogonal),s(cart(real,Q110681),Y))),s(cart(real,Q110681),X))) ).
fof(aORTHOGONALu_LNEG,axiom,
! [Q110704,X,Y] : s(bool,i(s(fun(cart(real,Q110704),bool),i(s(fun(cart(real,Q110704),fun(cart(real,Q110704),bool)),orthogonal),s(cart(real,Q110704),i(s(fun(cart(real,Q110704),cart(real,Q110704)),vectoru_neg),s(cart(real,Q110704),X))))),s(cart(real,Q110704),Y))) = s(bool,i(s(fun(cart(real,Q110704),bool),i(s(fun(cart(real,Q110704),fun(cart(real,Q110704),bool)),orthogonal),s(cart(real,Q110704),X))),s(cart(real,Q110704),Y))) ).
fof(aORTHOGONALu_RNEG,axiom,
! [Q110725,X,Y] : s(bool,i(s(fun(cart(real,Q110725),bool),i(s(fun(cart(real,Q110725),fun(cart(real,Q110725),bool)),orthogonal),s(cart(real,Q110725),X))),s(cart(real,Q110725),i(s(fun(cart(real,Q110725),cart(real,Q110725)),vectoru_neg),s(cart(real,Q110725),Y))))) = s(bool,i(s(fun(cart(real,Q110725),bool),i(s(fun(cart(real,Q110725),fun(cart(real,Q110725),bool)),orthogonal),s(cart(real,Q110725),X))),s(cart(real,Q110725),Y))) ).
fof(aORTHOGONALu_BASIS,axiom,
! [N,X,I0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) )
=> ( p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,I0))))),s(cart(real,N),X))))
<=> s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ) ).
fof(aORTHOGONALu_BASISu_BASIS,axiom,
! [N,I0,J0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,J0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,J0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) )
=> ( p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,I0))))),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,J0))))))
<=> s(num,I0) != s(num,J0) ) ) ).
fof(aORTHOGONALu_CLAUSESu_conjunct0,axiom,
! [Q110833,A5] : p(s(bool,i(s(fun(cart(real,Q110833),bool),i(s(fun(cart(real,Q110833),fun(cart(real,Q110833),bool)),orthogonal),s(cart(real,Q110833),A5))),s(cart(real,Q110833),i(s(fun(num,cart(real,Q110833)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) ).
fof(aORTHOGONALu_CLAUSESu_conjunct1,axiom,
! [Q110858,A5,X,C0] :
( p(s(bool,i(s(fun(cart(real,Q110858),bool),i(s(fun(cart(real,Q110858),fun(cart(real,Q110858),bool)),orthogonal),s(cart(real,Q110858),A5))),s(cart(real,Q110858),X))))
=> p(s(bool,i(s(fun(cart(real,Q110858),bool),i(s(fun(cart(real,Q110858),fun(cart(real,Q110858),bool)),orthogonal),s(cart(real,Q110858),A5))),s(cart(real,Q110858),i(s(fun(cart(real,Q110858),cart(real,Q110858)),i(s(fun(real,fun(cart(real,Q110858),cart(real,Q110858))),r_),s(real,C0))),s(cart(real,Q110858),X)))))) ) ).
fof(aORTHOGONALu_CLAUSESu_conjunct2,axiom,
! [Q111053,A5,X] :
( p(s(bool,i(s(fun(cart(real,Q111053),bool),i(s(fun(cart(real,Q111053),fun(cart(real,Q111053),bool)),orthogonal),s(cart(real,Q111053),A5))),s(cart(real,Q111053),X))))
=> p(s(bool,i(s(fun(cart(real,Q111053),bool),i(s(fun(cart(real,Q111053),fun(cart(real,Q111053),bool)),orthogonal),s(cart(real,Q111053),A5))),s(cart(real,Q111053),i(s(fun(cart(real,Q111053),cart(real,Q111053)),vectoru_neg),s(cart(real,Q111053),X)))))) ) ).
fof(aORTHOGONALu_CLAUSESu_conjunct3,axiom,
! [Q111054,A5,X,Y] :
( ( p(s(bool,i(s(fun(cart(real,Q111054),bool),i(s(fun(cart(real,Q111054),fun(cart(real,Q111054),bool)),orthogonal),s(cart(real,Q111054),A5))),s(cart(real,Q111054),X))))
& p(s(bool,i(s(fun(cart(real,Q111054),bool),i(s(fun(cart(real,Q111054),fun(cart(real,Q111054),bool)),orthogonal),s(cart(real,Q111054),A5))),s(cart(real,Q111054),Y)))) )
=> p(s(bool,i(s(fun(cart(real,Q111054),bool),i(s(fun(cart(real,Q111054),fun(cart(real,Q111054),bool)),orthogonal),s(cart(real,Q111054),A5))),s(cart(real,Q111054),i(s(fun(cart(real,Q111054),cart(real,Q111054)),i(s(fun(cart(real,Q111054),fun(cart(real,Q111054),cart(real,Q111054))),vectoru_add),s(cart(real,Q111054),X))),s(cart(real,Q111054),Y)))))) ) ).
fof(aORTHOGONALu_CLAUSESu_conjunct4,axiom,
! [Q111055,A5,X,Y] :
( ( p(s(bool,i(s(fun(cart(real,Q111055),bool),i(s(fun(cart(real,Q111055),fun(cart(real,Q111055),bool)),orthogonal),s(cart(real,Q111055),A5))),s(cart(real,Q111055),X))))
& p(s(bool,i(s(fun(cart(real,Q111055),bool),i(s(fun(cart(real,Q111055),fun(cart(real,Q111055),bool)),orthogonal),s(cart(real,Q111055),A5))),s(cart(real,Q111055),Y)))) )
=> p(s(bool,i(s(fun(cart(real,Q111055),bool),i(s(fun(cart(real,Q111055),fun(cart(real,Q111055),bool)),orthogonal),s(cart(real,Q111055),A5))),s(cart(real,Q111055),i(s(fun(cart(real,Q111055),cart(real,Q111055)),i(s(fun(cart(real,Q111055),fun(cart(real,Q111055),cart(real,Q111055))),vectoru_sub),s(cart(real,Q111055),X))),s(cart(real,Q111055),Y)))))) ) ).
fof(aORTHOGONALu_CLAUSESu_conjunct5,axiom,
! [Q110949,A5] : p(s(bool,i(s(fun(cart(real,Q110949),bool),i(s(fun(cart(real,Q110949),fun(cart(real,Q110949),bool)),orthogonal),s(cart(real,Q110949),i(s(fun(num,cart(real,Q110949)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(real,Q110949),A5)))) ).
fof(aORTHOGONALu_CLAUSESu_conjunct6,axiom,
! [Q110968,A5,X,C0] :
( p(s(bool,i(s(fun(cart(real,Q110968),bool),i(s(fun(cart(real,Q110968),fun(cart(real,Q110968),bool)),orthogonal),s(cart(real,Q110968),X))),s(cart(real,Q110968),A5))))
=> p(s(bool,i(s(fun(cart(real,Q110968),bool),i(s(fun(cart(real,Q110968),fun(cart(real,Q110968),bool)),orthogonal),s(cart(real,Q110968),i(s(fun(cart(real,Q110968),cart(real,Q110968)),i(s(fun(real,fun(cart(real,Q110968),cart(real,Q110968))),r_),s(real,C0))),s(cart(real,Q110968),X))))),s(cart(real,Q110968),A5)))) ) ).
fof(aORTHOGONALu_CLAUSESu_conjunct7,axiom,
! [Q111056,A5,X] :
( p(s(bool,i(s(fun(cart(real,Q111056),bool),i(s(fun(cart(real,Q111056),fun(cart(real,Q111056),bool)),orthogonal),s(cart(real,Q111056),X))),s(cart(real,Q111056),A5))))
=> p(s(bool,i(s(fun(cart(real,Q111056),bool),i(s(fun(cart(real,Q111056),fun(cart(real,Q111056),bool)),orthogonal),s(cart(real,Q111056),i(s(fun(cart(real,Q111056),cart(real,Q111056)),vectoru_neg),s(cart(real,Q111056),X))))),s(cart(real,Q111056),A5)))) ) ).
fof(aORTHOGONALu_CLAUSESu_conjunct8,axiom,
! [Q111057,A5,X,Y] :
( ( p(s(bool,i(s(fun(cart(real,Q111057),bool),i(s(fun(cart(real,Q111057),fun(cart(real,Q111057),bool)),orthogonal),s(cart(real,Q111057),X))),s(cart(real,Q111057),A5))))
& p(s(bool,i(s(fun(cart(real,Q111057),bool),i(s(fun(cart(real,Q111057),fun(cart(real,Q111057),bool)),orthogonal),s(cart(real,Q111057),Y))),s(cart(real,Q111057),A5)))) )
=> p(s(bool,i(s(fun(cart(real,Q111057),bool),i(s(fun(cart(real,Q111057),fun(cart(real,Q111057),bool)),orthogonal),s(cart(real,Q111057),i(s(fun(cart(real,Q111057),cart(real,Q111057)),i(s(fun(cart(real,Q111057),fun(cart(real,Q111057),cart(real,Q111057))),vectoru_add),s(cart(real,Q111057),X))),s(cart(real,Q111057),Y))))),s(cart(real,Q111057),A5)))) ) ).
fof(aORTHOGONALu_CLAUSESu_conjunct9,axiom,
! [Q111058,A5,X,Y] :
( ( p(s(bool,i(s(fun(cart(real,Q111058),bool),i(s(fun(cart(real,Q111058),fun(cart(real,Q111058),bool)),orthogonal),s(cart(real,Q111058),X))),s(cart(real,Q111058),A5))))
& p(s(bool,i(s(fun(cart(real,Q111058),bool),i(s(fun(cart(real,Q111058),fun(cart(real,Q111058),bool)),orthogonal),s(cart(real,Q111058),Y))),s(cart(real,Q111058),A5)))) )
=> p(s(bool,i(s(fun(cart(real,Q111058),bool),i(s(fun(cart(real,Q111058),fun(cart(real,Q111058),bool)),orthogonal),s(cart(real,Q111058),i(s(fun(cart(real,Q111058),cart(real,Q111058)),i(s(fun(cart(real,Q111058),fun(cart(real,Q111058),cart(real,Q111058))),vectoru_sub),s(cart(real,Q111058),X))),s(cart(real,Q111058),Y))))),s(cart(real,Q111058),A5)))) ) ).
fof(aORTHOGONALu_RVSUM,axiom,
! [A,N,F0,S0,X] :
( ( p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0))))
& ! [Y] :
( p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),S0))))
=> p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal),s(cart(real,N),X))),s(cart(real,N),i(s(fun(A,cart(real,N)),F0),s(A,Y)))))) ) )
=> p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal),s(cart(real,N),X))),s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,N)),F0)))))) ) ).
fof(aORTHOGONALu_LVSUM,axiom,
! [A,N,F0,S0,Y] :
( ( p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0))))
& ! [X] :
( p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))
=> p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal),s(cart(real,N),i(s(fun(A,cart(real,N)),F0),s(A,X))))),s(cart(real,N),Y)))) ) )
=> p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal),s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,N)),F0))))),s(cart(real,N),Y)))) ) ).
fof(aVECTORu_1,axiom,
! [A] : s(A,i(s(fun(num,A),i(s(fun(cart(A,n10),fun(num,A)),d_),s(cart(A,n10),i(s(fun(list(A),cart(A,n10)),vector),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,x))),s(list(A),nil))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(A,x) ).
fof(aVECTORu_2u_conjunct0,axiom,
! [A] : s(A,i(s(fun(num,A),i(s(fun(cart(A,n20),fun(num,A)),d_),s(cart(A,n20),i(s(fun(list(A),cart(A,n20)),vector),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,x))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,y))),s(list(A),nil))))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(A,x) ).
fof(aVECTORu_2u_conjunct1,axiom,
! [A] : s(A,i(s(fun(num,A),i(s(fun(cart(A,n20),fun(num,A)),d_),s(cart(A,n20),i(s(fun(list(A),cart(A,n20)),vector),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,x))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,y))),s(list(A),nil))))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(A,y) ).
fof(aVECTORu_3u_conjunct0,axiom,
! [A] : s(A,i(s(fun(num,A),i(s(fun(cart(A,n3),fun(num,A)),d_),s(cart(A,n3),i(s(fun(list(A),cart(A,n3)),vector),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,x))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,y))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,z))),s(list(A),nil))))))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(A,x) ).
fof(aVECTORu_3u_conjunct1,axiom,
! [A] : s(A,i(s(fun(num,A),i(s(fun(cart(A,n3),fun(num,A)),d_),s(cart(A,n3),i(s(fun(list(A),cart(A,n3)),vector),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,x))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,y))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,z))),s(list(A),nil))))))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(A,y) ).
fof(aVECTORu_3u_conjunct2,axiom,
! [A] : s(A,i(s(fun(num,A),i(s(fun(cart(A,n3),fun(num,A)),d_),s(cart(A,n3),i(s(fun(list(A),cart(A,n3)),vector),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,x))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,y))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,z))),s(list(A),nil))))))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(A,z) ).
fof(aFORALLu_VECTORu_1,axiom,
! [A] :
( ! [V] : p(s(bool,i(s(fun(cart(A,n10),bool),p0),s(cart(A,n10),V))))
<=> ! [X] : p(s(bool,i(s(fun(cart(A,n10),bool),p0),s(cart(A,n10),i(s(fun(list(A),cart(A,n10)),vector),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,X))),s(list(A),nil)))))))) ) ).
fof(aFORALLu_VECTORu_2,axiom,
! [A] :
( ! [V] : p(s(bool,i(s(fun(cart(A,n20),bool),p0),s(cart(A,n20),V))))
<=> ! [X,Y] : p(s(bool,i(s(fun(cart(A,n20),bool),p0),s(cart(A,n20),i(s(fun(list(A),cart(A,n20)),vector),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,X))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,Y))),s(list(A),nil)))))))))) ) ).
fof(aFORALLu_VECTORu_3,axiom,
! [A] :
( ! [V] : p(s(bool,i(s(fun(cart(A,n3),bool),p0),s(cart(A,n3),V))))
<=> ! [X,Y,Z0] : p(s(bool,i(s(fun(cart(A,n3),bool),p0),s(cart(A,n3),i(s(fun(list(A),cart(A,n3)),vector),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,X))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,Y))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,Z0))),s(list(A),nil)))))))))))) ) ).
fof(aEXISTSu_VECTORu_1,axiom,
! [A] :
( ? [V] : p(s(bool,i(s(fun(cart(A,n10),bool),p0),s(cart(A,n10),V))))
<=> ? [X] : p(s(bool,i(s(fun(cart(A,n10),bool),p0),s(cart(A,n10),i(s(fun(list(A),cart(A,n10)),vector),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,X))),s(list(A),nil)))))))) ) ).
fof(aEXISTSu_VECTORu_2,axiom,
! [A] :
( ? [V] : p(s(bool,i(s(fun(cart(A,n20),bool),p0),s(cart(A,n20),V))))
<=> ? [X,Y] : p(s(bool,i(s(fun(cart(A,n20),bool),p0),s(cart(A,n20),i(s(fun(list(A),cart(A,n20)),vector),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,X))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,Y))),s(list(A),nil)))))))))) ) ).
fof(aEXISTSu_VECTORu_3,axiom,
! [A] :
( ? [V] : p(s(bool,i(s(fun(cart(A,n3),bool),p0),s(cart(A,n3),V))))
<=> ? [X,Y,Z0] : p(s(bool,i(s(fun(cart(A,n3),bool),p0),s(cart(A,n3),i(s(fun(list(A),cart(A,n3)),vector),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,X))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,Y))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,Z0))),s(list(A),nil)))))))))))) ) ).
fof(alinear,axiom,
! [N,M,F0] :
( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
<=> ( ! [X,Y] : s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),i(s(fun(cart(real,M),fun(cart(real,M),cart(real,M))),vectoru_add),s(cart(real,M),X))),s(cart(real,M),Y))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),Y)))))
& ! [C0,X] : s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),i(s(fun(real,fun(cart(real,M),cart(real,M))),r_),s(real,C0))),s(cart(real,M),X))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,C0))),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))) ) ) ).
fof(aLINEARu_COMPOSEu_CMUL,axiom,
! [Q111564,Q111562,U_0] :
( ! [C0,F0,X] : s(cart(real,Q111562),i(s(fun(cart(real,Q111564),cart(real,Q111562)),i(s(fun(fun(cart(real,Q111564),cart(real,Q111562)),fun(cart(real,Q111564),cart(real,Q111562))),i(s(fun(real,fun(fun(cart(real,Q111564),cart(real,Q111562)),fun(cart(real,Q111564),cart(real,Q111562)))),U_0),s(real,C0))),s(fun(cart(real,Q111564),cart(real,Q111562)),F0))),s(cart(real,Q111564),X))) = s(cart(real,Q111562),i(s(fun(cart(real,Q111562),cart(real,Q111562)),i(s(fun(real,fun(cart(real,Q111562),cart(real,Q111562))),r_),s(real,C0))),s(cart(real,Q111562),i(s(fun(cart(real,Q111564),cart(real,Q111562)),F0),s(cart(real,Q111564),X)))))
=> ! [F0,C0] :
( p(s(bool,i(s(fun(fun(cart(real,Q111564),cart(real,Q111562)),bool),linear),s(fun(cart(real,Q111564),cart(real,Q111562)),F0))))
=> p(s(bool,i(s(fun(fun(cart(real,Q111564),cart(real,Q111562)),bool),linear),s(fun(cart(real,Q111564),cart(real,Q111562)),i(s(fun(fun(cart(real,Q111564),cart(real,Q111562)),fun(cart(real,Q111564),cart(real,Q111562))),i(s(fun(real,fun(fun(cart(real,Q111564),cart(real,Q111562)),fun(cart(real,Q111564),cart(real,Q111562)))),U_0),s(real,C0))),s(fun(cart(real,Q111564),cart(real,Q111562)),F0)))))) ) ) ).
fof(aLINEARu_COMPOSEu_NEG,axiom,
! [Q111583,Q111590,U_0] :
( ! [F0,X] : s(cart(real,Q111590),i(s(fun(cart(real,Q111583),cart(real,Q111590)),i(s(fun(fun(cart(real,Q111583),cart(real,Q111590)),fun(cart(real,Q111583),cart(real,Q111590))),U_0),s(fun(cart(real,Q111583),cart(real,Q111590)),F0))),s(cart(real,Q111583),X))) = s(cart(real,Q111590),i(s(fun(cart(real,Q111590),cart(real,Q111590)),vectoru_neg),s(cart(real,Q111590),i(s(fun(cart(real,Q111583),cart(real,Q111590)),F0),s(cart(real,Q111583),X)))))
=> ! [F0] :
( p(s(bool,i(s(fun(fun(cart(real,Q111583),cart(real,Q111590)),bool),linear),s(fun(cart(real,Q111583),cart(real,Q111590)),F0))))
=> p(s(bool,i(s(fun(fun(cart(real,Q111583),cart(real,Q111590)),bool),linear),s(fun(cart(real,Q111583),cart(real,Q111590)),i(s(fun(fun(cart(real,Q111583),cart(real,Q111590)),fun(cart(real,Q111583),cart(real,Q111590))),U_0),s(fun(cart(real,Q111583),cart(real,Q111590)),F0)))))) ) ) ).
fof(aLINEARu_COMPOSEu_ADD,axiom,
! [Q111612,Q111621,U_0] :
( ! [F0,G0,X] : s(cart(real,Q111621),i(s(fun(cart(real,Q111612),cart(real,Q111621)),i(s(fun(fun(cart(real,Q111612),cart(real,Q111621)),fun(cart(real,Q111612),cart(real,Q111621))),i(s(fun(fun(cart(real,Q111612),cart(real,Q111621)),fun(fun(cart(real,Q111612),cart(real,Q111621)),fun(cart(real,Q111612),cart(real,Q111621)))),U_0),s(fun(cart(real,Q111612),cart(real,Q111621)),F0))),s(fun(cart(real,Q111612),cart(real,Q111621)),G0))),s(cart(real,Q111612),X))) = s(cart(real,Q111621),i(s(fun(cart(real,Q111621),cart(real,Q111621)),i(s(fun(cart(real,Q111621),fun(cart(real,Q111621),cart(real,Q111621))),vectoru_add),s(cart(real,Q111621),i(s(fun(cart(real,Q111612),cart(real,Q111621)),F0),s(cart(real,Q111612),X))))),s(cart(real,Q111621),i(s(fun(cart(real,Q111612),cart(real,Q111621)),G0),s(cart(real,Q111612),X)))))
=> ! [F0,G0] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q111612),cart(real,Q111621)),bool),linear),s(fun(cart(real,Q111612),cart(real,Q111621)),F0))))
& p(s(bool,i(s(fun(fun(cart(real,Q111612),cart(real,Q111621)),bool),linear),s(fun(cart(real,Q111612),cart(real,Q111621)),G0)))) )
=> p(s(bool,i(s(fun(fun(cart(real,Q111612),cart(real,Q111621)),bool),linear),s(fun(cart(real,Q111612),cart(real,Q111621)),i(s(fun(fun(cart(real,Q111612),cart(real,Q111621)),fun(cart(real,Q111612),cart(real,Q111621))),i(s(fun(fun(cart(real,Q111612),cart(real,Q111621)),fun(fun(cart(real,Q111612),cart(real,Q111621)),fun(cart(real,Q111612),cart(real,Q111621)))),U_0),s(fun(cart(real,Q111612),cart(real,Q111621)),F0))),s(fun(cart(real,Q111612),cart(real,Q111621)),G0)))))) ) ) ).
fof(aLINEARu_COMPOSEu_SUB,axiom,
! [Q111643,Q111652,U_0] :
( ! [F0,G0,X] : s(cart(real,Q111652),i(s(fun(cart(real,Q111643),cart(real,Q111652)),i(s(fun(fun(cart(real,Q111643),cart(real,Q111652)),fun(cart(real,Q111643),cart(real,Q111652))),i(s(fun(fun(cart(real,Q111643),cart(real,Q111652)),fun(fun(cart(real,Q111643),cart(real,Q111652)),fun(cart(real,Q111643),cart(real,Q111652)))),U_0),s(fun(cart(real,Q111643),cart(real,Q111652)),F0))),s(fun(cart(real,Q111643),cart(real,Q111652)),G0))),s(cart(real,Q111643),X))) = s(cart(real,Q111652),i(s(fun(cart(real,Q111652),cart(real,Q111652)),i(s(fun(cart(real,Q111652),fun(cart(real,Q111652),cart(real,Q111652))),vectoru_sub),s(cart(real,Q111652),i(s(fun(cart(real,Q111643),cart(real,Q111652)),F0),s(cart(real,Q111643),X))))),s(cart(real,Q111652),i(s(fun(cart(real,Q111643),cart(real,Q111652)),G0),s(cart(real,Q111643),X)))))
=> ! [F0,G0] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q111643),cart(real,Q111652)),bool),linear),s(fun(cart(real,Q111643),cart(real,Q111652)),F0))))
& p(s(bool,i(s(fun(fun(cart(real,Q111643),cart(real,Q111652)),bool),linear),s(fun(cart(real,Q111643),cart(real,Q111652)),G0)))) )
=> p(s(bool,i(s(fun(fun(cart(real,Q111643),cart(real,Q111652)),bool),linear),s(fun(cart(real,Q111643),cart(real,Q111652)),i(s(fun(fun(cart(real,Q111643),cart(real,Q111652)),fun(cart(real,Q111643),cart(real,Q111652))),i(s(fun(fun(cart(real,Q111643),cart(real,Q111652)),fun(fun(cart(real,Q111643),cart(real,Q111652)),fun(cart(real,Q111643),cart(real,Q111652)))),U_0),s(fun(cart(real,Q111643),cart(real,Q111652)),F0))),s(fun(cart(real,Q111643),cart(real,Q111652)),G0)))))) ) ) ).
fof(aLINEARu_COMPOSE,axiom,
! [Q111672,Q111668,Q111669,F0,G0] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q111668),cart(real,Q111669)),bool),linear),s(fun(cart(real,Q111668),cart(real,Q111669)),F0))))
& p(s(bool,i(s(fun(fun(cart(real,Q111669),cart(real,Q111672)),bool),linear),s(fun(cart(real,Q111669),cart(real,Q111672)),G0)))) )
=> p(s(bool,i(s(fun(fun(cart(real,Q111668),cart(real,Q111672)),bool),linear),s(fun(cart(real,Q111668),cart(real,Q111672)),i(s(fun(fun(cart(real,Q111668),cart(real,Q111669)),fun(cart(real,Q111668),cart(real,Q111672))),i(s(fun(fun(cart(real,Q111669),cart(real,Q111672)),fun(fun(cart(real,Q111668),cart(real,Q111669)),fun(cart(real,Q111668),cart(real,Q111672)))),o),s(fun(cart(real,Q111669),cart(real,Q111672)),G0))),s(fun(cart(real,Q111668),cart(real,Q111669)),F0)))))) ) ).
fof(aLINEARu_ID,axiom,
! [Q111683,U_0] :
( ! [X] : s(cart(real,Q111683),i(s(fun(cart(real,Q111683),cart(real,Q111683)),U_0),s(cart(real,Q111683),X))) = s(cart(real,Q111683),X)
=> p(s(bool,i(s(fun(fun(cart(real,Q111683),cart(real,Q111683)),bool),linear),s(fun(cart(real,Q111683),cart(real,Q111683)),U_0)))) ) ).
fof(aLINEARu_I,axiom,
! [Q111690] : p(s(bool,i(s(fun(fun(cart(real,Q111690),cart(real,Q111690)),bool),linear),s(fun(cart(real,Q111690),cart(real,Q111690)),i1)))) ).
fof(aLINEARu_ZERO,axiom,
! [Q111694,Q111699,U_0] :
( ! [X] : s(cart(real,Q111699),i(s(fun(cart(real,Q111694),cart(real,Q111699)),U_0),s(cart(real,Q111694),X))) = s(cart(real,Q111699),i(s(fun(num,cart(real,Q111699)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
=> p(s(bool,i(s(fun(fun(cart(real,Q111694),cart(real,Q111699)),bool),linear),s(fun(cart(real,Q111694),cart(real,Q111699)),U_0)))) ) ).
fof(aLINEARu_NEGATION,axiom,
! [Q111705] : p(s(bool,i(s(fun(fun(cart(real,Q111705),cart(real,Q111705)),bool),linear),s(fun(cart(real,Q111705),cart(real,Q111705)),vectoru_neg)))) ).
fof(aLINEARu_COMPOSEu_VSUM,axiom,
! [Q111747,Q111736,Q111733,U_1] :
( ! [F0,X,A5] : s(cart(real,Q111733),i(s(fun(Q111747,cart(real,Q111733)),i(s(fun(cart(real,Q111736),fun(Q111747,cart(real,Q111733))),i(s(fun(fun(Q111747,fun(cart(real,Q111736),cart(real,Q111733))),fun(cart(real,Q111736),fun(Q111747,cart(real,Q111733)))),U_1),s(fun(Q111747,fun(cart(real,Q111736),cart(real,Q111733))),F0))),s(cart(real,Q111736),X))),s(Q111747,A5))) = s(cart(real,Q111733),i(s(fun(cart(real,Q111736),cart(real,Q111733)),i(s(fun(Q111747,fun(cart(real,Q111736),cart(real,Q111733))),F0),s(Q111747,A5))),s(cart(real,Q111736),X)))
=> ! [U_0] :
( ! [S0,F0,X] : s(cart(real,Q111733),i(s(fun(cart(real,Q111736),cart(real,Q111733)),i(s(fun(fun(Q111747,fun(cart(real,Q111736),cart(real,Q111733))),fun(cart(real,Q111736),cart(real,Q111733))),i(s(fun(fun(Q111747,bool),fun(fun(Q111747,fun(cart(real,Q111736),cart(real,Q111733))),fun(cart(real,Q111736),cart(real,Q111733)))),U_0),s(fun(Q111747,bool),S0))),s(fun(Q111747,fun(cart(real,Q111736),cart(real,Q111733))),F0))),s(cart(real,Q111736),X))) = s(cart(real,Q111733),i(s(fun(fun(Q111747,cart(real,Q111733)),cart(real,Q111733)),i(s(fun(fun(Q111747,bool),fun(fun(Q111747,cart(real,Q111733)),cart(real,Q111733))),vsum),s(fun(Q111747,bool),S0))),s(fun(Q111747,cart(real,Q111733)),i(s(fun(cart(real,Q111736),fun(Q111747,cart(real,Q111733))),i(s(fun(fun(Q111747,fun(cart(real,Q111736),cart(real,Q111733))),fun(cart(real,Q111736),fun(Q111747,cart(real,Q111733)))),U_1),s(fun(Q111747,fun(cart(real,Q111736),cart(real,Q111733))),F0))),s(cart(real,Q111736),X)))))
=> ! [F0,S0] :
( ( p(s(bool,i(s(fun(fun(Q111747,bool),bool),finite),s(fun(Q111747,bool),S0))))
& ! [A5] :
( p(s(bool,i(s(fun(fun(Q111747,bool),bool),i(s(fun(Q111747,fun(fun(Q111747,bool),bool)),in),s(Q111747,A5))),s(fun(Q111747,bool),S0))))
=> p(s(bool,i(s(fun(fun(cart(real,Q111736),cart(real,Q111733)),bool),linear),s(fun(cart(real,Q111736),cart(real,Q111733)),i(s(fun(Q111747,fun(cart(real,Q111736),cart(real,Q111733))),F0),s(Q111747,A5)))))) ) )
=> p(s(bool,i(s(fun(fun(cart(real,Q111736),cart(real,Q111733)),bool),linear),s(fun(cart(real,Q111736),cart(real,Q111733)),i(s(fun(fun(Q111747,fun(cart(real,Q111736),cart(real,Q111733))),fun(cart(real,Q111736),cart(real,Q111733))),i(s(fun(fun(Q111747,bool),fun(fun(Q111747,fun(cart(real,Q111736),cart(real,Q111733))),fun(cart(real,Q111736),cart(real,Q111733)))),U_0),s(fun(Q111747,bool),S0))),s(fun(Q111747,fun(cart(real,Q111736),cart(real,Q111733))),F0)))))) ) ) ) ).
fof(aLINEARu_VMULu_COMPONENT,axiom,
! [M,N,Q111786,U_0] :
( ! [F0,K0,V,X] : s(cart(real,Q111786),i(s(fun(cart(real,M),cart(real,Q111786)),i(s(fun(cart(real,Q111786),fun(cart(real,M),cart(real,Q111786))),i(s(fun(num,fun(cart(real,Q111786),fun(cart(real,M),cart(real,Q111786)))),i(s(fun(fun(cart(real,M),cart(real,N)),fun(num,fun(cart(real,Q111786),fun(cart(real,M),cart(real,Q111786))))),U_0),s(fun(cart(real,M),cart(real,N)),F0))),s(num,K0))),s(cart(real,Q111786),V))),s(cart(real,M),X))) = s(cart(real,Q111786),i(s(fun(cart(real,Q111786),cart(real,Q111786)),i(s(fun(real,fun(cart(real,Q111786),cart(real,Q111786))),r_),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))),s(num,K0))))),s(cart(real,Q111786),V)))
=> ! [F0,V,K0] :
( ( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,K0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,K0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) )
=> p(s(bool,i(s(fun(fun(cart(real,M),cart(real,Q111786)),bool),linear),s(fun(cart(real,M),cart(real,Q111786)),i(s(fun(cart(real,Q111786),fun(cart(real,M),cart(real,Q111786))),i(s(fun(num,fun(cart(real,Q111786),fun(cart(real,M),cart(real,Q111786)))),i(s(fun(fun(cart(real,M),cart(real,N)),fun(num,fun(cart(real,Q111786),fun(cart(real,M),cart(real,Q111786))))),U_0),s(fun(cart(real,M),cart(real,N)),F0))),s(num,K0))),s(cart(real,Q111786),V)))))) ) ) ).
fof(aLINEARu_0,axiom,
! [Q111807,Q111809,F0] :
( p(s(bool,i(s(fun(fun(cart(real,Q111807),cart(real,Q111809)),bool),linear),s(fun(cart(real,Q111807),cart(real,Q111809)),F0))))
=> s(cart(real,Q111809),i(s(fun(cart(real,Q111807),cart(real,Q111809)),F0),s(cart(real,Q111807),i(s(fun(num,cart(real,Q111807)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(cart(real,Q111809),i(s(fun(num,cart(real,Q111809)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ).
fof(aLINEARu_CMUL,axiom,
! [Q111837,Q111834,F0,C0,X] :
( p(s(bool,i(s(fun(fun(cart(real,Q111834),cart(real,Q111837)),bool),linear),s(fun(cart(real,Q111834),cart(real,Q111837)),F0))))
=> s(cart(real,Q111837),i(s(fun(cart(real,Q111834),cart(real,Q111837)),F0),s(cart(real,Q111834),i(s(fun(cart(real,Q111834),cart(real,Q111834)),i(s(fun(real,fun(cart(real,Q111834),cart(real,Q111834))),r_),s(real,C0))),s(cart(real,Q111834),X))))) = s(cart(real,Q111837),i(s(fun(cart(real,Q111837),cart(real,Q111837)),i(s(fun(real,fun(cart(real,Q111837),cart(real,Q111837))),r_),s(real,C0))),s(cart(real,Q111837),i(s(fun(cart(real,Q111834),cart(real,Q111837)),F0),s(cart(real,Q111834),X))))) ) ).
fof(aLINEARu_NEG,axiom,
! [Q111863,Q111862,F0,X] :
( p(s(bool,i(s(fun(fun(cart(real,Q111862),cart(real,Q111863)),bool),linear),s(fun(cart(real,Q111862),cart(real,Q111863)),F0))))
=> s(cart(real,Q111863),i(s(fun(cart(real,Q111862),cart(real,Q111863)),F0),s(cart(real,Q111862),i(s(fun(cart(real,Q111862),cart(real,Q111862)),vectoru_neg),s(cart(real,Q111862),X))))) = s(cart(real,Q111863),i(s(fun(cart(real,Q111863),cart(real,Q111863)),vectoru_neg),s(cart(real,Q111863),i(s(fun(cart(real,Q111862),cart(real,Q111863)),F0),s(cart(real,Q111862),X))))) ) ).
fof(aLINEARu_ADD,axiom,
! [Q111897,Q111896,F0,X,Y] :
( p(s(bool,i(s(fun(fun(cart(real,Q111896),cart(real,Q111897)),bool),linear),s(fun(cart(real,Q111896),cart(real,Q111897)),F0))))
=> s(cart(real,Q111897),i(s(fun(cart(real,Q111896),cart(real,Q111897)),F0),s(cart(real,Q111896),i(s(fun(cart(real,Q111896),cart(real,Q111896)),i(s(fun(cart(real,Q111896),fun(cart(real,Q111896),cart(real,Q111896))),vectoru_add),s(cart(real,Q111896),X))),s(cart(real,Q111896),Y))))) = s(cart(real,Q111897),i(s(fun(cart(real,Q111897),cart(real,Q111897)),i(s(fun(cart(real,Q111897),fun(cart(real,Q111897),cart(real,Q111897))),vectoru_add),s(cart(real,Q111897),i(s(fun(cart(real,Q111896),cart(real,Q111897)),F0),s(cart(real,Q111896),X))))),s(cart(real,Q111897),i(s(fun(cart(real,Q111896),cart(real,Q111897)),F0),s(cart(real,Q111896),Y))))) ) ).
fof(aLINEARu_SUB,axiom,
! [Q111931,Q111930,F0,X,Y] :
( p(s(bool,i(s(fun(fun(cart(real,Q111930),cart(real,Q111931)),bool),linear),s(fun(cart(real,Q111930),cart(real,Q111931)),F0))))
=> s(cart(real,Q111931),i(s(fun(cart(real,Q111930),cart(real,Q111931)),F0),s(cart(real,Q111930),i(s(fun(cart(real,Q111930),cart(real,Q111930)),i(s(fun(cart(real,Q111930),fun(cart(real,Q111930),cart(real,Q111930))),vectoru_sub),s(cart(real,Q111930),X))),s(cart(real,Q111930),Y))))) = s(cart(real,Q111931),i(s(fun(cart(real,Q111931),cart(real,Q111931)),i(s(fun(cart(real,Q111931),fun(cart(real,Q111931),cart(real,Q111931))),vectoru_sub),s(cart(real,Q111931),i(s(fun(cart(real,Q111930),cart(real,Q111931)),F0),s(cart(real,Q111930),X))))),s(cart(real,Q111931),i(s(fun(cart(real,Q111930),cart(real,Q111931)),F0),s(cart(real,Q111930),Y))))) ) ).
fof(aLINEARu_VSUM,axiom,
! [Q111967,Q111971,Q111963,F0,G0,S0] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q111963),cart(real,Q111967)),bool),linear),s(fun(cart(real,Q111963),cart(real,Q111967)),F0))))
& p(s(bool,i(s(fun(fun(Q111971,bool),bool),finite),s(fun(Q111971,bool),S0)))) )
=> s(cart(real,Q111967),i(s(fun(cart(real,Q111963),cart(real,Q111967)),F0),s(cart(real,Q111963),i(s(fun(fun(Q111971,cart(real,Q111963)),cart(real,Q111963)),i(s(fun(fun(Q111971,bool),fun(fun(Q111971,cart(real,Q111963)),cart(real,Q111963))),vsum),s(fun(Q111971,bool),S0))),s(fun(Q111971,cart(real,Q111963)),G0))))) = s(cart(real,Q111967),i(s(fun(fun(Q111971,cart(real,Q111967)),cart(real,Q111967)),i(s(fun(fun(Q111971,bool),fun(fun(Q111971,cart(real,Q111967)),cart(real,Q111967))),vsum),s(fun(Q111971,bool),S0))),s(fun(Q111971,cart(real,Q111967)),i(s(fun(fun(Q111971,cart(real,Q111963)),fun(Q111971,cart(real,Q111967))),i(s(fun(fun(cart(real,Q111963),cart(real,Q111967)),fun(fun(Q111971,cart(real,Q111963)),fun(Q111971,cart(real,Q111967)))),o),s(fun(cart(real,Q111963),cart(real,Q111967)),F0))),s(fun(Q111971,cart(real,Q111963)),G0))))) ) ).
fof(aLINEARu_VSUMu_MUL,axiom,
! [Q112022,Q112025,Q112011,U_1] :
( ! [C0,F0,V,I0] : s(cart(real,Q112022),i(s(fun(Q112025,cart(real,Q112022)),i(s(fun(fun(Q112025,cart(real,Q112011)),fun(Q112025,cart(real,Q112022))),i(s(fun(fun(cart(real,Q112011),cart(real,Q112022)),fun(fun(Q112025,cart(real,Q112011)),fun(Q112025,cart(real,Q112022)))),i(s(fun(fun(Q112025,real),fun(fun(cart(real,Q112011),cart(real,Q112022)),fun(fun(Q112025,cart(real,Q112011)),fun(Q112025,cart(real,Q112022))))),U_1),s(fun(Q112025,real),C0))),s(fun(cart(real,Q112011),cart(real,Q112022)),F0))),s(fun(Q112025,cart(real,Q112011)),V))),s(Q112025,I0))) = s(cart(real,Q112022),i(s(fun(cart(real,Q112022),cart(real,Q112022)),i(s(fun(real,fun(cart(real,Q112022),cart(real,Q112022))),r_),s(real,i(s(fun(Q112025,real),C0),s(Q112025,I0))))),s(cart(real,Q112022),i(s(fun(cart(real,Q112011),cart(real,Q112022)),F0),s(cart(real,Q112011),i(s(fun(Q112025,cart(real,Q112011)),V),s(Q112025,I0)))))))
=> ! [U_0] :
( ! [C0,V,I0] : s(cart(real,Q112011),i(s(fun(Q112025,cart(real,Q112011)),i(s(fun(fun(Q112025,cart(real,Q112011)),fun(Q112025,cart(real,Q112011))),i(s(fun(fun(Q112025,real),fun(fun(Q112025,cart(real,Q112011)),fun(Q112025,cart(real,Q112011)))),U_0),s(fun(Q112025,real),C0))),s(fun(Q112025,cart(real,Q112011)),V))),s(Q112025,I0))) = s(cart(real,Q112011),i(s(fun(cart(real,Q112011),cart(real,Q112011)),i(s(fun(real,fun(cart(real,Q112011),cart(real,Q112011))),r_),s(real,i(s(fun(Q112025,real),C0),s(Q112025,I0))))),s(cart(real,Q112011),i(s(fun(Q112025,cart(real,Q112011)),V),s(Q112025,I0)))))
=> ! [F0,S0,C0,V] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q112011),cart(real,Q112022)),bool),linear),s(fun(cart(real,Q112011),cart(real,Q112022)),F0))))
& p(s(bool,i(s(fun(fun(Q112025,bool),bool),finite),s(fun(Q112025,bool),S0)))) )
=> s(cart(real,Q112022),i(s(fun(cart(real,Q112011),cart(real,Q112022)),F0),s(cart(real,Q112011),i(s(fun(fun(Q112025,cart(real,Q112011)),cart(real,Q112011)),i(s(fun(fun(Q112025,bool),fun(fun(Q112025,cart(real,Q112011)),cart(real,Q112011))),vsum),s(fun(Q112025,bool),S0))),s(fun(Q112025,cart(real,Q112011)),i(s(fun(fun(Q112025,cart(real,Q112011)),fun(Q112025,cart(real,Q112011))),i(s(fun(fun(Q112025,real),fun(fun(Q112025,cart(real,Q112011)),fun(Q112025,cart(real,Q112011)))),U_0),s(fun(Q112025,real),C0))),s(fun(Q112025,cart(real,Q112011)),V))))))) = s(cart(real,Q112022),i(s(fun(fun(Q112025,cart(real,Q112022)),cart(real,Q112022)),i(s(fun(fun(Q112025,bool),fun(fun(Q112025,cart(real,Q112022)),cart(real,Q112022))),vsum),s(fun(Q112025,bool),S0))),s(fun(Q112025,cart(real,Q112022)),i(s(fun(fun(Q112025,cart(real,Q112011)),fun(Q112025,cart(real,Q112022))),i(s(fun(fun(cart(real,Q112011),cart(real,Q112022)),fun(fun(Q112025,cart(real,Q112011)),fun(Q112025,cart(real,Q112022)))),i(s(fun(fun(Q112025,real),fun(fun(cart(real,Q112011),cart(real,Q112022)),fun(fun(Q112025,cart(real,Q112011)),fun(Q112025,cart(real,Q112022))))),U_1),s(fun(Q112025,real),C0))),s(fun(cart(real,Q112011),cart(real,Q112022)),F0))),s(fun(Q112025,cart(real,Q112011)),V))))) ) ) ) ).
fof(aLINEARu_INJECTIVEu_0,axiom,
! [Q112067,Q112072,F0] :
( p(s(bool,i(s(fun(fun(cart(real,Q112072),cart(real,Q112067)),bool),linear),s(fun(cart(real,Q112072),cart(real,Q112067)),F0))))
=> ( ! [X,Y] :
( s(cart(real,Q112067),i(s(fun(cart(real,Q112072),cart(real,Q112067)),F0),s(cart(real,Q112072),X))) = s(cart(real,Q112067),i(s(fun(cart(real,Q112072),cart(real,Q112067)),F0),s(cart(real,Q112072),Y)))
=> s(cart(real,Q112072),X) = s(cart(real,Q112072),Y) )
<=> ! [X] :
( s(cart(real,Q112067),i(s(fun(cart(real,Q112072),cart(real,Q112067)),F0),s(cart(real,Q112072),X))) = s(cart(real,Q112067),i(s(fun(num,cart(real,Q112067)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
=> s(cart(real,Q112072),X) = s(cart(real,Q112072),i(s(fun(num,cart(real,Q112072)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ) ) ).
fof(aLINEARu_BOUNDED,axiom,
! [N,M,F0] :
( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
=> ? [B0] :
! [X] : p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,B0))),s(real,i(s(fun(cart(real,M),real),vectoru_norm),s(cart(real,M),X)))))))) ) ).
fof(aLINEARu_BOUNDEDu_POS,axiom,
! [N,M,F0] :
( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
=> ? [B0] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,B0))))
& ! [X] : p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,B0))),s(real,i(s(fun(cart(real,M),real),vectoru_norm),s(cart(real,M),X)))))))) ) ) ).
fof(aSYMMETRICu_LINEARu_IMAGE,axiom,
! [Q112240,Q112239,F0,S0] :
( ( ! [X] :
( p(s(bool,i(s(fun(fun(cart(real,Q112239),bool),bool),i(s(fun(cart(real,Q112239),fun(fun(cart(real,Q112239),bool),bool)),in),s(cart(real,Q112239),X))),s(fun(cart(real,Q112239),bool),S0))))
=> p(s(bool,i(s(fun(fun(cart(real,Q112239),bool),bool),i(s(fun(cart(real,Q112239),fun(fun(cart(real,Q112239),bool),bool)),in),s(cart(real,Q112239),i(s(fun(cart(real,Q112239),cart(real,Q112239)),vectoru_neg),s(cart(real,Q112239),X))))),s(fun(cart(real,Q112239),bool),S0)))) )
& p(s(bool,i(s(fun(fun(cart(real,Q112239),cart(real,Q112240)),bool),linear),s(fun(cart(real,Q112239),cart(real,Q112240)),F0)))) )
=> ! [X] :
( p(s(bool,i(s(fun(fun(cart(real,Q112240),bool),bool),i(s(fun(cart(real,Q112240),fun(fun(cart(real,Q112240),bool),bool)),in),s(cart(real,Q112240),X))),s(fun(cart(real,Q112240),bool),i(s(fun(fun(cart(real,Q112239),bool),fun(cart(real,Q112240),bool)),i(s(fun(fun(cart(real,Q112239),cart(real,Q112240)),fun(fun(cart(real,Q112239),bool),fun(cart(real,Q112240),bool))),image),s(fun(cart(real,Q112239),cart(real,Q112240)),F0))),s(fun(cart(real,Q112239),bool),S0))))))
=> p(s(bool,i(s(fun(fun(cart(real,Q112240),bool),bool),i(s(fun(cart(real,Q112240),fun(fun(cart(real,Q112240),bool),bool)),in),s(cart(real,Q112240),i(s(fun(cart(real,Q112240),cart(real,Q112240)),vectoru_neg),s(cart(real,Q112240),X))))),s(fun(cart(real,Q112240),bool),i(s(fun(fun(cart(real,Q112239),bool),fun(cart(real,Q112240),bool)),i(s(fun(fun(cart(real,Q112239),cart(real,Q112240)),fun(fun(cart(real,Q112239),bool),fun(cart(real,Q112240),bool))),image),s(fun(cart(real,Q112239),cart(real,Q112240)),F0))),s(fun(cart(real,Q112239),bool),S0)))))) ) ) ).
fof(abilinear,axiom,
! [Q112265,Q112255,Q112254,U_1] :
( ! [F0,Y,X] : s(cart(real,Q112255),i(s(fun(cart(real,Q112265),cart(real,Q112255)),i(s(fun(cart(real,Q112254),fun(cart(real,Q112265),cart(real,Q112255))),i(s(fun(fun(cart(real,Q112265),fun(cart(real,Q112254),cart(real,Q112255))),fun(cart(real,Q112254),fun(cart(real,Q112265),cart(real,Q112255)))),U_1),s(fun(cart(real,Q112265),fun(cart(real,Q112254),cart(real,Q112255))),F0))),s(cart(real,Q112254),Y))),s(cart(real,Q112265),X))) = s(cart(real,Q112255),i(s(fun(cart(real,Q112254),cart(real,Q112255)),i(s(fun(cart(real,Q112265),fun(cart(real,Q112254),cart(real,Q112255))),F0),s(cart(real,Q112265),X))),s(cart(real,Q112254),Y)))
=> ! [U_0] :
( ! [F0,X,Y] : s(cart(real,Q112255),i(s(fun(cart(real,Q112254),cart(real,Q112255)),i(s(fun(cart(real,Q112265),fun(cart(real,Q112254),cart(real,Q112255))),i(s(fun(fun(cart(real,Q112265),fun(cart(real,Q112254),cart(real,Q112255))),fun(cart(real,Q112265),fun(cart(real,Q112254),cart(real,Q112255)))),U_0),s(fun(cart(real,Q112265),fun(cart(real,Q112254),cart(real,Q112255))),F0))),s(cart(real,Q112265),X))),s(cart(real,Q112254),Y))) = s(cart(real,Q112255),i(s(fun(cart(real,Q112254),cart(real,Q112255)),i(s(fun(cart(real,Q112265),fun(cart(real,Q112254),cart(real,Q112255))),F0),s(cart(real,Q112265),X))),s(cart(real,Q112254),Y)))
=> ! [F0] :
( p(s(bool,i(s(fun(fun(cart(real,Q112265),fun(cart(real,Q112254),cart(real,Q112255))),bool),bilinear),s(fun(cart(real,Q112265),fun(cart(real,Q112254),cart(real,Q112255))),F0))))
<=> ( ! [X] : p(s(bool,i(s(fun(fun(cart(real,Q112254),cart(real,Q112255)),bool),linear),s(fun(cart(real,Q112254),cart(real,Q112255)),i(s(fun(cart(real,Q112265),fun(cart(real,Q112254),cart(real,Q112255))),i(s(fun(fun(cart(real,Q112265),fun(cart(real,Q112254),cart(real,Q112255))),fun(cart(real,Q112265),fun(cart(real,Q112254),cart(real,Q112255)))),U_0),s(fun(cart(real,Q112265),fun(cart(real,Q112254),cart(real,Q112255))),F0))),s(cart(real,Q112265),X))))))
& ! [Y] : p(s(bool,i(s(fun(fun(cart(real,Q112265),cart(real,Q112255)),bool),linear),s(fun(cart(real,Q112265),cart(real,Q112255)),i(s(fun(cart(real,Q112254),fun(cart(real,Q112265),cart(real,Q112255))),i(s(fun(fun(cart(real,Q112265),fun(cart(real,Q112254),cart(real,Q112255))),fun(cart(real,Q112254),fun(cart(real,Q112265),cart(real,Q112255)))),U_1),s(fun(cart(real,Q112265),fun(cart(real,Q112254),cart(real,Q112255))),F0))),s(cart(real,Q112254),Y)))))) ) ) ) ) ).
fof(aBILINEARu_LADD,axiom,
! [Q112310,Q112309,Q112292,H0,X,Y,Z0] :
( p(s(bool,i(s(fun(fun(cart(real,Q112309),fun(cart(real,Q112292),cart(real,Q112310))),bool),bilinear),s(fun(cart(real,Q112309),fun(cart(real,Q112292),cart(real,Q112310))),H0))))
=> s(cart(real,Q112310),i(s(fun(cart(real,Q112292),cart(real,Q112310)),i(s(fun(cart(real,Q112309),fun(cart(real,Q112292),cart(real,Q112310))),H0),s(cart(real,Q112309),i(s(fun(cart(real,Q112309),cart(real,Q112309)),i(s(fun(cart(real,Q112309),fun(cart(real,Q112309),cart(real,Q112309))),vectoru_add),s(cart(real,Q112309),X))),s(cart(real,Q112309),Y))))),s(cart(real,Q112292),Z0))) = s(cart(real,Q112310),i(s(fun(cart(real,Q112310),cart(real,Q112310)),i(s(fun(cart(real,Q112310),fun(cart(real,Q112310),cart(real,Q112310))),vectoru_add),s(cart(real,Q112310),i(s(fun(cart(real,Q112292),cart(real,Q112310)),i(s(fun(cart(real,Q112309),fun(cart(real,Q112292),cart(real,Q112310))),H0),s(cart(real,Q112309),X))),s(cart(real,Q112292),Z0))))),s(cart(real,Q112310),i(s(fun(cart(real,Q112292),cart(real,Q112310)),i(s(fun(cart(real,Q112309),fun(cart(real,Q112292),cart(real,Q112310))),H0),s(cart(real,Q112309),Y))),s(cart(real,Q112292),Z0))))) ) ).
fof(aBILINEARu_RADD,axiom,
! [Q112352,Q112333,Q112351,H0,X,Y,Z0] :
( p(s(bool,i(s(fun(fun(cart(real,Q112333),fun(cart(real,Q112351),cart(real,Q112352))),bool),bilinear),s(fun(cart(real,Q112333),fun(cart(real,Q112351),cart(real,Q112352))),H0))))
=> s(cart(real,Q112352),i(s(fun(cart(real,Q112351),cart(real,Q112352)),i(s(fun(cart(real,Q112333),fun(cart(real,Q112351),cart(real,Q112352))),H0),s(cart(real,Q112333),X))),s(cart(real,Q112351),i(s(fun(cart(real,Q112351),cart(real,Q112351)),i(s(fun(cart(real,Q112351),fun(cart(real,Q112351),cart(real,Q112351))),vectoru_add),s(cart(real,Q112351),Y))),s(cart(real,Q112351),Z0))))) = s(cart(real,Q112352),i(s(fun(cart(real,Q112352),cart(real,Q112352)),i(s(fun(cart(real,Q112352),fun(cart(real,Q112352),cart(real,Q112352))),vectoru_add),s(cart(real,Q112352),i(s(fun(cart(real,Q112351),cart(real,Q112352)),i(s(fun(cart(real,Q112333),fun(cart(real,Q112351),cart(real,Q112352))),H0),s(cart(real,Q112333),X))),s(cart(real,Q112351),Y))))),s(cart(real,Q112352),i(s(fun(cart(real,Q112351),cart(real,Q112352)),i(s(fun(cart(real,Q112333),fun(cart(real,Q112351),cart(real,Q112352))),H0),s(cart(real,Q112333),X))),s(cart(real,Q112351),Z0))))) ) ).
fof(aBILINEARu_LMUL,axiom,
! [Q112388,Q112385,Q112376,H0,C0,X,Y] :
( p(s(bool,i(s(fun(fun(cart(real,Q112385),fun(cart(real,Q112376),cart(real,Q112388))),bool),bilinear),s(fun(cart(real,Q112385),fun(cart(real,Q112376),cart(real,Q112388))),H0))))
=> s(cart(real,Q112388),i(s(fun(cart(real,Q112376),cart(real,Q112388)),i(s(fun(cart(real,Q112385),fun(cart(real,Q112376),cart(real,Q112388))),H0),s(cart(real,Q112385),i(s(fun(cart(real,Q112385),cart(real,Q112385)),i(s(fun(real,fun(cart(real,Q112385),cart(real,Q112385))),r_),s(real,C0))),s(cart(real,Q112385),X))))),s(cart(real,Q112376),Y))) = s(cart(real,Q112388),i(s(fun(cart(real,Q112388),cart(real,Q112388)),i(s(fun(real,fun(cart(real,Q112388),cart(real,Q112388))),r_),s(real,C0))),s(cart(real,Q112388),i(s(fun(cart(real,Q112376),cart(real,Q112388)),i(s(fun(cart(real,Q112385),fun(cart(real,Q112376),cart(real,Q112388))),H0),s(cart(real,Q112385),X))),s(cart(real,Q112376),Y))))) ) ).
fof(aBILINEARu_RMUL,axiom,
! [Q112424,Q112411,Q112421,H0,C0,X,Y] :
( p(s(bool,i(s(fun(fun(cart(real,Q112411),fun(cart(real,Q112421),cart(real,Q112424))),bool),bilinear),s(fun(cart(real,Q112411),fun(cart(real,Q112421),cart(real,Q112424))),H0))))
=> s(cart(real,Q112424),i(s(fun(cart(real,Q112421),cart(real,Q112424)),i(s(fun(cart(real,Q112411),fun(cart(real,Q112421),cart(real,Q112424))),H0),s(cart(real,Q112411),X))),s(cart(real,Q112421),i(s(fun(cart(real,Q112421),cart(real,Q112421)),i(s(fun(real,fun(cart(real,Q112421),cart(real,Q112421))),r_),s(real,C0))),s(cart(real,Q112421),Y))))) = s(cart(real,Q112424),i(s(fun(cart(real,Q112424),cart(real,Q112424)),i(s(fun(real,fun(cart(real,Q112424),cart(real,Q112424))),r_),s(real,C0))),s(cart(real,Q112424),i(s(fun(cart(real,Q112421),cart(real,Q112424)),i(s(fun(cart(real,Q112411),fun(cart(real,Q112421),cart(real,Q112424))),H0),s(cart(real,Q112411),X))),s(cart(real,Q112421),Y))))) ) ).
fof(aBILINEARu_LNEG,axiom,
! [Q112458,Q112457,Q112444,H0,X,Y] :
( p(s(bool,i(s(fun(fun(cart(real,Q112457),fun(cart(real,Q112444),cart(real,Q112458))),bool),bilinear),s(fun(cart(real,Q112457),fun(cart(real,Q112444),cart(real,Q112458))),H0))))
=> s(cart(real,Q112458),i(s(fun(cart(real,Q112444),cart(real,Q112458)),i(s(fun(cart(real,Q112457),fun(cart(real,Q112444),cart(real,Q112458))),H0),s(cart(real,Q112457),i(s(fun(cart(real,Q112457),cart(real,Q112457)),vectoru_neg),s(cart(real,Q112457),X))))),s(cart(real,Q112444),Y))) = s(cart(real,Q112458),i(s(fun(cart(real,Q112458),cart(real,Q112458)),vectoru_neg),s(cart(real,Q112458),i(s(fun(cart(real,Q112444),cart(real,Q112458)),i(s(fun(cart(real,Q112457),fun(cart(real,Q112444),cart(real,Q112458))),H0),s(cart(real,Q112457),X))),s(cart(real,Q112444),Y))))) ) ).
fof(aBILINEARu_RNEG,axiom,
! [Q112492,Q112477,Q112491,H0,X,Y] :
( p(s(bool,i(s(fun(fun(cart(real,Q112477),fun(cart(real,Q112491),cart(real,Q112492))),bool),bilinear),s(fun(cart(real,Q112477),fun(cart(real,Q112491),cart(real,Q112492))),H0))))
=> s(cart(real,Q112492),i(s(fun(cart(real,Q112491),cart(real,Q112492)),i(s(fun(cart(real,Q112477),fun(cart(real,Q112491),cart(real,Q112492))),H0),s(cart(real,Q112477),X))),s(cart(real,Q112491),i(s(fun(cart(real,Q112491),cart(real,Q112491)),vectoru_neg),s(cart(real,Q112491),Y))))) = s(cart(real,Q112492),i(s(fun(cart(real,Q112492),cart(real,Q112492)),vectoru_neg),s(cart(real,Q112492),i(s(fun(cart(real,Q112491),cart(real,Q112492)),i(s(fun(cart(real,Q112477),fun(cart(real,Q112491),cart(real,Q112492))),H0),s(cart(real,Q112477),X))),s(cart(real,Q112491),Y))))) ) ).
fof(aBILINEARu_LZERO,axiom,
! [Q112532,Q112524,Q112534,H0,X] :
( p(s(bool,i(s(fun(fun(cart(real,Q112532),fun(cart(real,Q112524),cart(real,Q112534))),bool),bilinear),s(fun(cart(real,Q112532),fun(cart(real,Q112524),cart(real,Q112534))),H0))))
=> s(cart(real,Q112534),i(s(fun(cart(real,Q112524),cart(real,Q112534)),i(s(fun(cart(real,Q112532),fun(cart(real,Q112524),cart(real,Q112534))),H0),s(cart(real,Q112532),i(s(fun(num,cart(real,Q112532)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(real,Q112524),X))) = s(cart(real,Q112534),i(s(fun(num,cart(real,Q112534)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ).
fof(aBILINEARu_RZERO,axiom,
! [Q112563,Q112572,Q112574,H0,X] :
( p(s(bool,i(s(fun(fun(cart(real,Q112563),fun(cart(real,Q112572),cart(real,Q112574))),bool),bilinear),s(fun(cart(real,Q112563),fun(cart(real,Q112572),cart(real,Q112574))),H0))))
=> s(cart(real,Q112574),i(s(fun(cart(real,Q112572),cart(real,Q112574)),i(s(fun(cart(real,Q112563),fun(cart(real,Q112572),cart(real,Q112574))),H0),s(cart(real,Q112563),X))),s(cart(real,Q112572),i(s(fun(num,cart(real,Q112572)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(cart(real,Q112574),i(s(fun(num,cart(real,Q112574)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ).
fof(aBILINEARu_LSUB,axiom,
! [Q112614,Q112613,Q112596,H0,X,Y,Z0] :
( p(s(bool,i(s(fun(fun(cart(real,Q112613),fun(cart(real,Q112596),cart(real,Q112614))),bool),bilinear),s(fun(cart(real,Q112613),fun(cart(real,Q112596),cart(real,Q112614))),H0))))
=> s(cart(real,Q112614),i(s(fun(cart(real,Q112596),cart(real,Q112614)),i(s(fun(cart(real,Q112613),fun(cart(real,Q112596),cart(real,Q112614))),H0),s(cart(real,Q112613),i(s(fun(cart(real,Q112613),cart(real,Q112613)),i(s(fun(cart(real,Q112613),fun(cart(real,Q112613),cart(real,Q112613))),vectoru_sub),s(cart(real,Q112613),X))),s(cart(real,Q112613),Y))))),s(cart(real,Q112596),Z0))) = s(cart(real,Q112614),i(s(fun(cart(real,Q112614),cart(real,Q112614)),i(s(fun(cart(real,Q112614),fun(cart(real,Q112614),cart(real,Q112614))),vectoru_sub),s(cart(real,Q112614),i(s(fun(cart(real,Q112596),cart(real,Q112614)),i(s(fun(cart(real,Q112613),fun(cart(real,Q112596),cart(real,Q112614))),H0),s(cart(real,Q112613),X))),s(cart(real,Q112596),Z0))))),s(cart(real,Q112614),i(s(fun(cart(real,Q112596),cart(real,Q112614)),i(s(fun(cart(real,Q112613),fun(cart(real,Q112596),cart(real,Q112614))),H0),s(cart(real,Q112613),Y))),s(cart(real,Q112596),Z0))))) ) ).
fof(aBILINEARu_RSUB,axiom,
! [Q112656,Q112637,Q112655,H0,X,Y,Z0] :
( p(s(bool,i(s(fun(fun(cart(real,Q112637),fun(cart(real,Q112655),cart(real,Q112656))),bool),bilinear),s(fun(cart(real,Q112637),fun(cart(real,Q112655),cart(real,Q112656))),H0))))
=> s(cart(real,Q112656),i(s(fun(cart(real,Q112655),cart(real,Q112656)),i(s(fun(cart(real,Q112637),fun(cart(real,Q112655),cart(real,Q112656))),H0),s(cart(real,Q112637),X))),s(cart(real,Q112655),i(s(fun(cart(real,Q112655),cart(real,Q112655)),i(s(fun(cart(real,Q112655),fun(cart(real,Q112655),cart(real,Q112655))),vectoru_sub),s(cart(real,Q112655),Y))),s(cart(real,Q112655),Z0))))) = s(cart(real,Q112656),i(s(fun(cart(real,Q112656),cart(real,Q112656)),i(s(fun(cart(real,Q112656),fun(cart(real,Q112656),cart(real,Q112656))),vectoru_sub),s(cart(real,Q112656),i(s(fun(cart(real,Q112655),cart(real,Q112656)),i(s(fun(cart(real,Q112637),fun(cart(real,Q112655),cart(real,Q112656))),H0),s(cart(real,Q112637),X))),s(cart(real,Q112655),Y))))),s(cart(real,Q112656),i(s(fun(cart(real,Q112655),cart(real,Q112656)),i(s(fun(cart(real,Q112637),fun(cart(real,Q112655),cart(real,Q112656))),H0),s(cart(real,Q112637),X))),s(cart(real,Q112655),Z0))))) ) ).
fof(aBILINEARu_VSUM,axiom,
! [Q112722,Q112723,M,N,P,U_0] :
( ! [H0,F0] :
( p(s(bool,i(s(fun(fun(prod(Q112722,Q112723),cart(real,P)),bool),i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),fun(fun(prod(Q112722,Q112723),cart(real,P)),bool)),U_0),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0))),s(fun(prod(Q112722,Q112723),cart(real,P)),F0))))
<=> ! [I0,J0] : p(s(bool,i(s(fun(cart(real,P),bool),i(s(fun(cart(real,P),fun(cart(real,P),bool)),geq),s(cart(real,P),i(s(fun(prod(Q112722,Q112723),cart(real,P)),F0),s(prod(Q112722,Q112723),i(s(fun(Q112723,prod(Q112722,Q112723)),i(s(fun(Q112722,fun(Q112723,prod(Q112722,Q112723))),c_),s(Q112722,I0))),s(Q112723,J0))))))),s(cart(real,P),i(s(fun(cart(real,N),cart(real,P)),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0),s(cart(real,M),i(s(fun(Q112722,cart(real,M)),f),s(Q112722,I0))))),s(cart(real,N),i(s(fun(Q112723,cart(real,N)),g),s(Q112723,J0)))))))) )
=> ! [H0] :
( ( p(s(bool,i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),bool),bilinear),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0))))
& p(s(bool,i(s(fun(fun(Q112722,bool),bool),finite),s(fun(Q112722,bool),s0))))
& p(s(bool,i(s(fun(fun(Q112723,bool),bool),finite),s(fun(Q112723,bool),t0)))) )
=> s(cart(real,P),i(s(fun(cart(real,N),cart(real,P)),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0),s(cart(real,M),i(s(fun(fun(Q112722,cart(real,M)),cart(real,M)),i(s(fun(fun(Q112722,bool),fun(fun(Q112722,cart(real,M)),cart(real,M))),vsum),s(fun(Q112722,bool),s0))),s(fun(Q112722,cart(real,M)),f))))),s(cart(real,N),i(s(fun(fun(Q112723,cart(real,N)),cart(real,N)),i(s(fun(fun(Q112723,bool),fun(fun(Q112723,cart(real,N)),cart(real,N))),vsum),s(fun(Q112723,bool),t0))),s(fun(Q112723,cart(real,N)),g))))) = s(cart(real,P),i(s(fun(fun(prod(Q112722,Q112723),cart(real,P)),cart(real,P)),i(s(fun(fun(prod(Q112722,Q112723),bool),fun(fun(prod(Q112722,Q112723),cart(real,P)),cart(real,P))),vsum),s(fun(prod(Q112722,Q112723),bool),i(s(fun(fun(Q112723,bool),fun(prod(Q112722,Q112723),bool)),i(s(fun(fun(Q112722,bool),fun(fun(Q112723,bool),fun(prod(Q112722,Q112723),bool))),cross0),s(fun(Q112722,bool),s0))),s(fun(Q112723,bool),t0))))),s(fun(prod(Q112722,Q112723),cart(real,P)),i(s(fun(fun(fun(prod(Q112722,Q112723),cart(real,P)),bool),fun(prod(Q112722,Q112723),cart(real,P))),gabs),s(fun(fun(prod(Q112722,Q112723),cart(real,P)),bool),i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),fun(fun(prod(Q112722,Q112723),cart(real,P)),bool)),U_0),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0))))))) ) ) ).
fof(aBILINEARu_BOUNDED,axiom,
! [P,M,N,H0] :
( p(s(bool,i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),bool),bilinear),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0))))
=> ? [B0] :
! [X,Y] : p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,P),real),vectoru_norm),s(cart(real,P),i(s(fun(cart(real,N),cart(real,P)),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0),s(cart(real,M),X))),s(cart(real,N),Y))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,B0))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(cart(real,M),real),vectoru_norm),s(cart(real,M),X))))),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),Y)))))))))) ) ).
fof(aBILINEARu_BOUNDEDu_POS,axiom,
! [Q112837,Q112835,Q112836,H0] :
( p(s(bool,i(s(fun(fun(cart(real,Q112835),fun(cart(real,Q112836),cart(real,Q112837))),bool),bilinear),s(fun(cart(real,Q112835),fun(cart(real,Q112836),cart(real,Q112837))),H0))))
=> ? [B0] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,B0))))
& ! [X,Y] : p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,Q112837),real),vectoru_norm),s(cart(real,Q112837),i(s(fun(cart(real,Q112836),cart(real,Q112837)),i(s(fun(cart(real,Q112835),fun(cart(real,Q112836),cart(real,Q112837))),H0),s(cart(real,Q112835),X))),s(cart(real,Q112836),Y))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,B0))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(cart(real,Q112835),real),vectoru_norm),s(cart(real,Q112835),X))))),s(real,i(s(fun(cart(real,Q112836),real),vectoru_norm),s(cart(real,Q112836),Y)))))))))) ) ) ).
fof(aBILINEARu_VSUMu_PARTIALu_SUC,axiom,
! [M,N,P,U_1] :
( ! [H0,F0,G0,K0] : s(cart(real,P),i(s(fun(num,cart(real,P)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,P))),i(s(fun(fun(num,cart(real,M)),fun(fun(num,cart(real,N)),fun(num,cart(real,P)))),i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),fun(fun(num,cart(real,M)),fun(fun(num,cart(real,N)),fun(num,cart(real,P))))),U_1),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0))),s(fun(num,cart(real,M)),F0))),s(fun(num,cart(real,N)),G0))),s(num,K0))) = s(cart(real,P),i(s(fun(cart(real,N),cart(real,P)),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0),s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),i(s(fun(cart(real,M),fun(cart(real,M),cart(real,M))),vectoru_sub),s(cart(real,M),i(s(fun(num,cart(real,M)),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,K0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(cart(real,M),i(s(fun(num,cart(real,M)),F0),s(num,K0))))))),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,K0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))
=> ! [U_0] :
( ! [H0,F0,G0,K0] : s(cart(real,P),i(s(fun(num,cart(real,P)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,P))),i(s(fun(fun(num,cart(real,M)),fun(fun(num,cart(real,N)),fun(num,cart(real,P)))),i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),fun(fun(num,cart(real,M)),fun(fun(num,cart(real,N)),fun(num,cart(real,P))))),U_0),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0))),s(fun(num,cart(real,M)),F0))),s(fun(num,cart(real,N)),G0))),s(num,K0))) = s(cart(real,P),i(s(fun(cart(real,N),cart(real,P)),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0),s(cart(real,M),i(s(fun(num,cart(real,M)),F0),s(num,K0))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,K0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,K0)))))))
=> ! [F0,G0,H0,M0,N0] :
( p(s(bool,i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),bool),bilinear),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0))))
=> s(cart(real,P),i(s(fun(fun(num,cart(real,P)),cart(real,P)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,P)),cart(real,P))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,P)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,P))),i(s(fun(fun(num,cart(real,M)),fun(fun(num,cart(real,N)),fun(num,cart(real,P)))),i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),fun(fun(num,cart(real,M)),fun(fun(num,cart(real,N)),fun(num,cart(real,P))))),U_0),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0))),s(fun(num,cart(real,M)),F0))),s(fun(num,cart(real,N)),G0))))) = s(cart(real,P),i(s(fun(cart(real,P),cart(real,P)),i(s(fun(cart(real,P),fun(cart(real,P),cart(real,P))),i(s(fun(bool,fun(cart(real,P),fun(cart(real,P),cart(real,P)))),cond),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0))))),s(cart(real,P),i(s(fun(cart(real,P),cart(real,P)),i(s(fun(cart(real,P),fun(cart(real,P),cart(real,P))),vectoru_sub),s(cart(real,P),i(s(fun(cart(real,P),cart(real,P)),i(s(fun(cart(real,P),fun(cart(real,P),cart(real,P))),vectoru_sub),s(cart(real,P),i(s(fun(cart(real,N),cart(real,P)),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0),s(cart(real,M),i(s(fun(num,cart(real,M)),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))),s(cart(real,P),i(s(fun(cart(real,N),cart(real,P)),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0),s(cart(real,M),i(s(fun(num,cart(real,M)),F0),s(num,M0))))),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,M0))))))))),s(cart(real,P),i(s(fun(fun(num,cart(real,P)),cart(real,P)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,P)),cart(real,P))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,P)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,P))),i(s(fun(fun(num,cart(real,M)),fun(fun(num,cart(real,N)),fun(num,cart(real,P)))),i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),fun(fun(num,cart(real,M)),fun(fun(num,cart(real,N)),fun(num,cart(real,P))))),U_1),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0))),s(fun(num,cart(real,M)),F0))),s(fun(num,cart(real,N)),G0))))))))),s(cart(real,P),i(s(fun(num,cart(real,P)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) ) ) ) ).
fof(aBILINEARu_VSUMu_PARTIALu_PRE,axiom,
! [M,N,P,U_1] :
( ! [H0,F0,G0,K0] : s(cart(real,P),i(s(fun(num,cart(real,P)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,P))),i(s(fun(fun(num,cart(real,M)),fun(fun(num,cart(real,N)),fun(num,cart(real,P)))),i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),fun(fun(num,cart(real,M)),fun(fun(num,cart(real,N)),fun(num,cart(real,P))))),U_1),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0))),s(fun(num,cart(real,M)),F0))),s(fun(num,cart(real,N)),G0))),s(num,K0))) = s(cart(real,P),i(s(fun(cart(real,N),cart(real,P)),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0),s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),i(s(fun(cart(real,M),fun(cart(real,M),cart(real,M))),vectoru_sub),s(cart(real,M),i(s(fun(num,cart(real,M)),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,K0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(cart(real,M),i(s(fun(num,cart(real,M)),F0),s(num,K0))))))),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,K0)))))
=> ! [U_0] :
( ! [H0,F0,G0,K0] : s(cart(real,P),i(s(fun(num,cart(real,P)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,P))),i(s(fun(fun(num,cart(real,M)),fun(fun(num,cart(real,N)),fun(num,cart(real,P)))),i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),fun(fun(num,cart(real,M)),fun(fun(num,cart(real,N)),fun(num,cart(real,P))))),U_0),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0))),s(fun(num,cart(real,M)),F0))),s(fun(num,cart(real,N)),G0))),s(num,K0))) = s(cart(real,P),i(s(fun(cart(real,N),cart(real,P)),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0),s(cart(real,M),i(s(fun(num,cart(real,M)),F0),s(num,K0))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,K0))))),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,K0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))))
=> ! [F0,G0,H0,M0,N0] :
( p(s(bool,i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),bool),bilinear),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0))))
=> s(cart(real,P),i(s(fun(fun(num,cart(real,P)),cart(real,P)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,P)),cart(real,P))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,P)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,P))),i(s(fun(fun(num,cart(real,M)),fun(fun(num,cart(real,N)),fun(num,cart(real,P)))),i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),fun(fun(num,cart(real,M)),fun(fun(num,cart(real,N)),fun(num,cart(real,P))))),U_0),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0))),s(fun(num,cart(real,M)),F0))),s(fun(num,cart(real,N)),G0))))) = s(cart(real,P),i(s(fun(cart(real,P),cart(real,P)),i(s(fun(cart(real,P),fun(cart(real,P),cart(real,P))),i(s(fun(bool,fun(cart(real,P),fun(cart(real,P),cart(real,P)))),cond),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0))))),s(cart(real,P),i(s(fun(cart(real,P),cart(real,P)),i(s(fun(cart(real,P),fun(cart(real,P),cart(real,P))),vectoru_sub),s(cart(real,P),i(s(fun(cart(real,P),cart(real,P)),i(s(fun(cart(real,P),fun(cart(real,P),cart(real,P))),vectoru_sub),s(cart(real,P),i(s(fun(cart(real,N),cart(real,P)),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0),s(cart(real,M),i(s(fun(num,cart(real,M)),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,N0))))))),s(cart(real,P),i(s(fun(cart(real,N),cart(real,P)),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0),s(cart(real,M),i(s(fun(num,cart(real,M)),F0),s(num,M0))))),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,M0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))))),s(cart(real,P),i(s(fun(fun(num,cart(real,P)),cart(real,P)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,P)),cart(real,P))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,P)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,P))),i(s(fun(fun(num,cart(real,M)),fun(fun(num,cart(real,N)),fun(num,cart(real,P)))),i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),fun(fun(num,cart(real,M)),fun(fun(num,cart(real,N)),fun(num,cart(real,P))))),U_1),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0))),s(fun(num,cart(real,M)),F0))),s(fun(num,cart(real,N)),G0))))))))),s(cart(real,P),i(s(fun(num,cart(real,P)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) ) ) ) ).
fof(aadjoint,axiom,
! [M,N,U_0] :
( ! [F0,FI_] :
( p(s(bool,i(s(fun(fun(cart(real,N),cart(real,M)),bool),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,N),cart(real,M)),bool)),U_0),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,N),cart(real,M)),FI_))))
<=> ! [X,Y] : s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))),s(cart(real,N),Y))) = s(real,i(s(fun(cart(real,M),real),i(s(fun(cart(real,M),fun(cart(real,M),real)),dot),s(cart(real,M),X))),s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),FI_),s(cart(real,N),Y))))) )
=> ! [F0] : s(fun(cart(real,N),cart(real,M)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,N),cart(real,M))),adjoint),s(fun(cart(real,M),cart(real,N)),F0))) = s(fun(cart(real,N),cart(real,M)),i(s(fun(fun(fun(cart(real,N),cart(real,M)),bool),fun(cart(real,N),cart(real,M))),h_),s(fun(fun(cart(real,N),cart(real,M)),bool),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,N),cart(real,M)),bool)),U_0),s(fun(cart(real,M),cart(real,N)),F0))))) ) ).
fof(aADJOINTu_WORKS,axiom,
! [M,N,F0] :
( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
=> ! [X,Y] : s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))),s(cart(real,N),Y))) = s(real,i(s(fun(cart(real,M),real),i(s(fun(cart(real,M),fun(cart(real,M),real)),dot),s(cart(real,M),X))),s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,N),cart(real,M))),adjoint),s(fun(cart(real,M),cart(real,N)),F0))),s(cart(real,N),Y))))) ) ).
fof(aADJOINTu_LINEAR,axiom,
! [M,N,F0] :
( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
=> p(s(bool,i(s(fun(fun(cart(real,N),cart(real,M)),bool),linear),s(fun(cart(real,N),cart(real,M)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,N),cart(real,M))),adjoint),s(fun(cart(real,M),cart(real,N)),F0)))))) ) ).
fof(aADJOINTu_CLAUSES,axiom,
! [N,M,F0] :
( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
=> ( ! [X,Y] : s(real,i(s(fun(cart(real,M),real),i(s(fun(cart(real,M),fun(cart(real,M),real)),dot),s(cart(real,M),X))),s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,N),cart(real,M))),adjoint),s(fun(cart(real,M),cart(real,N)),F0))),s(cart(real,N),Y))))) = s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))),s(cart(real,N),Y)))
& ! [X,Y] : s(real,i(s(fun(cart(real,M),real),i(s(fun(cart(real,M),fun(cart(real,M),real)),dot),s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,N),cart(real,M))),adjoint),s(fun(cart(real,M),cart(real,N)),F0))),s(cart(real,N),Y))))),s(cart(real,M),X))) = s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),Y))),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))) ) ) ).
fof(aADJOINTu_ADJOINT,axiom,
! [M,N,F0] :
( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
=> s(fun(cart(real,M),cart(real,N)),i(s(fun(fun(cart(real,N),cart(real,M)),fun(cart(real,M),cart(real,N))),adjoint),s(fun(cart(real,N),cart(real,M)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,N),cart(real,M))),adjoint),s(fun(cart(real,M),cart(real,N)),F0))))) = s(fun(cart(real,M),cart(real,N)),F0) ) ).
fof(aADJOINTu_UNIQUE,axiom,
! [Q113333,Q113332,F0,FI_] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q113333),cart(real,Q113332)),bool),linear),s(fun(cart(real,Q113333),cart(real,Q113332)),F0))))
& ! [X,Y] : s(real,i(s(fun(cart(real,Q113333),real),i(s(fun(cart(real,Q113333),fun(cart(real,Q113333),real)),dot),s(cart(real,Q113333),i(s(fun(cart(real,Q113332),cart(real,Q113333)),FI_),s(cart(real,Q113332),X))))),s(cart(real,Q113333),Y))) = s(real,i(s(fun(cart(real,Q113332),real),i(s(fun(cart(real,Q113332),fun(cart(real,Q113332),real)),dot),s(cart(real,Q113332),X))),s(cart(real,Q113332),i(s(fun(cart(real,Q113333),cart(real,Q113332)),F0),s(cart(real,Q113333),Y))))) )
=> s(fun(cart(real,Q113332),cart(real,Q113333)),FI_) = s(fun(cart(real,Q113332),cart(real,Q113333)),i(s(fun(fun(cart(real,Q113333),cart(real,Q113332)),fun(cart(real,Q113332),cart(real,Q113333))),adjoint),s(fun(cart(real,Q113333),cart(real,Q113332)),F0))) ) ).
fof(amatrixu_cmul,axiom,
! [N,M,U_1] :
( ! [C0,A5,I0,J0] : s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(num,fun(num,real))),i(s(fun(real,fun(cart(cart(real,N),M),fun(num,fun(num,real)))),U_1),s(real,C0))),s(cart(cart(real,N),M),A5))),s(num,I0))),s(num,J0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,C0))),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),A5))),s(num,I0))))),s(num,J0)))))
=> ! [U_0] :
( ! [C0,A5,I0] : s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),i(s(fun(real,fun(cart(cart(real,N),M),fun(num,cart(real,N)))),U_0),s(real,C0))),s(cart(cart(real,N),M),A5))),s(num,I0))) = s(cart(real,N),i(s(fun(fun(num,real),cart(real,N)),lambda),s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(num,fun(num,real))),i(s(fun(real,fun(cart(cart(real,N),M),fun(num,fun(num,real)))),U_1),s(real,C0))),s(cart(cart(real,N),M),A5))),s(num,I0)))))
=> ! [C0,A5] : s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(real,fun(cart(cart(real,N),M),cart(cart(real,N),M))),r_r_),s(real,C0))),s(cart(cart(real,N),M),A5))) = s(cart(cart(real,N),M),i(s(fun(fun(num,cart(real,N)),cart(cart(real,N),M)),lambda),s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),i(s(fun(real,fun(cart(cart(real,N),M),fun(num,cart(real,N)))),U_0),s(real,C0))),s(cart(cart(real,N),M),A5))))) ) ) ).
fof(amatrixu_neg,axiom,
! [N,M,U_1] :
( ! [A5,I0,J0] : s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(num,fun(num,real))),U_1),s(cart(cart(real,N),M),A5))),s(num,I0))),s(num,J0))) = s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),A5))),s(num,I0))))),s(num,J0)))))
=> ! [U_0] :
( ! [A5,I0] : s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),U_0),s(cart(cart(real,N),M),A5))),s(num,I0))) = s(cart(real,N),i(s(fun(fun(num,real),cart(real,N)),lambda),s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(num,fun(num,real))),U_1),s(cart(cart(real,N),M),A5))),s(num,I0)))))
=> ! [A5] : s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),matrixu_neg),s(cart(cart(real,N),M),A5))) = s(cart(cart(real,N),M),i(s(fun(fun(num,cart(real,N)),cart(cart(real,N),M)),lambda),s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),U_0),s(cart(cart(real,N),M),A5))))) ) ) ).
fof(amatrixu_add,axiom,
! [N,M,U_1] :
( ! [A5,B0,I0,J0] : s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(num,fun(num,real))),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),fun(num,fun(num,real)))),U_1),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))),s(num,I0))),s(num,J0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),A5))),s(num,I0))))),s(num,J0))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),B0))),s(num,I0))))),s(num,J0)))))
=> ! [U_0] :
( ! [A5,B0,I0] : s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),fun(num,cart(real,N)))),U_0),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))),s(num,I0))) = s(cart(real,N),i(s(fun(fun(num,real),cart(real,N)),lambda),s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(num,fun(num,real))),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),fun(num,fun(num,real)))),U_1),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))),s(num,I0)))))
=> ! [A5,B0] : s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))) = s(cart(cart(real,N),M),i(s(fun(fun(num,cart(real,N)),cart(cart(real,N),M)),lambda),s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),fun(num,cart(real,N)))),U_0),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))))) ) ) ).
fof(amatrixu_sub,axiom,
! [N,M,U_1] :
( ! [A5,B0,I0,J0] : s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(num,fun(num,real))),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),fun(num,fun(num,real)))),U_1),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))),s(num,I0))),s(num,J0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),A5))),s(num,I0))))),s(num,J0))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),B0))),s(num,I0))))),s(num,J0)))))
=> ! [U_0] :
( ! [A5,B0,I0] : s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),fun(num,cart(real,N)))),U_0),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))),s(num,I0))) = s(cart(real,N),i(s(fun(fun(num,real),cart(real,N)),lambda),s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(num,fun(num,real))),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),fun(num,fun(num,real)))),U_1),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))),s(num,I0)))))
=> ! [A5,B0] : s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_sub),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))) = s(cart(cart(real,N),M),i(s(fun(fun(num,cart(real,N)),cart(cart(real,N),M)),lambda),s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),fun(num,cart(real,N)))),U_0),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))))) ) ) ).
fof(amatrixu_mul,axiom,
! [M,P,N,U_2] :
( ! [A5,I0,B0,J0,K0] : s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(cart(real,P),N),fun(num,fun(num,real))),i(s(fun(num,fun(cart(cart(real,P),N),fun(num,fun(num,real)))),i(s(fun(cart(cart(real,N),M),fun(num,fun(cart(cart(real,P),N),fun(num,fun(num,real))))),U_2),s(cart(cart(real,N),M),A5))),s(num,I0))),s(cart(cart(real,P),N),B0))),s(num,J0))),s(num,K0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),A5))),s(num,I0))))),s(num,K0))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,P),fun(num,real)),d_),s(cart(real,P),i(s(fun(num,cart(real,P)),i(s(fun(cart(cart(real,P),N),fun(num,cart(real,P))),d_),s(cart(cart(real,P),N),B0))),s(num,K0))))),s(num,J0)))))
=> ! [U_1] :
( ! [A5,I0,B0,J0] : s(real,i(s(fun(num,real),i(s(fun(cart(cart(real,P),N),fun(num,real)),i(s(fun(num,fun(cart(cart(real,P),N),fun(num,real))),i(s(fun(cart(cart(real,N),M),fun(num,fun(cart(cart(real,P),N),fun(num,real)))),U_1),s(cart(cart(real,N),M),A5))),s(num,I0))),s(cart(cart(real,P),N),B0))),s(num,J0))) = s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))),s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(cart(real,P),N),fun(num,fun(num,real))),i(s(fun(num,fun(cart(cart(real,P),N),fun(num,fun(num,real)))),i(s(fun(cart(cart(real,N),M),fun(num,fun(cart(cart(real,P),N),fun(num,fun(num,real))))),U_2),s(cart(cart(real,N),M),A5))),s(num,I0))),s(cart(cart(real,P),N),B0))),s(num,J0)))))
=> ! [U_0] :
( ! [A5,B0,I0] : s(cart(real,P),i(s(fun(num,cart(real,P)),i(s(fun(cart(cart(real,P),N),fun(num,cart(real,P))),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),fun(num,cart(real,P)))),U_0),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),B0))),s(num,I0))) = s(cart(real,P),i(s(fun(fun(num,real),cart(real,P)),lambda),s(fun(num,real),i(s(fun(cart(cart(real,P),N),fun(num,real)),i(s(fun(num,fun(cart(cart(real,P),N),fun(num,real))),i(s(fun(cart(cart(real,N),M),fun(num,fun(cart(cart(real,P),N),fun(num,real)))),U_1),s(cart(cart(real,N),M),A5))),s(num,I0))),s(cart(cart(real,P),N),B0)))))
=> ! [A5,B0] : s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),B0))) = s(cart(cart(real,P),M),i(s(fun(fun(num,cart(real,P)),cart(cart(real,P),M)),lambda),s(fun(num,cart(real,P)),i(s(fun(cart(cart(real,P),N),fun(num,cart(real,P))),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),fun(num,cart(real,P)))),U_0),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),B0))))) ) ) ) ).
fof(amatrixu_vectoru_mul,axiom,
! [M,N,U_1] :
( ! [A5,I0,X,J0] : s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),i(s(fun(num,fun(cart(real,N),fun(num,real))),i(s(fun(cart(cart(real,N),M),fun(num,fun(cart(real,N),fun(num,real)))),U_1),s(cart(cart(real,N),M),A5))),s(num,I0))),s(cart(real,N),X))),s(num,J0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),A5))),s(num,I0))))),s(num,J0))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,J0)))))
=> ! [U_0] :
( ! [A5,X,I0] : s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),fun(num,real))),U_0),s(cart(cart(real,N),M),A5))),s(cart(real,N),X))),s(num,I0))) = s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))),s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),i(s(fun(num,fun(cart(real,N),fun(num,real))),i(s(fun(cart(cart(real,N),M),fun(num,fun(cart(real,N),fun(num,real)))),U_1),s(cart(cart(real,N),M),A5))),s(num,I0))),s(cart(real,N),X)))))
=> ! [A5,X] : s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),A5))),s(cart(real,N),X))) = s(cart(real,M),i(s(fun(fun(num,real),cart(real,M)),lambda),s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),fun(num,real))),U_0),s(cart(cart(real,N),M),A5))),s(cart(real,N),X))))) ) ) ).
fof(avectoru_matrixu_mul,axiom,
! [N,M,U_1] :
( ! [A5,J0,X,I0] : s(real,i(s(fun(num,real),i(s(fun(cart(real,M),fun(num,real)),i(s(fun(num,fun(cart(real,M),fun(num,real))),i(s(fun(cart(cart(real,N),M),fun(num,fun(cart(real,M),fun(num,real)))),U_1),s(cart(cart(real,N),M),A5))),s(num,J0))),s(cart(real,M),X))),s(num,I0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),A5))),s(num,I0))))),s(num,J0))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,M),fun(num,real)),d_),s(cart(real,M),X))),s(num,I0)))))
=> ! [U_0] :
( ! [A5,X,J0] : s(real,i(s(fun(num,real),i(s(fun(cart(real,M),fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(cart(real,M),fun(num,real))),U_0),s(cart(cart(real,N),M),A5))),s(cart(real,M),X))),s(num,J0))) = s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ))))))),s(fun(num,real),i(s(fun(cart(real,M),fun(num,real)),i(s(fun(num,fun(cart(real,M),fun(num,real))),i(s(fun(cart(cart(real,N),M),fun(num,fun(cart(real,M),fun(num,real)))),U_1),s(cart(cart(real,N),M),A5))),s(num,J0))),s(cart(real,M),X)))))
=> ! [A5,X] : s(cart(real,N),i(s(fun(cart(cart(real,N),M),cart(real,N)),i(s(fun(cart(real,M),fun(cart(cart(real,N),M),cart(real,N))),vectoru_matrixu_mul),s(cart(real,M),X))),s(cart(cart(real,N),M),A5))) = s(cart(real,N),i(s(fun(fun(num,real),cart(real,N)),lambda),s(fun(num,real),i(s(fun(cart(real,M),fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(cart(real,M),fun(num,real))),U_0),s(cart(cart(real,N),M),A5))),s(cart(real,M),X))))) ) ) ).
fof(amat,axiom,
! [M,N,U_1] :
( ! [I0,K0,J0] :
? [V] :
( ( p(s(bool,V))
<=> s(num,I0) = s(num,J0) )
& s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(num,fun(num,fun(num,real))),U_1),s(num,I0))),s(num,K0))),s(num,J0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,V))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,K0))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) )
=> ! [U_0] :
( ! [K0,I0] : s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(num,fun(num,cart(real,N))),U_0),s(num,K0))),s(num,I0))) = s(cart(real,N),i(s(fun(fun(num,real),cart(real,N)),lambda),s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(num,fun(num,fun(num,real))),U_1),s(num,I0))),s(num,K0)))))
=> ! [K0] : s(cart(cart(real,N),M),i(s(fun(num,cart(cart(real,N),M)),mat),s(num,K0))) = s(cart(cart(real,N),M),i(s(fun(fun(num,cart(real,N)),cart(cart(real,N),M)),lambda),s(fun(num,cart(real,N)),i(s(fun(num,fun(num,cart(real,N))),U_0),s(num,K0))))) ) ) ).
fof(atransp,axiom,
! [N,M,U_1] :
( ! [A5,I0,J0] : s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(num,fun(num,real))),U_1),s(cart(cart(real,N),M),A5))),s(num,I0))),s(num,J0))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),A5))),s(num,J0))))),s(num,I0)))
=> ! [U_0] :
( ! [A5,I0] : s(cart(real,M),i(s(fun(num,cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,M))),U_0),s(cart(cart(real,N),M),A5))),s(num,I0))) = s(cart(real,M),i(s(fun(fun(num,real),cart(real,M)),lambda),s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(num,fun(num,real))),U_1),s(cart(cart(real,N),M),A5))),s(num,I0)))))
=> ! [A5] : s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),A5))) = s(cart(cart(real,M),N),i(s(fun(fun(num,cart(real,M)),cart(cart(real,M),N)),lambda),s(fun(num,cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,M))),U_0),s(cart(cart(real,N),M),A5))))) ) ) ).
fof(arow,axiom,
! [N,M,U_0] :
( ! [A5,I0,J0] : s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(num,fun(num,real))),U_0),s(cart(cart(real,N),M),A5))),s(num,I0))),s(num,J0))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),A5))),s(num,I0))))),s(num,J0)))
=> ! [A5,I0] : s(cart(real,N),i(s(fun(cart(cart(real,N),M),cart(real,N)),i(s(fun(num,fun(cart(cart(real,N),M),cart(real,N))),row),s(num,I0))),s(cart(cart(real,N),M),A5))) = s(cart(real,N),i(s(fun(fun(num,real),cart(real,N)),lambda),s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(num,fun(num,real))),U_0),s(cart(cart(real,N),M),A5))),s(num,I0))))) ) ).
fof(acolumn,axiom,
! [N,M,U_0] :
( ! [A5,J0,I0] : s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(num,fun(num,real))),U_0),s(cart(cart(real,N),M),A5))),s(num,J0))),s(num,I0))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),A5))),s(num,I0))))),s(num,J0)))
=> ! [A5,J0] : s(cart(real,M),i(s(fun(cart(cart(real,N),M),cart(real,M)),i(s(fun(num,fun(cart(cart(real,N),M),cart(real,M))),column),s(num,J0))),s(cart(cart(real,N),M),A5))) = s(cart(real,M),i(s(fun(fun(num,real),cart(real,M)),lambda),s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(num,fun(num,real))),U_0),s(cart(cart(real,N),M),A5))),s(num,J0))))) ) ).
fof(arows,axiom,
! [N,M,U_0] :
( ! [A5,GENR_PVARR_291] :
( p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),bool)),U_0),s(cart(cart(real,N),M),A5))),s(cart(real,N),GENR_PVARR_291))))
<=> ? [I0,V] :
( ( p(s(bool,V))
<=> ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ)))))) ) )
& p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(bool,fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(bool,fun(cart(real,N),bool))),setspec),s(cart(real,N),GENR_PVARR_291))),s(bool,V))),s(cart(real,N),i(s(fun(cart(cart(real,N),M),cart(real,N)),i(s(fun(num,fun(cart(cart(real,N),M),cart(real,N))),row),s(num,I0))),s(cart(cart(real,N),M),A5)))))) ) )
=> ! [A5] : s(fun(cart(real,N),bool),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),bool)),rows),s(cart(cart(real,N),M),A5))) = s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),gspec),s(fun(cart(real,N),bool),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),bool)),U_0),s(cart(cart(real,N),M),A5))))) ) ).
fof(acolumns,axiom,
! [N,M,U_0] :
( ! [A5,GENR_PVARR_292] :
( p(s(bool,i(s(fun(cart(real,M),bool),i(s(fun(cart(cart(real,N),M),fun(cart(real,M),bool)),U_0),s(cart(cart(real,N),M),A5))),s(cart(real,M),GENR_PVARR_292))))
<=> ? [I0,V] :
( ( p(s(bool,V))
<=> ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) ) )
& p(s(bool,i(s(fun(cart(real,M),bool),i(s(fun(bool,fun(cart(real,M),bool)),i(s(fun(cart(real,M),fun(bool,fun(cart(real,M),bool))),setspec),s(cart(real,M),GENR_PVARR_292))),s(bool,V))),s(cart(real,M),i(s(fun(cart(cart(real,N),M),cart(real,M)),i(s(fun(num,fun(cart(cart(real,N),M),cart(real,M))),column),s(num,I0))),s(cart(cart(real,N),M),A5)))))) ) )
=> ! [A5] : s(fun(cart(real,M),bool),i(s(fun(cart(cart(real,N),M),fun(cart(real,M),bool)),columns),s(cart(cart(real,N),M),A5))) = s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),gspec),s(fun(cart(real,M),bool),i(s(fun(cart(cart(real,N),M),fun(cart(real,M),bool)),U_0),s(cart(cart(real,N),M),A5))))) ) ).
fof(aMATRIXu_CMULu_COMPONENT,axiom,
! [N,M,C0,A5,I0] : s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(real,fun(cart(cart(real,N),M),cart(cart(real,N),M))),r_r_),s(real,C0))),s(cart(cart(real,N),M),A5))))),s(num,I0))))),s(num,j))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,C0))),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),A5))),s(num,I0))))),s(num,j))))) ).
fof(aMATRIXu_ADDu_COMPONENT,axiom,
! [N,M,A5,B0,I0,J0] : s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))))),s(num,I0))))),s(num,J0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),A5))),s(num,I0))))),s(num,J0))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),B0))),s(num,I0))))),s(num,J0))))) ).
fof(aMATRIXu_SUBu_COMPONENT,axiom,
! [N,M,A5,B0,I0,J0] : s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_sub),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))))),s(num,I0))))),s(num,J0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),A5))),s(num,I0))))),s(num,J0))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),B0))),s(num,I0))))),s(num,J0))))) ).
fof(aMATRIXu_NEGu_COMPONENT,axiom,
! [N,M,A5,I0,J0] : s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),matrixu_neg),s(cart(cart(real,N),M),A5))))),s(num,I0))))),s(num,J0))) = s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),A5))),s(num,I0))))),s(num,J0))))) ).
fof(aTRANSPu_COMPONENT,axiom,
! [N,M,A5,I0,J0] : s(real,i(s(fun(num,real),i(s(fun(cart(real,M),fun(num,real)),d_),s(cart(real,M),i(s(fun(num,cart(real,M)),i(s(fun(cart(cart(real,M),N),fun(num,cart(real,M))),d_),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),A5))))),s(num,I0))))),s(num,J0))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),A5))),s(num,J0))))),s(num,I0))) ).
fof(aMATu_COMPONENT,axiom,
! [N,M,N0,I0,J0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ))))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,J0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,J0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) )
=> ? [V] :
( ( p(s(bool,V))
<=> s(num,I0) = s(num,J0) )
& s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),i(s(fun(num,cart(cart(real,N),M)),mat),s(num,N0))))),s(num,I0))))),s(num,J0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,V))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) ) ) ).
fof(aMATRIXu_CMULu_ASSOC,axiom,
! [M,N,A5,B0,X] : s(cart(cart(real,M),N),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),N)),i(s(fun(real,fun(cart(cart(real,M),N),cart(cart(real,M),N))),r_r_),s(real,A5))),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),N)),i(s(fun(real,fun(cart(cart(real,M),N),cart(cart(real,M),N))),r_r_),s(real,B0))),s(cart(cart(real,M),N),X))))) = s(cart(cart(real,M),N),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),N)),i(s(fun(real,fun(cart(cart(real,M),N),cart(cart(real,M),N))),r_r_),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,A5))),s(real,B0))))),s(cart(cart(real,M),N),X))) ).
fof(aMATRIXu_CMULu_LID,axiom,
! [M,N,X] : s(cart(cart(real,M),N),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),N)),i(s(fun(real,fun(cart(cart(real,M),N),cart(cart(real,M),N))),r_r_),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(cart(cart(real,M),N),X))) = s(cart(cart(real,M),N),X) ).
fof(aMATRIXu_ADDu_SYM,axiom,
! [N,M,A5,B0] : s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),B0))),s(cart(cart(real,N),M),A5))) ).
fof(aMATRIXu_ADDu_ASSOC,axiom,
! [N,M,A5,B0,C0] : s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),B0))),s(cart(cart(real,N),M),C0))))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))))),s(cart(cart(real,N),M),C0))) ).
fof(aMATRIXu_ADDu_LID,axiom,
! [Q114603,Q114604,A5] : s(cart(cart(real,Q114603),Q114604),i(s(fun(cart(cart(real,Q114603),Q114604),cart(cart(real,Q114603),Q114604)),i(s(fun(cart(cart(real,Q114603),Q114604),fun(cart(cart(real,Q114603),Q114604),cart(cart(real,Q114603),Q114604))),matrixu_add),s(cart(cart(real,Q114603),Q114604),i(s(fun(num,cart(cart(real,Q114603),Q114604)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(cart(real,Q114603),Q114604),A5))) = s(cart(cart(real,Q114603),Q114604),A5) ).
fof(aMATRIXu_ADDu_RID,axiom,
! [Q114621,Q114622,A5] : s(cart(cart(real,Q114621),Q114622),i(s(fun(cart(cart(real,Q114621),Q114622),cart(cart(real,Q114621),Q114622)),i(s(fun(cart(cart(real,Q114621),Q114622),fun(cart(cart(real,Q114621),Q114622),cart(cart(real,Q114621),Q114622))),matrixu_add),s(cart(cart(real,Q114621),Q114622),A5))),s(cart(cart(real,Q114621),Q114622),i(s(fun(num,cart(cart(real,Q114621),Q114622)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(cart(cart(real,Q114621),Q114622),A5) ).
fof(aMATRIXu_ADDu_LNEG,axiom,
! [Q114643,Q114644,A5] : s(cart(cart(real,Q114643),Q114644),i(s(fun(cart(cart(real,Q114643),Q114644),cart(cart(real,Q114643),Q114644)),i(s(fun(cart(cart(real,Q114643),Q114644),fun(cart(cart(real,Q114643),Q114644),cart(cart(real,Q114643),Q114644))),matrixu_add),s(cart(cart(real,Q114643),Q114644),i(s(fun(cart(cart(real,Q114643),Q114644),cart(cart(real,Q114643),Q114644)),matrixu_neg),s(cart(cart(real,Q114643),Q114644),A5))))),s(cart(cart(real,Q114643),Q114644),A5))) = s(cart(cart(real,Q114643),Q114644),i(s(fun(num,cart(cart(real,Q114643),Q114644)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ).
fof(aMATRIXu_ADDu_RNEG,axiom,
! [Q114667,Q114668,A5] : s(cart(cart(real,Q114667),Q114668),i(s(fun(cart(cart(real,Q114667),Q114668),cart(cart(real,Q114667),Q114668)),i(s(fun(cart(cart(real,Q114667),Q114668),fun(cart(cart(real,Q114667),Q114668),cart(cart(real,Q114667),Q114668))),matrixu_add),s(cart(cart(real,Q114667),Q114668),A5))),s(cart(cart(real,Q114667),Q114668),i(s(fun(cart(cart(real,Q114667),Q114668),cart(cart(real,Q114667),Q114668)),matrixu_neg),s(cart(cart(real,Q114667),Q114668),A5))))) = s(cart(cart(real,Q114667),Q114668),i(s(fun(num,cart(cart(real,Q114667),Q114668)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ).
fof(aMATRIXu_SUB,axiom,
! [N,M,A5,B0] : s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_sub),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),matrixu_neg),s(cart(cart(real,N),M),B0))))) ).
fof(aMATRIXu_SUBu_REFL,axiom,
! [Q114719,Q114720,A5] : s(cart(cart(real,Q114719),Q114720),i(s(fun(cart(cart(real,Q114719),Q114720),cart(cart(real,Q114719),Q114720)),i(s(fun(cart(cart(real,Q114719),Q114720),fun(cart(cart(real,Q114719),Q114720),cart(cart(real,Q114719),Q114720))),matrixu_sub),s(cart(cart(real,Q114719),Q114720),A5))),s(cart(cart(real,Q114719),Q114720),A5))) = s(cart(cart(real,Q114719),Q114720),i(s(fun(num,cart(cart(real,Q114719),Q114720)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ).
fof(aMATRIXu_ADDu_LDISTRIB,axiom,
! [M,P,N,A5,B0,C0] : s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),N)),i(s(fun(cart(cart(real,P),N),fun(cart(cart(real,P),N),cart(cart(real,P),N))),matrixu_add),s(cart(cart(real,P),N),B0))),s(cart(cart(real,P),N),C0))))) = s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),M),cart(cart(real,P),M)),i(s(fun(cart(cart(real,P),M),fun(cart(cart(real,P),M),cart(cart(real,P),M))),matrixu_add),s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),B0))))),s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),C0))))) ).
fof(aMATRIXu_MULu_LID,axiom,
! [N,M,A5] : s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,M),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_mul),s(cart(cart(real,M),M),i(s(fun(num,cart(cart(real,M),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(cart(cart(real,N),M),A5))) = s(cart(cart(real,N),M),A5) ).
fof(aMATRIXu_MULu_RID,axiom,
! [N,M,A5] : s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),N),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),N),cart(cart(real,N),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),N),i(s(fun(num,cart(cart(real,N),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(cart(cart(real,N),M),A5) ).
fof(aMATRIXu_MULu_ASSOC,axiom,
! [M,N,Q,P,A5,B0,C0] : s(cart(cart(real,Q),M),i(s(fun(cart(cart(real,Q),N),cart(cart(real,Q),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,Q),N),cart(cart(real,Q),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,Q),N),i(s(fun(cart(cart(real,Q),P),cart(cart(real,Q),N)),i(s(fun(cart(cart(real,P),N),fun(cart(cart(real,Q),P),cart(cart(real,Q),N))),matrixu_mul),s(cart(cart(real,P),N),B0))),s(cart(cart(real,Q),P),C0))))) = s(cart(cart(real,Q),M),i(s(fun(cart(cart(real,Q),P),cart(cart(real,Q),M)),i(s(fun(cart(cart(real,P),M),fun(cart(cart(real,Q),P),cart(cart(real,Q),M))),matrixu_mul),s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),B0))))),s(cart(cart(real,Q),P),C0))) ).
fof(aMATRIXu_MULu_LZERO,axiom,
! [N,P,M,A5] : s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),i(s(fun(num,cart(cart(real,N),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(cart(real,P),N),A5))) = s(cart(cart(real,P),M),i(s(fun(num,cart(cart(real,P),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ).
fof(aMATRIXu_MULu_RZERO,axiom,
! [N,P,M,A5] : s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),i(s(fun(num,cart(cart(real,P),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(cart(cart(real,P),M),i(s(fun(num,cart(cart(real,P),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ).
fof(aMATRIXu_ADDu_RDISTRIB,axiom,
! [M,P,N,A5,B0,C0] : s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))))),s(cart(cart(real,P),N),C0))) = s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),M),cart(cart(real,P),M)),i(s(fun(cart(cart(real,P),M),fun(cart(cart(real,P),M),cart(cart(real,P),M))),matrixu_add),s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),C0))))),s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),B0))),s(cart(cart(real,P),N),C0))))) ).
fof(aMATRIXu_SUBu_LDISTRIB,axiom,
! [M,P,N,A5,B0,C0] : s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),N)),i(s(fun(cart(cart(real,P),N),fun(cart(cart(real,P),N),cart(cart(real,P),N))),matrixu_sub),s(cart(cart(real,P),N),B0))),s(cart(cart(real,P),N),C0))))) = s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),M),cart(cart(real,P),M)),i(s(fun(cart(cart(real,P),M),fun(cart(cart(real,P),M),cart(cart(real,P),M))),matrixu_sub),s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),B0))))),s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),C0))))) ).
fof(aMATRIXu_SUBu_RDISTRIB,axiom,
! [M,P,N,A5,B0,C0] : s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_sub),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))))),s(cart(cart(real,P),N),C0))) = s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),M),cart(cart(real,P),M)),i(s(fun(cart(cart(real,P),M),fun(cart(cart(real,P),M),cart(cart(real,P),M))),matrixu_sub),s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),C0))))),s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),B0))),s(cart(cart(real,P),N),C0))))) ).
fof(aMATRIXu_MULu_LMUL,axiom,
! [M,P,N,A5,B0,C0] : s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(real,fun(cart(cart(real,N),M),cart(cart(real,N),M))),r_r_),s(real,C0))),s(cart(cart(real,N),M),A5))))),s(cart(cart(real,P),N),B0))) = s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),M),cart(cart(real,P),M)),i(s(fun(real,fun(cart(cart(real,P),M),cart(cart(real,P),M))),r_r_),s(real,C0))),s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),B0))))) ).
fof(aMATRIXu_MULu_RMUL,axiom,
! [M,P,N,A5,B0,C0] : s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),N)),i(s(fun(real,fun(cart(cart(real,P),N),cart(cart(real,P),N))),r_r_),s(real,C0))),s(cart(cart(real,P),N),B0))))) = s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),M),cart(cart(real,P),M)),i(s(fun(real,fun(cart(cart(real,P),M),cart(cart(real,P),M))),r_r_),s(real,C0))),s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),B0))))) ).
fof(aMATRIXu_CMULu_ADDu_LDISTRIB,axiom,
! [N,M,A5,B0,C0] : s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(real,fun(cart(cart(real,N),M),cart(cart(real,N),M))),r_r_),s(real,C0))),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(real,fun(cart(cart(real,N),M),cart(cart(real,N),M))),r_r_),s(real,C0))),s(cart(cart(real,N),M),A5))))),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(real,fun(cart(cart(real,N),M),cart(cart(real,N),M))),r_r_),s(real,C0))),s(cart(cart(real,N),M),B0))))) ).
fof(aMATRIXu_CMULu_SUBu_LDISTRIB,axiom,
! [N,M,A5,B0,C0] : s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(real,fun(cart(cart(real,N),M),cart(cart(real,N),M))),r_r_),s(real,C0))),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_sub),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_sub),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(real,fun(cart(cart(real,N),M),cart(cart(real,N),M))),r_r_),s(real,C0))),s(cart(cart(real,N),M),A5))))),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(real,fun(cart(cart(real,N),M),cart(cart(real,N),M))),r_r_),s(real,C0))),s(cart(cart(real,N),M),B0))))) ).
fof(aMATRIXu_CMULu_ADDu_RDISTRIB,axiom,
! [N,M,A5,B0,C0] : s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(real,fun(cart(cart(real,N),M),cart(cart(real,N),M))),r_r_),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,B0))),s(real,C0))))),s(cart(cart(real,N),M),A5))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(real,fun(cart(cart(real,N),M),cart(cart(real,N),M))),r_r_),s(real,B0))),s(cart(cart(real,N),M),A5))))),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(real,fun(cart(cart(real,N),M),cart(cart(real,N),M))),r_r_),s(real,C0))),s(cart(cart(real,N),M),A5))))) ).
fof(aMATRIXu_CMULu_SUBu_RDISTRIB,axiom,
! [N,M,A5,B0,C0] : s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(real,fun(cart(cart(real,N),M),cart(cart(real,N),M))),r_r_),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,B0))),s(real,C0))))),s(cart(cart(real,N),M),A5))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_sub),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(real,fun(cart(cart(real,N),M),cart(cart(real,N),M))),r_r_),s(real,B0))),s(cart(cart(real,N),M),A5))))),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(real,fun(cart(cart(real,N),M),cart(cart(real,N),M))),r_r_),s(real,C0))),s(cart(cart(real,N),M),A5))))) ).
fof(aMATRIXu_CMULu_RZERO,axiom,
! [Q115612,Q115613,C0] : s(cart(cart(real,Q115612),Q115613),i(s(fun(cart(cart(real,Q115612),Q115613),cart(cart(real,Q115612),Q115613)),i(s(fun(real,fun(cart(cart(real,Q115612),Q115613),cart(cart(real,Q115612),Q115613))),r_r_),s(real,C0))),s(cart(cart(real,Q115612),Q115613),i(s(fun(num,cart(cart(real,Q115612),Q115613)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(cart(cart(real,Q115612),Q115613),i(s(fun(num,cart(cart(real,Q115612),Q115613)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ).
fof(aMATRIXu_CMULu_LZERO,axiom,
! [Q115629,Q115630,A5] : s(cart(cart(real,Q115629),Q115630),i(s(fun(cart(cart(real,Q115629),Q115630),cart(cart(real,Q115629),Q115630)),i(s(fun(real,fun(cart(cart(real,Q115629),Q115630),cart(cart(real,Q115629),Q115630))),r_r_),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(cart(real,Q115629),Q115630),A5))) = s(cart(cart(real,Q115629),Q115630),i(s(fun(num,cart(cart(real,Q115629),Q115630)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ).
fof(aMATRIXu_NEGu_MINUS1,axiom,
! [N,M,A5] : s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),matrixu_neg),s(cart(cart(real,N),M),A5))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(real,fun(cart(cart(real,N),M),cart(cart(real,N),M))),r_r_),s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(cart(cart(real,N),M),A5))) ).
fof(aMATRIXu_ADDu_ACu_conjunct0,axiom,
! [N,M] : s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),a))),s(cart(cart(real,N),M),b))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),b))),s(cart(cart(real,N),M),a))) ).
fof(aMATRIXu_ADDu_ACu_conjunct1,axiom,
! [N,M] : s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),a))),s(cart(cart(real,N),M),b))))),s(cart(cart(real,N),M),c0))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),a))),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),b))),s(cart(cart(real,N),M),c0))))) ).
fof(aMATRIXu_ADDu_ACu_conjunct2,axiom,
! [N,M] : s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),a))),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),b))),s(cart(cart(real,N),M),c0))))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),b))),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),a))),s(cart(cart(real,N),M),c0))))) ).
fof(aMATRIXu_NEGu_ADD,axiom,
! [N,M,A5,B0] : s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),matrixu_neg),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),matrixu_neg),s(cart(cart(real,N),M),A5))))),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),matrixu_neg),s(cart(cart(real,N),M),B0))))) ).
fof(aMATRIXu_NEGu_SUB,axiom,
! [N,M,A5,B0] : s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),matrixu_neg),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_sub),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_sub),s(cart(cart(real,N),M),B0))),s(cart(cart(real,N),M),A5))) ).
fof(aMATRIXu_NEGu_0,axiom,
! [Q115825,Q115826] : s(cart(cart(real,Q115825),Q115826),i(s(fun(cart(cart(real,Q115825),Q115826),cart(cart(real,Q115825),Q115826)),matrixu_neg),s(cart(cart(real,Q115825),Q115826),i(s(fun(num,cart(cart(real,Q115825),Q115826)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(cart(cart(real,Q115825),Q115826),i(s(fun(num,cart(cart(real,Q115825),Q115826)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ).
fof(aMATRIXu_SUBu_RZERO,axiom,
! [N,M,A5] : s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_sub),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),i(s(fun(num,cart(cart(real,N),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(cart(cart(real,N),M),A5) ).
fof(aMATRIXu_SUBu_LZERO,axiom,
! [N,M,A5] : s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_sub),s(cart(cart(real,N),M),i(s(fun(num,cart(cart(real,N),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(cart(real,N),M),A5))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),matrixu_neg),s(cart(cart(real,N),M),A5))) ).
fof(aMATRIXu_NEGu_EQu_0,axiom,
! [N,M,A5] :
( s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),matrixu_neg),s(cart(cart(real,N),M),A5))) = s(cart(cart(real,N),M),i(s(fun(num,cart(cart(real,N),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
<=> s(cart(cart(real,N),M),A5) = s(cart(cart(real,N),M),i(s(fun(num,cart(cart(real,N),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ).
fof(aMATRIXu_VECTORu_MULu_ASSOC,axiom,
! [M,N,P,A5,B0,X] : s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),A5))),s(cart(real,N),i(s(fun(cart(real,P),cart(real,N)),i(s(fun(cart(cart(real,P),N),fun(cart(real,P),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,P),N),B0))),s(cart(real,P),X))))) = s(cart(real,M),i(s(fun(cart(real,P),cart(real,M)),i(s(fun(cart(cart(real,P),M),fun(cart(real,P),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),B0))))),s(cart(real,P),X))) ).
fof(aMATRIXu_VECTORu_MULu_LID,axiom,
! [N,X] : s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(cart(real,N),N),fun(cart(real,N),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,N),N),i(s(fun(num,cart(cart(real,N),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(cart(real,N),X))) = s(cart(real,N),X) ).
fof(aMATRIXu_VECTORu_MULu_LZERO,axiom,
! [N,Q116015,X] : s(cart(real,Q116015),i(s(fun(cart(real,N),cart(real,Q116015)),i(s(fun(cart(cart(real,N),Q116015),fun(cart(real,N),cart(real,Q116015))),matrixu_vectoru_mul),s(cart(cart(real,N),Q116015),i(s(fun(num,cart(cart(real,N),Q116015)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(real,N),X))) = s(cart(real,Q116015),i(s(fun(num,cart(real,Q116015)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ).
fof(aMATRIXu_VECTORu_MULu_RZERO,axiom,
! [M,N,A5] : s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),i(s(fun(num,cart(real,M)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ).
fof(aMATRIXu_VECTORu_MULu_ADDu_LDISTRIB,axiom,
! [N,M,A5,X,Y] : s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),i(s(fun(cart(real,M),fun(cart(real,M),cart(real,M))),vectoru_add),s(cart(real,M),X))),s(cart(real,M),Y))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),X))))),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),Y))))) ).
fof(aMATRIXu_VECTORu_MULu_SUBu_LDISTRIB,axiom,
! [N,M,A5,X,Y] : s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),i(s(fun(cart(real,M),fun(cart(real,M),cart(real,M))),vectoru_sub),s(cart(real,M),X))),s(cart(real,M),Y))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),X))))),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),Y))))) ).
fof(aMATRIXu_VECTORu_MULu_ADDu_RDISTRIB,axiom,
! [N,M,A5,B0,X] : s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),N)),i(s(fun(cart(cart(real,M),N),fun(cart(cart(real,M),N),cart(cart(real,M),N))),matrixu_add),s(cart(cart(real,M),N),A5))),s(cart(cart(real,M),N),B0))))),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),X))))),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),B0))),s(cart(real,M),X))))) ).
fof(aMATRIXu_VECTORu_MULu_SUBu_RDISTRIB,axiom,
! [N,M,A5,B0,X] : s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),N)),i(s(fun(cart(cart(real,M),N),fun(cart(cart(real,M),N),cart(cart(real,M),N))),matrixu_sub),s(cart(cart(real,M),N),A5))),s(cart(cart(real,M),N),B0))))),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),X))))),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),B0))),s(cart(real,M),X))))) ).
fof(aMATRIXu_VECTORu_MULu_RMUL,axiom,
! [N,M,A5,X,C0] : s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),i(s(fun(real,fun(cart(real,M),cart(real,M))),r_),s(real,C0))),s(cart(real,M),X))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,C0))),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),X))))) ).
fof(aMATRIXu_TRANSPu_MUL,axiom,
! [Q116425,Q116423,Q116424,A5,B0] : s(cart(cart(real,Q116424),Q116425),i(s(fun(cart(cart(real,Q116425),Q116424),cart(cart(real,Q116424),Q116425)),transp),s(cart(cart(real,Q116425),Q116424),i(s(fun(cart(cart(real,Q116425),Q116423),cart(cart(real,Q116425),Q116424)),i(s(fun(cart(cart(real,Q116423),Q116424),fun(cart(cart(real,Q116425),Q116423),cart(cart(real,Q116425),Q116424))),matrixu_mul),s(cart(cart(real,Q116423),Q116424),A5))),s(cart(cart(real,Q116425),Q116423),B0))))) = s(cart(cart(real,Q116424),Q116425),i(s(fun(cart(cart(real,Q116424),Q116423),cart(cart(real,Q116424),Q116425)),i(s(fun(cart(cart(real,Q116423),Q116425),fun(cart(cart(real,Q116424),Q116423),cart(cart(real,Q116424),Q116425))),matrixu_mul),s(cart(cart(real,Q116423),Q116425),i(s(fun(cart(cart(real,Q116425),Q116423),cart(cart(real,Q116423),Q116425)),transp),s(cart(cart(real,Q116425),Q116423),B0))))),s(cart(cart(real,Q116424),Q116423),i(s(fun(cart(cart(real,Q116423),Q116424),cart(cart(real,Q116424),Q116423)),transp),s(cart(cart(real,Q116423),Q116424),A5))))) ).
fof(aMATRIXu_EQ,axiom,
! [M,N,A5,B0] :
( s(cart(cart(real,N),M),A5) = s(cart(cart(real,N),M),B0)
<=> ! [X] : s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),A5))),s(cart(real,N),X))) = s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),B0))),s(cart(real,N),X))) ) ).
fof(aMATRIXu_VECTORu_MULu_COMPONENT,axiom,
! [M,N,A5,X,K0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,K0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,K0))),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ)))))) )
=> s(real,i(s(fun(num,real),i(s(fun(cart(real,M),fun(num,real)),d_),s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),A5))),s(cart(real,N),X))))),s(num,K0))) = s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),A5))),s(num,K0))))),s(cart(real,N),X))) ) ).
fof(aDOTu_LMULu_MATRIX,axiom,
! [M,N,A5,X,Y] : s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),i(s(fun(cart(cart(real,N),M),cart(real,N)),i(s(fun(cart(real,M),fun(cart(cart(real,N),M),cart(real,N))),vectoru_matrixu_mul),s(cart(real,M),X))),s(cart(cart(real,N),M),A5))))),s(cart(real,N),Y))) = s(real,i(s(fun(cart(real,M),real),i(s(fun(cart(real,M),fun(cart(real,M),real)),dot),s(cart(real,M),X))),s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),A5))),s(cart(real,N),Y))))) ).
fof(aTRANSPu_MATRIXu_CMUL,axiom,
! [M,N,A5,C0] : s(cart(cart(real,N),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,N),M)),transp),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),N)),i(s(fun(real,fun(cart(cart(real,M),N),cart(cart(real,M),N))),r_r_),s(real,C0))),s(cart(cart(real,M),N),A5))))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(real,fun(cart(cart(real,N),M),cart(cart(real,N),M))),r_r_),s(real,C0))),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,N),M)),transp),s(cart(cart(real,M),N),A5))))) ).
fof(aTRANSPu_MATRIXu_ADD,axiom,
! [N,M,A5,B0] : s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))))) = s(cart(cart(real,M),N),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),N)),i(s(fun(cart(cart(real,M),N),fun(cart(cart(real,M),N),cart(cart(real,M),N))),matrixu_add),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),A5))))),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),B0))))) ).
fof(aTRANSPu_MATRIXu_SUB,axiom,
! [N,M,A5,B0] : s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_sub),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))))) = s(cart(cart(real,M),N),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),N)),i(s(fun(cart(cart(real,M),N),fun(cart(cart(real,M),N),cart(cart(real,M),N))),matrixu_sub),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),A5))))),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),B0))))) ).
fof(aTRANSPu_MATRIXu_NEG,axiom,
! [N,M,A5] : s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),matrixu_neg),s(cart(cart(real,N),M),A5))))) = s(cart(cart(real,M),N),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),N)),matrixu_neg),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),A5))))) ).
fof(aTRANSPu_MAT,axiom,
! [Q116735,Q116736,N0] : s(cart(cart(real,Q116735),Q116736),i(s(fun(cart(cart(real,Q116736),Q116735),cart(cart(real,Q116735),Q116736)),transp),s(cart(cart(real,Q116736),Q116735),i(s(fun(num,cart(cart(real,Q116736),Q116735)),mat),s(num,N0))))) = s(cart(cart(real,Q116735),Q116736),i(s(fun(num,cart(cart(real,Q116735),Q116736)),mat),s(num,N0))) ).
fof(aTRANSPu_TRANSP,axiom,
! [N,M,A5] : s(cart(cart(real,N),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,N),M)),transp),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),A5))))) = s(cart(cart(real,N),M),A5) ).
fof(aTRANSPu_EQ,axiom,
! [M,N,A5,B0] :
( s(cart(cart(real,N),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,N),M)),transp),s(cart(cart(real,M),N),A5))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,N),M)),transp),s(cart(cart(real,M),N),B0)))
<=> s(cart(cart(real,M),N),A5) = s(cart(cart(real,M),N),B0) ) ).
fof(aROWu_TRANSP,axiom,
! [N,M,A5,I0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) )
=> s(cart(real,M),i(s(fun(cart(cart(real,M),N),cart(real,M)),i(s(fun(num,fun(cart(cart(real,M),N),cart(real,M))),row),s(num,I0))),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),A5))))) = s(cart(real,M),i(s(fun(cart(cart(real,N),M),cart(real,M)),i(s(fun(num,fun(cart(cart(real,N),M),cart(real,M))),column),s(num,I0))),s(cart(cart(real,N),M),A5))) ) ).
fof(aCOLUMNu_TRANSP,axiom,
! [N,M,A5,I0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ)))))) )
=> s(cart(real,N),i(s(fun(cart(cart(real,M),N),cart(real,N)),i(s(fun(num,fun(cart(cart(real,M),N),cart(real,N))),column),s(num,I0))),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),A5))))) = s(cart(real,N),i(s(fun(cart(cart(real,N),M),cart(real,N)),i(s(fun(num,fun(cart(cart(real,N),M),cart(real,N))),row),s(num,I0))),s(cart(cart(real,N),M),A5))) ) ).
fof(aROWSu_TRANSP,axiom,
! [N,M,A5] : s(fun(cart(real,M),bool),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),bool)),rows),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),A5))))) = s(fun(cart(real,M),bool),i(s(fun(cart(cart(real,N),M),fun(cart(real,M),bool)),columns),s(cart(cart(real,N),M),A5))) ).
fof(aCOLUMNSu_TRANSP,axiom,
! [N,M,A5] : s(fun(cart(real,N),bool),i(s(fun(cart(cart(real,M),N),fun(cart(real,N),bool)),columns),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),A5))))) = s(fun(cart(real,N),bool),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),bool)),rows),s(cart(cart(real,N),M),A5))) ).
fof(aVECTORu_MATRIXu_MULu_TRANSP,axiom,
! [M,N,A5,X] : s(cart(real,M),i(s(fun(cart(cart(real,M),N),cart(real,M)),i(s(fun(cart(real,N),fun(cart(cart(real,M),N),cart(real,M))),vectoru_matrixu_mul),s(cart(real,N),X))),s(cart(cart(real,M),N),A5))) = s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,N),M)),transp),s(cart(cart(real,M),N),A5))))),s(cart(real,N),X))) ).
fof(aMATRIXu_VECTORu_MULu_TRANSP,axiom,
! [M,N,A5,X] : s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(cart(real,N),M),cart(real,N)),i(s(fun(cart(real,M),fun(cart(cart(real,N),M),cart(real,N))),vectoru_matrixu_mul),s(cart(real,M),X))),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,N),M)),transp),s(cart(cart(real,M),N),A5))))) ).
fof(aFINITEu_ROWS,axiom,
! [N,M,A5] : p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),bool)),rows),s(cart(cart(real,N),M),A5)))))) ).
fof(aFINITEu_COLUMNS,axiom,
! [N,M,A5] : p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),finite),s(fun(cart(real,M),bool),i(s(fun(cart(cart(real,N),M),fun(cart(real,M),bool)),columns),s(cart(cart(real,N),M),A5)))))) ).
fof(aMATRIXu_EQUALu_ROWS,axiom,
! [N,M,A5,B0] :
( s(cart(cart(real,N),M),A5) = s(cart(cart(real,N),M),B0)
<=> ! [I0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ)))))) )
=> s(cart(real,N),i(s(fun(cart(cart(real,N),M),cart(real,N)),i(s(fun(num,fun(cart(cart(real,N),M),cart(real,N))),row),s(num,I0))),s(cart(cart(real,N),M),A5))) = s(cart(real,N),i(s(fun(cart(cart(real,N),M),cart(real,N)),i(s(fun(num,fun(cart(cart(real,N),M),cart(real,N))),row),s(num,I0))),s(cart(cart(real,N),M),B0))) ) ) ).
fof(aMATRIXu_EQUALu_COLUMNS,axiom,
! [N,M,A5,B0] :
( s(cart(cart(real,N),M),A5) = s(cart(cart(real,N),M),B0)
<=> ! [I0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) )
=> s(cart(real,M),i(s(fun(cart(cart(real,N),M),cart(real,M)),i(s(fun(num,fun(cart(cart(real,N),M),cart(real,M))),column),s(num,I0))),s(cart(cart(real,N),M),A5))) = s(cart(real,M),i(s(fun(cart(cart(real,N),M),cart(real,M)),i(s(fun(num,fun(cart(cart(real,N),M),cart(real,M))),column),s(num,I0))),s(cart(cart(real,N),M),B0))) ) ) ).
fof(aMATRIXu_MULu_DOT,axiom,
! [M,N,U_0] :
( ! [A5,X,I0] : s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),fun(num,real))),U_0),s(cart(cart(real,N),M),A5))),s(cart(real,N),X))),s(num,I0))) = s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),A5))),s(num,I0))))),s(cart(real,N),X)))
=> ! [A5,X] : s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),A5))),s(cart(real,N),X))) = s(cart(real,M),i(s(fun(fun(num,real),cart(real,M)),lambda),s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),fun(num,real))),U_0),s(cart(cart(real,N),M),A5))),s(cart(real,N),X))))) ) ).
fof(aMATRIXu_MULu_VSUM,axiom,
! [N,M,U_0] :
( ! [X,A5,I0] : s(cart(real,M),i(s(fun(num,cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,M))),i(s(fun(cart(real,N),fun(cart(cart(real,N),M),fun(num,cart(real,M)))),U_0),s(cart(real,N),X))),s(cart(cart(real,N),M),A5))),s(num,I0))) = s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),i(s(fun(real,fun(cart(real,M),cart(real,M))),r_),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))))),s(cart(real,M),i(s(fun(cart(cart(real,N),M),cart(real,M)),i(s(fun(num,fun(cart(cart(real,N),M),cart(real,M))),column),s(num,I0))),s(cart(cart(real,N),M),A5)))))
=> ! [A5,X] : s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),A5))),s(cart(real,N),X))) = s(cart(real,M),i(s(fun(fun(num,cart(real,M)),cart(real,M)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,M)),cart(real,M))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))),s(fun(num,cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,M))),i(s(fun(cart(real,N),fun(cart(cart(real,N),M),fun(num,cart(real,M)))),U_0),s(cart(real,N),X))),s(cart(cart(real,N),M),A5))))) ) ).
fof(aVECTORu_COMPONENTWISE,axiom,
! [N,U_1] :
( ! [X,J0,I0] : s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(real,N),fun(num,fun(num,real))),U_1),s(cart(real,N),X))),s(num,J0))),s(num,I0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,I0))))),s(num,J0)))))
=> ! [U_0] :
( ! [X,J0] : s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),U_0),s(cart(real,N),X))),s(num,J0))) = s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))),s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(real,N),fun(num,fun(num,real))),U_1),s(cart(real,N),X))),s(num,J0)))))
=> ! [X] : s(cart(real,N),X) = s(cart(real,N),i(s(fun(fun(num,real),cart(real,N)),lambda),s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),U_0),s(cart(real,N),X))))) ) ) ).
fof(aLINEARu_COMPONENTWISE,axiom,
! [M,N,U_0] :
( ! [X,F0,J0,I0] : s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(num,fun(num,real))),i(s(fun(cart(real,M),fun(fun(cart(real,M),cart(real,N)),fun(num,fun(num,real)))),U_0),s(cart(real,M),X))),s(fun(cart(real,M),cart(real,N)),F0))),s(num,J0))),s(num,I0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),i(s(fun(cart(real,M),fun(num,real)),d_),s(cart(real,M),X))),s(num,I0))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),i(s(fun(num,cart(real,M)),basis),s(num,I0))))))),s(num,J0)))))
=> ! [F0] :
( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
=> ! [X,J0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,J0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,J0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) )
=> s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))),s(num,J0))) = s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ))))))),s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(num,fun(num,real))),i(s(fun(cart(real,M),fun(fun(cart(real,M),cart(real,N)),fun(num,fun(num,real)))),U_0),s(cart(real,M),X))),s(fun(cart(real,M),cart(real,N)),F0))),s(num,J0))))) ) ) ) ).
fof(ainvertible,axiom,
! [M,N,A5] :
( p(s(bool,i(s(fun(cart(cart(real,N),M),bool),invertible),s(cart(cart(real,N),M),A5))))
<=> ? [AI_] :
( s(cart(cart(real,M),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,M),N),cart(cart(real,M),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,M),N),AI_))) = s(cart(cart(real,M),M),i(s(fun(num,cart(cart(real,M),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))
& s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),N)),i(s(fun(cart(cart(real,M),N),fun(cart(cart(real,N),M),cart(cart(real,N),N))),matrixu_mul),s(cart(cart(real,M),N),AI_))),s(cart(cart(real,N),M),A5))) = s(cart(cart(real,N),N),i(s(fun(num,cart(cart(real,N),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) ) ) ).
fof(amatrixu_inv,axiom,
! [N,M,U_0] :
( ! [A5,AI_] :
( p(s(bool,i(s(fun(cart(cart(real,M),N),bool),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,M),N),bool)),U_0),s(cart(cart(real,N),M),A5))),s(cart(cart(real,M),N),AI_))))
<=> ( s(cart(cart(real,M),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,M),N),cart(cart(real,M),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,M),N),AI_))) = s(cart(cart(real,M),M),i(s(fun(num,cart(cart(real,M),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))
& s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),N)),i(s(fun(cart(cart(real,M),N),fun(cart(cart(real,N),M),cart(cart(real,N),N))),matrixu_mul),s(cart(cart(real,M),N),AI_))),s(cart(cart(real,N),M),A5))) = s(cart(cart(real,N),N),i(s(fun(num,cart(cart(real,N),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) ) )
=> ! [A5] : s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),matrixu_inv),s(cart(cart(real,N),M),A5))) = s(cart(cart(real,M),N),i(s(fun(fun(cart(cart(real,M),N),bool),cart(cart(real,M),N)),h_),s(fun(cart(cart(real,M),N),bool),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,M),N),bool)),U_0),s(cart(cart(real,N),M),A5))))) ) ).
fof(aMATRIXu_INV,axiom,
! [M,N,A5] :
( p(s(bool,i(s(fun(cart(cart(real,N),M),bool),invertible),s(cart(cart(real,N),M),A5))))
=> ( s(cart(cart(real,M),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,M),N),cart(cart(real,M),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),matrixu_inv),s(cart(cart(real,N),M),A5))))) = s(cart(cart(real,M),M),i(s(fun(num,cart(cart(real,M),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))
& s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),N)),i(s(fun(cart(cart(real,M),N),fun(cart(cart(real,N),M),cart(cart(real,N),N))),matrixu_mul),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),matrixu_inv),s(cart(cart(real,N),M),A5))))),s(cart(cart(real,N),M),A5))) = s(cart(cart(real,N),N),i(s(fun(num,cart(cart(real,N),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) ) ) ).
fof(amatrix,axiom,
! [M,N,U_1] :
( ! [F0,I0,J0] : s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(num,fun(num,real))),U_1),s(fun(cart(real,M),cart(real,N)),F0))),s(num,I0))),s(num,J0))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),i(s(fun(num,cart(real,M)),basis),s(num,J0))))))),s(num,I0)))
=> ! [U_0] :
( ! [F0,I0] : s(cart(real,M),i(s(fun(num,cart(real,M)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(num,cart(real,M))),U_0),s(fun(cart(real,M),cart(real,N)),F0))),s(num,I0))) = s(cart(real,M),i(s(fun(fun(num,real),cart(real,M)),lambda),s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(num,fun(num,real))),U_1),s(fun(cart(real,M),cart(real,N)),F0))),s(num,I0)))))
=> ! [F0] : s(cart(cart(real,M),N),i(s(fun(fun(cart(real,M),cart(real,N)),cart(cart(real,M),N)),matrix),s(fun(cart(real,M),cart(real,N)),F0))) = s(cart(cart(real,M),N),i(s(fun(fun(num,cart(real,M)),cart(cart(real,M),N)),lambda),s(fun(num,cart(real,M)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(num,cart(real,M))),U_0),s(fun(cart(real,M),cart(real,N)),F0))))) ) ) ).
fof(aMATRIXu_VECTORu_MULu_LINEAR,axiom,
! [N,M,U_0] :
( ! [A5,X] : s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),U_0),s(cart(cart(real,N),M),A5))),s(cart(real,N),X))) = s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),A5))),s(cart(real,N),X)))
=> ! [A5] : p(s(bool,i(s(fun(fun(cart(real,N),cart(real,M)),bool),linear),s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),U_0),s(cart(cart(real,N),M),A5)))))) ) ).
fof(aMATRIXu_WORKS,axiom,
! [N,M,F0] :
( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
=> ! [X] : s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),i(s(fun(fun(cart(real,M),cart(real,N)),cart(cart(real,M),N)),matrix),s(fun(cart(real,M),cart(real,N)),F0))))),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) ) ).
fof(aMATRIXu_VECTORu_MUL,axiom,
! [N,M,F0] :
( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
=> ! [X] : s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),i(s(fun(fun(cart(real,M),cart(real,N)),cart(cart(real,M),N)),matrix),s(fun(cart(real,M),cart(real,N)),F0))))),s(cart(real,M),X))) ) ).
fof(aMATRIXu_OFu_MATRIXu_VECTORu_MUL,axiom,
! [N,M,U_0] :
( ! [A5,X] : s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),U_0),s(cart(cart(real,N),M),A5))),s(cart(real,N),X))) = s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),A5))),s(cart(real,N),X)))
=> ! [A5] : s(cart(cart(real,N),M),i(s(fun(fun(cart(real,N),cart(real,M)),cart(cart(real,N),M)),matrix),s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),U_0),s(cart(cart(real,N),M),A5))))) = s(cart(cart(real,N),M),A5) ) ).
fof(aMATRIXu_COMPOSE,axiom,
! [Q117654,Q117653,Q117652,F0,G0] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q117653),cart(real,Q117652)),bool),linear),s(fun(cart(real,Q117653),cart(real,Q117652)),F0))))
& p(s(bool,i(s(fun(fun(cart(real,Q117652),cart(real,Q117654)),bool),linear),s(fun(cart(real,Q117652),cart(real,Q117654)),G0)))) )
=> s(cart(cart(real,Q117653),Q117654),i(s(fun(fun(cart(real,Q117653),cart(real,Q117654)),cart(cart(real,Q117653),Q117654)),matrix),s(fun(cart(real,Q117653),cart(real,Q117654)),i(s(fun(fun(cart(real,Q117653),cart(real,Q117652)),fun(cart(real,Q117653),cart(real,Q117654))),i(s(fun(fun(cart(real,Q117652),cart(real,Q117654)),fun(fun(cart(real,Q117653),cart(real,Q117652)),fun(cart(real,Q117653),cart(real,Q117654)))),o),s(fun(cart(real,Q117652),cart(real,Q117654)),G0))),s(fun(cart(real,Q117653),cart(real,Q117652)),F0))))) = s(cart(cart(real,Q117653),Q117654),i(s(fun(cart(cart(real,Q117653),Q117652),cart(cart(real,Q117653),Q117654)),i(s(fun(cart(cart(real,Q117652),Q117654),fun(cart(cart(real,Q117653),Q117652),cart(cart(real,Q117653),Q117654))),matrixu_mul),s(cart(cart(real,Q117652),Q117654),i(s(fun(fun(cart(real,Q117652),cart(real,Q117654)),cart(cart(real,Q117652),Q117654)),matrix),s(fun(cart(real,Q117652),cart(real,Q117654)),G0))))),s(cart(cart(real,Q117653),Q117652),i(s(fun(fun(cart(real,Q117653),cart(real,Q117652)),cart(cart(real,Q117653),Q117652)),matrix),s(fun(cart(real,Q117653),cart(real,Q117652)),F0))))) ) ).
fof(aMATRIXu_VECTORu_COLUMN,axiom,
! [N,M,U_0] :
( ! [X,A5,I0] : s(cart(real,M),i(s(fun(num,cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,M))),i(s(fun(cart(real,N),fun(cart(cart(real,N),M),fun(num,cart(real,M)))),U_0),s(cart(real,N),X))),s(cart(cart(real,N),M),A5))),s(num,I0))) = s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),i(s(fun(real,fun(cart(real,M),cart(real,M))),r_),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))))),s(cart(real,M),i(s(fun(num,cart(real,M)),i(s(fun(cart(cart(real,M),N),fun(num,cart(real,M))),d_),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),A5))))),s(num,I0)))))
=> ! [A5,X] : s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),A5))),s(cart(real,N),X))) = s(cart(real,M),i(s(fun(fun(num,cart(real,M)),cart(real,M)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,M)),cart(real,M))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))),s(fun(num,cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,M))),i(s(fun(cart(real,N),fun(cart(cart(real,N),M),fun(num,cart(real,M)))),U_0),s(cart(real,N),X))),s(cart(cart(real,N),M),A5))))) ) ).
fof(aMATRIXu_MULu_COMPONENT,axiom,
! [N,I0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) )
=> s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),N),fun(num,cart(real,N))),d_),s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),N),cart(cart(real,N),N)),i(s(fun(cart(cart(real,N),N),fun(cart(cart(real,N),N),cart(cart(real,N),N))),matrixu_mul),s(cart(cart(real,N),N),a))),s(cart(cart(real,N),N),b))))),s(num,I0))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(cart(real,N),N),fun(cart(real,N),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),N),cart(cart(real,N),N)),transp),s(cart(cart(real,N),N),b))))),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),N),fun(num,cart(real,N))),d_),s(cart(cart(real,N),N),a))),s(num,I0))))) ) ).
fof(aADJOINTu_MATRIX,axiom,
! [N,M,U_0] :
( ! [A5,X] : s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),U_0),s(cart(cart(real,N),M),A5))),s(cart(real,N),X))) = s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),A5))),s(cart(real,N),X)))
=> ! [A5,X] : s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(fun(cart(real,N),cart(real,M)),fun(cart(real,M),cart(real,N))),adjoint),s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),U_0),s(cart(cart(real,N),M),A5))))),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),A5))))),s(cart(real,M),X))) ) ).
fof(aMATRIXu_ADJOINT,axiom,
! [Q117843,Q117844,F0] :
( p(s(bool,i(s(fun(fun(cart(real,Q117843),cart(real,Q117844)),bool),linear),s(fun(cart(real,Q117843),cart(real,Q117844)),F0))))
=> s(cart(cart(real,Q117844),Q117843),i(s(fun(fun(cart(real,Q117844),cart(real,Q117843)),cart(cart(real,Q117844),Q117843)),matrix),s(fun(cart(real,Q117844),cart(real,Q117843)),i(s(fun(fun(cart(real,Q117843),cart(real,Q117844)),fun(cart(real,Q117844),cart(real,Q117843))),adjoint),s(fun(cart(real,Q117843),cart(real,Q117844)),F0))))) = s(cart(cart(real,Q117844),Q117843),i(s(fun(cart(cart(real,Q117843),Q117844),cart(cart(real,Q117844),Q117843)),transp),s(cart(cart(real,Q117843),Q117844),i(s(fun(fun(cart(real,Q117843),cart(real,Q117844)),cart(cart(real,Q117843),Q117844)),matrix),s(fun(cart(real,Q117843),cart(real,Q117844)),F0))))) ) ).
fof(aMATRIXu_ID,axiom,
! [Q117856,U_0] :
( ! [X] : s(cart(real,Q117856),i(s(fun(cart(real,Q117856),cart(real,Q117856)),U_0),s(cart(real,Q117856),X))) = s(cart(real,Q117856),X)
=> s(cart(cart(real,Q117856),Q117856),i(s(fun(fun(cart(real,Q117856),cart(real,Q117856)),cart(cart(real,Q117856),Q117856)),matrix),s(fun(cart(real,Q117856),cart(real,Q117856)),U_0))) = s(cart(cart(real,Q117856),Q117856),i(s(fun(num,cart(cart(real,Q117856),Q117856)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) ) ).
fof(aMATRIXu_I,axiom,
! [Q117867] : s(cart(cart(real,Q117867),Q117867),i(s(fun(fun(cart(real,Q117867),cart(real,Q117867)),cart(cart(real,Q117867),Q117867)),matrix),s(fun(cart(real,Q117867),cart(real,Q117867)),i1))) = s(cart(cart(real,Q117867),Q117867),i(s(fun(num,cart(cart(real,Q117867),Q117867)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) ).
fof(aLINEARu_EQu_MATRIX,axiom,
! [Q117887,Q117888,F0,G0] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q117887),cart(real,Q117888)),bool),linear),s(fun(cart(real,Q117887),cart(real,Q117888)),F0))))
& p(s(bool,i(s(fun(fun(cart(real,Q117887),cart(real,Q117888)),bool),linear),s(fun(cart(real,Q117887),cart(real,Q117888)),G0))))
& s(cart(cart(real,Q117887),Q117888),i(s(fun(fun(cart(real,Q117887),cart(real,Q117888)),cart(cart(real,Q117887),Q117888)),matrix),s(fun(cart(real,Q117887),cart(real,Q117888)),F0))) = s(cart(cart(real,Q117887),Q117888),i(s(fun(fun(cart(real,Q117887),cart(real,Q117888)),cart(cart(real,Q117887),Q117888)),matrix),s(fun(cart(real,Q117887),cart(real,Q117888)),G0))) )
=> s(fun(cart(real,Q117887),cart(real,Q117888)),F0) = s(fun(cart(real,Q117887),cart(real,Q117888)),G0) ) ).
fof(aMATRIXu_SELFu_ADJOINT,axiom,
! [Q117930,F0] :
( p(s(bool,i(s(fun(fun(cart(real,Q117930),cart(real,Q117930)),bool),linear),s(fun(cart(real,Q117930),cart(real,Q117930)),F0))))
=> ( s(fun(cart(real,Q117930),cart(real,Q117930)),i(s(fun(fun(cart(real,Q117930),cart(real,Q117930)),fun(cart(real,Q117930),cart(real,Q117930))),adjoint),s(fun(cart(real,Q117930),cart(real,Q117930)),F0))) = s(fun(cart(real,Q117930),cart(real,Q117930)),F0)
<=> s(cart(cart(real,Q117930),Q117930),i(s(fun(cart(cart(real,Q117930),Q117930),cart(cart(real,Q117930),Q117930)),transp),s(cart(cart(real,Q117930),Q117930),i(s(fun(fun(cart(real,Q117930),cart(real,Q117930)),cart(cart(real,Q117930),Q117930)),matrix),s(fun(cart(real,Q117930),cart(real,Q117930)),F0))))) = s(cart(cart(real,Q117930),Q117930),i(s(fun(fun(cart(real,Q117930),cart(real,Q117930)),cart(cart(real,Q117930),Q117930)),matrix),s(fun(cart(real,Q117930),cart(real,Q117930)),F0))) ) ) ).
fof(aLINEARu_MATRIXu_EXISTS,axiom,
! [N,M,F0] :
( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
<=> ? [A5] :
! [X] : s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),X))) ) ).
fof(aLINEARu_1,axiom,
! [F0] :
( p(s(bool,i(s(fun(fun(cart(real,n10),cart(real,n10)),bool),linear),s(fun(cart(real,n10),cart(real,n10)),F0))))
<=> ? [C0] :
! [X] : s(cart(real,n10),i(s(fun(cart(real,n10),cart(real,n10)),F0),s(cart(real,n10),X))) = s(cart(real,n10),i(s(fun(cart(real,n10),cart(real,n10)),i(s(fun(real,fun(cart(real,n10),cart(real,n10))),r_),s(real,C0))),s(cart(real,n10),X))) ) ).
fof(aonorm,axiom,
! [M,N,U_0] :
( ! [F0,GENR_PVARR_293] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(fun(cart(real,M),cart(real,N)),fun(real,bool)),U_0),s(fun(cart(real,M),cart(real,N)),F0))),s(real,GENR_PVARR_293))))
<=> ? [X,V] :
( ( p(s(bool,V))
<=> s(real,i(s(fun(cart(real,M),real),vectoru_norm),s(cart(real,M),X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) )
& p(s(bool,i(s(fun(real,bool),i(s(fun(bool,fun(real,bool)),i(s(fun(real,fun(bool,fun(real,bool))),setspec),s(real,GENR_PVARR_293))),s(bool,V))),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X)))))))) ) )
=> ! [F0] : s(real,i(s(fun(fun(cart(real,M),cart(real,N)),real),onorm),s(fun(cart(real,M),cart(real,N)),F0))) = s(real,i(s(fun(fun(real,bool),real),sup),s(fun(real,bool),i(s(fun(fun(real,bool),fun(real,bool)),gspec),s(fun(real,bool),i(s(fun(fun(cart(real,M),cart(real,N)),fun(real,bool)),U_0),s(fun(cart(real,M),cart(real,N)),F0))))))) ) ).
fof(aNORMu_BOUNDu_GENERALIZE,axiom,
! [N,M,F0,B0] :
( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
=> ( ! [X] :
( s(real,i(s(fun(cart(real,M),real),vectoru_norm),s(cart(real,M),X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))))),s(real,B0)))) )
<=> ! [X] : p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,B0))),s(real,i(s(fun(cart(real,M),real),vectoru_norm),s(cart(real,M),X)))))))) ) ) ).
fof(aONORM,axiom,
! [M,N,F0] :
( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
=> ( ! [X] : p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(fun(cart(real,M),cart(real,N)),real),onorm),s(fun(cart(real,M),cart(real,N)),F0))))),s(real,i(s(fun(cart(real,M),real),vectoru_norm),s(cart(real,M),X))))))))
& ! [B0] :
( ! [X] : p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,B0))),s(real,i(s(fun(cart(real,M),real),vectoru_norm),s(cart(real,M),X))))))))
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(fun(cart(real,M),cart(real,N)),real),onorm),s(fun(cart(real,M),cart(real,N)),F0))))),s(real,B0)))) ) ) ) ).
fof(aONORMu_POSu_LE,axiom,
! [Q118203,Q118204,F0] :
( p(s(bool,i(s(fun(fun(cart(real,Q118203),cart(real,Q118204)),bool),linear),s(fun(cart(real,Q118203),cart(real,Q118204)),F0))))
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(fun(cart(real,Q118203),cart(real,Q118204)),real),onorm),s(fun(cart(real,Q118203),cart(real,Q118204)),F0)))))) ) ).
fof(aONORMu_EQu_0,axiom,
! [M,N,F0] :
( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
=> ( s(real,i(s(fun(fun(cart(real,M),cart(real,N)),real),onorm),s(fun(cart(real,M),cart(real,N)),F0))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
<=> ! [X] : s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ) ).
fof(aONORMu_CONST,axiom,
! [M,N,U_0] :
( ! [Y,X] : s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,M),cart(real,N))),U_0),s(cart(real,N),Y))),s(cart(real,M),X))) = s(cart(real,N),Y)
=> ! [Y] : s(real,i(s(fun(fun(cart(real,M),cart(real,N)),real),onorm),s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,M),cart(real,N))),U_0),s(cart(real,N),Y))))) = s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),Y))) ) ).
fof(aONORMu_POSu_LT,axiom,
! [Q118333,Q118355,F0] :
( p(s(bool,i(s(fun(fun(cart(real,Q118333),cart(real,Q118355)),bool),linear),s(fun(cart(real,Q118333),cart(real,Q118355)),F0))))
=> ( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(fun(cart(real,Q118333),cart(real,Q118355)),real),onorm),s(fun(cart(real,Q118333),cart(real,Q118355)),F0))))))
<=> ~ ! [X] : s(cart(real,Q118355),i(s(fun(cart(real,Q118333),cart(real,Q118355)),F0),s(cart(real,Q118333),X))) = s(cart(real,Q118355),i(s(fun(num,cart(real,Q118355)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ) ).
fof(aONORMu_COMPOSE,axiom,
! [Q118371,Q118373,Q118374,F0,G0] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q118374),cart(real,Q118371)),bool),linear),s(fun(cart(real,Q118374),cart(real,Q118371)),F0))))
& p(s(bool,i(s(fun(fun(cart(real,Q118373),cart(real,Q118374)),bool),linear),s(fun(cart(real,Q118373),cart(real,Q118374)),G0)))) )
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(fun(cart(real,Q118373),cart(real,Q118371)),real),onorm),s(fun(cart(real,Q118373),cart(real,Q118371)),i(s(fun(fun(cart(real,Q118373),cart(real,Q118374)),fun(cart(real,Q118373),cart(real,Q118371))),i(s(fun(fun(cart(real,Q118374),cart(real,Q118371)),fun(fun(cart(real,Q118373),cart(real,Q118374)),fun(cart(real,Q118373),cart(real,Q118371)))),o),s(fun(cart(real,Q118374),cart(real,Q118371)),F0))),s(fun(cart(real,Q118373),cart(real,Q118374)),G0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(fun(cart(real,Q118374),cart(real,Q118371)),real),onorm),s(fun(cart(real,Q118374),cart(real,Q118371)),F0))))),s(real,i(s(fun(fun(cart(real,Q118373),cart(real,Q118374)),real),onorm),s(fun(cart(real,Q118373),cart(real,Q118374)),G0)))))))) ) ).
fof(aONORMu_NEGu_LEMMA,axiom,
! [Q118409,Q118421,U_0] :
( ! [F0,X] : s(cart(real,Q118421),i(s(fun(cart(real,Q118409),cart(real,Q118421)),i(s(fun(fun(cart(real,Q118409),cart(real,Q118421)),fun(cart(real,Q118409),cart(real,Q118421))),U_0),s(fun(cart(real,Q118409),cart(real,Q118421)),F0))),s(cart(real,Q118409),X))) = s(cart(real,Q118421),i(s(fun(cart(real,Q118421),cart(real,Q118421)),vectoru_neg),s(cart(real,Q118421),i(s(fun(cart(real,Q118409),cart(real,Q118421)),F0),s(cart(real,Q118409),X)))))
=> ! [F0] :
( p(s(bool,i(s(fun(fun(cart(real,Q118409),cart(real,Q118421)),bool),linear),s(fun(cart(real,Q118409),cart(real,Q118421)),F0))))
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(fun(cart(real,Q118409),cart(real,Q118421)),real),onorm),s(fun(cart(real,Q118409),cart(real,Q118421)),i(s(fun(fun(cart(real,Q118409),cart(real,Q118421)),fun(cart(real,Q118409),cart(real,Q118421))),U_0),s(fun(cart(real,Q118409),cart(real,Q118421)),F0))))))),s(real,i(s(fun(fun(cart(real,Q118409),cart(real,Q118421)),real),onorm),s(fun(cart(real,Q118409),cart(real,Q118421)),F0)))))) ) ) ).
fof(aONORMu_NEG,axiom,
! [M,N,U_0] :
( ! [F0,X] : s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),cart(real,N))),U_0),s(fun(cart(real,M),cart(real,N)),F0))),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),vectoru_neg),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X)))))
=> ! [F0] :
( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
=> s(real,i(s(fun(fun(cart(real,M),cart(real,N)),real),onorm),s(fun(cart(real,M),cart(real,N)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),cart(real,N))),U_0),s(fun(cart(real,M),cart(real,N)),F0))))) = s(real,i(s(fun(fun(cart(real,M),cart(real,N)),real),onorm),s(fun(cart(real,M),cart(real,N)),F0))) ) ) ).
fof(aONORMu_TRIANGLE,axiom,
! [M,N,U_0] :
( ! [F0,G0,X] : s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),cart(real,N))),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),cart(real,N)))),U_0),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,M),cart(real,N)),G0))),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),G0),s(cart(real,M),X)))))
=> ! [F0,G0] :
( ( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
& p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),G0)))) )
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(fun(cart(real,M),cart(real,N)),real),onorm),s(fun(cart(real,M),cart(real,N)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),cart(real,N))),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),cart(real,N)))),U_0),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,M),cart(real,N)),G0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(fun(cart(real,M),cart(real,N)),real),onorm),s(fun(cart(real,M),cart(real,N)),F0))))),s(real,i(s(fun(fun(cart(real,M),cart(real,N)),real),onorm),s(fun(cart(real,M),cart(real,N)),G0)))))))) ) ) ).
fof(aONORMu_TRIANGLEu_LE,axiom,
! [Q118562,Q118573,U_0] :
( ! [F0,G0,X] : s(cart(real,Q118573),i(s(fun(cart(real,Q118562),cart(real,Q118573)),i(s(fun(fun(cart(real,Q118562),cart(real,Q118573)),fun(cart(real,Q118562),cart(real,Q118573))),i(s(fun(fun(cart(real,Q118562),cart(real,Q118573)),fun(fun(cart(real,Q118562),cart(real,Q118573)),fun(cart(real,Q118562),cart(real,Q118573)))),U_0),s(fun(cart(real,Q118562),cart(real,Q118573)),F0))),s(fun(cart(real,Q118562),cart(real,Q118573)),G0))),s(cart(real,Q118562),X))) = s(cart(real,Q118573),i(s(fun(cart(real,Q118573),cart(real,Q118573)),i(s(fun(cart(real,Q118573),fun(cart(real,Q118573),cart(real,Q118573))),vectoru_add),s(cart(real,Q118573),i(s(fun(cart(real,Q118562),cart(real,Q118573)),F0),s(cart(real,Q118562),X))))),s(cart(real,Q118573),i(s(fun(cart(real,Q118562),cart(real,Q118573)),G0),s(cart(real,Q118562),X)))))
=> ! [F0,G0] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q118562),cart(real,Q118573)),bool),linear),s(fun(cart(real,Q118562),cart(real,Q118573)),F0))))
& p(s(bool,i(s(fun(fun(cart(real,Q118562),cart(real,Q118573)),bool),linear),s(fun(cart(real,Q118562),cart(real,Q118573)),G0))))
& p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(fun(cart(real,Q118562),cart(real,Q118573)),real),onorm),s(fun(cart(real,Q118562),cart(real,Q118573)),F0))))),s(real,i(s(fun(fun(cart(real,Q118562),cart(real,Q118573)),real),onorm),s(fun(cart(real,Q118562),cart(real,Q118573)),G0))))))),s(real,e0)))) )
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(fun(cart(real,Q118562),cart(real,Q118573)),real),onorm),s(fun(cart(real,Q118562),cart(real,Q118573)),i(s(fun(fun(cart(real,Q118562),cart(real,Q118573)),fun(cart(real,Q118562),cart(real,Q118573))),i(s(fun(fun(cart(real,Q118562),cart(real,Q118573)),fun(fun(cart(real,Q118562),cart(real,Q118573)),fun(cart(real,Q118562),cart(real,Q118573)))),U_0),s(fun(cart(real,Q118562),cart(real,Q118573)),F0))),s(fun(cart(real,Q118562),cart(real,Q118573)),G0))))))),s(real,e0)))) ) ) ).
fof(aONORMu_TRIANGLEu_LT,axiom,
! [Q118614,Q118625,U_0] :
( ! [F0,G0,X] : s(cart(real,Q118625),i(s(fun(cart(real,Q118614),cart(real,Q118625)),i(s(fun(fun(cart(real,Q118614),cart(real,Q118625)),fun(cart(real,Q118614),cart(real,Q118625))),i(s(fun(fun(cart(real,Q118614),cart(real,Q118625)),fun(fun(cart(real,Q118614),cart(real,Q118625)),fun(cart(real,Q118614),cart(real,Q118625)))),U_0),s(fun(cart(real,Q118614),cart(real,Q118625)),F0))),s(fun(cart(real,Q118614),cart(real,Q118625)),G0))),s(cart(real,Q118614),X))) = s(cart(real,Q118625),i(s(fun(cart(real,Q118625),cart(real,Q118625)),i(s(fun(cart(real,Q118625),fun(cart(real,Q118625),cart(real,Q118625))),vectoru_add),s(cart(real,Q118625),i(s(fun(cart(real,Q118614),cart(real,Q118625)),F0),s(cart(real,Q118614),X))))),s(cart(real,Q118625),i(s(fun(cart(real,Q118614),cart(real,Q118625)),G0),s(cart(real,Q118614),X)))))
=> ! [F0,G0] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q118614),cart(real,Q118625)),bool),linear),s(fun(cart(real,Q118614),cart(real,Q118625)),F0))))
& p(s(bool,i(s(fun(fun(cart(real,Q118614),cart(real,Q118625)),bool),linear),s(fun(cart(real,Q118614),cart(real,Q118625)),G0))))
& p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(fun(cart(real,Q118614),cart(real,Q118625)),real),onorm),s(fun(cart(real,Q118614),cart(real,Q118625)),F0))))),s(real,i(s(fun(fun(cart(real,Q118614),cart(real,Q118625)),real),onorm),s(fun(cart(real,Q118614),cart(real,Q118625)),G0))))))),s(real,e0)))) )
=> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(fun(cart(real,Q118614),cart(real,Q118625)),real),onorm),s(fun(cart(real,Q118614),cart(real,Q118625)),i(s(fun(fun(cart(real,Q118614),cart(real,Q118625)),fun(cart(real,Q118614),cart(real,Q118625))),i(s(fun(fun(cart(real,Q118614),cart(real,Q118625)),fun(fun(cart(real,Q118614),cart(real,Q118625)),fun(cart(real,Q118614),cart(real,Q118625)))),U_0),s(fun(cart(real,Q118614),cart(real,Q118625)),F0))),s(fun(cart(real,Q118614),cart(real,Q118625)),G0))))))),s(real,e0)))) ) ) ).
fof(aONORMu_ID,axiom,
! [N,U_0] :
( ! [X] : s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),U_0),s(cart(real,N),X))) = s(cart(real,N),X)
=> s(real,i(s(fun(fun(cart(real,N),cart(real,N)),real),onorm),s(fun(cart(real,N),cart(real,N)),U_0))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) ) ).
fof(aONORMu_I,axiom,
! [N] : s(real,i(s(fun(fun(cart(real,N),cart(real,N)),real),onorm),s(fun(cart(real,N),cart(real,N)),i1))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) ).
fof(alift,axiom,
! [U_0] :
( ! [X,I0] : s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),U_0),s(real,X))),s(num,I0))) = s(real,X)
=> ! [X] : s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X))) = s(cart(real,n10),i(s(fun(fun(num,real),cart(real,n10)),lambda),s(fun(num,real),i(s(fun(real,fun(num,real)),U_0),s(real,X))))) ) ).
fof(adrop,axiom,
! [X] : s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,n10),fun(num,real)),d_),s(cart(real,n10),X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) ).
fof(aLIFTu_COMPONENT,axiom,
! [X] : s(real,i(s(fun(num,real),i(s(fun(cart(real,n10),fun(num,real)),d_),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(real,X) ).
fof(aLIFTu_DROPu_conjunct0,axiom,
! [X] : s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X))))) = s(cart(real,n10),X) ).
fof(aLIFTu_DROPu_conjunct1,axiom,
! [X] : s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X))))) = s(real,X) ).
fof(aIMAGEu_LIFTu_DROPu_conjunct0,axiom,
! [S0] : s(fun(cart(real,n10),bool),i(s(fun(fun(cart(real,n10),bool),fun(cart(real,n10),bool)),i(s(fun(fun(cart(real,n10),cart(real,n10)),fun(fun(cart(real,n10),bool),fun(cart(real,n10),bool))),image),s(fun(cart(real,n10),cart(real,n10)),i(s(fun(fun(cart(real,n10),real),fun(cart(real,n10),cart(real,n10))),i(s(fun(fun(real,cart(real,n10)),fun(fun(cart(real,n10),real),fun(cart(real,n10),cart(real,n10)))),o),s(fun(real,cart(real,n10)),lift))),s(fun(cart(real,n10),real),drop))))),s(fun(cart(real,n10),bool),S0))) = s(fun(cart(real,n10),bool),S0) ).
fof(aIMAGEu_LIFTu_DROPu_conjunct1,axiom,
! [S0] : s(fun(real,bool),i(s(fun(fun(real,bool),fun(real,bool)),i(s(fun(fun(real,real),fun(fun(real,bool),fun(real,bool))),image),s(fun(real,real),i(s(fun(fun(real,cart(real,n10)),fun(real,real)),i(s(fun(fun(cart(real,n10),real),fun(fun(real,cart(real,n10)),fun(real,real))),o),s(fun(cart(real,n10),real),drop))),s(fun(real,cart(real,n10)),lift))))),s(fun(real,bool),S0))) = s(fun(real,bool),S0) ).
fof(aINu_IMAGEu_LIFTu_DROPu_conjunct0,axiom,
! [X,S0] : s(bool,i(s(fun(fun(cart(real,n10),bool),bool),i(s(fun(cart(real,n10),fun(fun(cart(real,n10),bool),bool)),in),s(cart(real,n10),X))),s(fun(cart(real,n10),bool),i(s(fun(fun(real,bool),fun(cart(real,n10),bool)),i(s(fun(fun(real,cart(real,n10)),fun(fun(real,bool),fun(cart(real,n10),bool))),image),s(fun(real,cart(real,n10)),lift))),s(fun(real,bool),S0))))) = s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X))))),s(fun(real,bool),S0))) ).
fof(aINu_IMAGEu_LIFTu_DROPu_conjunct1,axiom,
! [X,S0] : s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),i(s(fun(fun(cart(real,n10),bool),fun(real,bool)),i(s(fun(fun(cart(real,n10),real),fun(fun(cart(real,n10),bool),fun(real,bool))),image),s(fun(cart(real,n10),real),drop))),s(fun(cart(real,n10),bool),S0))))) = s(bool,i(s(fun(fun(cart(real,n10),bool),bool),i(s(fun(cart(real,n10),fun(fun(cart(real,n10),bool),bool)),in),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X))))),s(fun(cart(real,n10),bool),S0))) ).
fof(aFORALLu_LIFT,axiom,
( ! [X] : p(s(bool,i(s(fun(cart(real,n10),bool),p0),s(cart(real,n10),X))))
<=> ! [X] : p(s(bool,i(s(fun(cart(real,n10),bool),p0),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X)))))) ) ).
fof(aEXISTSu_LIFT,axiom,
( ? [X] : p(s(bool,i(s(fun(cart(real,n10),bool),p0),s(cart(real,n10),X))))
<=> ? [X] : p(s(bool,i(s(fun(cart(real,n10),bool),p0),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X)))))) ) ).
fof(aFORALLu_DROP,axiom,
( ! [X] : p(s(bool,i(s(fun(real,bool),p0),s(real,X))))
<=> ! [X] : p(s(bool,i(s(fun(real,bool),p0),s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X)))))) ) ).
fof(aEXISTSu_DROP,axiom,
( ? [X] : p(s(bool,i(s(fun(real,bool),p0),s(real,X))))
<=> ? [X] : p(s(bool,i(s(fun(real,bool),p0),s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X)))))) ) ).
fof(aFORALLu_LIFTu_FUN,axiom,
! [A,P0] :
( ! [F0] : p(s(bool,i(s(fun(fun(A,cart(real,n10)),bool),P0),s(fun(A,cart(real,n10)),F0))))
<=> ! [F0] : p(s(bool,i(s(fun(fun(A,cart(real,n10)),bool),P0),s(fun(A,cart(real,n10)),i(s(fun(fun(A,real),fun(A,cart(real,n10))),i(s(fun(fun(real,cart(real,n10)),fun(fun(A,real),fun(A,cart(real,n10)))),o),s(fun(real,cart(real,n10)),lift))),s(fun(A,real),F0)))))) ) ).
fof(aFORALLu_DROPu_FUN,axiom,
! [A,P0] :
( ! [F0] : p(s(bool,i(s(fun(fun(A,real),bool),P0),s(fun(A,real),F0))))
<=> ! [F0] : p(s(bool,i(s(fun(fun(A,real),bool),P0),s(fun(A,real),i(s(fun(fun(A,cart(real,n10)),fun(A,real)),i(s(fun(fun(cart(real,n10),real),fun(fun(A,cart(real,n10)),fun(A,real))),o),s(fun(cart(real,n10),real),drop))),s(fun(A,cart(real,n10)),F0)))))) ) ).
fof(aEXISTSu_LIFTu_FUN,axiom,
! [A,P0] :
( ? [F0] : p(s(bool,i(s(fun(fun(A,cart(real,n10)),bool),P0),s(fun(A,cart(real,n10)),F0))))
<=> ? [F0] : p(s(bool,i(s(fun(fun(A,cart(real,n10)),bool),P0),s(fun(A,cart(real,n10)),i(s(fun(fun(A,real),fun(A,cart(real,n10))),i(s(fun(fun(real,cart(real,n10)),fun(fun(A,real),fun(A,cart(real,n10)))),o),s(fun(real,cart(real,n10)),lift))),s(fun(A,real),F0)))))) ) ).
fof(aEXISTSu_DROPu_FUN,axiom,
! [A,P0] :
( ? [F0] : p(s(bool,i(s(fun(fun(A,real),bool),P0),s(fun(A,real),F0))))
<=> ? [F0] : p(s(bool,i(s(fun(fun(A,real),bool),P0),s(fun(A,real),i(s(fun(fun(A,cart(real,n10)),fun(A,real)),i(s(fun(fun(cart(real,n10),real),fun(fun(A,cart(real,n10)),fun(A,real))),o),s(fun(cart(real,n10),real),drop))),s(fun(A,cart(real,n10)),F0)))))) ) ).
fof(aLIFTu_EQ,axiom,
! [X,Y] :
( s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X))) = s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,Y)))
<=> s(real,X) = s(real,Y) ) ).
fof(aDROPu_EQ,axiom,
! [X,Y] :
( s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X))) = s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),Y)))
<=> s(cart(real,n10),X) = s(cart(real,n10),Y) ) ).
fof(aLIFTu_INu_IMAGEu_LIFT,axiom,
! [X,S0] : s(bool,i(s(fun(fun(cart(real,n10),bool),bool),i(s(fun(cart(real,n10),fun(fun(cart(real,n10),bool),bool)),in),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X))))),s(fun(cart(real,n10),bool),i(s(fun(fun(real,bool),fun(cart(real,n10),bool)),i(s(fun(fun(real,cart(real,n10)),fun(fun(real,bool),fun(cart(real,n10),bool))),image),s(fun(real,cart(real,n10)),lift))),s(fun(real,bool),S0))))) = s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0))) ).
fof(aFORALLu_LIFTu_IMAGE,axiom,
! [P0] :
( ! [S0] : p(s(bool,i(s(fun(fun(cart(real,n10),bool),bool),P0),s(fun(cart(real,n10),bool),S0))))
<=> ! [S0] : p(s(bool,i(s(fun(fun(cart(real,n10),bool),bool),P0),s(fun(cart(real,n10),bool),i(s(fun(fun(real,bool),fun(cart(real,n10),bool)),i(s(fun(fun(real,cart(real,n10)),fun(fun(real,bool),fun(cart(real,n10),bool))),image),s(fun(real,cart(real,n10)),lift))),s(fun(real,bool),S0)))))) ) ).
fof(aEXISTSu_LIFTu_IMAGE,axiom,
! [P0] :
( ? [S0] : p(s(bool,i(s(fun(fun(cart(real,n10),bool),bool),P0),s(fun(cart(real,n10),bool),S0))))
<=> ? [S0] : p(s(bool,i(s(fun(fun(cart(real,n10),bool),bool),P0),s(fun(cart(real,n10),bool),i(s(fun(fun(real,bool),fun(cart(real,n10),bool)),i(s(fun(fun(real,cart(real,n10)),fun(fun(real,bool),fun(cart(real,n10),bool))),image),s(fun(real,cart(real,n10)),lift))),s(fun(real,bool),S0)))))) ) ).
fof(aSUBSETu_LIFTu_IMAGE,axiom,
! [S0,T0] : s(bool,i(s(fun(fun(cart(real,n10),bool),bool),i(s(fun(fun(cart(real,n10),bool),fun(fun(cart(real,n10),bool),bool)),subset),s(fun(cart(real,n10),bool),i(s(fun(fun(real,bool),fun(cart(real,n10),bool)),i(s(fun(fun(real,cart(real,n10)),fun(fun(real,bool),fun(cart(real,n10),bool))),image),s(fun(real,cart(real,n10)),lift))),s(fun(real,bool),S0))))),s(fun(cart(real,n10),bool),i(s(fun(fun(real,bool),fun(cart(real,n10),bool)),i(s(fun(fun(real,cart(real,n10)),fun(fun(real,bool),fun(cart(real,n10),bool))),image),s(fun(real,cart(real,n10)),lift))),s(fun(real,bool),T0))))) = s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(fun(real,bool),fun(fun(real,bool),bool)),subset),s(fun(real,bool),S0))),s(fun(real,bool),T0))) ).
fof(aFORALLu_DROPu_IMAGE,axiom,
! [P0] :
( ! [S0] : p(s(bool,i(s(fun(fun(real,bool),bool),P0),s(fun(real,bool),S0))))
<=> ! [S0] : p(s(bool,i(s(fun(fun(real,bool),bool),P0),s(fun(real,bool),i(s(fun(fun(cart(real,n10),bool),fun(real,bool)),i(s(fun(fun(cart(real,n10),real),fun(fun(cart(real,n10),bool),fun(real,bool))),image),s(fun(cart(real,n10),real),drop))),s(fun(cart(real,n10),bool),S0)))))) ) ).
fof(aEXISTSu_DROPu_IMAGE,axiom,
! [P0] :
( ? [S0] : p(s(bool,i(s(fun(fun(real,bool),bool),P0),s(fun(real,bool),S0))))
<=> ? [S0] : p(s(bool,i(s(fun(fun(real,bool),bool),P0),s(fun(real,bool),i(s(fun(fun(cart(real,n10),bool),fun(real,bool)),i(s(fun(fun(cart(real,n10),real),fun(fun(cart(real,n10),bool),fun(real,bool))),image),s(fun(cart(real,n10),real),drop))),s(fun(cart(real,n10),bool),S0)))))) ) ).
fof(aSUBSETu_DROPu_IMAGE,axiom,
! [S0,T0] : s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(fun(real,bool),fun(fun(real,bool),bool)),subset),s(fun(real,bool),i(s(fun(fun(cart(real,n10),bool),fun(real,bool)),i(s(fun(fun(cart(real,n10),real),fun(fun(cart(real,n10),bool),fun(real,bool))),image),s(fun(cart(real,n10),real),drop))),s(fun(cart(real,n10),bool),S0))))),s(fun(real,bool),i(s(fun(fun(cart(real,n10),bool),fun(real,bool)),i(s(fun(fun(cart(real,n10),real),fun(fun(cart(real,n10),bool),fun(real,bool))),image),s(fun(cart(real,n10),real),drop))),s(fun(cart(real,n10),bool),T0))))) = s(bool,i(s(fun(fun(cart(real,n10),bool),bool),i(s(fun(fun(cart(real,n10),bool),fun(fun(cart(real,n10),bool),bool)),subset),s(fun(cart(real,n10),bool),S0))),s(fun(cart(real,n10),bool),T0))) ).
fof(aDROPu_INu_IMAGEu_DROP,axiom,
! [X,S0] : s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X))))),s(fun(real,bool),i(s(fun(fun(cart(real,n10),bool),fun(real,bool)),i(s(fun(fun(cart(real,n10),real),fun(fun(cart(real,n10),bool),fun(real,bool))),image),s(fun(cart(real,n10),real),drop))),s(fun(cart(real,n10),bool),S0))))) = s(bool,i(s(fun(fun(cart(real,n10),bool),bool),i(s(fun(cart(real,n10),fun(fun(cart(real,n10),bool),bool)),in),s(cart(real,n10),X))),s(fun(cart(real,n10),bool),S0))) ).
fof(aLIFTu_NUM,axiom,
! [N0] : s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0))))) = s(cart(real,n10),i(s(fun(num,cart(real,n10)),vec),s(num,N0))) ).
fof(aLIFTu_ADD,axiom,
! [X,Y] : s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Y))))) = s(cart(real,n10),i(s(fun(cart(real,n10),cart(real,n10)),i(s(fun(cart(real,n10),fun(cart(real,n10),cart(real,n10))),vectoru_add),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X))))),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,Y))))) ).
fof(aLIFTu_SUB,axiom,
! [X,Y] : s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,Y))))) = s(cart(real,n10),i(s(fun(cart(real,n10),cart(real,n10)),i(s(fun(cart(real,n10),fun(cart(real,n10),cart(real,n10))),vectoru_sub),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X))))),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,Y))))) ).
fof(aLIFTu_CMUL,axiom,
! [X,C0] : s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,C0))),s(real,X))))) = s(cart(real,n10),i(s(fun(cart(real,n10),cart(real,n10)),i(s(fun(real,fun(cart(real,n10),cart(real,n10))),r_),s(real,C0))),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X))))) ).
fof(aLIFTu_NEG,axiom,
! [X] : s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,i(s(fun(real,real),realu_neg),s(real,X))))) = s(cart(real,n10),i(s(fun(cart(real,n10),cart(real,n10)),vectoru_neg),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X))))) ).
fof(aLIFTu_EQu_CMUL,axiom,
! [X] : s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X))) = s(cart(real,n10),i(s(fun(cart(real,n10),cart(real,n10)),i(s(fun(real,fun(cart(real,n10),cart(real,n10))),r_),s(real,X))),s(cart(real,n10),i(s(fun(num,cart(real,n10)),vec),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) ).
fof(aLIFTu_SUM,axiom,
! [Q119381,K0,X] :
( p(s(bool,i(s(fun(fun(Q119381,bool),bool),finite),s(fun(Q119381,bool),K0))))
=> s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,i(s(fun(fun(Q119381,real),real),i(s(fun(fun(Q119381,bool),fun(fun(Q119381,real),real)),sum),s(fun(Q119381,bool),K0))),s(fun(Q119381,real),X))))) = s(cart(real,n10),i(s(fun(fun(Q119381,cart(real,n10)),cart(real,n10)),i(s(fun(fun(Q119381,bool),fun(fun(Q119381,cart(real,n10)),cart(real,n10))),vsum),s(fun(Q119381,bool),K0))),s(fun(Q119381,cart(real,n10)),i(s(fun(fun(Q119381,real),fun(Q119381,cart(real,n10))),i(s(fun(fun(real,cart(real,n10)),fun(fun(Q119381,real),fun(Q119381,cart(real,n10)))),o),s(fun(real,cart(real,n10)),lift))),s(fun(Q119381,real),X))))) ) ).
fof(aDROPu_LAMBDA,axiom,
! [U_0] :
( ! [X,I0] : s(real,i(s(fun(num,real),i(s(fun(fun(num,real),fun(num,real)),U_0),s(fun(num,real),X))),s(num,I0))) = s(real,i(s(fun(num,real),X),s(num,I0)))
=> ! [X] : s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),i(s(fun(fun(num,real),cart(real,n10)),lambda),s(fun(num,real),i(s(fun(fun(num,real),fun(num,real)),U_0),s(fun(num,real),X))))))) = s(real,i(s(fun(num,real),X),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) ) ).
fof(aDROPu_VEC,axiom,
! [N0] : s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),i(s(fun(num,cart(real,n10)),vec),s(num,N0))))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0))) ).
fof(aDROPu_ADD,axiom,
! [X,Y] : s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),i(s(fun(cart(real,n10),cart(real,n10)),i(s(fun(cart(real,n10),fun(cart(real,n10),cart(real,n10))),vectoru_add),s(cart(real,n10),X))),s(cart(real,n10),Y))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X))))),s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),Y))))) ).
fof(aDROPu_SUB,axiom,
! [X,Y] : s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),i(s(fun(cart(real,n10),cart(real,n10)),i(s(fun(cart(real,n10),fun(cart(real,n10),cart(real,n10))),vectoru_sub),s(cart(real,n10),X))),s(cart(real,n10),Y))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X))))),s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),Y))))) ).
fof(aDROPu_CMUL,axiom,
! [X,C0] : s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),i(s(fun(cart(real,n10),cart(real,n10)),i(s(fun(real,fun(cart(real,n10),cart(real,n10))),r_),s(real,C0))),s(cart(real,n10),X))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,C0))),s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X))))) ).
fof(aDROPu_NEG,axiom,
! [X] : s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),i(s(fun(cart(real,n10),cart(real,n10)),vectoru_neg),s(cart(real,n10),X))))) = s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X))))) ).
fof(aDROPu_VSUM,axiom,
! [Q119533,K0,X] :
( p(s(bool,i(s(fun(fun(Q119533,bool),bool),finite),s(fun(Q119533,bool),K0))))
=> s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),i(s(fun(fun(Q119533,cart(real,n10)),cart(real,n10)),i(s(fun(fun(Q119533,bool),fun(fun(Q119533,cart(real,n10)),cart(real,n10))),vsum),s(fun(Q119533,bool),K0))),s(fun(Q119533,cart(real,n10)),X))))) = s(real,i(s(fun(fun(Q119533,real),real),i(s(fun(fun(Q119533,bool),fun(fun(Q119533,real),real)),sum),s(fun(Q119533,bool),K0))),s(fun(Q119533,real),i(s(fun(fun(Q119533,cart(real,n10)),fun(Q119533,real)),i(s(fun(fun(cart(real,n10),real),fun(fun(Q119533,cart(real,n10)),fun(Q119533,real))),o),s(fun(cart(real,n10),real),drop))),s(fun(Q119533,cart(real,n10)),X))))) ) ).
fof(aABSu_DROP,axiom,
! [X] : s(real,i(s(fun(cart(real,n10),real),vectoru_norm),s(cart(real,n10),X))) = s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X))))) ).
fof(aNORMu_1u_POS,axiom,
! [X] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X))))))
=> s(real,i(s(fun(cart(real,n10),real),vectoru_norm),s(cart(real,n10),X))) = s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X))) ) ).
fof(aNORMu_LIFT,axiom,
! [X] : s(real,i(s(fun(cart(real,n10),real),vectoru_norm),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X))))) = s(real,i(s(fun(real,real),realu_abs),s(real,X))) ).
fof(aDISTu_LIFT,axiom,
! [X,Y] : s(real,i(s(fun(prod(cart(real,n10),cart(real,n10)),real),distance),s(prod(cart(real,n10),cart(real,n10)),i(s(fun(cart(real,n10),prod(cart(real,n10),cart(real,n10))),i(s(fun(cart(real,n10),fun(cart(real,n10),prod(cart(real,n10),cart(real,n10)))),c_),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X))))),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,Y))))))) = s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,Y))))) ).
fof(aLINEARu_VMULu_DROP,axiom,
! [Q119643,Q119649,U_0] :
( ! [F0,V,X] : s(cart(real,Q119649),i(s(fun(cart(real,Q119643),cart(real,Q119649)),i(s(fun(cart(real,Q119649),fun(cart(real,Q119643),cart(real,Q119649))),i(s(fun(fun(cart(real,Q119643),cart(real,n10)),fun(cart(real,Q119649),fun(cart(real,Q119643),cart(real,Q119649)))),U_0),s(fun(cart(real,Q119643),cart(real,n10)),F0))),s(cart(real,Q119649),V))),s(cart(real,Q119643),X))) = s(cart(real,Q119649),i(s(fun(cart(real,Q119649),cart(real,Q119649)),i(s(fun(real,fun(cart(real,Q119649),cart(real,Q119649))),r_),s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),i(s(fun(cart(real,Q119643),cart(real,n10)),F0),s(cart(real,Q119643),X))))))),s(cart(real,Q119649),V)))
=> ! [F0,V] :
( p(s(bool,i(s(fun(fun(cart(real,Q119643),cart(real,n10)),bool),linear),s(fun(cart(real,Q119643),cart(real,n10)),F0))))
=> p(s(bool,i(s(fun(fun(cart(real,Q119643),cart(real,Q119649)),bool),linear),s(fun(cart(real,Q119643),cart(real,Q119649)),i(s(fun(cart(real,Q119649),fun(cart(real,Q119643),cart(real,Q119649))),i(s(fun(fun(cart(real,Q119643),cart(real,n10)),fun(cart(real,Q119649),fun(cart(real,Q119643),cart(real,Q119649)))),U_0),s(fun(cart(real,Q119643),cart(real,n10)),F0))),s(cart(real,Q119649),V)))))) ) ) ).
fof(aLINEARu_FROMu_REALS,axiom,
! [N,F0] :
( p(s(bool,i(s(fun(fun(cart(real,n10),cart(real,N)),bool),linear),s(fun(cart(real,n10),cart(real,N)),F0))))
=> ! [X] : s(cart(real,N),i(s(fun(cart(real,n10),cart(real,N)),F0),s(cart(real,n10),X))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X))))),s(cart(real,N),i(s(fun(cart(cart(real,n10),N),cart(real,N)),i(s(fun(num,fun(cart(cart(real,n10),N),cart(real,N))),column),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(cart(cart(real,n10),N),i(s(fun(fun(cart(real,n10),cart(real,N)),cart(cart(real,n10),N)),matrix),s(fun(cart(real,n10),cart(real,N)),F0))))))) ) ).
fof(aLINEARu_TOu_REALS,axiom,
! [N,F0] :
( p(s(bool,i(s(fun(fun(cart(real,N),cart(real,n10)),bool),linear),s(fun(cart(real,N),cart(real,n10)),F0))))
=> ! [X] : s(cart(real,n10),i(s(fun(cart(real,N),cart(real,n10)),F0),s(cart(real,N),X))) = s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),i(s(fun(cart(cart(real,N),n10),cart(real,N)),i(s(fun(num,fun(cart(cart(real,N),n10),cart(real,N))),row),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(cart(cart(real,N),n10),i(s(fun(fun(cart(real,N),cart(real,n10)),cart(cart(real,N),n10)),matrix),s(fun(cart(real,N),cart(real,n10)),F0))))))),s(cart(real,N),X))))) ) ).
fof(aDROPu_EQu_0,axiom,
! [X] :
( s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
<=> s(cart(real,n10),X) = s(cart(real,n10),i(s(fun(num,cart(real,n10)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ).
fof(aVSUMu_REAL,axiom,
! [Q119749,F0,S0] :
( p(s(bool,i(s(fun(fun(Q119749,bool),bool),finite),s(fun(Q119749,bool),S0))))
=> s(cart(real,n10),i(s(fun(fun(Q119749,cart(real,n10)),cart(real,n10)),i(s(fun(fun(Q119749,bool),fun(fun(Q119749,cart(real,n10)),cart(real,n10))),vsum),s(fun(Q119749,bool),S0))),s(fun(Q119749,cart(real,n10)),F0))) = s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,i(s(fun(fun(Q119749,real),real),i(s(fun(fun(Q119749,bool),fun(fun(Q119749,real),real)),sum),s(fun(Q119749,bool),S0))),s(fun(Q119749,real),i(s(fun(fun(Q119749,cart(real,n10)),fun(Q119749,real)),i(s(fun(fun(cart(real,n10),real),fun(fun(Q119749,cart(real,n10)),fun(Q119749,real))),o),s(fun(cart(real,n10),real),drop))),s(fun(Q119749,cart(real,n10)),F0))))))) ) ).
fof(aDROPu_WLOGu_LE,axiom,
( ( ! [X,Y] : s(bool,i(s(fun(cart(real,n10),bool),i(s(fun(cart(real,n10),fun(cart(real,n10),bool)),p0),s(cart(real,n10),X))),s(cart(real,n10),Y))) = s(bool,i(s(fun(cart(real,n10),bool),i(s(fun(cart(real,n10),fun(cart(real,n10),bool)),p0),s(cart(real,n10),Y))),s(cart(real,n10),X)))
& ! [X,Y] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X))))),s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),Y))))))
=> p(s(bool,i(s(fun(cart(real,n10),bool),i(s(fun(cart(real,n10),fun(cart(real,n10),bool)),p0),s(cart(real,n10),X))),s(cart(real,n10),Y)))) ) )
=> ! [X,Y] : p(s(bool,i(s(fun(cart(real,n10),bool),i(s(fun(cart(real,n10),fun(cart(real,n10),bool)),p0),s(cart(real,n10),X))),s(cart(real,n10),Y)))) ) ).
fof(aIMAGEu_LIFTu_UNIV,axiom,
s(fun(cart(real,n10),bool),i(s(fun(fun(real,bool),fun(cart(real,n10),bool)),i(s(fun(fun(real,cart(real,n10)),fun(fun(real,bool),fun(cart(real,n10),bool))),image),s(fun(real,cart(real,n10)),lift))),s(fun(real,bool),univ))) = s(fun(cart(real,n10),bool),univ) ).
fof(aIMAGEu_DROPu_UNIV,axiom,
s(fun(real,bool),i(s(fun(fun(cart(real,n10),bool),fun(real,bool)),i(s(fun(fun(cart(real,n10),real),fun(fun(cart(real,n10),bool),fun(real,bool))),image),s(fun(cart(real,n10),real),drop))),s(fun(cart(real,n10),bool),univ))) = s(fun(real,bool),univ) ).
fof(aSUMu_VSUM,axiom,
! [Q119844,F0,S0] :
( p(s(bool,i(s(fun(fun(Q119844,bool),bool),finite),s(fun(Q119844,bool),S0))))
=> s(real,i(s(fun(fun(Q119844,real),real),i(s(fun(fun(Q119844,bool),fun(fun(Q119844,real),real)),sum),s(fun(Q119844,bool),S0))),s(fun(Q119844,real),F0))) = s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),i(s(fun(fun(Q119844,cart(real,n10)),cart(real,n10)),i(s(fun(fun(Q119844,bool),fun(fun(Q119844,cart(real,n10)),cart(real,n10))),vsum),s(fun(Q119844,bool),S0))),s(fun(Q119844,cart(real,n10)),i(s(fun(fun(Q119844,real),fun(Q119844,cart(real,n10))),i(s(fun(fun(real,cart(real,n10)),fun(fun(Q119844,real),fun(Q119844,cart(real,n10)))),o),s(fun(real,cart(real,n10)),lift))),s(fun(Q119844,real),F0))))))) ) ).
fof(aLINEARu_LIFTu_DOT,axiom,
! [Q119852,U_0] :
( ! [A5,X] : s(cart(real,n10),i(s(fun(cart(real,Q119852),cart(real,n10)),i(s(fun(cart(real,Q119852),fun(cart(real,Q119852),cart(real,n10))),U_0),s(cart(real,Q119852),A5))),s(cart(real,Q119852),X))) = s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,i(s(fun(cart(real,Q119852),real),i(s(fun(cart(real,Q119852),fun(cart(real,Q119852),real)),dot),s(cart(real,Q119852),A5))),s(cart(real,Q119852),X)))))
=> ! [A5] : p(s(bool,i(s(fun(fun(cart(real,Q119852),cart(real,n10)),bool),linear),s(fun(cart(real,Q119852),cart(real,n10)),i(s(fun(cart(real,Q119852),fun(cart(real,Q119852),cart(real,n10))),U_0),s(cart(real,Q119852),A5)))))) ) ).
fof(aLINEARu_LIFTu_COMPONENT,axiom,
! [N,U_0] :
( ! [K0,X] : s(cart(real,n10),i(s(fun(cart(real,N),cart(real,n10)),i(s(fun(num,fun(cart(real,N),cart(real,n10))),U_0),s(num,K0))),s(cart(real,N),X))) = s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,K0)))))
=> ! [K0] : p(s(bool,i(s(fun(fun(cart(real,N),cart(real,n10)),bool),linear),s(fun(cart(real,N),cart(real,n10)),i(s(fun(num,fun(cart(real,N),cart(real,n10))),U_0),s(num,K0)))))) ) ).
fof(aLINEARu_FSTCART,axiom,
! [Q119933,Q119935] : p(s(bool,i(s(fun(fun(cart(real,finite_sum(Q119935,Q119933)),cart(real,Q119935)),bool),linear),s(fun(cart(real,finite_sum(Q119935,Q119933)),cart(real,Q119935)),fstcart)))) ).
fof(aLINEARu_SNDCART,axiom,
! [Q119985,Q119987] : p(s(bool,i(s(fun(fun(cart(real,finite_sum(Q119985,Q119987)),cart(real,Q119987)),bool),linear),s(fun(cart(real,finite_sum(Q119985,Q119987)),cart(real,Q119987)),sndcart)))) ).
fof(aFSTCARTu_VEC,axiom,
! [Q120015,Q120021,N0] : s(cart(real,Q120021),i(s(fun(cart(real,finite_sum(Q120021,Q120015)),cart(real,Q120021)),fstcart),s(cart(real,finite_sum(Q120021,Q120015)),i(s(fun(num,cart(real,finite_sum(Q120021,Q120015))),vec),s(num,N0))))) = s(cart(real,Q120021),i(s(fun(num,cart(real,Q120021)),vec),s(num,N0))) ).
fof(aFSTCARTu_ADD,axiom,
! [M,N,X,Y] : s(cart(real,M),i(s(fun(cart(real,finite_sum(M,N)),cart(real,M)),fstcart),s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N))),i(s(fun(cart(real,finite_sum(M,N)),fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N)))),vectoru_add),s(cart(real,finite_sum(M,N)),X))),s(cart(real,finite_sum(M,N)),Y))))) = s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),i(s(fun(cart(real,M),fun(cart(real,M),cart(real,M))),vectoru_add),s(cart(real,M),i(s(fun(cart(real,finite_sum(M,N)),cart(real,M)),fstcart),s(cart(real,finite_sum(M,N)),X))))),s(cart(real,M),i(s(fun(cart(real,finite_sum(M,N)),cart(real,M)),fstcart),s(cart(real,finite_sum(M,N)),Y))))) ).
fof(aFSTCARTu_CMUL,axiom,
! [M,N,X,C0] : s(cart(real,M),i(s(fun(cart(real,finite_sum(M,N)),cart(real,M)),fstcart),s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N))),i(s(fun(real,fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N)))),r_),s(real,C0))),s(cart(real,finite_sum(M,N)),X))))) = s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),i(s(fun(real,fun(cart(real,M),cart(real,M))),r_),s(real,C0))),s(cart(real,M),i(s(fun(cart(real,finite_sum(M,N)),cart(real,M)),fstcart),s(cart(real,finite_sum(M,N)),X))))) ).
fof(aFSTCARTu_NEG,axiom,
! [M,N,X] : s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),vectoru_neg),s(cart(real,M),i(s(fun(cart(real,finite_sum(M,N)),cart(real,M)),fstcart),s(cart(real,finite_sum(M,N)),X))))) = s(cart(real,M),i(s(fun(cart(real,finite_sum(M,N)),cart(real,M)),fstcart),s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N))),vectoru_neg),s(cart(real,finite_sum(M,N)),X))))) ).
fof(aFSTCARTu_SUB,axiom,
! [M,N,X,Y] : s(cart(real,M),i(s(fun(cart(real,finite_sum(M,N)),cart(real,M)),fstcart),s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N))),i(s(fun(cart(real,finite_sum(M,N)),fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N)))),vectoru_sub),s(cart(real,finite_sum(M,N)),X))),s(cart(real,finite_sum(M,N)),Y))))) = s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),i(s(fun(cart(real,M),fun(cart(real,M),cart(real,M))),vectoru_sub),s(cart(real,M),i(s(fun(cart(real,finite_sum(M,N)),cart(real,M)),fstcart),s(cart(real,finite_sum(M,N)),X))))),s(cart(real,M),i(s(fun(cart(real,finite_sum(M,N)),cart(real,M)),fstcart),s(cart(real,finite_sum(M,N)),Y))))) ).
fof(aFSTCARTu_VSUM,axiom,
! [Q120217,Q120216,Q120214,U_0] :
( ! [X,I0] : s(cart(real,Q120216),i(s(fun(Q120217,cart(real,Q120216)),i(s(fun(fun(Q120217,cart(real,finite_sum(Q120216,Q120214))),fun(Q120217,cart(real,Q120216))),U_0),s(fun(Q120217,cart(real,finite_sum(Q120216,Q120214))),X))),s(Q120217,I0))) = s(cart(real,Q120216),i(s(fun(cart(real,finite_sum(Q120216,Q120214)),cart(real,Q120216)),fstcart),s(cart(real,finite_sum(Q120216,Q120214)),i(s(fun(Q120217,cart(real,finite_sum(Q120216,Q120214))),X),s(Q120217,I0)))))
=> ! [K0,X] :
( p(s(bool,i(s(fun(fun(Q120217,bool),bool),finite),s(fun(Q120217,bool),K0))))
=> s(cart(real,Q120216),i(s(fun(cart(real,finite_sum(Q120216,Q120214)),cart(real,Q120216)),fstcart),s(cart(real,finite_sum(Q120216,Q120214)),i(s(fun(fun(Q120217,cart(real,finite_sum(Q120216,Q120214))),cart(real,finite_sum(Q120216,Q120214))),i(s(fun(fun(Q120217,bool),fun(fun(Q120217,cart(real,finite_sum(Q120216,Q120214))),cart(real,finite_sum(Q120216,Q120214)))),vsum),s(fun(Q120217,bool),K0))),s(fun(Q120217,cart(real,finite_sum(Q120216,Q120214))),X))))) = s(cart(real,Q120216),i(s(fun(fun(Q120217,cart(real,Q120216)),cart(real,Q120216)),i(s(fun(fun(Q120217,bool),fun(fun(Q120217,cart(real,Q120216)),cart(real,Q120216))),vsum),s(fun(Q120217,bool),K0))),s(fun(Q120217,cart(real,Q120216)),i(s(fun(fun(Q120217,cart(real,finite_sum(Q120216,Q120214))),fun(Q120217,cart(real,Q120216))),U_0),s(fun(Q120217,cart(real,finite_sum(Q120216,Q120214))),X))))) ) ) ).
fof(aSNDCARTu_VEC,axiom,
! [Q120272,Q120278,N0] : s(cart(real,Q120278),i(s(fun(cart(real,finite_sum(Q120272,Q120278)),cart(real,Q120278)),sndcart),s(cart(real,finite_sum(Q120272,Q120278)),i(s(fun(num,cart(real,finite_sum(Q120272,Q120278))),vec),s(num,N0))))) = s(cart(real,Q120278),i(s(fun(num,cart(real,Q120278)),vec),s(num,N0))) ).
fof(aSNDCARTu_ADD,axiom,
! [M,N,X,Y] : s(cart(real,N),i(s(fun(cart(real,finite_sum(M,N)),cart(real,N)),sndcart),s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N))),i(s(fun(cart(real,finite_sum(M,N)),fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N)))),vectoru_add),s(cart(real,finite_sum(M,N)),X))),s(cart(real,finite_sum(M,N)),Y))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(cart(real,finite_sum(M,N)),cart(real,N)),sndcart),s(cart(real,finite_sum(M,N)),X))))),s(cart(real,N),i(s(fun(cart(real,finite_sum(M,N)),cart(real,N)),sndcart),s(cart(real,finite_sum(M,N)),Y))))) ).
fof(aSNDCARTu_CMUL,axiom,
! [M,N,X,C0] : s(cart(real,N),i(s(fun(cart(real,finite_sum(M,N)),cart(real,N)),sndcart),s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N))),i(s(fun(real,fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N)))),r_),s(real,C0))),s(cart(real,finite_sum(M,N)),X))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,C0))),s(cart(real,N),i(s(fun(cart(real,finite_sum(M,N)),cart(real,N)),sndcart),s(cart(real,finite_sum(M,N)),X))))) ).
fof(aSNDCARTu_NEG,axiom,
! [M,N,X] : s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),vectoru_neg),s(cart(real,N),i(s(fun(cart(real,finite_sum(M,N)),cart(real,N)),sndcart),s(cart(real,finite_sum(M,N)),X))))) = s(cart(real,N),i(s(fun(cart(real,finite_sum(M,N)),cart(real,N)),sndcart),s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N))),vectoru_neg),s(cart(real,finite_sum(M,N)),X))))) ).
fof(aSNDCARTu_SUB,axiom,
! [M,N,X,Y] : s(cart(real,N),i(s(fun(cart(real,finite_sum(M,N)),cart(real,N)),sndcart),s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N))),i(s(fun(cart(real,finite_sum(M,N)),fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N)))),vectoru_sub),s(cart(real,finite_sum(M,N)),X))),s(cart(real,finite_sum(M,N)),Y))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),i(s(fun(cart(real,finite_sum(M,N)),cart(real,N)),sndcart),s(cart(real,finite_sum(M,N)),X))))),s(cart(real,N),i(s(fun(cart(real,finite_sum(M,N)),cart(real,N)),sndcart),s(cart(real,finite_sum(M,N)),Y))))) ).
fof(aSNDCARTu_VSUM,axiom,
! [Q120474,Q120471,Q120473,U_0] :
( ! [X,I0] : s(cart(real,Q120473),i(s(fun(Q120474,cart(real,Q120473)),i(s(fun(fun(Q120474,cart(real,finite_sum(Q120471,Q120473))),fun(Q120474,cart(real,Q120473))),U_0),s(fun(Q120474,cart(real,finite_sum(Q120471,Q120473))),X))),s(Q120474,I0))) = s(cart(real,Q120473),i(s(fun(cart(real,finite_sum(Q120471,Q120473)),cart(real,Q120473)),sndcart),s(cart(real,finite_sum(Q120471,Q120473)),i(s(fun(Q120474,cart(real,finite_sum(Q120471,Q120473))),X),s(Q120474,I0)))))
=> ! [K0,X] :
( p(s(bool,i(s(fun(fun(Q120474,bool),bool),finite),s(fun(Q120474,bool),K0))))
=> s(cart(real,Q120473),i(s(fun(cart(real,finite_sum(Q120471,Q120473)),cart(real,Q120473)),sndcart),s(cart(real,finite_sum(Q120471,Q120473)),i(s(fun(fun(Q120474,cart(real,finite_sum(Q120471,Q120473))),cart(real,finite_sum(Q120471,Q120473))),i(s(fun(fun(Q120474,bool),fun(fun(Q120474,cart(real,finite_sum(Q120471,Q120473))),cart(real,finite_sum(Q120471,Q120473)))),vsum),s(fun(Q120474,bool),K0))),s(fun(Q120474,cart(real,finite_sum(Q120471,Q120473))),X))))) = s(cart(real,Q120473),i(s(fun(fun(Q120474,cart(real,Q120473)),cart(real,Q120473)),i(s(fun(fun(Q120474,bool),fun(fun(Q120474,cart(real,Q120473)),cart(real,Q120473))),vsum),s(fun(Q120474,bool),K0))),s(fun(Q120474,cart(real,Q120473)),i(s(fun(fun(Q120474,cart(real,finite_sum(Q120471,Q120473))),fun(Q120474,cart(real,Q120473))),U_0),s(fun(Q120474,cart(real,finite_sum(Q120471,Q120473))),X))))) ) ) ).
fof(aPASTECARTu_VEC,axiom,
! [Q120489,Q120491,N0] : s(cart(real,finite_sum(Q120489,Q120491)),i(s(fun(cart(real,Q120491),cart(real,finite_sum(Q120489,Q120491))),i(s(fun(cart(real,Q120489),fun(cart(real,Q120491),cart(real,finite_sum(Q120489,Q120491)))),pastecart),s(cart(real,Q120489),i(s(fun(num,cart(real,Q120489)),vec),s(num,N0))))),s(cart(real,Q120491),i(s(fun(num,cart(real,Q120491)),vec),s(num,N0))))) = s(cart(real,finite_sum(Q120489,Q120491)),i(s(fun(num,cart(real,finite_sum(Q120489,Q120491))),vec),s(num,N0))) ).
fof(aPASTECARTu_ADD,axiom,
! [M,N,X1,Y1,X2,Y2] : s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N))),i(s(fun(cart(real,finite_sum(M,N)),fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N)))),vectoru_add),s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,N),cart(real,finite_sum(M,N))),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,finite_sum(M,N)))),pastecart),s(cart(real,M),X1))),s(cart(real,N),Y1))))),s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,N),cart(real,finite_sum(M,N))),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,finite_sum(M,N)))),pastecart),s(cart(real,M),X2))),s(cart(real,N),Y2))))) = s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,N),cart(real,finite_sum(M,N))),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,finite_sum(M,N)))),pastecart),s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),i(s(fun(cart(real,M),fun(cart(real,M),cart(real,M))),vectoru_add),s(cart(real,M),X1))),s(cart(real,M),X2))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),Y1))),s(cart(real,N),Y2))))) ).
fof(aPASTECARTu_CMUL,axiom,
! [Q120589,Q120590,X1,Y1,C0] : s(cart(real,finite_sum(Q120589,Q120590)),i(s(fun(cart(real,Q120590),cart(real,finite_sum(Q120589,Q120590))),i(s(fun(cart(real,Q120589),fun(cart(real,Q120590),cart(real,finite_sum(Q120589,Q120590)))),pastecart),s(cart(real,Q120589),i(s(fun(cart(real,Q120589),cart(real,Q120589)),i(s(fun(real,fun(cart(real,Q120589),cart(real,Q120589))),r_),s(real,C0))),s(cart(real,Q120589),X1))))),s(cart(real,Q120590),i(s(fun(cart(real,Q120590),cart(real,Q120590)),i(s(fun(real,fun(cart(real,Q120590),cart(real,Q120590))),r_),s(real,C0))),s(cart(real,Q120590),Y1))))) = s(cart(real,finite_sum(Q120589,Q120590)),i(s(fun(cart(real,finite_sum(Q120589,Q120590)),cart(real,finite_sum(Q120589,Q120590))),i(s(fun(real,fun(cart(real,finite_sum(Q120589,Q120590)),cart(real,finite_sum(Q120589,Q120590)))),r_),s(real,C0))),s(cart(real,finite_sum(Q120589,Q120590)),i(s(fun(cart(real,Q120590),cart(real,finite_sum(Q120589,Q120590))),i(s(fun(cart(real,Q120589),fun(cart(real,Q120590),cart(real,finite_sum(Q120589,Q120590)))),pastecart),s(cart(real,Q120589),X1))),s(cart(real,Q120590),Y1))))) ).
fof(aPASTECARTu_NEG,axiom,
! [M,N,X,Y] : s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,N),cart(real,finite_sum(M,N))),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,finite_sum(M,N)))),pastecart),s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),vectoru_neg),s(cart(real,M),X))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),vectoru_neg),s(cart(real,N),Y))))) = s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N))),vectoru_neg),s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,N),cart(real,finite_sum(M,N))),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,finite_sum(M,N)))),pastecart),s(cart(real,M),X))),s(cart(real,N),Y))))) ).
fof(aPASTECARTu_SUB,axiom,
! [M,N,X1,Y1,X2,Y2] : s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N))),i(s(fun(cart(real,finite_sum(M,N)),fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N)))),vectoru_sub),s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,N),cart(real,finite_sum(M,N))),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,finite_sum(M,N)))),pastecart),s(cart(real,M),X1))),s(cart(real,N),Y1))))),s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,N),cart(real,finite_sum(M,N))),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,finite_sum(M,N)))),pastecart),s(cart(real,M),X2))),s(cart(real,N),Y2))))) = s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,N),cart(real,finite_sum(M,N))),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,finite_sum(M,N)))),pastecart),s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),i(s(fun(cart(real,M),fun(cart(real,M),cart(real,M))),vectoru_sub),s(cart(real,M),X1))),s(cart(real,M),X2))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),Y1))),s(cart(real,N),Y2))))) ).
fof(aPASTECARTu_VSUM,axiom,
! [Q120760,Q120763,Q120761,U_0] :
( ! [X,Y,I0] : s(cart(real,finite_sum(Q120760,Q120761)),i(s(fun(Q120763,cart(real,finite_sum(Q120760,Q120761))),i(s(fun(fun(Q120763,cart(real,Q120761)),fun(Q120763,cart(real,finite_sum(Q120760,Q120761)))),i(s(fun(fun(Q120763,cart(real,Q120760)),fun(fun(Q120763,cart(real,Q120761)),fun(Q120763,cart(real,finite_sum(Q120760,Q120761))))),U_0),s(fun(Q120763,cart(real,Q120760)),X))),s(fun(Q120763,cart(real,Q120761)),Y))),s(Q120763,I0))) = s(cart(real,finite_sum(Q120760,Q120761)),i(s(fun(cart(real,Q120761),cart(real,finite_sum(Q120760,Q120761))),i(s(fun(cart(real,Q120760),fun(cart(real,Q120761),cart(real,finite_sum(Q120760,Q120761)))),pastecart),s(cart(real,Q120760),i(s(fun(Q120763,cart(real,Q120760)),X),s(Q120763,I0))))),s(cart(real,Q120761),i(s(fun(Q120763,cart(real,Q120761)),Y),s(Q120763,I0)))))
=> ! [K0,X,Y] :
( p(s(bool,i(s(fun(fun(Q120763,bool),bool),finite),s(fun(Q120763,bool),K0))))
=> s(cart(real,finite_sum(Q120760,Q120761)),i(s(fun(cart(real,Q120761),cart(real,finite_sum(Q120760,Q120761))),i(s(fun(cart(real,Q120760),fun(cart(real,Q120761),cart(real,finite_sum(Q120760,Q120761)))),pastecart),s(cart(real,Q120760),i(s(fun(fun(Q120763,cart(real,Q120760)),cart(real,Q120760)),i(s(fun(fun(Q120763,bool),fun(fun(Q120763,cart(real,Q120760)),cart(real,Q120760))),vsum),s(fun(Q120763,bool),K0))),s(fun(Q120763,cart(real,Q120760)),X))))),s(cart(real,Q120761),i(s(fun(fun(Q120763,cart(real,Q120761)),cart(real,Q120761)),i(s(fun(fun(Q120763,bool),fun(fun(Q120763,cart(real,Q120761)),cart(real,Q120761))),vsum),s(fun(Q120763,bool),K0))),s(fun(Q120763,cart(real,Q120761)),Y))))) = s(cart(real,finite_sum(Q120760,Q120761)),i(s(fun(fun(Q120763,cart(real,finite_sum(Q120760,Q120761))),cart(real,finite_sum(Q120760,Q120761))),i(s(fun(fun(Q120763,bool),fun(fun(Q120763,cart(real,finite_sum(Q120760,Q120761))),cart(real,finite_sum(Q120760,Q120761)))),vsum),s(fun(Q120763,bool),K0))),s(fun(Q120763,cart(real,finite_sum(Q120760,Q120761))),i(s(fun(fun(Q120763,cart(real,Q120761)),fun(Q120763,cart(real,finite_sum(Q120760,Q120761)))),i(s(fun(fun(Q120763,cart(real,Q120760)),fun(fun(Q120763,cart(real,Q120761)),fun(Q120763,cart(real,finite_sum(Q120760,Q120761))))),U_0),s(fun(Q120763,cart(real,Q120760)),X))),s(fun(Q120763,cart(real,Q120761)),Y))))) ) ) ).
fof(aPASTECARTu_EQu_VEC,axiom,
! [Q120795,Q120800,X,Y,N0] :
( s(cart(real,finite_sum(Q120795,Q120800)),i(s(fun(cart(real,Q120800),cart(real,finite_sum(Q120795,Q120800))),i(s(fun(cart(real,Q120795),fun(cart(real,Q120800),cart(real,finite_sum(Q120795,Q120800)))),pastecart),s(cart(real,Q120795),X))),s(cart(real,Q120800),Y))) = s(cart(real,finite_sum(Q120795,Q120800)),i(s(fun(num,cart(real,finite_sum(Q120795,Q120800))),vec),s(num,N0)))
<=> ( s(cart(real,Q120795),X) = s(cart(real,Q120795),i(s(fun(num,cart(real,Q120795)),vec),s(num,N0)))
& s(cart(real,Q120800),Y) = s(cart(real,Q120800),i(s(fun(num,cart(real,Q120800)),vec),s(num,N0))) ) ) ).
fof(aNORMu_FSTCART,axiom,
! [Q120851,Q120849,X] : p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,Q120851),real),vectoru_norm),s(cart(real,Q120851),i(s(fun(cart(real,finite_sum(Q120851,Q120849)),cart(real,Q120851)),fstcart),s(cart(real,finite_sum(Q120851,Q120849)),X))))))),s(real,i(s(fun(cart(real,finite_sum(Q120851,Q120849)),real),vectoru_norm),s(cart(real,finite_sum(Q120851,Q120849)),X)))))) ).
fof(aDISTu_FSTCART,axiom,
! [Q120883,Q120881,X,Y] : p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(prod(cart(real,Q120883),cart(real,Q120883)),real),distance),s(prod(cart(real,Q120883),cart(real,Q120883)),i(s(fun(cart(real,Q120883),prod(cart(real,Q120883),cart(real,Q120883))),i(s(fun(cart(real,Q120883),fun(cart(real,Q120883),prod(cart(real,Q120883),cart(real,Q120883)))),c_),s(cart(real,Q120883),i(s(fun(cart(real,finite_sum(Q120883,Q120881)),cart(real,Q120883)),fstcart),s(cart(real,finite_sum(Q120883,Q120881)),X))))),s(cart(real,Q120883),i(s(fun(cart(real,finite_sum(Q120883,Q120881)),cart(real,Q120883)),fstcart),s(cart(real,finite_sum(Q120883,Q120881)),Y))))))))),s(real,i(s(fun(prod(cart(real,finite_sum(Q120883,Q120881)),cart(real,finite_sum(Q120883,Q120881))),real),distance),s(prod(cart(real,finite_sum(Q120883,Q120881)),cart(real,finite_sum(Q120883,Q120881))),i(s(fun(cart(real,finite_sum(Q120883,Q120881)),prod(cart(real,finite_sum(Q120883,Q120881)),cart(real,finite_sum(Q120883,Q120881)))),i(s(fun(cart(real,finite_sum(Q120883,Q120881)),fun(cart(real,finite_sum(Q120883,Q120881)),prod(cart(real,finite_sum(Q120883,Q120881)),cart(real,finite_sum(Q120883,Q120881))))),c_),s(cart(real,finite_sum(Q120883,Q120881)),X))),s(cart(real,finite_sum(Q120883,Q120881)),Y)))))))) ).
fof(aNORMu_SNDCART,axiom,
! [Q120961,Q120963,X] : p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,Q120963),real),vectoru_norm),s(cart(real,Q120963),i(s(fun(cart(real,finite_sum(Q120961,Q120963)),cart(real,Q120963)),sndcart),s(cart(real,finite_sum(Q120961,Q120963)),X))))))),s(real,i(s(fun(cart(real,finite_sum(Q120961,Q120963)),real),vectoru_norm),s(cart(real,finite_sum(Q120961,Q120963)),X)))))) ).
fof(aDISTu_SNDCART,axiom,
! [Q120993,Q120995,X,Y] : p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(prod(cart(real,Q120995),cart(real,Q120995)),real),distance),s(prod(cart(real,Q120995),cart(real,Q120995)),i(s(fun(cart(real,Q120995),prod(cart(real,Q120995),cart(real,Q120995))),i(s(fun(cart(real,Q120995),fun(cart(real,Q120995),prod(cart(real,Q120995),cart(real,Q120995)))),c_),s(cart(real,Q120995),i(s(fun(cart(real,finite_sum(Q120993,Q120995)),cart(real,Q120995)),sndcart),s(cart(real,finite_sum(Q120993,Q120995)),X))))),s(cart(real,Q120995),i(s(fun(cart(real,finite_sum(Q120993,Q120995)),cart(real,Q120995)),sndcart),s(cart(real,finite_sum(Q120993,Q120995)),Y))))))))),s(real,i(s(fun(prod(cart(real,finite_sum(Q120993,Q120995)),cart(real,finite_sum(Q120993,Q120995))),real),distance),s(prod(cart(real,finite_sum(Q120993,Q120995)),cart(real,finite_sum(Q120993,Q120995))),i(s(fun(cart(real,finite_sum(Q120993,Q120995)),prod(cart(real,finite_sum(Q120993,Q120995)),cart(real,finite_sum(Q120993,Q120995)))),i(s(fun(cart(real,finite_sum(Q120993,Q120995)),fun(cart(real,finite_sum(Q120993,Q120995)),prod(cart(real,finite_sum(Q120993,Q120995)),cart(real,finite_sum(Q120993,Q120995))))),c_),s(cart(real,finite_sum(Q120993,Q120995)),X))),s(cart(real,finite_sum(Q120993,Q120995)),Y)))))))) ).
fof(aDOTu_PASTECART,axiom,
! [Q121075,Q121076,X1,X2,Y1,Y2] : s(real,i(s(fun(cart(real,finite_sum(Q121075,Q121076)),real),i(s(fun(cart(real,finite_sum(Q121075,Q121076)),fun(cart(real,finite_sum(Q121075,Q121076)),real)),dot),s(cart(real,finite_sum(Q121075,Q121076)),i(s(fun(cart(real,Q121076),cart(real,finite_sum(Q121075,Q121076))),i(s(fun(cart(real,Q121075),fun(cart(real,Q121076),cart(real,finite_sum(Q121075,Q121076)))),pastecart),s(cart(real,Q121075),X1))),s(cart(real,Q121076),X2))))),s(cart(real,finite_sum(Q121075,Q121076)),i(s(fun(cart(real,Q121076),cart(real,finite_sum(Q121075,Q121076))),i(s(fun(cart(real,Q121075),fun(cart(real,Q121076),cart(real,finite_sum(Q121075,Q121076)))),pastecart),s(cart(real,Q121075),Y1))),s(cart(real,Q121076),Y2))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(cart(real,Q121075),real),i(s(fun(cart(real,Q121075),fun(cart(real,Q121075),real)),dot),s(cart(real,Q121075),X1))),s(cart(real,Q121075),Y1))))),s(real,i(s(fun(cart(real,Q121076),real),i(s(fun(cart(real,Q121076),fun(cart(real,Q121076),real)),dot),s(cart(real,Q121076),X2))),s(cart(real,Q121076),Y2))))) ).
fof(aNORMu_PASTECART,axiom,
! [Q121103,Q121104,X,Y] : s(real,i(s(fun(cart(real,finite_sum(Q121103,Q121104)),real),vectoru_norm),s(cart(real,finite_sum(Q121103,Q121104)),i(s(fun(cart(real,Q121104),cart(real,finite_sum(Q121103,Q121104))),i(s(fun(cart(real,Q121103),fun(cart(real,Q121104),cart(real,finite_sum(Q121103,Q121104)))),pastecart),s(cart(real,Q121103),X))),s(cart(real,Q121104),Y))))) = s(real,i(s(fun(real,real),sqrt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,Q121103),real),vectoru_norm),s(cart(real,Q121103),X))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,Q121104),real),vectoru_norm),s(cart(real,Q121104),Y))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))) ).
fof(aNORMu_PASTECARTu_LE,axiom,
! [Q121142,Q121143,X,Y] : p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,finite_sum(Q121142,Q121143)),real),vectoru_norm),s(cart(real,finite_sum(Q121142,Q121143)),i(s(fun(cart(real,Q121143),cart(real,finite_sum(Q121142,Q121143))),i(s(fun(cart(real,Q121142),fun(cart(real,Q121143),cart(real,finite_sum(Q121142,Q121143)))),pastecart),s(cart(real,Q121142),X))),s(cart(real,Q121143),Y))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(cart(real,Q121142),real),vectoru_norm),s(cart(real,Q121142),X))))),s(real,i(s(fun(cart(real,Q121143),real),vectoru_norm),s(cart(real,Q121143),Y)))))))) ).
fof(aNORMu_LEu_PASTECART,axiom,
! [M,N,X,Y] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,M),real),vectoru_norm),s(cart(real,M),X))))),s(real,i(s(fun(cart(real,finite_sum(M,N)),real),vectoru_norm),s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,N),cart(real,finite_sum(M,N))),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,finite_sum(M,N)))),pastecart),s(cart(real,M),X))),s(cart(real,N),Y))))))))
& p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),Y))))),s(real,i(s(fun(cart(real,finite_sum(M,N)),real),vectoru_norm),s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,N),cart(real,finite_sum(M,N))),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,finite_sum(M,N)))),pastecart),s(cart(real,M),X))),s(cart(real,N),Y)))))))) ) ).
fof(aNORMu_PASTECARTu_0u_conjunct0,axiom,
! [Q121218,Q121215,X] : s(real,i(s(fun(cart(real,finite_sum(Q121215,Q121218)),real),vectoru_norm),s(cart(real,finite_sum(Q121215,Q121218)),i(s(fun(cart(real,Q121218),cart(real,finite_sum(Q121215,Q121218))),i(s(fun(cart(real,Q121215),fun(cart(real,Q121218),cart(real,finite_sum(Q121215,Q121218)))),pastecart),s(cart(real,Q121215),X))),s(cart(real,Q121218),i(s(fun(num,cart(real,Q121218)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))) = s(real,i(s(fun(cart(real,Q121215),real),vectoru_norm),s(cart(real,Q121215),X))) ).
fof(aNORMu_PASTECARTu_0u_conjunct1,axiom,
! [Q121236,Q121234,Y] : s(real,i(s(fun(cart(real,finite_sum(Q121236,Q121234)),real),vectoru_norm),s(cart(real,finite_sum(Q121236,Q121234)),i(s(fun(cart(real,Q121234),cart(real,finite_sum(Q121236,Q121234))),i(s(fun(cart(real,Q121236),fun(cart(real,Q121234),cart(real,finite_sum(Q121236,Q121234)))),pastecart),s(cart(real,Q121236),i(s(fun(num,cart(real,Q121236)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(real,Q121234),Y))))) = s(real,i(s(fun(cart(real,Q121234),real),vectoru_norm),s(cart(real,Q121234),Y))) ).
fof(aDISTu_PASTECARTu_CANCELu_conjunct0,axiom,
! [Q121280,Q121279,X,XI_,Y] : s(real,i(s(fun(prod(cart(real,finite_sum(Q121279,Q121280)),cart(real,finite_sum(Q121279,Q121280))),real),distance),s(prod(cart(real,finite_sum(Q121279,Q121280)),cart(real,finite_sum(Q121279,Q121280))),i(s(fun(cart(real,finite_sum(Q121279,Q121280)),prod(cart(real,finite_sum(Q121279,Q121280)),cart(real,finite_sum(Q121279,Q121280)))),i(s(fun(cart(real,finite_sum(Q121279,Q121280)),fun(cart(real,finite_sum(Q121279,Q121280)),prod(cart(real,finite_sum(Q121279,Q121280)),cart(real,finite_sum(Q121279,Q121280))))),c_),s(cart(real,finite_sum(Q121279,Q121280)),i(s(fun(cart(real,Q121280),cart(real,finite_sum(Q121279,Q121280))),i(s(fun(cart(real,Q121279),fun(cart(real,Q121280),cart(real,finite_sum(Q121279,Q121280)))),pastecart),s(cart(real,Q121279),X))),s(cart(real,Q121280),Y))))),s(cart(real,finite_sum(Q121279,Q121280)),i(s(fun(cart(real,Q121280),cart(real,finite_sum(Q121279,Q121280))),i(s(fun(cart(real,Q121279),fun(cart(real,Q121280),cart(real,finite_sum(Q121279,Q121280)))),pastecart),s(cart(real,Q121279),XI_))),s(cart(real,Q121280),Y))))))) = s(real,i(s(fun(prod(cart(real,Q121279),cart(real,Q121279)),real),distance),s(prod(cart(real,Q121279),cart(real,Q121279)),i(s(fun(cart(real,Q121279),prod(cart(real,Q121279),cart(real,Q121279))),i(s(fun(cart(real,Q121279),fun(cart(real,Q121279),prod(cart(real,Q121279),cart(real,Q121279)))),c_),s(cart(real,Q121279),X))),s(cart(real,Q121279),XI_))))) ).
fof(aDISTu_PASTECARTu_CANCELu_conjunct1,axiom,
! [Q121316,Q121317,X,Y,YI_] : s(real,i(s(fun(prod(cart(real,finite_sum(Q121316,Q121317)),cart(real,finite_sum(Q121316,Q121317))),real),distance),s(prod(cart(real,finite_sum(Q121316,Q121317)),cart(real,finite_sum(Q121316,Q121317))),i(s(fun(cart(real,finite_sum(Q121316,Q121317)),prod(cart(real,finite_sum(Q121316,Q121317)),cart(real,finite_sum(Q121316,Q121317)))),i(s(fun(cart(real,finite_sum(Q121316,Q121317)),fun(cart(real,finite_sum(Q121316,Q121317)),prod(cart(real,finite_sum(Q121316,Q121317)),cart(real,finite_sum(Q121316,Q121317))))),c_),s(cart(real,finite_sum(Q121316,Q121317)),i(s(fun(cart(real,Q121317),cart(real,finite_sum(Q121316,Q121317))),i(s(fun(cart(real,Q121316),fun(cart(real,Q121317),cart(real,finite_sum(Q121316,Q121317)))),pastecart),s(cart(real,Q121316),X))),s(cart(real,Q121317),Y))))),s(cart(real,finite_sum(Q121316,Q121317)),i(s(fun(cart(real,Q121317),cart(real,finite_sum(Q121316,Q121317))),i(s(fun(cart(real,Q121316),fun(cart(real,Q121317),cart(real,finite_sum(Q121316,Q121317)))),pastecart),s(cart(real,Q121316),X))),s(cart(real,Q121317),YI_))))))) = s(real,i(s(fun(prod(cart(real,Q121317),cart(real,Q121317)),real),distance),s(prod(cart(real,Q121317),cart(real,Q121317)),i(s(fun(cart(real,Q121317),prod(cart(real,Q121317),cart(real,Q121317))),i(s(fun(cart(real,Q121317),fun(cart(real,Q121317),prod(cart(real,Q121317),cart(real,Q121317)))),c_),s(cart(real,Q121317),Y))),s(cart(real,Q121317),YI_))))) ).
fof(asubspace,axiom,
! [Q121390,S0] :
( p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),subspace),s(fun(cart(real,Q121390),bool),S0))))
<=> ( p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),i(s(fun(num,cart(real,Q121390)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,Q121390),bool),S0))))
& ! [X,Y] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),X))),s(fun(cart(real,Q121390),bool),S0))))
& p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),Y))),s(fun(cart(real,Q121390),bool),S0)))) )
=> p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),i(s(fun(cart(real,Q121390),cart(real,Q121390)),i(s(fun(cart(real,Q121390),fun(cart(real,Q121390),cart(real,Q121390))),vectoru_add),s(cart(real,Q121390),X))),s(cart(real,Q121390),Y))))),s(fun(cart(real,Q121390),bool),S0)))) )
& ! [C0,X] :
( p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),X))),s(fun(cart(real,Q121390),bool),S0))))
=> p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),i(s(fun(cart(real,Q121390),cart(real,Q121390)),i(s(fun(real,fun(cart(real,Q121390),cart(real,Q121390))),r_),s(real,C0))),s(cart(real,Q121390),X))))),s(fun(cart(real,Q121390),bool),S0)))) ) ) ) ).
fof(aspan,axiom,
! [Q121402,S0] : s(fun(cart(real,Q121402),bool),i(s(fun(fun(cart(real,Q121402),bool),fun(cart(real,Q121402),bool)),span),s(fun(cart(real,Q121402),bool),S0))) = s(fun(cart(real,Q121402),bool),i(s(fun(fun(cart(real,Q121402),bool),fun(cart(real,Q121402),bool)),i(s(fun(fun(fun(cart(real,Q121402),bool),bool),fun(fun(cart(real,Q121402),bool),fun(cart(real,Q121402),bool))),hull),s(fun(fun(cart(real,Q121402),bool),bool),subspace))),s(fun(cart(real,Q121402),bool),S0))) ).
fof(adependent,axiom,
! [Q121420,S0] :
( p(s(bool,i(s(fun(fun(cart(real,Q121420),bool),bool),dependent),s(fun(cart(real,Q121420),bool),S0))))
<=> ? [A5] :
( p(s(bool,i(s(fun(fun(cart(real,Q121420),bool),bool),i(s(fun(cart(real,Q121420),fun(fun(cart(real,Q121420),bool),bool)),in),s(cart(real,Q121420),A5))),s(fun(cart(real,Q121420),bool),S0))))
& p(s(bool,i(s(fun(fun(cart(real,Q121420),bool),bool),i(s(fun(cart(real,Q121420),fun(fun(cart(real,Q121420),bool),bool)),in),s(cart(real,Q121420),A5))),s(fun(cart(real,Q121420),bool),i(s(fun(fun(cart(real,Q121420),bool),fun(cart(real,Q121420),bool)),span),s(fun(cart(real,Q121420),bool),i(s(fun(cart(real,Q121420),fun(cart(real,Q121420),bool)),i(s(fun(fun(cart(real,Q121420),bool),fun(cart(real,Q121420),fun(cart(real,Q121420),bool))),delete),s(fun(cart(real,Q121420),bool),S0))),s(cart(real,Q121420),A5)))))))) ) ) ).
fof(aindependent,axiom,
! [Q121430,S0] :
( p(s(bool,i(s(fun(fun(cart(real,Q121430),bool),bool),independent),s(fun(cart(real,Q121430),bool),S0))))
<=> ~ p(s(bool,i(s(fun(fun(cart(real,Q121430),bool),bool),dependent),s(fun(cart(real,Q121430),bool),S0)))) ) ).
fof(aSUBSPACEu_UNIV,axiom,
! [N] : p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),subspace),s(fun(cart(real,N),bool),univ)))) ).
fof(aSUBSPACEu_IMPu_NONEMPTY,axiom,
! [Q121443,S0] :
( p(s(bool,i(s(fun(fun(cart(real,Q121443),bool),bool),subspace),s(fun(cart(real,Q121443),bool),S0))))
=> s(fun(cart(real,Q121443),bool),S0) != s(fun(cart(real,Q121443),bool),empty) ) ).
fof(aSUBSPACEu_0,axiom,
! [Q121453] :
( p(s(bool,i(s(fun(fun(cart(real,Q121453),bool),bool),subspace),s(fun(cart(real,Q121453),bool),s0))))
=> p(s(bool,i(s(fun(fun(cart(real,Q121453),bool),bool),i(s(fun(cart(real,Q121453),fun(fun(cart(real,Q121453),bool),bool)),in),s(cart(real,Q121453),i(s(fun(num,cart(real,Q121453)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,Q121453),bool),s0)))) ) ).
fof(aSUBSPACEu_ADD,axiom,
! [Q121494,X,Y,S0] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q121494),bool),bool),subspace),s(fun(cart(real,Q121494),bool),S0))))
& p(s(bool,i(s(fun(fun(cart(real,Q121494),bool),bool),i(s(fun(cart(real,Q121494),fun(fun(cart(real,Q121494),bool),bool)),in),s(cart(real,Q121494),X))),s(fun(cart(real,Q121494),bool),S0))))
& p(s(bool,i(s(fun(fun(cart(real,Q121494),bool),bool),i(s(fun(cart(real,Q121494),fun(fun(cart(real,Q121494),bool),bool)),in),s(cart(real,Q121494),Y))),s(fun(cart(real,Q121494),bool),S0)))) )
=> p(s(bool,i(s(fun(fun(cart(real,Q121494),bool),bool),i(s(fun(cart(real,Q121494),fun(fun(cart(real,Q121494),bool),bool)),in),s(cart(real,Q121494),i(s(fun(cart(real,Q121494),cart(real,Q121494)),i(s(fun(cart(real,Q121494),fun(cart(real,Q121494),cart(real,Q121494))),vectoru_add),s(cart(real,Q121494),X))),s(cart(real,Q121494),Y))))),s(fun(cart(real,Q121494),bool),S0)))) ) ).
fof(aSUBSPACEu_MUL,axiom,
! [Q121516,X,C0,S0] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q121516),bool),bool),subspace),s(fun(cart(real,Q121516),bool),S0))))
& p(s(bool,i(s(fun(fun(cart(real,Q121516),bool),bool),i(s(fun(cart(real,Q121516),fun(fun(cart(real,Q121516),bool),bool)),in),s(cart(real,Q121516),X))),s(fun(cart(real,Q121516),bool),S0)))) )
=> p(s(bool,i(s(fun(fun(cart(real,Q121516),bool),bool),i(s(fun(cart(real,Q121516),fun(fun(cart(real,Q121516),bool),bool)),in),s(cart(real,Q121516),i(s(fun(cart(real,Q121516),cart(real,Q121516)),i(s(fun(real,fun(cart(real,Q121516),cart(real,Q121516))),r_),s(real,C0))),s(cart(real,Q121516),X))))),s(fun(cart(real,Q121516),bool),S0)))) ) ).
fof(aSUBSPACEu_NEG,axiom,
! [Q121570,X,S0] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q121570),bool),bool),subspace),s(fun(cart(real,Q121570),bool),S0))))
& p(s(bool,i(s(fun(fun(cart(real,Q121570),bool),bool),i(s(fun(cart(real,Q121570),fun(fun(cart(real,Q121570),bool),bool)),in),s(cart(real,Q121570),X))),s(fun(cart(real,Q121570),bool),S0)))) )
=> p(s(bool,i(s(fun(fun(cart(real,Q121570),bool),bool),i(s(fun(cart(real,Q121570),fun(fun(cart(real,Q121570),bool),bool)),in),s(cart(real,Q121570),i(s(fun(cart(real,Q121570),cart(real,Q121570)),vectoru_neg),s(cart(real,Q121570),X))))),s(fun(cart(real,Q121570),bool),S0)))) ) ).
fof(aSUBSPACEu_SUB,axiom,
! [Q121609,X,Y,S0] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q121609),bool),bool),subspace),s(fun(cart(real,Q121609),bool),S0))))
& p(s(bool,i(s(fun(fun(cart(real,Q121609),bool),bool),i(s(fun(cart(real,Q121609),fun(fun(cart(real,Q121609),bool),bool)),in),s(cart(real,Q121609),X))),s(fun(cart(real,Q121609),bool),S0))))
& p(s(bool,i(s(fun(fun(cart(real,Q121609),bool),bool),i(s(fun(cart(real,Q121609),fun(fun(cart(real,Q121609),bool),bool)),in),s(cart(real,Q121609),Y))),s(fun(cart(real,Q121609),bool),S0)))) )
=> p(s(bool,i(s(fun(fun(cart(real,Q121609),bool),bool),i(s(fun(cart(real,Q121609),fun(fun(cart(real,Q121609),bool),bool)),in),s(cart(real,Q121609),i(s(fun(cart(real,Q121609),cart(real,Q121609)),i(s(fun(cart(real,Q121609),fun(cart(real,Q121609),cart(real,Q121609))),vectoru_sub),s(cart(real,Q121609),X))),s(cart(real,Q121609),Y))))),s(fun(cart(real,Q121609),bool),S0)))) ) ).
fof(aSUBSPACEu_VSUM,axiom,
! [Q121648,Q121655,S0,F0,T0] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q121655),bool),bool),subspace),s(fun(cart(real,Q121655),bool),S0))))
& p(s(bool,i(s(fun(fun(Q121648,bool),bool),finite),s(fun(Q121648,bool),T0))))
& ! [X] :
( p(s(bool,i(s(fun(fun(Q121648,bool),bool),i(s(fun(Q121648,fun(fun(Q121648,bool),bool)),in),s(Q121648,X))),s(fun(Q121648,bool),T0))))
=> p(s(bool,i(s(fun(fun(cart(real,Q121655),bool),bool),i(s(fun(cart(real,Q121655),fun(fun(cart(real,Q121655),bool),bool)),in),s(cart(real,Q121655),i(s(fun(Q121648,cart(real,Q121655)),F0),s(Q121648,X))))),s(fun(cart(real,Q121655),bool),S0)))) ) )
=> p(s(bool,i(s(fun(fun(cart(real,Q121655),bool),bool),i(s(fun(cart(real,Q121655),fun(fun(cart(real,Q121655),bool),bool)),in),s(cart(real,Q121655),i(s(fun(fun(Q121648,cart(real,Q121655)),cart(real,Q121655)),i(s(fun(fun(Q121648,bool),fun(fun(Q121648,cart(real,Q121655)),cart(real,Q121655))),vsum),s(fun(Q121648,bool),T0))),s(fun(Q121648,cart(real,Q121655)),F0))))),s(fun(cart(real,Q121655),bool),S0)))) ) ).
fof(aSUBSPACEu_LINEARu_IMAGE,axiom,
! [Q121671,Q121673,F0,S0] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q121673),cart(real,Q121671)),bool),linear),s(fun(cart(real,Q121673),cart(real,Q121671)),F0))))
& p(s(bool,i(s(fun(fun(cart(real,Q121673),bool),bool),subspace),s(fun(cart(real,Q121673),bool),S0)))) )
=> p(s(bool,i(s(fun(fun(cart(real,Q121671),bool),bool),subspace),s(fun(cart(real,Q121671),bool),i(s(fun(fun(cart(real,Q121673),bool),fun(cart(real,Q121671),bool)),i(s(fun(fun(cart(real,Q121673),cart(real,Q121671)),fun(fun(cart(real,Q121673),bool),fun(cart(real,Q121671),bool))),image),s(fun(cart(real,Q121673),cart(real,Q121671)),F0))),s(fun(cart(real,Q121673),bool),S0)))))) ) ).
fof(aSUBSPACEu_LINEARu_PREIMAGE,axiom,
! [Q121694,Q121697,U_0] :
( ! [F0,S0,GENR_PVARR_297] :
( p(s(bool,i(s(fun(cart(real,Q121694),bool),i(s(fun(fun(cart(real,Q121697),bool),fun(cart(real,Q121694),bool)),i(s(fun(fun(cart(real,Q121694),cart(real,Q121697)),fun(fun(cart(real,Q121697),bool),fun(cart(real,Q121694),bool))),U_0),s(fun(cart(real,Q121694),cart(real,Q121697)),F0))),s(fun(cart(real,Q121697),bool),S0))),s(cart(real,Q121694),GENR_PVARR_297))))
<=> ? [X] : p(s(bool,i(s(fun(cart(real,Q121694),bool),i(s(fun(bool,fun(cart(real,Q121694),bool)),i(s(fun(cart(real,Q121694),fun(bool,fun(cart(real,Q121694),bool))),setspec),s(cart(real,Q121694),GENR_PVARR_297))),s(bool,i(s(fun(fun(cart(real,Q121697),bool),bool),i(s(fun(cart(real,Q121697),fun(fun(cart(real,Q121697),bool),bool)),in),s(cart(real,Q121697),i(s(fun(cart(real,Q121694),cart(real,Q121697)),F0),s(cart(real,Q121694),X))))),s(fun(cart(real,Q121697),bool),S0))))),s(cart(real,Q121694),X)))) )
=> ! [F0,S0] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q121694),cart(real,Q121697)),bool),linear),s(fun(cart(real,Q121694),cart(real,Q121697)),F0))))
& p(s(bool,i(s(fun(fun(cart(real,Q121697),bool),bool),subspace),s(fun(cart(real,Q121697),bool),S0)))) )
=> p(s(bool,i(s(fun(fun(cart(real,Q121694),bool),bool),subspace),s(fun(cart(real,Q121694),bool),i(s(fun(fun(cart(real,Q121694),bool),fun(cart(real,Q121694),bool)),gspec),s(fun(cart(real,Q121694),bool),i(s(fun(fun(cart(real,Q121697),bool),fun(cart(real,Q121694),bool)),i(s(fun(fun(cart(real,Q121694),cart(real,Q121697)),fun(fun(cart(real,Q121697),bool),fun(cart(real,Q121694),bool))),U_0),s(fun(cart(real,Q121694),cart(real,Q121697)),F0))),s(fun(cart(real,Q121697),bool),S0)))))))) ) ) ).
fof(aSUBSPACEu_TRIVIAL,axiom,
! [Q121723] : p(s(bool,i(s(fun(fun(cart(real,Q121723),bool),bool),subspace),s(fun(cart(real,Q121723),bool),i(s(fun(fun(cart(real,Q121723),bool),fun(cart(real,Q121723),bool)),i(s(fun(cart(real,Q121723),fun(fun(cart(real,Q121723),bool),fun(cart(real,Q121723),bool))),insert),s(cart(real,Q121723),i(s(fun(num,cart(real,Q121723)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,Q121723),bool),empty)))))) ).
fof(aSUBSPACEu_INTER,axiom,
! [Q121741,S0,T0] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q121741),bool),bool),subspace),s(fun(cart(real,Q121741),bool),S0))))
& p(s(bool,i(s(fun(fun(cart(real,Q121741),bool),bool),subspace),s(fun(cart(real,Q121741),bool),T0)))) )
=> p(s(bool,i(s(fun(fun(cart(real,Q121741),bool),bool),subspace),s(fun(cart(real,Q121741),bool),i(s(fun(fun(cart(real,Q121741),bool),fun(cart(real,Q121741),bool)),i(s(fun(fun(cart(real,Q121741),bool),fun(fun(cart(real,Q121741),bool),fun(cart(real,Q121741),bool))),inter),s(fun(cart(real,Q121741),bool),S0))),s(fun(cart(real,Q121741),bool),T0)))))) ) ).
fof(aSUBSPACEu_INTERS,axiom,
! [Q121764,F0] :
( ! [S0] :
( p(s(bool,i(s(fun(fun(fun(cart(real,Q121764),bool),bool),bool),i(s(fun(fun(cart(real,Q121764),bool),fun(fun(fun(cart(real,Q121764),bool),bool),bool)),in),s(fun(cart(real,Q121764),bool),S0))),s(fun(fun(cart(real,Q121764),bool),bool),F0))))
=> p(s(bool,i(s(fun(fun(cart(real,Q121764),bool),bool),subspace),s(fun(cart(real,Q121764),bool),S0)))) )
=> p(s(bool,i(s(fun(fun(cart(real,Q121764),bool),bool),subspace),s(fun(cart(real,Q121764),bool),i(s(fun(fun(fun(cart(real,Q121764),bool),bool),fun(cart(real,Q121764),bool)),inters),s(fun(fun(cart(real,Q121764),bool),bool),F0)))))) ) ).
fof(aLINEARu_INJECTIVEu_0u_SUBSPACE,axiom,
! [N,M,F0,S0] :
( ( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
& p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),subspace),s(fun(cart(real,M),bool),S0)))) )
=> ( ! [X,Y] :
( ( p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),S0))))
& p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),Y))),s(fun(cart(real,M),bool),S0))))
& s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),Y))) )
=> s(cart(real,M),X) = s(cart(real,M),Y) )
<=> ! [X] :
( ( p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),S0))))
& s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) )
=> s(cart(real,M),X) = s(cart(real,M),i(s(fun(num,cart(real,M)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ) ) ).
fof(aSUBSPACEu_UNIONu_CHAIN,axiom,
! [N,S0,T0] :
( ( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),subspace),s(fun(cart(real,N),bool),S0))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),subspace),s(fun(cart(real,N),bool),T0))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),subspace),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),union),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),T0)))))) )
=> ( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),T0))))
| p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),T0))),s(fun(cart(real,N),bool),S0)))) ) ) ).
fof(aSPANu_SPAN,axiom,
! [Q121985,S0] : s(fun(cart(real,Q121985),bool),i(s(fun(fun(cart(real,Q121985),bool),fun(cart(real,Q121985),bool)),span),s(fun(cart(real,Q121985),bool),i(s(fun(fun(cart(real,Q121985),bool),fun(cart(real,Q121985),bool)),span),s(fun(cart(real,Q121985),bool),S0))))) = s(fun(cart(real,Q121985),bool),i(s(fun(fun(cart(real,Q121985),bool),fun(cart(real,Q121985),bool)),span),s(fun(cart(real,Q121985),bool),S0))) ).
fof(aSPANu_MONO,axiom,
! [Q122006,S0,T0] :
( p(s(bool,i(s(fun(fun(cart(real,Q122006),bool),bool),i(s(fun(fun(cart(real,Q122006),bool),fun(fun(cart(real,Q122006),bool),bool)),subset),s(fun(cart(real,Q122006),bool),S0))),s(fun(cart(real,Q122006),bool),T0))))
=> p(s(bool,i(s(fun(fun(cart(real,Q122006),bool),bool),i(s(fun(fun(cart(real,Q122006),bool),fun(fun(cart(real,Q122006),bool),bool)),subset),s(fun(cart(real,Q122006),bool),i(s(fun(fun(cart(real,Q122006),bool),fun(cart(real,Q122006),bool)),span),s(fun(cart(real,Q122006),bool),S0))))),s(fun(cart(real,Q122006),bool),i(s(fun(fun(cart(real,Q122006),bool),fun(cart(real,Q122006),bool)),span),s(fun(cart(real,Q122006),bool),T0)))))) ) ).
fof(aSUBSPACEu_SPAN,axiom,
! [Q122015,S0] : p(s(bool,i(s(fun(fun(cart(real,Q122015),bool),bool),subspace),s(fun(cart(real,Q122015),bool),i(s(fun(fun(cart(real,Q122015),bool),fun(cart(real,Q122015),bool)),span),s(fun(cart(real,Q122015),bool),S0)))))) ).
fof(aSPANu_CLAUSESu_conjunct0,axiom,
! [Q122036,A5,S0] :
( p(s(bool,i(s(fun(fun(cart(real,Q122036),bool),bool),i(s(fun(cart(real,Q122036),fun(fun(cart(real,Q122036),bool),bool)),in),s(cart(real,Q122036),A5))),s(fun(cart(real,Q122036),bool),S0))))
=> p(s(bool,i(s(fun(fun(cart(real,Q122036),bool),bool),i(s(fun(cart(real,Q122036),fun(fun(cart(real,Q122036),bool),bool)),in),s(cart(real,Q122036),A5))),s(fun(cart(real,Q122036),bool),i(s(fun(fun(cart(real,Q122036),bool),fun(cart(real,Q122036),bool)),span),s(fun(cart(real,Q122036),bool),S0)))))) ) ).
fof(aSPANu_CLAUSESu_conjunct1,axiom,
! [Q122045] : p(s(bool,i(s(fun(fun(cart(real,Q122045),bool),bool),i(s(fun(cart(real,Q122045),fun(fun(cart(real,Q122045),bool),bool)),in),s(cart(real,Q122045),i(s(fun(num,cart(real,Q122045)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,Q122045),bool),i(s(fun(fun(cart(real,Q122045),bool),fun(cart(real,Q122045),bool)),span),s(fun(cart(real,Q122045),bool),s0)))))) ).
fof(aSPANu_CLAUSESu_conjunct2,axiom,
! [Q122111,X,Y,S0] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q122111),bool),bool),i(s(fun(cart(real,Q122111),fun(fun(cart(real,Q122111),bool),bool)),in),s(cart(real,Q122111),X))),s(fun(cart(real,Q122111),bool),i(s(fun(fun(cart(real,Q122111),bool),fun(cart(real,Q122111),bool)),span),s(fun(cart(real,Q122111),bool),S0))))))
& p(s(bool,i(s(fun(fun(cart(real,Q122111),bool),bool),i(s(fun(cart(real,Q122111),fun(fun(cart(real,Q122111),bool),bool)),in),s(cart(real,Q122111),Y))),s(fun(cart(real,Q122111),bool),i(s(fun(fun(cart(real,Q122111),bool),fun(cart(real,Q122111),bool)),span),s(fun(cart(real,Q122111),bool),S0)))))) )
=> p(s(bool,i(s(fun(fun(cart(real,Q122111),bool),bool),i(s(fun(cart(real,Q122111),fun(fun(cart(real,Q122111),bool),bool)),in),s(cart(real,Q122111),i(s(fun(cart(real,Q122111),cart(real,Q122111)),i(s(fun(cart(real,Q122111),fun(cart(real,Q122111),cart(real,Q122111))),vectoru_add),s(cart(real,Q122111),X))),s(cart(real,Q122111),Y))))),s(fun(cart(real,Q122111),bool),i(s(fun(fun(cart(real,Q122111),bool),fun(cart(real,Q122111),bool)),span),s(fun(cart(real,Q122111),bool),S0)))))) ) ).
fof(aSPANu_CLAUSESu_conjunct3,axiom,
! [Q122108,X,C0,S0] :
( p(s(bool,i(s(fun(fun(cart(real,Q122108),bool),bool),i(s(fun(cart(real,Q122108),fun(fun(cart(real,Q122108),bool),bool)),in),s(cart(real,Q122108),X))),s(fun(cart(real,Q122108),bool),i(s(fun(fun(cart(real,Q122108),bool),fun(cart(real,Q122108),bool)),span),s(fun(cart(real,Q122108),bool),S0))))))
=> p(s(bool,i(s(fun(fun(cart(real,Q122108),bool),bool),i(s(fun(cart(real,Q122108),fun(fun(cart(real,Q122108),bool),bool)),in),s(cart(real,Q122108),i(s(fun(cart(real,Q122108),cart(real,Q122108)),i(s(fun(real,fun(cart(real,Q122108),cart(real,Q122108))),r_),s(real,C0))),s(cart(real,Q122108),X))))),s(fun(cart(real,Q122108),bool),i(s(fun(fun(cart(real,Q122108),bool),fun(cart(real,Q122108),bool)),span),s(fun(cart(real,Q122108),bool),S0)))))) ) ).
fof(aSPANu_INDUCT,axiom,
! [Q122152,S0,H0] :
( ( ! [X] :
( p(s(bool,i(s(fun(fun(cart(real,Q122152),bool),bool),i(s(fun(cart(real,Q122152),fun(fun(cart(real,Q122152),bool),bool)),in),s(cart(real,Q122152),X))),s(fun(cart(real,Q122152),bool),S0))))
=> p(s(bool,i(s(fun(fun(cart(real,Q122152),bool),bool),i(s(fun(cart(real,Q122152),fun(fun(cart(real,Q122152),bool),bool)),in),s(cart(real,Q122152),X))),s(fun(cart(real,Q122152),bool),H0)))) )
& p(s(bool,i(s(fun(fun(cart(real,Q122152),bool),bool),subspace),s(fun(cart(real,Q122152),bool),H0)))) )
=> ! [X] :
( p(s(bool,i(s(fun(fun(cart(real,Q122152),bool),bool),i(s(fun(cart(real,Q122152),fun(fun(cart(real,Q122152),bool),bool)),in),s(cart(real,Q122152),X))),s(fun(cart(real,Q122152),bool),i(s(fun(fun(cart(real,Q122152),bool),fun(cart(real,Q122152),bool)),span),s(fun(cart(real,Q122152),bool),S0))))))
=> p(s(bool,i(s(fun(cart(real,Q122152),bool),H0),s(cart(real,Q122152),X)))) ) ) ).
fof(aSPANu_EMPTY,axiom,
! [Q122165] : s(fun(cart(real,Q122165),bool),i(s(fun(fun(cart(real,Q122165),bool),fun(cart(real,Q122165),bool)),span),s(fun(cart(real,Q122165),bool),empty))) = s(fun(cart(real,Q122165),bool),i(s(fun(fun(cart(real,Q122165),bool),fun(cart(real,Q122165),bool)),i(s(fun(cart(real,Q122165),fun(fun(cart(real,Q122165),bool),fun(cart(real,Q122165),bool))),insert),s(cart(real,Q122165),i(s(fun(num,cart(real,Q122165)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,Q122165),bool),empty))) ).
fof(aINDEPENDENTu_EMPTY,axiom,
! [Q122169] : p(s(bool,i(s(fun(fun(cart(real,Q122169),bool),bool),independent),s(fun(cart(real,Q122169),bool),empty)))) ).
fof(aINDEPENDENTu_NONZERO,axiom,
! [Q122179,S0] :
( p(s(bool,i(s(fun(fun(cart(real,Q122179),bool),bool),independent),s(fun(cart(real,Q122179),bool),S0))))
=> ~ p(s(bool,i(s(fun(fun(cart(real,Q122179),bool),bool),i(s(fun(cart(real,Q122179),fun(fun(cart(real,Q122179),bool),bool)),in),s(cart(real,Q122179),i(s(fun(num,cart(real,Q122179)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,Q122179),bool),S0)))) ) ).
fof(aINDEPENDENTu_MONO,axiom,
! [Q122205,S0,T0] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q122205),bool),bool),independent),s(fun(cart(real,Q122205),bool),T0))))
& p(s(bool,i(s(fun(fun(cart(real,Q122205),bool),bool),i(s(fun(fun(cart(real,Q122205),bool),fun(fun(cart(real,Q122205),bool),bool)),subset),s(fun(cart(real,Q122205),bool),S0))),s(fun(cart(real,Q122205),bool),T0)))) )
=> p(s(bool,i(s(fun(fun(cart(real,Q122205),bool),bool),independent),s(fun(cart(real,Q122205),bool),S0)))) ) ).
fof(aDEPENDENTu_MONO,axiom,
! [N,S0,T0] :
( ( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),dependent),s(fun(cart(real,N),bool),S0))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),T0)))) )
=> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),dependent),s(fun(cart(real,N),bool),T0)))) ) ).
fof(aSPANu_SUBSPACE,axiom,
! [Q122268,B0,S0] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q122268),bool),bool),i(s(fun(fun(cart(real,Q122268),bool),fun(fun(cart(real,Q122268),bool),bool)),subset),s(fun(cart(real,Q122268),bool),B0))),s(fun(cart(real,Q122268),bool),S0))))
& p(s(bool,i(s(fun(fun(cart(real,Q122268),bool),bool),i(s(fun(fun(cart(real,Q122268),bool),fun(fun(cart(real,Q122268),bool),bool)),subset),s(fun(cart(real,Q122268),bool),S0))),s(fun(cart(real,Q122268),bool),i(s(fun(fun(cart(real,Q122268),bool),fun(cart(real,Q122268),bool)),span),s(fun(cart(real,Q122268),bool),B0))))))
& p(s(bool,i(s(fun(fun(cart(real,Q122268),bool),bool),subspace),s(fun(cart(real,Q122268),bool),S0)))) )
=> s(fun(cart(real,Q122268),bool),i(s(fun(fun(cart(real,Q122268),bool),fun(cart(real,Q122268),bool)),span),s(fun(cart(real,Q122268),bool),B0))) = s(fun(cart(real,Q122268),bool),S0) ) ).
fof(aSPANu_INDUCTu_ALT,axiom,
! [N,S0,H0] :
( ( p(s(bool,i(s(fun(cart(real,N),bool),H0),s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))
& ! [C0,X,Y] :
( ( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),X))),s(fun(cart(real,N),bool),S0))))
& p(s(bool,i(s(fun(cart(real,N),bool),H0),s(cart(real,N),Y)))) )
=> p(s(bool,i(s(fun(cart(real,N),bool),H0),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,C0))),s(cart(real,N),X))))),s(cart(real,N),Y)))))) ) )
=> ! [X] :
( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),X))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0))))))
=> p(s(bool,i(s(fun(cart(real,N),bool),H0),s(cart(real,N),X)))) ) ) ).
fof(aSPANu_SUPERSET,axiom,
! [Q122358,X] :
( p(s(bool,i(s(fun(fun(cart(real,Q122358),bool),bool),i(s(fun(cart(real,Q122358),fun(fun(cart(real,Q122358),bool),bool)),in),s(cart(real,Q122358),X))),s(fun(cart(real,Q122358),bool),s0))))
=> p(s(bool,i(s(fun(fun(cart(real,Q122358),bool),bool),i(s(fun(cart(real,Q122358),fun(fun(cart(real,Q122358),bool),bool)),in),s(cart(real,Q122358),X))),s(fun(cart(real,Q122358),bool),i(s(fun(fun(cart(real,Q122358),bool),fun(cart(real,Q122358),bool)),span),s(fun(cart(real,Q122358),bool),s0)))))) ) ).
fof(aSPANu_INC,axiom,
! [Q122368,S0] : p(s(bool,i(s(fun(fun(cart(real,Q122368),bool),bool),i(s(fun(fun(cart(real,Q122368),bool),fun(fun(cart(real,Q122368),bool),bool)),subset),s(fun(cart(real,Q122368),bool),S0))),s(fun(cart(real,Q122368),bool),i(s(fun(fun(cart(real,Q122368),bool),fun(cart(real,Q122368),bool)),span),s(fun(cart(real,Q122368),bool),S0)))))) ).
fof(aSPANu_UNIONu_SUBSET,axiom,
! [Q122389,S0,T0] : p(s(bool,i(s(fun(fun(cart(real,Q122389),bool),bool),i(s(fun(fun(cart(real,Q122389),bool),fun(fun(cart(real,Q122389),bool),bool)),subset),s(fun(cart(real,Q122389),bool),i(s(fun(fun(cart(real,Q122389),bool),fun(cart(real,Q122389),bool)),i(s(fun(fun(cart(real,Q122389),bool),fun(fun(cart(real,Q122389),bool),fun(cart(real,Q122389),bool))),union),s(fun(cart(real,Q122389),bool),i(s(fun(fun(cart(real,Q122389),bool),fun(cart(real,Q122389),bool)),span),s(fun(cart(real,Q122389),bool),S0))))),s(fun(cart(real,Q122389),bool),i(s(fun(fun(cart(real,Q122389),bool),fun(cart(real,Q122389),bool)),span),s(fun(cart(real,Q122389),bool),T0))))))),s(fun(cart(real,Q122389),bool),i(s(fun(fun(cart(real,Q122389),bool),fun(cart(real,Q122389),bool)),span),s(fun(cart(real,Q122389),bool),i(s(fun(fun(cart(real,Q122389),bool),fun(cart(real,Q122389),bool)),i(s(fun(fun(cart(real,Q122389),bool),fun(fun(cart(real,Q122389),bool),fun(cart(real,Q122389),bool))),union),s(fun(cart(real,Q122389),bool),S0))),s(fun(cart(real,Q122389),bool),T0)))))))) ).
fof(aSPANu_UNIV,axiom,
! [N] : s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),univ))) = s(fun(cart(real,N),bool),univ) ).
fof(aSPANu_0,axiom,
! [Q122419] : p(s(bool,i(s(fun(fun(cart(real,Q122419),bool),bool),i(s(fun(cart(real,Q122419),fun(fun(cart(real,Q122419),bool),bool)),in),s(cart(real,Q122419),i(s(fun(num,cart(real,Q122419)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,Q122419),bool),i(s(fun(fun(cart(real,Q122419),bool),fun(cart(real,Q122419),bool)),span),s(fun(cart(real,Q122419),bool),s0)))))) ).
fof(aSPANu_ADD,axiom,
! [Q122457,X,Y,S0] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q122457),bool),bool),i(s(fun(cart(real,Q122457),fun(fun(cart(real,Q122457),bool),bool)),in),s(cart(real,Q122457),X))),s(fun(cart(real,Q122457),bool),i(s(fun(fun(cart(real,Q122457),bool),fun(cart(real,Q122457),bool)),span),s(fun(cart(real,Q122457),bool),S0))))))
& p(s(bool,i(s(fun(fun(cart(real,Q122457),bool),bool),i(s(fun(cart(real,Q122457),fun(fun(cart(real,Q122457),bool),bool)),in),s(cart(real,Q122457),Y))),s(fun(cart(real,Q122457),bool),i(s(fun(fun(cart(real,Q122457),bool),fun(cart(real,Q122457),bool)),span),s(fun(cart(real,Q122457),bool),S0)))))) )
=> p(s(bool,i(s(fun(fun(cart(real,Q122457),bool),bool),i(s(fun(cart(real,Q122457),fun(fun(cart(real,Q122457),bool),bool)),in),s(cart(real,Q122457),i(s(fun(cart(real,Q122457),cart(real,Q122457)),i(s(fun(cart(real,Q122457),fun(cart(real,Q122457),cart(real,Q122457))),vectoru_add),s(cart(real,Q122457),X))),s(cart(real,Q122457),Y))))),s(fun(cart(real,Q122457),bool),i(s(fun(fun(cart(real,Q122457),bool),fun(cart(real,Q122457),bool)),span),s(fun(cart(real,Q122457),bool),S0)))))) ) ).
fof(aSPANu_MUL,axiom,
! [Q122488,X,C0,S0] :
( p(s(bool,i(s(fun(fun(cart(real,Q122488),bool),bool),i(s(fun(cart(real,Q122488),fun(fun(cart(real,Q122488),bool),bool)),in),s(cart(real,Q122488),X))),s(fun(cart(real,Q122488),bool),i(s(fun(fun(cart(real,Q122488),bool),fun(cart(real,Q122488),bool)),span),s(fun(cart(real,Q122488),bool),S0))))))
=> p(s(bool,i(s(fun(fun(cart(real,Q122488),bool),bool),i(s(fun(cart(real,Q122488),fun(fun(cart(real,Q122488),bool),bool)),in),s(cart(real,Q122488),i(s(fun(cart(real,Q122488),cart(real,Q122488)),i(s(fun(real,fun(cart(real,Q122488),cart(real,Q122488))),r_),s(real,C0))),s(cart(real,Q122488),X))))),s(fun(cart(real,Q122488),bool),i(s(fun(fun(cart(real,Q122488),bool),fun(cart(real,Q122488),bool)),span),s(fun(cart(real,Q122488),bool),S0)))))) ) ).
fof(aSPANu_MULu_EQ,axiom,
! [N,X,C0,S0] :
( s(real,C0) != s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
=> s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,C0))),s(cart(real,N),X))))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0))))) = s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),X))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0))))) ) ).
fof(aSPANu_NEG,axiom,
! [Q122563,X,S0] :
( p(s(bool,i(s(fun(fun(cart(real,Q122563),bool),bool),i(s(fun(cart(real,Q122563),fun(fun(cart(real,Q122563),bool),bool)),in),s(cart(real,Q122563),X))),s(fun(cart(real,Q122563),bool),i(s(fun(fun(cart(real,Q122563),bool),fun(cart(real,Q122563),bool)),span),s(fun(cart(real,Q122563),bool),S0))))))
=> p(s(bool,i(s(fun(fun(cart(real,Q122563),bool),bool),i(s(fun(cart(real,Q122563),fun(fun(cart(real,Q122563),bool),bool)),in),s(cart(real,Q122563),i(s(fun(cart(real,Q122563),cart(real,Q122563)),vectoru_neg),s(cart(real,Q122563),X))))),s(fun(cart(real,Q122563),bool),i(s(fun(fun(cart(real,Q122563),bool),fun(cart(real,Q122563),bool)),span),s(fun(cart(real,Q122563),bool),S0)))))) ) ).
fof(aSPANu_NEGu_EQ,axiom,
! [Q122592,X,S0] : s(bool,i(s(fun(fun(cart(real,Q122592),bool),bool),i(s(fun(cart(real,Q122592),fun(fun(cart(real,Q122592),bool),bool)),in),s(cart(real,Q122592),i(s(fun(cart(real,Q122592),cart(real,Q122592)),vectoru_neg),s(cart(real,Q122592),X))))),s(fun(cart(real,Q122592),bool),i(s(fun(fun(cart(real,Q122592),bool),fun(cart(real,Q122592),bool)),span),s(fun(cart(real,Q122592),bool),S0))))) = s(bool,i(s(fun(fun(cart(real,Q122592),bool),bool),i(s(fun(cart(real,Q122592),fun(fun(cart(real,Q122592),bool),bool)),in),s(cart(real,Q122592),X))),s(fun(cart(real,Q122592),bool),i(s(fun(fun(cart(real,Q122592),bool),fun(cart(real,Q122592),bool)),span),s(fun(cart(real,Q122592),bool),S0))))) ).
fof(aSPANu_SUB,axiom,
! [Q122633,X,Y,S0] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q122633),bool),bool),i(s(fun(cart(real,Q122633),fun(fun(cart(real,Q122633),bool),bool)),in),s(cart(real,Q122633),X))),s(fun(cart(real,Q122633),bool),i(s(fun(fun(cart(real,Q122633),bool),fun(cart(real,Q122633),bool)),span),s(fun(cart(real,Q122633),bool),S0))))))
& p(s(bool,i(s(fun(fun(cart(real,Q122633),bool),bool),i(s(fun(cart(real,Q122633),fun(fun(cart(real,Q122633),bool),bool)),in),s(cart(real,Q122633),Y))),s(fun(cart(real,Q122633),bool),i(s(fun(fun(cart(real,Q122633),bool),fun(cart(real,Q122633),bool)),span),s(fun(cart(real,Q122633),bool),S0)))))) )
=> p(s(bool,i(s(fun(fun(cart(real,Q122633),bool),bool),i(s(fun(cart(real,Q122633),fun(fun(cart(real,Q122633),bool),bool)),in),s(cart(real,Q122633),i(s(fun(cart(real,Q122633),cart(real,Q122633)),i(s(fun(cart(real,Q122633),fun(cart(real,Q122633),cart(real,Q122633))),vectoru_sub),s(cart(real,Q122633),X))),s(cart(real,Q122633),Y))))),s(fun(cart(real,Q122633),bool),i(s(fun(fun(cart(real,Q122633),bool),fun(cart(real,Q122633),bool)),span),s(fun(cart(real,Q122633),bool),S0)))))) ) ).
fof(aSPANu_VSUM,axiom,
! [Q122668,Q122679,S0,F0,T0] :
( ( p(s(bool,i(s(fun(fun(Q122668,bool),bool),finite),s(fun(Q122668,bool),T0))))
& ! [X] :
( p(s(bool,i(s(fun(fun(Q122668,bool),bool),i(s(fun(Q122668,fun(fun(Q122668,bool),bool)),in),s(Q122668,X))),s(fun(Q122668,bool),T0))))
=> p(s(bool,i(s(fun(fun(cart(real,Q122679),bool),bool),i(s(fun(cart(real,Q122679),fun(fun(cart(real,Q122679),bool),bool)),in),s(cart(real,Q122679),i(s(fun(Q122668,cart(real,Q122679)),F0),s(Q122668,X))))),s(fun(cart(real,Q122679),bool),i(s(fun(fun(cart(real,Q122679),bool),fun(cart(real,Q122679),bool)),span),s(fun(cart(real,Q122679),bool),S0)))))) ) )
=> p(s(bool,i(s(fun(fun(cart(real,Q122679),bool),bool),i(s(fun(cart(real,Q122679),fun(fun(cart(real,Q122679),bool),bool)),in),s(cart(real,Q122679),i(s(fun(fun(Q122668,cart(real,Q122679)),cart(real,Q122679)),i(s(fun(fun(Q122668,bool),fun(fun(Q122668,cart(real,Q122679)),cart(real,Q122679))),vsum),s(fun(Q122668,bool),T0))),s(fun(Q122668,cart(real,Q122679)),F0))))),s(fun(cart(real,Q122679),bool),i(s(fun(fun(cart(real,Q122679),bool),fun(cart(real,Q122679),bool)),span),s(fun(cart(real,Q122679),bool),S0)))))) ) ).
fof(aSPANu_ADDu_EQ,axiom,
! [Q122739,S0,X,Y] :
( p(s(bool,i(s(fun(fun(cart(real,Q122739),bool),bool),i(s(fun(cart(real,Q122739),fun(fun(cart(real,Q122739),bool),bool)),in),s(cart(real,Q122739),X))),s(fun(cart(real,Q122739),bool),i(s(fun(fun(cart(real,Q122739),bool),fun(cart(real,Q122739),bool)),span),s(fun(cart(real,Q122739),bool),S0))))))
=> s(bool,i(s(fun(fun(cart(real,Q122739),bool),bool),i(s(fun(cart(real,Q122739),fun(fun(cart(real,Q122739),bool),bool)),in),s(cart(real,Q122739),i(s(fun(cart(real,Q122739),cart(real,Q122739)),i(s(fun(cart(real,Q122739),fun(cart(real,Q122739),cart(real,Q122739))),vectoru_add),s(cart(real,Q122739),X))),s(cart(real,Q122739),Y))))),s(fun(cart(real,Q122739),bool),i(s(fun(fun(cart(real,Q122739),bool),fun(cart(real,Q122739),bool)),span),s(fun(cart(real,Q122739),bool),S0))))) = s(bool,i(s(fun(fun(cart(real,Q122739),bool),bool),i(s(fun(cart(real,Q122739),fun(fun(cart(real,Q122739),bool),bool)),in),s(cart(real,Q122739),Y))),s(fun(cart(real,Q122739),bool),i(s(fun(fun(cart(real,Q122739),bool),fun(cart(real,Q122739),bool)),span),s(fun(cart(real,Q122739),bool),S0))))) ) ).
fof(aSPANu_EQu_SELF,axiom,
! [Q122754,S0] :
( s(fun(cart(real,Q122754),bool),i(s(fun(fun(cart(real,Q122754),bool),fun(cart(real,Q122754),bool)),span),s(fun(cart(real,Q122754),bool),S0))) = s(fun(cart(real,Q122754),bool),S0)
<=> p(s(bool,i(s(fun(fun(cart(real,Q122754),bool),bool),subspace),s(fun(cart(real,Q122754),bool),S0)))) ) ).
fof(aSPANu_SUBSETu_SUBSPACE,axiom,
! [N,S0,T0] :
( ( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),T0))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),subspace),s(fun(cart(real,N),bool),T0)))) )
=> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0))))),s(fun(cart(real,N),bool),T0)))) ) ).
fof(aSUBSPACEu_TRANSLATIONu_SELF,axiom,
! [Q122839,U_0] :
( ! [A5,X] : s(cart(real,Q122839),i(s(fun(cart(real,Q122839),cart(real,Q122839)),i(s(fun(cart(real,Q122839),fun(cart(real,Q122839),cart(real,Q122839))),U_0),s(cart(real,Q122839),A5))),s(cart(real,Q122839),X))) = s(cart(real,Q122839),i(s(fun(cart(real,Q122839),cart(real,Q122839)),i(s(fun(cart(real,Q122839),fun(cart(real,Q122839),cart(real,Q122839))),vectoru_add),s(cart(real,Q122839),A5))),s(cart(real,Q122839),X)))
=> ! [S0,A5] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q122839),bool),bool),subspace),s(fun(cart(real,Q122839),bool),S0))))
& p(s(bool,i(s(fun(fun(cart(real,Q122839),bool),bool),i(s(fun(cart(real,Q122839),fun(fun(cart(real,Q122839),bool),bool)),in),s(cart(real,Q122839),A5))),s(fun(cart(real,Q122839),bool),S0)))) )
=> s(fun(cart(real,Q122839),bool),i(s(fun(fun(cart(real,Q122839),bool),fun(cart(real,Q122839),bool)),i(s(fun(fun(cart(real,Q122839),cart(real,Q122839)),fun(fun(cart(real,Q122839),bool),fun(cart(real,Q122839),bool))),image),s(fun(cart(real,Q122839),cart(real,Q122839)),i(s(fun(cart(real,Q122839),fun(cart(real,Q122839),cart(real,Q122839))),U_0),s(cart(real,Q122839),A5))))),s(fun(cart(real,Q122839),bool),S0))) = s(fun(cart(real,Q122839),bool),S0) ) ) ).
fof(aSUBSPACEu_TRANSLATIONu_SELFu_EQ,axiom,
! [N,U_0] :
( ! [A5,X] : s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),U_0),s(cart(real,N),A5))),s(cart(real,N),X))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),A5))),s(cart(real,N),X)))
=> ! [S0,A5] :
( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),subspace),s(fun(cart(real,N),bool),S0))))
=> ( s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,N),cart(real,N)),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),U_0),s(cart(real,N),A5))))),s(fun(cart(real,N),bool),S0))) = s(fun(cart(real,N),bool),S0)
<=> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),A5))),s(fun(cart(real,N),bool),S0)))) ) ) ) ).
fof(aSUBSPACEu_SUMS,axiom,
! [Q122994,U_0] :
( ! [S0,T0,GENR_PVARR_298] :
( p(s(bool,i(s(fun(cart(real,Q122994),bool),i(s(fun(fun(cart(real,Q122994),bool),fun(cart(real,Q122994),bool)),i(s(fun(fun(cart(real,Q122994),bool),fun(fun(cart(real,Q122994),bool),fun(cart(real,Q122994),bool))),U_0),s(fun(cart(real,Q122994),bool),S0))),s(fun(cart(real,Q122994),bool),T0))),s(cart(real,Q122994),GENR_PVARR_298))))
<=> ? [X,Y,V] :
( ( p(s(bool,V))
<=> ( p(s(bool,i(s(fun(fun(cart(real,Q122994),bool),bool),i(s(fun(cart(real,Q122994),fun(fun(cart(real,Q122994),bool),bool)),in),s(cart(real,Q122994),X))),s(fun(cart(real,Q122994),bool),S0))))
& p(s(bool,i(s(fun(fun(cart(real,Q122994),bool),bool),i(s(fun(cart(real,Q122994),fun(fun(cart(real,Q122994),bool),bool)),in),s(cart(real,Q122994),Y))),s(fun(cart(real,Q122994),bool),T0)))) ) )
& p(s(bool,i(s(fun(cart(real,Q122994),bool),i(s(fun(bool,fun(cart(real,Q122994),bool)),i(s(fun(cart(real,Q122994),fun(bool,fun(cart(real,Q122994),bool))),setspec),s(cart(real,Q122994),GENR_PVARR_298))),s(bool,V))),s(cart(real,Q122994),i(s(fun(cart(real,Q122994),cart(real,Q122994)),i(s(fun(cart(real,Q122994),fun(cart(real,Q122994),cart(real,Q122994))),vectoru_add),s(cart(real,Q122994),X))),s(cart(real,Q122994),Y)))))) ) )
=> ! [S0,T0] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q122994),bool),bool),subspace),s(fun(cart(real,Q122994),bool),S0))))
& p(s(bool,i(s(fun(fun(cart(real,Q122994),bool),bool),subspace),s(fun(cart(real,Q122994),bool),T0)))) )
=> p(s(bool,i(s(fun(fun(cart(real,Q122994),bool),bool),subspace),s(fun(cart(real,Q122994),bool),i(s(fun(fun(cart(real,Q122994),bool),fun(cart(real,Q122994),bool)),gspec),s(fun(cart(real,Q122994),bool),i(s(fun(fun(cart(real,Q122994),bool),fun(cart(real,Q122994),bool)),i(s(fun(fun(cart(real,Q122994),bool),fun(fun(cart(real,Q122994),bool),fun(cart(real,Q122994),bool))),U_0),s(fun(cart(real,Q122994),bool),S0))),s(fun(cart(real,Q122994),bool),T0)))))))) ) ) ).
fof(aSPANu_UNION,axiom,
! [N,U_0] :
( ! [S0,T0,GENR_PVARR_299] :
( p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),U_0),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),T0))),s(cart(real,N),GENR_PVARR_299))))
<=> ? [X,Y,V] :
( ( p(s(bool,V))
<=> ( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),X))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0))))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),Y))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),T0)))))) ) )
& p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(bool,fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(bool,fun(cart(real,N),bool))),setspec),s(cart(real,N),GENR_PVARR_299))),s(bool,V))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),X))),s(cart(real,N),Y)))))) ) )
=> ! [S0,T0] : s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),union),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),T0))))) = s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),gspec),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),U_0),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),T0))))) ) ).
fof(aSPANu_LINEARu_IMAGE,axiom,
! [N,M,F0,S0] :
( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
=> s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,M),bool),S0))))) = s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),span),s(fun(cart(real,M),bool),S0))))) ) ).
fof(aDEPENDENTu_LINEARu_IMAGEu_EQ,axiom,
! [N,M,F0,S0] :
( ( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
& ! [X,Y] :
( s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),Y)))
=> s(cart(real,M),X) = s(cart(real,M),Y) ) )
=> s(bool,i(s(fun(fun(cart(real,N),bool),bool),dependent),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,M),bool),S0))))) = s(bool,i(s(fun(fun(cart(real,M),bool),bool),dependent),s(fun(cart(real,M),bool),S0))) ) ).
fof(aDEPENDENTu_LINEARu_IMAGE,axiom,
! [N,M,F0,S0] :
( ( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
& ! [X,Y] :
( ( p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),S0))))
& p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),Y))),s(fun(cart(real,M),bool),S0))))
& s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),Y))) )
=> s(cart(real,M),X) = s(cart(real,M),Y) )
& p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),dependent),s(fun(cart(real,M),bool),S0)))) )
=> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),dependent),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,M),bool),S0)))))) ) ).
fof(aINDEPENDENTu_LINEARu_IMAGEu_EQ,axiom,
! [N,M,F0,S0] :
( ( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
& ! [X,Y] :
( s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),Y)))
=> s(cart(real,M),X) = s(cart(real,M),Y) ) )
=> s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,M),bool),S0))))) = s(bool,i(s(fun(fun(cart(real,M),bool),bool),independent),s(fun(cart(real,M),bool),S0))) ) ).
fof(aSPANu_BREAKDOWN,axiom,
! [N,B0,S0,A5] :
( ( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),B0))),s(fun(cart(real,N),bool),S0))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),A5))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0)))))) )
=> ? [K0] : p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),A5))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,K0))),s(cart(real,N),B0))))))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(cart(real,N),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),fun(cart(real,N),bool))),delete),s(fun(cart(real,N),bool),S0))),s(cart(real,N),B0)))))))) ) ).
fof(aSPANu_BREAKDOWNu_EQ,axiom,
! [N,A5,S0] :
( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),x))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),A5))),s(fun(cart(real,N),bool),S0))))))))
<=> ? [K0] : p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),x))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,K0))),s(cart(real,N),A5))))))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0)))))) ) ).
fof(aSPANu_INSERTu_0,axiom,
! [Q123623,S0] : s(fun(cart(real,Q123623),bool),i(s(fun(fun(cart(real,Q123623),bool),fun(cart(real,Q123623),bool)),span),s(fun(cart(real,Q123623),bool),i(s(fun(fun(cart(real,Q123623),bool),fun(cart(real,Q123623),bool)),i(s(fun(cart(real,Q123623),fun(fun(cart(real,Q123623),bool),fun(cart(real,Q123623),bool))),insert),s(cart(real,Q123623),i(s(fun(num,cart(real,Q123623)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,Q123623),bool),S0))))) = s(fun(cart(real,Q123623),bool),i(s(fun(fun(cart(real,Q123623),bool),fun(cart(real,Q123623),bool)),span),s(fun(cart(real,Q123623),bool),S0))) ).
fof(aSPANu_SING,axiom,
! [Q123656,U_0] :
( ! [A5,GENR_PVARR_301] :
( p(s(bool,i(s(fun(cart(real,Q123656),bool),i(s(fun(cart(real,Q123656),fun(cart(real,Q123656),bool)),U_0),s(cart(real,Q123656),A5))),s(cart(real,Q123656),GENR_PVARR_301))))
<=> ? [U] : p(s(bool,i(s(fun(cart(real,Q123656),bool),i(s(fun(bool,fun(cart(real,Q123656),bool)),i(s(fun(cart(real,Q123656),fun(bool,fun(cart(real,Q123656),bool))),setspec),s(cart(real,Q123656),GENR_PVARR_301))),s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,U))),s(fun(real,bool),univ))))),s(cart(real,Q123656),i(s(fun(cart(real,Q123656),cart(real,Q123656)),i(s(fun(real,fun(cart(real,Q123656),cart(real,Q123656))),r_),s(real,U))),s(cart(real,Q123656),A5)))))) )
=> ! [A5] : s(fun(cart(real,Q123656),bool),i(s(fun(fun(cart(real,Q123656),bool),fun(cart(real,Q123656),bool)),span),s(fun(cart(real,Q123656),bool),i(s(fun(fun(cart(real,Q123656),bool),fun(cart(real,Q123656),bool)),i(s(fun(cart(real,Q123656),fun(fun(cart(real,Q123656),bool),fun(cart(real,Q123656),bool))),insert),s(cart(real,Q123656),A5))),s(fun(cart(real,Q123656),bool),empty))))) = s(fun(cart(real,Q123656),bool),i(s(fun(fun(cart(real,Q123656),bool),fun(cart(real,Q123656),bool)),gspec),s(fun(cart(real,Q123656),bool),i(s(fun(cart(real,Q123656),fun(cart(real,Q123656),bool)),U_0),s(cart(real,Q123656),A5))))) ) ).
fof(aSPANu_2,axiom,
! [Q123742,U_0] :
( ! [A5,B0,GENR_PVARR_302] :
( p(s(bool,i(s(fun(cart(real,Q123742),bool),i(s(fun(cart(real,Q123742),fun(cart(real,Q123742),bool)),i(s(fun(cart(real,Q123742),fun(cart(real,Q123742),fun(cart(real,Q123742),bool))),U_0),s(cart(real,Q123742),A5))),s(cart(real,Q123742),B0))),s(cart(real,Q123742),GENR_PVARR_302))))
<=> ? [U,V,V0] :
( ( p(s(bool,V0))
<=> ( p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,U))),s(fun(real,bool),univ))))
& p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,V))),s(fun(real,bool),univ)))) ) )
& p(s(bool,i(s(fun(cart(real,Q123742),bool),i(s(fun(bool,fun(cart(real,Q123742),bool)),i(s(fun(cart(real,Q123742),fun(bool,fun(cart(real,Q123742),bool))),setspec),s(cart(real,Q123742),GENR_PVARR_302))),s(bool,V0))),s(cart(real,Q123742),i(s(fun(cart(real,Q123742),cart(real,Q123742)),i(s(fun(cart(real,Q123742),fun(cart(real,Q123742),cart(real,Q123742))),vectoru_add),s(cart(real,Q123742),i(s(fun(cart(real,Q123742),cart(real,Q123742)),i(s(fun(real,fun(cart(real,Q123742),cart(real,Q123742))),r_),s(real,U))),s(cart(real,Q123742),A5))))),s(cart(real,Q123742),i(s(fun(cart(real,Q123742),cart(real,Q123742)),i(s(fun(real,fun(cart(real,Q123742),cart(real,Q123742))),r_),s(real,V))),s(cart(real,Q123742),B0)))))))) ) )
=> ! [A5,B0] : s(fun(cart(real,Q123742),bool),i(s(fun(fun(cart(real,Q123742),bool),fun(cart(real,Q123742),bool)),span),s(fun(cart(real,Q123742),bool),i(s(fun(fun(cart(real,Q123742),bool),fun(cart(real,Q123742),bool)),i(s(fun(cart(real,Q123742),fun(fun(cart(real,Q123742),bool),fun(cart(real,Q123742),bool))),insert),s(cart(real,Q123742),A5))),s(fun(cart(real,Q123742),bool),i(s(fun(fun(cart(real,Q123742),bool),fun(cart(real,Q123742),bool)),i(s(fun(cart(real,Q123742),fun(fun(cart(real,Q123742),bool),fun(cart(real,Q123742),bool))),insert),s(cart(real,Q123742),B0))),s(fun(cart(real,Q123742),bool),empty))))))) = s(fun(cart(real,Q123742),bool),i(s(fun(fun(cart(real,Q123742),bool),fun(cart(real,Q123742),bool)),gspec),s(fun(cart(real,Q123742),bool),i(s(fun(cart(real,Q123742),fun(cart(real,Q123742),bool)),i(s(fun(cart(real,Q123742),fun(cart(real,Q123742),fun(cart(real,Q123742),bool))),U_0),s(cart(real,Q123742),A5))),s(cart(real,Q123742),B0))))) ) ).
fof(aSPANu_3,axiom,
! [Q123857,U_0] :
( ! [A5,B0,C0,GENR_PVARR_303] :
( p(s(bool,i(s(fun(cart(real,Q123857),bool),i(s(fun(cart(real,Q123857),fun(cart(real,Q123857),bool)),i(s(fun(cart(real,Q123857),fun(cart(real,Q123857),fun(cart(real,Q123857),bool))),i(s(fun(cart(real,Q123857),fun(cart(real,Q123857),fun(cart(real,Q123857),fun(cart(real,Q123857),bool)))),U_0),s(cart(real,Q123857),A5))),s(cart(real,Q123857),B0))),s(cart(real,Q123857),C0))),s(cart(real,Q123857),GENR_PVARR_303))))
<=> ? [U,V,W,V0] :
( ( p(s(bool,V0))
<=> ( p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,U))),s(fun(real,bool),univ))))
& p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,V))),s(fun(real,bool),univ))))
& p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,W))),s(fun(real,bool),univ)))) ) )
& p(s(bool,i(s(fun(cart(real,Q123857),bool),i(s(fun(bool,fun(cart(real,Q123857),bool)),i(s(fun(cart(real,Q123857),fun(bool,fun(cart(real,Q123857),bool))),setspec),s(cart(real,Q123857),GENR_PVARR_303))),s(bool,V0))),s(cart(real,Q123857),i(s(fun(cart(real,Q123857),cart(real,Q123857)),i(s(fun(cart(real,Q123857),fun(cart(real,Q123857),cart(real,Q123857))),vectoru_add),s(cart(real,Q123857),i(s(fun(cart(real,Q123857),cart(real,Q123857)),i(s(fun(real,fun(cart(real,Q123857),cart(real,Q123857))),r_),s(real,U))),s(cart(real,Q123857),A5))))),s(cart(real,Q123857),i(s(fun(cart(real,Q123857),cart(real,Q123857)),i(s(fun(cart(real,Q123857),fun(cart(real,Q123857),cart(real,Q123857))),vectoru_add),s(cart(real,Q123857),i(s(fun(cart(real,Q123857),cart(real,Q123857)),i(s(fun(real,fun(cart(real,Q123857),cart(real,Q123857))),r_),s(real,V))),s(cart(real,Q123857),B0))))),s(cart(real,Q123857),i(s(fun(cart(real,Q123857),cart(real,Q123857)),i(s(fun(real,fun(cart(real,Q123857),cart(real,Q123857))),r_),s(real,W))),s(cart(real,Q123857),C0)))))))))) ) )
=> ! [A5,B0,C0] : s(fun(cart(real,Q123857),bool),i(s(fun(fun(cart(real,Q123857),bool),fun(cart(real,Q123857),bool)),span),s(fun(cart(real,Q123857),bool),i(s(fun(fun(cart(real,Q123857),bool),fun(cart(real,Q123857),bool)),i(s(fun(cart(real,Q123857),fun(fun(cart(real,Q123857),bool),fun(cart(real,Q123857),bool))),insert),s(cart(real,Q123857),A5))),s(fun(cart(real,Q123857),bool),i(s(fun(fun(cart(real,Q123857),bool),fun(cart(real,Q123857),bool)),i(s(fun(cart(real,Q123857),fun(fun(cart(real,Q123857),bool),fun(cart(real,Q123857),bool))),insert),s(cart(real,Q123857),B0))),s(fun(cart(real,Q123857),bool),i(s(fun(fun(cart(real,Q123857),bool),fun(cart(real,Q123857),bool)),i(s(fun(cart(real,Q123857),fun(fun(cart(real,Q123857),bool),fun(cart(real,Q123857),bool))),insert),s(cart(real,Q123857),C0))),s(fun(cart(real,Q123857),bool),empty))))))))) = s(fun(cart(real,Q123857),bool),i(s(fun(fun(cart(real,Q123857),bool),fun(cart(real,Q123857),bool)),gspec),s(fun(cart(real,Q123857),bool),i(s(fun(cart(real,Q123857),fun(cart(real,Q123857),bool)),i(s(fun(cart(real,Q123857),fun(cart(real,Q123857),fun(cart(real,Q123857),bool))),i(s(fun(cart(real,Q123857),fun(cart(real,Q123857),fun(cart(real,Q123857),fun(cart(real,Q123857),bool)))),U_0),s(cart(real,Q123857),A5))),s(cart(real,Q123857),B0))),s(cart(real,Q123857),C0))))) ) ).
fof(aINu_SPANu_INSERT,axiom,
! [N,A5,B0,S0] :
( ( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),A5))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),B0))),s(fun(cart(real,N),bool),S0))))))))
& ~ p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),A5))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0)))))) )
=> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),B0))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),A5))),s(fun(cart(real,N),bool),S0)))))))) ) ).
fof(aINu_SPANu_DELETE,axiom,
! [Q124006,A5,B0,S0] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q124006),bool),bool),i(s(fun(cart(real,Q124006),fun(fun(cart(real,Q124006),bool),bool)),in),s(cart(real,Q124006),A5))),s(fun(cart(real,Q124006),bool),i(s(fun(fun(cart(real,Q124006),bool),fun(cart(real,Q124006),bool)),span),s(fun(cart(real,Q124006),bool),S0))))))
& ~ p(s(bool,i(s(fun(fun(cart(real,Q124006),bool),bool),i(s(fun(cart(real,Q124006),fun(fun(cart(real,Q124006),bool),bool)),in),s(cart(real,Q124006),A5))),s(fun(cart(real,Q124006),bool),i(s(fun(fun(cart(real,Q124006),bool),fun(cart(real,Q124006),bool)),span),s(fun(cart(real,Q124006),bool),i(s(fun(cart(real,Q124006),fun(cart(real,Q124006),bool)),i(s(fun(fun(cart(real,Q124006),bool),fun(cart(real,Q124006),fun(cart(real,Q124006),bool))),delete),s(fun(cart(real,Q124006),bool),S0))),s(cart(real,Q124006),B0)))))))) )
=> p(s(bool,i(s(fun(fun(cart(real,Q124006),bool),bool),i(s(fun(cart(real,Q124006),fun(fun(cart(real,Q124006),bool),bool)),in),s(cart(real,Q124006),B0))),s(fun(cart(real,Q124006),bool),i(s(fun(fun(cart(real,Q124006),bool),fun(cart(real,Q124006),bool)),span),s(fun(cart(real,Q124006),bool),i(s(fun(fun(cart(real,Q124006),bool),fun(cart(real,Q124006),bool)),i(s(fun(cart(real,Q124006),fun(fun(cart(real,Q124006),bool),fun(cart(real,Q124006),bool))),insert),s(cart(real,Q124006),A5))),s(fun(cart(real,Q124006),bool),i(s(fun(cart(real,Q124006),fun(cart(real,Q124006),bool)),i(s(fun(fun(cart(real,Q124006),bool),fun(cart(real,Q124006),fun(cart(real,Q124006),bool))),delete),s(fun(cart(real,Q124006),bool),S0))),s(cart(real,Q124006),B0)))))))))) ) ).
fof(aEQu_SPANu_INSERTu_EQ,axiom,
! [N,S0,X,Y] :
( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),X))),s(cart(real,N),Y))))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0))))))
=> s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),X))),s(fun(cart(real,N),bool),S0))))) = s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),Y))),s(fun(cart(real,N),bool),S0))))) ) ).
fof(aSPANu_TRANS,axiom,
! [N,X,Y,S0] :
( ( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),X))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0))))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),Y))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),X))),s(fun(cart(real,N),bool),S0)))))))) )
=> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),Y))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0)))))) ) ).
fof(aSPANu_EXPLICIT,axiom,
! [N,U_1] :
( ! [U,V] : s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),real),fun(cart(real,N),cart(real,N))),U_1),s(fun(cart(real,N),real),U))),s(cart(real,N),V))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(cart(real,N),real),U),s(cart(real,N),V))))),s(cart(real,N),V)))
=> ! [U_0] :
( ! [P0,GENR_PVARR_304] :
( p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),U_0),s(fun(cart(real,N),bool),P0))),s(cart(real,N),GENR_PVARR_304))))
<=> ? [Y,V] :
( ( p(s(bool,V))
<=> ? [S0,U] :
( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),S0))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),P0))))
& s(cart(real,N),i(s(fun(fun(cart(real,N),cart(real,N)),cart(real,N)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),cart(real,N)),cart(real,N))),vsum),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),real),fun(cart(real,N),cart(real,N))),U_1),s(fun(cart(real,N),real),U))))) = s(cart(real,N),Y) ) )
& p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(bool,fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(bool,fun(cart(real,N),bool))),setspec),s(cart(real,N),GENR_PVARR_304))),s(bool,V))),s(cart(real,N),Y)))) ) )
=> ! [P0] : s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),P0))) = s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),gspec),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),U_0),s(fun(cart(real,N),bool),P0))))) ) ) ).
fof(aDEPENDENTu_EXPLICIT,axiom,
! [N,U_0] :
( ! [U,V] : s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),real),fun(cart(real,N),cart(real,N))),U_0),s(fun(cart(real,N),real),U))),s(cart(real,N),V))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(cart(real,N),real),U),s(cart(real,N),V))))),s(cart(real,N),V)))
=> ! [P0] :
( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),dependent),s(fun(cart(real,N),bool),P0))))
<=> ? [S0,U] :
( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),S0))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),P0))))
& ? [V] :
( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),V))),s(fun(cart(real,N),bool),S0))))
& s(real,i(s(fun(cart(real,N),real),U),s(cart(real,N),V))) != s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) )
& s(cart(real,N),i(s(fun(fun(cart(real,N),cart(real,N)),cart(real,N)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),cart(real,N)),cart(real,N))),vsum),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),real),fun(cart(real,N),cart(real,N))),U_0),s(fun(cart(real,N),real),U))))) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ) ) ).
fof(aDEPENDENTu_FINITE,axiom,
! [N,U_0] :
( ! [U,V] : s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),real),fun(cart(real,N),cart(real,N))),U_0),s(fun(cart(real,N),real),U))),s(cart(real,N),V))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(cart(real,N),real),U),s(cart(real,N),V))))),s(cart(real,N),V)))
=> ! [S0] :
( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),S0))))
=> ( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),dependent),s(fun(cart(real,N),bool),S0))))
<=> ? [U] :
( ? [V] :
( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),V))),s(fun(cart(real,N),bool),S0))))
& s(real,i(s(fun(cart(real,N),real),U),s(cart(real,N),V))) != s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) )
& s(cart(real,N),i(s(fun(fun(cart(real,N),cart(real,N)),cart(real,N)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),cart(real,N)),cart(real,N))),vsum),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),real),fun(cart(real,N),cart(real,N))),U_0),s(fun(cart(real,N),real),U))))) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ) ) ) ).
fof(aSPANu_FINITE,axiom,
! [N,U_1] :
( ! [U,V] : s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),real),fun(cart(real,N),cart(real,N))),U_1),s(fun(cart(real,N),real),U))),s(cart(real,N),V))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(cart(real,N),real),U),s(cart(real,N),V))))),s(cart(real,N),V)))
=> ! [U_0] :
( ! [S0,GENR_PVARR_307] :
( p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),U_0),s(fun(cart(real,N),bool),S0))),s(cart(real,N),GENR_PVARR_307))))
<=> ? [Y,V] :
( ( p(s(bool,V))
<=> ? [U] : s(cart(real,N),i(s(fun(fun(cart(real,N),cart(real,N)),cart(real,N)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),cart(real,N)),cart(real,N))),vsum),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),real),fun(cart(real,N),cart(real,N))),U_1),s(fun(cart(real,N),real),U))))) = s(cart(real,N),Y) )
& p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(bool,fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(bool,fun(cart(real,N),bool))),setspec),s(cart(real,N),GENR_PVARR_307))),s(bool,V))),s(cart(real,N),Y)))) ) )
=> ! [S0] :
( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),S0))))
=> s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0))) = s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),gspec),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),U_0),s(fun(cart(real,N),bool),S0))))) ) ) ) ).
fof(aSPANu_STDBASIS,axiom,
! [N,U_0] :
( ! [GENR_PVARR_308] :
( p(s(bool,i(s(fun(cart(real,N),bool),U_0),s(cart(real,N),GENR_PVARR_308))))
<=> ? [I0,V] :
( ( p(s(bool,V))
<=> ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) ) )
& p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(bool,fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(bool,fun(cart(real,N),bool))),setspec),s(cart(real,N),GENR_PVARR_308))),s(bool,V))),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,I0)))))) ) )
=> s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),gspec),s(fun(cart(real,N),bool),U_0))))) = s(fun(cart(real,N),bool),univ) ) ).
fof(aHASu_SIZEu_STDBASIS,axiom,
! [N,U_0] :
( ! [GENR_PVARR_311] :
( p(s(bool,i(s(fun(cart(real,N),bool),U_0),s(cart(real,N),GENR_PVARR_311))))
<=> ? [I0,V] :
( ( p(s(bool,V))
<=> ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) ) )
& p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(bool,fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(bool,fun(cart(real,N),bool))),setspec),s(cart(real,N),GENR_PVARR_311))),s(bool,V))),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,I0)))))) ) )
=> p(s(bool,i(s(fun(num,bool),i(s(fun(fun(cart(real,N),bool),fun(num,bool)),hasu_size),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),gspec),s(fun(cart(real,N),bool),U_0))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) ) ).
fof(aFINITEu_STDBASIS,axiom,
! [N,U_0] :
( ! [GENR_PVARR_312] :
( p(s(bool,i(s(fun(cart(real,N),bool),U_0),s(cart(real,N),GENR_PVARR_312))))
<=> ? [I0,V] :
( ( p(s(bool,V))
<=> ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) ) )
& p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(bool,fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(bool,fun(cart(real,N),bool))),setspec),s(cart(real,N),GENR_PVARR_312))),s(bool,V))),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,I0)))))) ) )
=> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),gspec),s(fun(cart(real,N),bool),U_0)))))) ) ).
fof(aCARDu_STDBASIS,axiom,
! [N,U_0] :
( ! [GENR_PVARR_313] :
( p(s(bool,i(s(fun(cart(real,N),bool),U_0),s(cart(real,N),GENR_PVARR_313))))
<=> ? [I0,V] :
( ( p(s(bool,V))
<=> ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) ) )
& p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(bool,fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(bool,fun(cart(real,N),bool))),setspec),s(cart(real,N),GENR_PVARR_313))),s(bool,V))),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,I0)))))) ) )
=> s(num,i(s(fun(fun(cart(real,N),bool),num),card),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),gspec),s(fun(cart(real,N),bool),U_0))))) = s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))) ) ).
fof(aINu_SPANu_IMAGEu_BASIS,axiom,
! [N,X,S0] :
( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),X))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(fun(num,bool),fun(cart(real,N),bool)),i(s(fun(fun(num,cart(real,N)),fun(fun(num,bool),fun(cart(real,N),bool))),image),s(fun(num,cart(real,N)),basis))),s(fun(num,bool),S0))))))))
<=> ! [I0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))
& ~ p(s(bool,i(s(fun(fun(num,bool),bool),i(s(fun(num,fun(fun(num,bool),bool)),in),s(num,I0))),s(fun(num,bool),S0)))) )
=> s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ) ).
fof(aINDEPENDENTu_STDBASIS,axiom,
! [N,U_0] :
( ! [GENR_PVARR_318] :
( p(s(bool,i(s(fun(cart(real,N),bool),U_0),s(cart(real,N),GENR_PVARR_318))))
<=> ? [I0,V] :
( ( p(s(bool,V))
<=> ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) ) )
& p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(bool,fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(bool,fun(cart(real,N),bool))),setspec),s(cart(real,N),GENR_PVARR_318))),s(bool,V))),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,I0)))))) ) )
=> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),gspec),s(fun(cart(real,N),bool),U_0)))))) ) ).
fof(aINDEPENDENTu_INSERT,axiom,
! [N,A5,S0] :
? [V] :
( ( p(s(bool,V))
<=> ( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),S0))))
& ~ p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),A5))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0)))))) ) )
& s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),A5))),s(fun(cart(real,N),bool),S0))))) = s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),i(s(fun(bool,fun(bool,fun(bool,bool))),cond),s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),A5))),s(fun(cart(real,N),bool),S0))))),s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),S0))))),s(bool,V))) ) ).
fof(aSPANNINGu_SUBSETu_INDEPENDENT,axiom,
! [N,S0,T0] :
( ( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),T0))),s(fun(cart(real,N),bool),S0))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),S0))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),T0)))))) )
=> s(fun(cart(real,N),bool),S0) = s(fun(cart(real,N),bool),T0) ) ).
fof(aEXCHANGEu_LEMMA,axiom,
! [N,S0,T0] :
( ( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),T0))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),S0))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),T0)))))) )
=> ? [TI_] :
( p(s(bool,i(s(fun(num,bool),i(s(fun(fun(cart(real,N),bool),fun(num,bool)),hasu_size),s(fun(cart(real,N),bool),TI_))),s(num,i(s(fun(fun(cart(real,N),bool),num),card),s(fun(cart(real,N),bool),T0))))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),TI_))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),TI_))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),union),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),T0))))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),TI_)))))) ) ) ).
fof(aINDEPENDENTu_SPANu_BOUND,axiom,
! [Q125545,S0,T0] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q125545),bool),bool),finite),s(fun(cart(real,Q125545),bool),T0))))
& p(s(bool,i(s(fun(fun(cart(real,Q125545),bool),bool),independent),s(fun(cart(real,Q125545),bool),S0))))
& p(s(bool,i(s(fun(fun(cart(real,Q125545),bool),bool),i(s(fun(fun(cart(real,Q125545),bool),fun(fun(cart(real,Q125545),bool),bool)),subset),s(fun(cart(real,Q125545),bool),S0))),s(fun(cart(real,Q125545),bool),i(s(fun(fun(cart(real,Q125545),bool),fun(cart(real,Q125545),bool)),span),s(fun(cart(real,Q125545),bool),T0)))))) )
=> ( p(s(bool,i(s(fun(fun(cart(real,Q125545),bool),bool),finite),s(fun(cart(real,Q125545),bool),S0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(cart(real,Q125545),bool),num),card),s(fun(cart(real,Q125545),bool),S0))))),s(num,i(s(fun(fun(cart(real,Q125545),bool),num),card),s(fun(cart(real,Q125545),bool),T0)))))) ) ) ).
fof(aINDEPENDENTu_BOUND,axiom,
! [N,S0] :
( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),S0))))
=> ( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),S0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(cart(real,N),bool),num),card),s(fun(cart(real,N),bool),S0))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) ) ) ).
fof(aDEPENDENTu_BIGGERSET,axiom,
! [N,S0] :
( ( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),S0))))
=> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_),s(num,i(s(fun(fun(cart(real,N),bool),num),card),s(fun(cart(real,N),bool),S0))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) )
=> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),dependent),s(fun(cart(real,N),bool),S0)))) ) ).
fof(aINDEPENDENTu_IMPu_FINITE,axiom,
! [N,S0] :
( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),S0))))
=> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),S0)))) ) ).
fof(aINDEPENDENTu_EXPLICIT,axiom,
! [N,U_0] :
( ! [C0,V] : s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),real),fun(cart(real,N),cart(real,N))),U_0),s(fun(cart(real,N),real),C0))),s(cart(real,N),V))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(cart(real,N),real),C0),s(cart(real,N),V))))),s(cart(real,N),V)))
=> ! [B0] :
( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),B0))))
<=> ( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),B0))))
& ! [C0] :
( s(cart(real,N),i(s(fun(fun(cart(real,N),cart(real,N)),cart(real,N)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),cart(real,N)),cart(real,N))),vsum),s(fun(cart(real,N),bool),B0))),s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),real),fun(cart(real,N),cart(real,N))),U_0),s(fun(cart(real,N),real),C0))))) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
=> ! [V] :
( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),V))),s(fun(cart(real,N),bool),B0))))
=> s(real,i(s(fun(cart(real,N),real),C0),s(cart(real,N),V))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ) ) ) ) ).
fof(aINDEPENDENTu_SING,axiom,
! [Q125680,X] :
( p(s(bool,i(s(fun(fun(cart(real,Q125680),bool),bool),independent),s(fun(cart(real,Q125680),bool),i(s(fun(fun(cart(real,Q125680),bool),fun(cart(real,Q125680),bool)),i(s(fun(cart(real,Q125680),fun(fun(cart(real,Q125680),bool),fun(cart(real,Q125680),bool))),insert),s(cart(real,Q125680),X))),s(fun(cart(real,Q125680),bool),empty))))))
<=> s(cart(real,Q125680),X) != s(cart(real,Q125680),i(s(fun(num,cart(real,Q125680)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ).
fof(aDEPENDENTu_SING,axiom,
! [Q125698,X] :
( p(s(bool,i(s(fun(fun(cart(real,Q125698),bool),bool),dependent),s(fun(cart(real,Q125698),bool),i(s(fun(fun(cart(real,Q125698),bool),fun(cart(real,Q125698),bool)),i(s(fun(cart(real,Q125698),fun(fun(cart(real,Q125698),bool),fun(cart(real,Q125698),bool))),insert),s(cart(real,Q125698),X))),s(fun(cart(real,Q125698),bool),empty))))))
<=> s(cart(real,Q125698),X) = s(cart(real,Q125698),i(s(fun(num,cart(real,Q125698)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ).
fof(aDEPENDENTu_2,axiom,
! [N,A5,B0] :
? [V] :
( ( p(s(bool,V))
<=> ? [X,Y] :
( s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,X))),s(cart(real,N),A5))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,Y))),s(cart(real,N),B0))))) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
& ~ ( s(real,X) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
& s(real,Y) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ) )
& ? [VI_] :
( ( p(s(bool,VI_))
<=> s(cart(real,N),A5) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) )
& ? [VI_I_] :
( ( p(s(bool,VI_I_))
<=> s(cart(real,N),A5) = s(cart(real,N),B0) )
& s(bool,i(s(fun(fun(cart(real,N),bool),bool),dependent),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),A5))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),B0))),s(fun(cart(real,N),bool),empty))))))) = s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),i(s(fun(bool,fun(bool,fun(bool,bool))),cond),s(bool,VI_I_))),s(bool,VI_))),s(bool,V))) ) ) ) ).
fof(aDEPENDENTu_3,axiom,
! [N,A5,B0,C0] :
( ( s(cart(real,N),A5) != s(cart(real,N),B0)
& s(cart(real,N),A5) != s(cart(real,N),C0)
& s(cart(real,N),B0) != s(cart(real,N),C0) )
=> ( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),dependent),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),A5))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),B0))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),C0))),s(fun(cart(real,N),bool),empty))))))))))
<=> ? [X,Y,Z0] :
( s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,X))),s(cart(real,N),A5))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,Y))),s(cart(real,N),B0))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,Z0))),s(cart(real,N),C0))))))) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
& ~ ( s(real,X) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
& s(real,Y) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
& s(real,Z0) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ) ) ) ).
fof(aINDEPENDENTu_2,axiom,
! [N,A5,B0,X,Y] :
( ( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),A5))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),B0))),s(fun(cart(real,N),bool),empty))))))))
& s(cart(real,N),A5) != s(cart(real,N),B0) )
=> ( s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,X))),s(cart(real,N),A5))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,Y))),s(cart(real,N),B0))))) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
<=> ( s(real,X) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
& s(real,Y) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ) ) ).
fof(aINDEPENDENTu_3,axiom,
! [N,A5,B0,C0,X,Y,Z0] :
( ( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),A5))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),B0))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),C0))),s(fun(cart(real,N),bool),empty))))))))))
& s(cart(real,N),A5) != s(cart(real,N),B0)
& s(cart(real,N),A5) != s(cart(real,N),C0)
& s(cart(real,N),B0) != s(cart(real,N),C0) )
=> ( s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,X))),s(cart(real,N),A5))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,Y))),s(cart(real,N),B0))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,Z0))),s(cart(real,N),C0))))))) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
<=> ( s(real,X) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
& s(real,Y) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
& s(real,Z0) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ) ) ).
fof(aMAXIMALu_INDEPENDENTu_SUBSETu_EXTEND,axiom,
! [N,S0,V] :
( ( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),V))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),S0)))) )
=> ? [B0] :
( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),B0))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),B0))),s(fun(cart(real,N),bool),V))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),B0))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),V))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),B0)))))) ) ) ).
fof(aMAXIMALu_INDEPENDENTu_SUBSET,axiom,
! [N,V] :
? [B0] :
( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),B0))),s(fun(cart(real,N),bool),V))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),B0))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),V))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),B0)))))) ) ).
fof(aLINEARu_SUBSPACEu_GRAPH,axiom,
! [M,N,U_0] :
( ! [F0,GENR_PVARR_319] :
( p(s(bool,i(s(fun(cart(real,finite_sum(M,N)),bool),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,finite_sum(M,N)),bool)),U_0),s(fun(cart(real,M),cart(real,N)),F0))),s(cart(real,finite_sum(M,N)),GENR_PVARR_319))))
<=> ? [X] : p(s(bool,i(s(fun(cart(real,finite_sum(M,N)),bool),i(s(fun(bool,fun(cart(real,finite_sum(M,N)),bool)),i(s(fun(cart(real,finite_sum(M,N)),fun(bool,fun(cart(real,finite_sum(M,N)),bool))),setspec),s(cart(real,finite_sum(M,N)),GENR_PVARR_319))),s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),univ))))),s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,N),cart(real,finite_sum(M,N))),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,finite_sum(M,N)))),pastecart),s(cart(real,M),X))),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X)))))))) )
=> ! [F0] : s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))) = s(bool,i(s(fun(fun(cart(real,finite_sum(M,N)),bool),bool),subspace),s(fun(cart(real,finite_sum(M,N)),bool),i(s(fun(fun(cart(real,finite_sum(M,N)),bool),fun(cart(real,finite_sum(M,N)),bool)),gspec),s(fun(cart(real,finite_sum(M,N)),bool),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,finite_sum(M,N)),bool)),U_0),s(fun(cart(real,M),cart(real,N)),F0))))))) ) ).
fof(adim,axiom,
! [Q126331,U_0] :
( ! [V,N0] :
( p(s(bool,i(s(fun(num,bool),i(s(fun(fun(cart(real,Q126331),bool),fun(num,bool)),U_0),s(fun(cart(real,Q126331),bool),V))),s(num,N0))))
<=> ? [B0] :
( p(s(bool,i(s(fun(fun(cart(real,Q126331),bool),bool),i(s(fun(fun(cart(real,Q126331),bool),fun(fun(cart(real,Q126331),bool),bool)),subset),s(fun(cart(real,Q126331),bool),B0))),s(fun(cart(real,Q126331),bool),V))))
& p(s(bool,i(s(fun(fun(cart(real,Q126331),bool),bool),independent),s(fun(cart(real,Q126331),bool),B0))))
& p(s(bool,i(s(fun(fun(cart(real,Q126331),bool),bool),i(s(fun(fun(cart(real,Q126331),bool),fun(fun(cart(real,Q126331),bool),bool)),subset),s(fun(cart(real,Q126331),bool),V))),s(fun(cart(real,Q126331),bool),i(s(fun(fun(cart(real,Q126331),bool),fun(cart(real,Q126331),bool)),span),s(fun(cart(real,Q126331),bool),B0))))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(fun(cart(real,Q126331),bool),fun(num,bool)),hasu_size),s(fun(cart(real,Q126331),bool),B0))),s(num,N0)))) ) )
=> ! [V] : s(num,i(s(fun(fun(cart(real,Q126331),bool),num),dim),s(fun(cart(real,Q126331),bool),V))) = s(num,i(s(fun(fun(num,bool),num),h_),s(fun(num,bool),i(s(fun(fun(cart(real,Q126331),bool),fun(num,bool)),U_0),s(fun(cart(real,Q126331),bool),V))))) ) ).
fof(aBASISu_EXISTS,axiom,
! [Q126364,V] :
? [B0] :
( p(s(bool,i(s(fun(fun(cart(real,Q126364),bool),bool),i(s(fun(fun(cart(real,Q126364),bool),fun(fun(cart(real,Q126364),bool),bool)),subset),s(fun(cart(real,Q126364),bool),B0))),s(fun(cart(real,Q126364),bool),V))))
& p(s(bool,i(s(fun(fun(cart(real,Q126364),bool),bool),independent),s(fun(cart(real,Q126364),bool),B0))))
& p(s(bool,i(s(fun(fun(cart(real,Q126364),bool),bool),i(s(fun(fun(cart(real,Q126364),bool),fun(fun(cart(real,Q126364),bool),bool)),subset),s(fun(cart(real,Q126364),bool),V))),s(fun(cart(real,Q126364),bool),i(s(fun(fun(cart(real,Q126364),bool),fun(cart(real,Q126364),bool)),span),s(fun(cart(real,Q126364),bool),B0))))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(fun(cart(real,Q126364),bool),fun(num,bool)),hasu_size),s(fun(cart(real,Q126364),bool),B0))),s(num,i(s(fun(fun(cart(real,Q126364),bool),num),dim),s(fun(cart(real,Q126364),bool),V)))))) ) ).
fof(aBASISu_EXISTSu_FINITE,axiom,
! [Q126398,V] :
? [B0] :
( p(s(bool,i(s(fun(fun(cart(real,Q126398),bool),bool),finite),s(fun(cart(real,Q126398),bool),B0))))
& p(s(bool,i(s(fun(fun(cart(real,Q126398),bool),bool),i(s(fun(fun(cart(real,Q126398),bool),fun(fun(cart(real,Q126398),bool),bool)),subset),s(fun(cart(real,Q126398),bool),B0))),s(fun(cart(real,Q126398),bool),V))))
& p(s(bool,i(s(fun(fun(cart(real,Q126398),bool),bool),independent),s(fun(cart(real,Q126398),bool),B0))))
& p(s(bool,i(s(fun(fun(cart(real,Q126398),bool),bool),i(s(fun(fun(cart(real,Q126398),bool),fun(fun(cart(real,Q126398),bool),bool)),subset),s(fun(cart(real,Q126398),bool),V))),s(fun(cart(real,Q126398),bool),i(s(fun(fun(cart(real,Q126398),bool),fun(cart(real,Q126398),bool)),span),s(fun(cart(real,Q126398),bool),B0))))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(fun(cart(real,Q126398),bool),fun(num,bool)),hasu_size),s(fun(cart(real,Q126398),bool),B0))),s(num,i(s(fun(fun(cart(real,Q126398),bool),num),dim),s(fun(cart(real,Q126398),bool),V)))))) ) ).
fof(aBASISu_SUBSPACEu_EXISTS,axiom,
! [N,S0] :
( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),subspace),s(fun(cart(real,N),bool),S0))))
=> ? [B0] :
( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),B0))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),B0))),s(fun(cart(real,N),bool),S0))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),B0))))
& s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),B0))) = s(fun(cart(real,N),bool),S0)
& p(s(bool,i(s(fun(num,bool),i(s(fun(fun(cart(real,N),bool),fun(num,bool)),hasu_size),s(fun(cart(real,N),bool),B0))),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0)))))) ) ) ).
fof(aINDEPENDENTu_CARDu_LEu_DIM,axiom,
! [N,V,B0] :
( ( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),B0))),s(fun(cart(real,N),bool),V))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),B0)))) )
=> ( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),B0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(cart(real,N),bool),num),card),s(fun(cart(real,N),bool),B0))))),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),V)))))) ) ) ).
fof(aSPANu_CARDu_GEu_DIM,axiom,
! [N,V,B0] :
( ( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),V))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),B0))))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),B0)))) )
=> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),V))))),s(num,i(s(fun(fun(cart(real,N),bool),num),card),s(fun(cart(real,N),bool),B0)))))) ) ).
fof(aBASISu_CARDu_EQu_DIM,axiom,
! [Q126529,V,B0] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q126529),bool),bool),i(s(fun(fun(cart(real,Q126529),bool),fun(fun(cart(real,Q126529),bool),bool)),subset),s(fun(cart(real,Q126529),bool),B0))),s(fun(cart(real,Q126529),bool),V))))
& p(s(bool,i(s(fun(fun(cart(real,Q126529),bool),bool),i(s(fun(fun(cart(real,Q126529),bool),fun(fun(cart(real,Q126529),bool),bool)),subset),s(fun(cart(real,Q126529),bool),V))),s(fun(cart(real,Q126529),bool),i(s(fun(fun(cart(real,Q126529),bool),fun(cart(real,Q126529),bool)),span),s(fun(cart(real,Q126529),bool),B0))))))
& p(s(bool,i(s(fun(fun(cart(real,Q126529),bool),bool),independent),s(fun(cart(real,Q126529),bool),B0)))) )
=> ( p(s(bool,i(s(fun(fun(cart(real,Q126529),bool),bool),finite),s(fun(cart(real,Q126529),bool),B0))))
& s(num,i(s(fun(fun(cart(real,Q126529),bool),num),card),s(fun(cart(real,Q126529),bool),B0))) = s(num,i(s(fun(fun(cart(real,Q126529),bool),num),dim),s(fun(cart(real,Q126529),bool),V))) ) ) ).
fof(aBASISu_HASu_SIZEu_DIM,axiom,
! [Q126544,V,B0] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q126544),bool),bool),independent),s(fun(cart(real,Q126544),bool),B0))))
& s(fun(cart(real,Q126544),bool),i(s(fun(fun(cart(real,Q126544),bool),fun(cart(real,Q126544),bool)),span),s(fun(cart(real,Q126544),bool),B0))) = s(fun(cart(real,Q126544),bool),V) )
=> p(s(bool,i(s(fun(num,bool),i(s(fun(fun(cart(real,Q126544),bool),fun(num,bool)),hasu_size),s(fun(cart(real,Q126544),bool),B0))),s(num,i(s(fun(fun(cart(real,Q126544),bool),num),dim),s(fun(cart(real,Q126544),bool),V)))))) ) ).
fof(aDIMu_UNIQUE,axiom,
! [Q126589,V,B0] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q126589),bool),bool),i(s(fun(fun(cart(real,Q126589),bool),fun(fun(cart(real,Q126589),bool),bool)),subset),s(fun(cart(real,Q126589),bool),B0))),s(fun(cart(real,Q126589),bool),V))))
& p(s(bool,i(s(fun(fun(cart(real,Q126589),bool),bool),i(s(fun(fun(cart(real,Q126589),bool),fun(fun(cart(real,Q126589),bool),bool)),subset),s(fun(cart(real,Q126589),bool),V))),s(fun(cart(real,Q126589),bool),i(s(fun(fun(cart(real,Q126589),bool),fun(cart(real,Q126589),bool)),span),s(fun(cart(real,Q126589),bool),B0))))))
& p(s(bool,i(s(fun(fun(cart(real,Q126589),bool),bool),independent),s(fun(cart(real,Q126589),bool),B0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(fun(cart(real,Q126589),bool),fun(num,bool)),hasu_size),s(fun(cart(real,Q126589),bool),B0))),s(num,n)))) )
=> s(num,i(s(fun(fun(cart(real,Q126589),bool),num),dim),s(fun(cart(real,Q126589),bool),V))) = s(num,n) ) ).
fof(aDIMu_LEu_CARD,axiom,
! [Q126603,S0] :
( p(s(bool,i(s(fun(fun(cart(real,Q126603),bool),bool),finite),s(fun(cart(real,Q126603),bool),S0))))
=> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(cart(real,Q126603),bool),num),dim),s(fun(cart(real,Q126603),bool),S0))))),s(num,i(s(fun(fun(cart(real,Q126603),bool),num),card),s(fun(cart(real,Q126603),bool),S0)))))) ) ).
fof(aDIMu_UNIV,axiom,
! [N] : s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),univ))) = s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))) ).
fof(aDIMu_SUBSET,axiom,
! [N,S0,T0] :
( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),T0))))
=> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0))))),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),T0)))))) ) ).
fof(aDIMu_SUBSETu_UNIV,axiom,
! [N,S0] : p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) ).
fof(aBASISu_HASu_SIZEu_UNIV,axiom,
! [N,B0] :
( ( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),B0))))
& s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),B0))) = s(fun(cart(real,N),bool),univ) )
=> p(s(bool,i(s(fun(num,bool),i(s(fun(fun(cart(real,N),bool),fun(num,bool)),hasu_size),s(fun(cart(real,N),bool),B0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) ) ).
fof(aCARDu_GEu_DIMu_INDEPENDENT,axiom,
! [N,V,B0] :
( ( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),B0))),s(fun(cart(real,N),bool),V))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),B0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),V))))),s(num,i(s(fun(fun(cart(real,N),bool),num),card),s(fun(cart(real,N),bool),B0)))))) )
=> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),V))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),B0)))))) ) ).
fof(aCARDu_LEu_DIMu_SPANNING,axiom,
! [N,V,B0] :
( ( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),V))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),B0))))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),B0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(cart(real,N),bool),num),card),s(fun(cart(real,N),bool),B0))))),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),V)))))) )
=> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),B0)))) ) ).
fof(aCARDu_EQu_DIM,axiom,
! [Q126884,V,B0] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q126884),bool),bool),i(s(fun(fun(cart(real,Q126884),bool),fun(fun(cart(real,Q126884),bool),bool)),subset),s(fun(cart(real,Q126884),bool),B0))),s(fun(cart(real,Q126884),bool),V))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(fun(cart(real,Q126884),bool),fun(num,bool)),hasu_size),s(fun(cart(real,Q126884),bool),B0))),s(num,i(s(fun(fun(cart(real,Q126884),bool),num),dim),s(fun(cart(real,Q126884),bool),V)))))) )
=> s(bool,i(s(fun(fun(cart(real,Q126884),bool),bool),independent),s(fun(cart(real,Q126884),bool),B0))) = s(bool,i(s(fun(fun(cart(real,Q126884),bool),bool),i(s(fun(fun(cart(real,Q126884),bool),fun(fun(cart(real,Q126884),bool),bool)),subset),s(fun(cart(real,Q126884),bool),V))),s(fun(cart(real,Q126884),bool),i(s(fun(fun(cart(real,Q126884),bool),fun(cart(real,Q126884),bool)),span),s(fun(cart(real,Q126884),bool),B0))))) ) ).
fof(aINDEPENDENTu_BOUNDu_GENERAL,axiom,
! [N,S0] :
( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),S0))))
=> ( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),S0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(cart(real,N),bool),num),card),s(fun(cart(real,N),bool),S0))))),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0)))))) ) ) ).
fof(aDEPENDENTu_BIGGERSETu_GENERAL,axiom,
! [N,S0] :
( ( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),S0))))
=> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_),s(num,i(s(fun(fun(cart(real,N),bool),num),card),s(fun(cart(real,N),bool),S0))))),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0)))))) )
=> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),dependent),s(fun(cart(real,N),bool),S0)))) ) ).
fof(aDIMu_SPAN,axiom,
! [N,S0] : s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0))))) = s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0))) ).
fof(aDIMu_INSERTu_0,axiom,
! [N,S0] : s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,N),bool),S0))))) = s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0))) ).
fof(aDIMu_EQu_CARD,axiom,
! [N,S0] :
( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),S0))))
=> s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0))) = s(num,i(s(fun(fun(cart(real,N),bool),num),card),s(fun(cart(real,N),bool),S0))) ) ).
fof(aSUBSETu_LEu_DIM,axiom,
! [N,S0,T0] :
( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),T0))))))
=> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0))))),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),T0)))))) ) ).
fof(aSPANu_EQu_DIM,axiom,
! [Q127017,S0,T0] :
( s(fun(cart(real,Q127017),bool),i(s(fun(fun(cart(real,Q127017),bool),fun(cart(real,Q127017),bool)),span),s(fun(cart(real,Q127017),bool),S0))) = s(fun(cart(real,Q127017),bool),i(s(fun(fun(cart(real,Q127017),bool),fun(cart(real,Q127017),bool)),span),s(fun(cart(real,Q127017),bool),T0)))
=> s(num,i(s(fun(fun(cart(real,Q127017),bool),num),dim),s(fun(cart(real,Q127017),bool),S0))) = s(num,i(s(fun(fun(cart(real,Q127017),bool),num),dim),s(fun(cart(real,Q127017),bool),T0))) ) ).
fof(aSPANSu_IMAGE,axiom,
! [Q127058,Q127043,F0,B0,V] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q127043),cart(real,Q127058)),bool),linear),s(fun(cart(real,Q127043),cart(real,Q127058)),F0))))
& p(s(bool,i(s(fun(fun(cart(real,Q127043),bool),bool),i(s(fun(fun(cart(real,Q127043),bool),fun(fun(cart(real,Q127043),bool),bool)),subset),s(fun(cart(real,Q127043),bool),V))),s(fun(cart(real,Q127043),bool),i(s(fun(fun(cart(real,Q127043),bool),fun(cart(real,Q127043),bool)),span),s(fun(cart(real,Q127043),bool),B0)))))) )
=> p(s(bool,i(s(fun(fun(cart(real,Q127058),bool),bool),i(s(fun(fun(cart(real,Q127058),bool),fun(fun(cart(real,Q127058),bool),bool)),subset),s(fun(cart(real,Q127058),bool),i(s(fun(fun(cart(real,Q127043),bool),fun(cart(real,Q127058),bool)),i(s(fun(fun(cart(real,Q127043),cart(real,Q127058)),fun(fun(cart(real,Q127043),bool),fun(cart(real,Q127058),bool))),image),s(fun(cart(real,Q127043),cart(real,Q127058)),F0))),s(fun(cart(real,Q127043),bool),V))))),s(fun(cart(real,Q127058),bool),i(s(fun(fun(cart(real,Q127058),bool),fun(cart(real,Q127058),bool)),span),s(fun(cart(real,Q127058),bool),i(s(fun(fun(cart(real,Q127043),bool),fun(cart(real,Q127058),bool)),i(s(fun(fun(cart(real,Q127043),cart(real,Q127058)),fun(fun(cart(real,Q127043),bool),fun(cart(real,Q127058),bool))),image),s(fun(cart(real,Q127043),cart(real,Q127058)),F0))),s(fun(cart(real,Q127043),bool),B0)))))))) ) ).
fof(aDIMu_LINEARu_IMAGEu_LE,axiom,
! [N,M,F0,S0] :
( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
=> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,M),bool),S0))))))),s(num,i(s(fun(fun(cart(real,M),bool),num),dim),s(fun(cart(real,M),bool),S0)))))) ) ).
fof(aDIMu_EMPTY,axiom,
! [N] : s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),empty))) = s(num,i(s(fun(num,num),numeral),s(num,u_0))) ).
fof(aDIMu_INSERT,axiom,
! [N,X,S0] : s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),X))),s(fun(cart(real,N),bool),S0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),i(s(fun(bool,fun(num,fun(num,num))),cond),s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),X))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0))))))),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) ).
fof(aDIMu_SING,axiom,
! [Q127174,X] :
? [V] :
( ( p(s(bool,V))
<=> s(cart(real,Q127174),X) = s(cart(real,Q127174),i(s(fun(num,cart(real,Q127174)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) )
& s(num,i(s(fun(fun(cart(real,Q127174),bool),num),dim),s(fun(cart(real,Q127174),bool),i(s(fun(fun(cart(real,Q127174),bool),fun(cart(real,Q127174),bool)),i(s(fun(cart(real,Q127174),fun(fun(cart(real,Q127174),bool),fun(cart(real,Q127174),bool))),insert),s(cart(real,Q127174),X))),s(fun(cart(real,Q127174),bool),empty))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),i(s(fun(bool,fun(num,fun(num,num))),cond),s(bool,V))),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) ) ).
fof(aDIMu_EQu_0,axiom,
! [N,S0] :
( s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0))) = s(num,i(s(fun(num,num),numeral),s(num,u_0)))
<=> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,N),bool),empty)))))) ) ).
fof(aSPANNINGu_SURJECTIVEu_IMAGE,axiom,
! [N,M,F0,S0] :
( ( p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(fun(cart(real,M),bool),fun(fun(cart(real,M),bool),bool)),subset),s(fun(cart(real,M),bool),univ))),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),span),s(fun(cart(real,M),bool),S0))))))
& p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
& ! [Y] :
? [X] : s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),Y) )
=> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),univ))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,M),bool),S0)))))))) ) ).
fof(aINDEPENDENTu_INJECTIVEu_IMAGEu_GEN,axiom,
! [N,M,F0,S0] :
( ( p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),independent),s(fun(cart(real,M),bool),S0))))
& p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
& ! [X,Y] :
( ( p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),span),s(fun(cart(real,M),bool),S0))))))
& p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),Y))),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),span),s(fun(cart(real,M),bool),S0))))))
& s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),Y))) )
=> s(cart(real,M),X) = s(cart(real,M),Y) ) )
=> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,M),bool),S0)))))) ) ).
fof(aINDEPENDENTu_INJECTIVEu_IMAGE,axiom,
! [N,M,F0,S0] :
( ( p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),independent),s(fun(cart(real,M),bool),S0))))
& p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
& ! [X,Y] :
( s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),Y)))
=> s(cart(real,M),X) = s(cart(real,M),Y) ) )
=> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,M),bool),S0)))))) ) ).
fof(aVECTORu_SUBu_PROJECTu_ORTHOGONAL,axiom,
! [N,B0,X] : s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),B0))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),X))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),B0))),s(cart(real,N),X))))),s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),B0))),s(cart(real,N),B0))))))),s(cart(real,N),B0))))))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ).
fof(aBASISu_ORTHOGONAL,axiom,
! [N,B0] :
( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),B0))))
=> ? [C0] :
( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),C0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(cart(real,N),bool),num),card),s(fun(cart(real,N),bool),C0))))),s(num,i(s(fun(fun(cart(real,N),bool),num),card),s(fun(cart(real,N),bool),B0))))))
& s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),C0))) = s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),B0)))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),fun(cart(real,N),bool)),fun(fun(cart(real,N),bool),bool)),pairwise),s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal))),s(fun(cart(real,N),bool),C0)))) ) ) ).
fof(aORTHOGONALu_BASISu_EXISTS,axiom,
! [N,V] :
? [B0] :
( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),B0))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),B0))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),V))))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),V))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),B0))))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(fun(cart(real,N),bool),fun(num,bool)),hasu_size),s(fun(cart(real,N),bool),B0))),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),V))))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),fun(cart(real,N),bool)),fun(fun(cart(real,N),bool),bool)),pairwise),s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal))),s(fun(cart(real,N),bool),B0)))) ) ).
fof(aSPANu_EQ,axiom,
! [Q127738,S0,T0] :
( s(fun(cart(real,Q127738),bool),i(s(fun(fun(cart(real,Q127738),bool),fun(cart(real,Q127738),bool)),span),s(fun(cart(real,Q127738),bool),S0))) = s(fun(cart(real,Q127738),bool),i(s(fun(fun(cart(real,Q127738),bool),fun(cart(real,Q127738),bool)),span),s(fun(cart(real,Q127738),bool),T0)))
<=> ( p(s(bool,i(s(fun(fun(cart(real,Q127738),bool),bool),i(s(fun(fun(cart(real,Q127738),bool),fun(fun(cart(real,Q127738),bool),bool)),subset),s(fun(cart(real,Q127738),bool),S0))),s(fun(cart(real,Q127738),bool),i(s(fun(fun(cart(real,Q127738),bool),fun(cart(real,Q127738),bool)),span),s(fun(cart(real,Q127738),bool),T0))))))
& p(s(bool,i(s(fun(fun(cart(real,Q127738),bool),bool),i(s(fun(fun(cart(real,Q127738),bool),fun(fun(cart(real,Q127738),bool),bool)),subset),s(fun(cart(real,Q127738),bool),T0))),s(fun(cart(real,Q127738),bool),i(s(fun(fun(cart(real,Q127738),bool),fun(cart(real,Q127738),bool)),span),s(fun(cart(real,Q127738),bool),S0)))))) ) ) ).
fof(aSPANu_EQu_INSERT,axiom,
! [Q127771,S0,X] :
( s(fun(cart(real,Q127771),bool),i(s(fun(fun(cart(real,Q127771),bool),fun(cart(real,Q127771),bool)),span),s(fun(cart(real,Q127771),bool),i(s(fun(fun(cart(real,Q127771),bool),fun(cart(real,Q127771),bool)),i(s(fun(cart(real,Q127771),fun(fun(cart(real,Q127771),bool),fun(cart(real,Q127771),bool))),insert),s(cart(real,Q127771),X))),s(fun(cart(real,Q127771),bool),S0))))) = s(fun(cart(real,Q127771),bool),i(s(fun(fun(cart(real,Q127771),bool),fun(cart(real,Q127771),bool)),span),s(fun(cart(real,Q127771),bool),S0)))
<=> p(s(bool,i(s(fun(fun(cart(real,Q127771),bool),bool),i(s(fun(cart(real,Q127771),fun(fun(cart(real,Q127771),bool),bool)),in),s(cart(real,Q127771),X))),s(fun(cart(real,Q127771),bool),i(s(fun(fun(cart(real,Q127771),bool),fun(cart(real,Q127771),bool)),span),s(fun(cart(real,Q127771),bool),S0)))))) ) ).
fof(aLINEARu_INDEPu_IMAGEu_LEMMA,axiom,
! [N,M,F0,B0] :
( ( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
& p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),finite),s(fun(cart(real,M),bool),B0))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,M),bool),B0))))))
& ! [X,Y] :
( ( p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),B0))))
& p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),Y))),s(fun(cart(real,M),bool),B0))))
& s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),Y))) )
=> s(cart(real,M),X) = s(cart(real,M),Y) ) )
=> ! [X] :
( p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),span),s(fun(cart(real,M),bool),B0))))))
=> ( s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
=> s(cart(real,M),X) = s(cart(real,M),i(s(fun(num,cart(real,M)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ) ) ).
fof(aLINEARu_INDEPENDENTu_EXTENDu_LEMMA,axiom,
! [N,M,F0,B0] :
( p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),finite),s(fun(cart(real,M),bool),B0))))
=> ( p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),independent),s(fun(cart(real,M),bool),B0))))
=> ? [G0] :
( ! [X,Y] :
( ( p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),span),s(fun(cart(real,M),bool),B0))))))
& p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),Y))),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),span),s(fun(cart(real,M),bool),B0)))))) )
=> s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),G0),s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),i(s(fun(cart(real,M),fun(cart(real,M),cart(real,M))),vectoru_add),s(cart(real,M),X))),s(cart(real,M),Y))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),G0),s(cart(real,M),X))))),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),G0),s(cart(real,M),Y))))) )
& ! [X,C0] :
( p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),span),s(fun(cart(real,M),bool),B0))))))
=> s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),G0),s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),i(s(fun(real,fun(cart(real,M),cart(real,M))),r_),s(real,C0))),s(cart(real,M),X))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,C0))),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),G0),s(cart(real,M),X))))) )
& ! [X] :
( p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),B0))))
=> s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),G0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) ) ) ) ) ).
fof(aLINEARu_INDEPENDENTu_EXTEND,axiom,
! [N,M,F0,B0] :
( p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),independent),s(fun(cart(real,M),bool),B0))))
=> ? [G0] :
( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),G0))))
& ! [X] :
( p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),B0))))
=> s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),G0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) ) ) ) ).
fof(aSUBSPACEu_KERNEL,axiom,
! [Q128666,Q128687,U_0] :
( ! [F0,GENR_PVARR_321] :
( p(s(bool,i(s(fun(cart(real,Q128666),bool),i(s(fun(fun(cart(real,Q128666),cart(real,Q128687)),fun(cart(real,Q128666),bool)),U_0),s(fun(cart(real,Q128666),cart(real,Q128687)),F0))),s(cart(real,Q128666),GENR_PVARR_321))))
<=> ? [X,V] :
( ( p(s(bool,V))
<=> s(cart(real,Q128687),i(s(fun(cart(real,Q128666),cart(real,Q128687)),F0),s(cart(real,Q128666),X))) = s(cart(real,Q128687),i(s(fun(num,cart(real,Q128687)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) )
& p(s(bool,i(s(fun(cart(real,Q128666),bool),i(s(fun(bool,fun(cart(real,Q128666),bool)),i(s(fun(cart(real,Q128666),fun(bool,fun(cart(real,Q128666),bool))),setspec),s(cart(real,Q128666),GENR_PVARR_321))),s(bool,V))),s(cart(real,Q128666),X)))) ) )
=> ! [F0] :
( p(s(bool,i(s(fun(fun(cart(real,Q128666),cart(real,Q128687)),bool),linear),s(fun(cart(real,Q128666),cart(real,Q128687)),F0))))
=> p(s(bool,i(s(fun(fun(cart(real,Q128666),bool),bool),subspace),s(fun(cart(real,Q128666),bool),i(s(fun(fun(cart(real,Q128666),bool),fun(cart(real,Q128666),bool)),gspec),s(fun(cart(real,Q128666),bool),i(s(fun(fun(cart(real,Q128666),cart(real,Q128687)),fun(cart(real,Q128666),bool)),U_0),s(fun(cart(real,Q128666),cart(real,Q128687)),F0)))))))) ) ) ).
fof(aLINEARu_EQu_0u_SPAN,axiom,
! [M,N,F0,B0] :
( ( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
& ! [X] :
( p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),B0))))
=> s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) )
=> ! [X] :
( p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),span),s(fun(cart(real,M),bool),B0))))))
=> s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ) ).
fof(aLINEARu_EQu_0,axiom,
! [Q128763,Q128793,F0,B0,S0] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q128763),cart(real,Q128793)),bool),linear),s(fun(cart(real,Q128763),cart(real,Q128793)),F0))))
& p(s(bool,i(s(fun(fun(cart(real,Q128763),bool),bool),i(s(fun(fun(cart(real,Q128763),bool),fun(fun(cart(real,Q128763),bool),bool)),subset),s(fun(cart(real,Q128763),bool),S0))),s(fun(cart(real,Q128763),bool),i(s(fun(fun(cart(real,Q128763),bool),fun(cart(real,Q128763),bool)),span),s(fun(cart(real,Q128763),bool),B0))))))
& ! [X] :
( p(s(bool,i(s(fun(fun(cart(real,Q128763),bool),bool),i(s(fun(cart(real,Q128763),fun(fun(cart(real,Q128763),bool),bool)),in),s(cart(real,Q128763),X))),s(fun(cart(real,Q128763),bool),B0))))
=> s(cart(real,Q128793),i(s(fun(cart(real,Q128763),cart(real,Q128793)),F0),s(cart(real,Q128763),X))) = s(cart(real,Q128793),i(s(fun(num,cart(real,Q128793)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) )
=> ! [X] :
( p(s(bool,i(s(fun(fun(cart(real,Q128763),bool),bool),i(s(fun(cart(real,Q128763),fun(fun(cart(real,Q128763),bool),bool)),in),s(cart(real,Q128763),X))),s(fun(cart(real,Q128763),bool),S0))))
=> s(cart(real,Q128793),i(s(fun(cart(real,Q128763),cart(real,Q128793)),F0),s(cart(real,Q128763),X))) = s(cart(real,Q128793),i(s(fun(num,cart(real,Q128793)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ) ).
fof(aLINEARu_EQ,axiom,
! [Q128822,Q128829,F0,G0,B0,S0] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q128829),cart(real,Q128822)),bool),linear),s(fun(cart(real,Q128829),cart(real,Q128822)),F0))))
& p(s(bool,i(s(fun(fun(cart(real,Q128829),cart(real,Q128822)),bool),linear),s(fun(cart(real,Q128829),cart(real,Q128822)),G0))))
& p(s(bool,i(s(fun(fun(cart(real,Q128829),bool),bool),i(s(fun(fun(cart(real,Q128829),bool),fun(fun(cart(real,Q128829),bool),bool)),subset),s(fun(cart(real,Q128829),bool),S0))),s(fun(cart(real,Q128829),bool),i(s(fun(fun(cart(real,Q128829),bool),fun(cart(real,Q128829),bool)),span),s(fun(cart(real,Q128829),bool),B0))))))
& ! [X] :
( p(s(bool,i(s(fun(fun(cart(real,Q128829),bool),bool),i(s(fun(cart(real,Q128829),fun(fun(cart(real,Q128829),bool),bool)),in),s(cart(real,Q128829),X))),s(fun(cart(real,Q128829),bool),B0))))
=> s(cart(real,Q128822),i(s(fun(cart(real,Q128829),cart(real,Q128822)),F0),s(cart(real,Q128829),X))) = s(cart(real,Q128822),i(s(fun(cart(real,Q128829),cart(real,Q128822)),G0),s(cart(real,Q128829),X))) ) )
=> ! [X] :
( p(s(bool,i(s(fun(fun(cart(real,Q128829),bool),bool),i(s(fun(cart(real,Q128829),fun(fun(cart(real,Q128829),bool),bool)),in),s(cart(real,Q128829),X))),s(fun(cart(real,Q128829),bool),S0))))
=> s(cart(real,Q128822),i(s(fun(cart(real,Q128829),cart(real,Q128822)),F0),s(cart(real,Q128829),X))) = s(cart(real,Q128822),i(s(fun(cart(real,Q128829),cart(real,Q128822)),G0),s(cart(real,Q128829),X))) ) ) ).
fof(aLINEARu_EQu_STDBASIS,axiom,
! [M,N,F0,G0] :
( ( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
& p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),G0))))
& ! [I0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ)))))) )
=> s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),i(s(fun(num,cart(real,M)),basis),s(num,I0))))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),G0),s(cart(real,M),i(s(fun(num,cart(real,M)),basis),s(num,I0))))) ) )
=> s(fun(cart(real,M),cart(real,N)),F0) = s(fun(cart(real,M),cart(real,N)),G0) ) ).
fof(aBILINEARu_EQ,axiom,
! [P,M,N,F0,G0,B0,C0,S0] :
( ( p(s(bool,i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),bool),bilinear),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),F0))))
& p(s(bool,i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),bool),bilinear),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),G0))))
& p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(fun(cart(real,M),bool),fun(fun(cart(real,M),bool),bool)),subset),s(fun(cart(real,M),bool),S0))),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),span),s(fun(cart(real,M),bool),B0))))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),t0))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),C0))))))
& ! [X,Y] :
( ( p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),B0))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),Y))),s(fun(cart(real,N),bool),C0)))) )
=> s(cart(real,P),i(s(fun(cart(real,N),cart(real,P)),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),F0),s(cart(real,M),X))),s(cart(real,N),Y))) = s(cart(real,P),i(s(fun(cart(real,N),cart(real,P)),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),G0),s(cart(real,M),X))),s(cart(real,N),Y))) ) )
=> ! [X,Y] :
( ( p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),S0))))
& p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),Y))),s(fun(cart(real,N),bool),t0)))) )
=> s(cart(real,P),i(s(fun(cart(real,N),cart(real,P)),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),F0),s(cart(real,M),X))),s(cart(real,N),Y))) = s(cart(real,P),i(s(fun(cart(real,N),cart(real,P)),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),G0),s(cart(real,M),X))),s(cart(real,N),Y))) ) ) ).
fof(aBILINEARu_EQu_STDBASIS,axiom,
! [M,N,P,F0,G0] :
( ( p(s(bool,i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),bool),bilinear),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),F0))))
& p(s(bool,i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),bool),bilinear),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),G0))))
& ! [I0,J0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ))))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,J0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,J0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) )
=> s(cart(real,P),i(s(fun(cart(real,N),cart(real,P)),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),F0),s(cart(real,M),i(s(fun(num,cart(real,M)),basis),s(num,I0))))),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,J0))))) = s(cart(real,P),i(s(fun(cart(real,N),cart(real,P)),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),G0),s(cart(real,M),i(s(fun(num,cart(real,M)),basis),s(num,I0))))),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,J0))))) ) )
=> s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),F0) = s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),G0) ) ).
fof(aLEFTu_INVERTIBLEu_TRANSP,axiom,
! [N,M,A5] :
( ? [B0] : s(cart(cart(real,M),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,M),N),cart(cart(real,M),M))),matrixu_mul),s(cart(cart(real,N),M),B0))),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),A5))))) = s(cart(cart(real,M),M),i(s(fun(num,cart(cart(real,M),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))
<=> ? [B0] : s(cart(cart(real,M),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,M),N),cart(cart(real,M),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,M),N),B0))) = s(cart(cart(real,M),M),i(s(fun(num,cart(cart(real,M),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) ) ).
fof(aRIGHTu_INVERTIBLEu_TRANSP,axiom,
! [M,N,A5] :
( ? [B0] : s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),N)),i(s(fun(cart(cart(real,M),N),fun(cart(cart(real,N),M),cart(cart(real,N),N))),matrixu_mul),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),A5))))),s(cart(cart(real,N),M),B0))) = s(cart(cart(real,N),N),i(s(fun(num,cart(cart(real,N),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))
<=> ? [B0] : s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),N)),i(s(fun(cart(cart(real,M),N),fun(cart(cart(real,N),M),cart(cart(real,N),N))),matrixu_mul),s(cart(cart(real,M),N),B0))),s(cart(cart(real,N),M),A5))) = s(cart(cart(real,N),N),i(s(fun(num,cart(cart(real,N),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) ) ).
fof(aLINEARu_INJECTIVEu_LEFTu_INVERSE,axiom,
! [N,M,F0] :
( ( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
& ! [X,Y] :
( s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),Y)))
=> s(cart(real,M),X) = s(cart(real,M),Y) ) )
=> ? [G0] :
( p(s(bool,i(s(fun(fun(cart(real,N),cart(real,M)),bool),linear),s(fun(cart(real,N),cart(real,M)),G0))))
& s(fun(cart(real,M),cart(real,M)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),cart(real,M))),i(s(fun(fun(cart(real,N),cart(real,M)),fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),cart(real,M)))),o),s(fun(cart(real,N),cart(real,M)),G0))),s(fun(cart(real,M),cart(real,N)),F0))) = s(fun(cart(real,M),cart(real,M)),i1) ) ) ).
fof(aLINEARu_SURJECTIVEu_RIGHTu_INVERSE,axiom,
! [M,N,F0] :
( ( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
& ! [Y] :
? [X] : s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),Y) )
=> ? [G0] :
( p(s(bool,i(s(fun(fun(cart(real,N),cart(real,M)),bool),linear),s(fun(cart(real,N),cart(real,M)),G0))))
& s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),cart(real,M)),fun(cart(real,N),cart(real,N))),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,N),cart(real,M)),fun(cart(real,N),cart(real,N)))),o),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,N),cart(real,M)),G0))) = s(fun(cart(real,N),cart(real,N)),i1) ) ) ).
fof(aMATRIXu_LEFTu_INVERTIBLEu_INJECTIVE,axiom,
! [M,N,A5] :
( ? [B0] : s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),N)),i(s(fun(cart(cart(real,M),N),fun(cart(cart(real,N),M),cart(cart(real,N),N))),matrixu_mul),s(cart(cart(real,M),N),B0))),s(cart(cart(real,N),M),A5))) = s(cart(cart(real,N),N),i(s(fun(num,cart(cart(real,N),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))
<=> ! [X,Y] :
( s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),A5))),s(cart(real,N),X))) = s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),A5))),s(cart(real,N),Y)))
=> s(cart(real,N),X) = s(cart(real,N),Y) ) ) ).
fof(aMATRIXu_LEFTu_INVERTIBLEu_KER,axiom,
! [M,N,A5] :
( ? [B0] : s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),N)),i(s(fun(cart(cart(real,M),N),fun(cart(cart(real,N),M),cart(cart(real,N),N))),matrixu_mul),s(cart(cart(real,M),N),B0))),s(cart(cart(real,N),M),A5))) = s(cart(cart(real,N),N),i(s(fun(num,cart(cart(real,N),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))
<=> ! [X] :
( s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),A5))),s(cart(real,N),X))) = s(cart(real,M),i(s(fun(num,cart(real,M)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
=> s(cart(real,N),X) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ) ).
fof(aMATRIXu_RIGHTu_INVERTIBLEu_SURJECTIVE,axiom,
! [N,M,A5] :
( ? [B0] : s(cart(cart(real,M),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,M),N),cart(cart(real,M),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,M),N),B0))) = s(cart(cart(real,M),M),i(s(fun(num,cart(cart(real,M),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))
<=> ! [Y] :
? [X] : s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),A5))),s(cart(real,N),X))) = s(cart(real,M),Y) ) ).
fof(aMATRIXu_LEFTu_INVERTIBLEu_INDEPENDENTu_COLUMNS,axiom,
! [M,N,U_0] :
( ! [C0,A5,I0] : s(cart(real,M),i(s(fun(num,cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,M))),i(s(fun(fun(num,real),fun(cart(cart(real,N),M),fun(num,cart(real,M)))),U_0),s(fun(num,real),C0))),s(cart(cart(real,N),M),A5))),s(num,I0))) = s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),i(s(fun(real,fun(cart(real,M),cart(real,M))),r_),s(real,i(s(fun(num,real),C0),s(num,I0))))),s(cart(real,M),i(s(fun(cart(cart(real,N),M),cart(real,M)),i(s(fun(num,fun(cart(cart(real,N),M),cart(real,M))),column),s(num,I0))),s(cart(cart(real,N),M),A5)))))
=> ! [A5] :
( ? [B0] : s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),N)),i(s(fun(cart(cart(real,M),N),fun(cart(cart(real,N),M),cart(cart(real,N),N))),matrixu_mul),s(cart(cart(real,M),N),B0))),s(cart(cart(real,N),M),A5))) = s(cart(cart(real,N),N),i(s(fun(num,cart(cart(real,N),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))
<=> ! [C0] :
( s(cart(real,M),i(s(fun(fun(num,cart(real,M)),cart(real,M)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,M)),cart(real,M))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))),s(fun(num,cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,M))),i(s(fun(fun(num,real),fun(cart(cart(real,N),M),fun(num,cart(real,M)))),U_0),s(fun(num,real),C0))),s(cart(cart(real,N),M),A5))))) = s(cart(real,M),i(s(fun(num,cart(real,M)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
=> ! [I0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) )
=> s(real,i(s(fun(num,real),C0),s(num,I0))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ) ) ) ).
fof(aMATRIXu_RIGHTu_INVERTIBLEu_INDEPENDENTu_ROWS,axiom,
! [N,M,U_0] :
( ! [C0,A5,I0] : s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),i(s(fun(fun(num,real),fun(cart(cart(real,N),M),fun(num,cart(real,N)))),U_0),s(fun(num,real),C0))),s(cart(cart(real,N),M),A5))),s(num,I0))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(num,real),C0),s(num,I0))))),s(cart(real,N),i(s(fun(cart(cart(real,N),M),cart(real,N)),i(s(fun(num,fun(cart(cart(real,N),M),cart(real,N))),row),s(num,I0))),s(cart(cart(real,N),M),A5)))))
=> ! [A5] :
( ? [B0] : s(cart(cart(real,M),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,M),N),cart(cart(real,M),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,M),N),B0))) = s(cart(cart(real,M),M),i(s(fun(num,cart(cart(real,M),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))
<=> ! [C0] :
( s(cart(real,N),i(s(fun(fun(num,cart(real,N)),cart(real,N)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,N)),cart(real,N))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ))))))),s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),i(s(fun(fun(num,real),fun(cart(cart(real,N),M),fun(num,cart(real,N)))),U_0),s(fun(num,real),C0))),s(cart(cart(real,N),M),A5))))) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
=> ! [I0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ)))))) )
=> s(real,i(s(fun(num,real),C0),s(num,I0))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ) ) ) ).
fof(aMATRIXu_RIGHTu_INVERTIBLEu_SPANu_COLUMNS,axiom,
! [N,M,A5] :
( ? [B0] : s(cart(cart(real,M),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,M),N),cart(cart(real,M),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,M),N),B0))) = s(cart(cart(real,M),M),i(s(fun(num,cart(cart(real,M),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))
<=> s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),span),s(fun(cart(real,M),bool),i(s(fun(cart(cart(real,N),M),fun(cart(real,M),bool)),columns),s(cart(cart(real,N),M),A5))))) = s(fun(cart(real,M),bool),univ) ) ).
fof(aMATRIXu_LEFTu_INVERTIBLEu_SPANu_ROWS,axiom,
! [M,N,A5] :
( ? [B0] : s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),N)),i(s(fun(cart(cart(real,M),N),fun(cart(cart(real,N),M),cart(cart(real,N),N))),matrixu_mul),s(cart(cart(real,M),N),B0))),s(cart(cart(real,N),M),A5))) = s(cart(cart(real,N),N),i(s(fun(num,cart(cart(real,N),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))
<=> s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),bool)),rows),s(cart(cart(real,N),M),A5))))) = s(fun(cart(real,N),bool),univ) ) ).
fof(aLINEARu_INJECTIVEu_IMPu_SURJECTIVE,axiom,
! [N,F0] :
( ( p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),F0))))
& ! [X,Y] :
( s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),X))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),Y)))
=> s(cart(real,N),X) = s(cart(real,N),Y) ) )
=> ! [Y] :
? [X] : s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),X))) = s(cart(real,N),Y) ) ).
fof(aLINEARu_SURJECTIVEu_IMPu_INJECTIVE,axiom,
! [N,F0] :
( ( p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),F0))))
& ! [Y] :
? [X] : s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),X))) = s(cart(real,N),Y) )
=> ! [X,Y] :
( s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),X))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),Y)))
=> s(cart(real,N),X) = s(cart(real,N),Y) ) ) ).
fof(aLINEARu_SURJECTIVEu_IFFu_INJECTIVE,axiom,
! [N,F0] :
( p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),F0))))
=> ( ! [Y] :
? [X] : s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),X))) = s(cart(real,N),Y)
<=> ! [X,Y] :
( s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),X))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),Y)))
=> s(cart(real,N),X) = s(cart(real,N),Y) ) ) ) ).
fof(aLEFTu_RIGHTu_INVERSEu_EQ,axiom,
! [A,F0,G0,H0] :
( ( s(fun(A,A),i(s(fun(fun(A,A),fun(A,A)),i(s(fun(fun(A,A),fun(fun(A,A),fun(A,A))),o),s(fun(A,A),F0))),s(fun(A,A),G0))) = s(fun(A,A),i1)
& s(fun(A,A),i(s(fun(fun(A,A),fun(A,A)),i(s(fun(fun(A,A),fun(fun(A,A),fun(A,A))),o),s(fun(A,A),G0))),s(fun(A,A),H0))) = s(fun(A,A),i1) )
=> s(fun(A,A),F0) = s(fun(A,A),H0) ) ).
fof(aISOMORPHISMu_EXPAND,axiom,
! [Q130465,Q130466,F0,G0] :
( ( s(fun(Q130465,Q130465),i(s(fun(fun(Q130465,Q130466),fun(Q130465,Q130465)),i(s(fun(fun(Q130466,Q130465),fun(fun(Q130465,Q130466),fun(Q130465,Q130465))),o),s(fun(Q130466,Q130465),F0))),s(fun(Q130465,Q130466),G0))) = s(fun(Q130465,Q130465),i1)
& s(fun(Q130466,Q130466),i(s(fun(fun(Q130466,Q130465),fun(Q130466,Q130466)),i(s(fun(fun(Q130465,Q130466),fun(fun(Q130466,Q130465),fun(Q130466,Q130466))),o),s(fun(Q130465,Q130466),G0))),s(fun(Q130466,Q130465),F0))) = s(fun(Q130466,Q130466),i1) )
<=> ( ! [X] : s(Q130465,i(s(fun(Q130466,Q130465),F0),s(Q130466,i(s(fun(Q130465,Q130466),G0),s(Q130465,X))))) = s(Q130465,X)
& ! [X] : s(Q130466,i(s(fun(Q130465,Q130466),G0),s(Q130465,i(s(fun(Q130466,Q130465),F0),s(Q130466,X))))) = s(Q130466,X) ) ) ).
fof(aLINEARu_INJECTIVEu_ISOMORPHISM,axiom,
! [N,F0] :
( ( p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),F0))))
& ! [X,Y] :
( s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),X))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),Y)))
=> s(cart(real,N),X) = s(cart(real,N),Y) ) )
=> ? [FI_] :
( p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),FI_))))
& ! [X] : s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),FI_),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),X))))) = s(cart(real,N),X)
& ! [X] : s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),FI_),s(cart(real,N),X))))) = s(cart(real,N),X) ) ) ).
fof(aLINEARu_SURJECTIVEu_ISOMORPHISM,axiom,
! [N,F0] :
( ( p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),F0))))
& ! [Y] :
? [X] : s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),X))) = s(cart(real,N),Y) )
=> ? [FI_] :
( p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),FI_))))
& ! [X] : s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),FI_),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),X))))) = s(cart(real,N),X)
& ! [X] : s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),FI_),s(cart(real,N),X))))) = s(cart(real,N),X) ) ) ).
fof(aLINEARu_INVERSEu_LEFT,axiom,
! [N,F0,FI_] :
( ( p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),F0))))
& p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),FI_)))) )
=> ( s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),cart(real,N)),fun(cart(real,N),cart(real,N))),i(s(fun(fun(cart(real,N),cart(real,N)),fun(fun(cart(real,N),cart(real,N)),fun(cart(real,N),cart(real,N)))),o),s(fun(cart(real,N),cart(real,N)),F0))),s(fun(cart(real,N),cart(real,N)),FI_))) = s(fun(cart(real,N),cart(real,N)),i1)
<=> s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),cart(real,N)),fun(cart(real,N),cart(real,N))),i(s(fun(fun(cart(real,N),cart(real,N)),fun(fun(cart(real,N),cart(real,N)),fun(cart(real,N),cart(real,N)))),o),s(fun(cart(real,N),cart(real,N)),FI_))),s(fun(cart(real,N),cart(real,N)),F0))) = s(fun(cart(real,N),cart(real,N)),i1) ) ) ).
fof(aLEFTu_INVERSEu_LINEAR,axiom,
! [N,F0,G0] :
( ( p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),F0))))
& s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),cart(real,N)),fun(cart(real,N),cart(real,N))),i(s(fun(fun(cart(real,N),cart(real,N)),fun(fun(cart(real,N),cart(real,N)),fun(cart(real,N),cart(real,N)))),o),s(fun(cart(real,N),cart(real,N)),G0))),s(fun(cart(real,N),cart(real,N)),F0))) = s(fun(cart(real,N),cart(real,N)),i1) )
=> p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),G0)))) ) ).
fof(aRIGHTu_INVERSEu_LINEAR,axiom,
! [N,F0,G0] :
( ( p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),F0))))
& s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),cart(real,N)),fun(cart(real,N),cart(real,N))),i(s(fun(fun(cart(real,N),cart(real,N)),fun(fun(cart(real,N),cart(real,N)),fun(cart(real,N),cart(real,N)))),o),s(fun(cart(real,N),cart(real,N)),F0))),s(fun(cart(real,N),cart(real,N)),G0))) = s(fun(cart(real,N),cart(real,N)),i1) )
=> p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),G0)))) ) ).
fof(aLEFTu_RIGHTu_INVERSEu_LINEAR,axiom,
! [M,N,F0,G0] :
( ( p(s(bool,i(s(fun(fun(cart(real,N),cart(real,M)),bool),linear),s(fun(cart(real,N),cart(real,M)),F0))))
& s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),cart(real,M)),fun(cart(real,N),cart(real,N))),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,N),cart(real,M)),fun(cart(real,N),cart(real,N)))),o),s(fun(cart(real,M),cart(real,N)),G0))),s(fun(cart(real,N),cart(real,M)),F0))) = s(fun(cart(real,N),cart(real,N)),i1)
& s(fun(cart(real,M),cart(real,M)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),cart(real,M))),i(s(fun(fun(cart(real,N),cart(real,M)),fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),cart(real,M)))),o),s(fun(cart(real,N),cart(real,M)),F0))),s(fun(cart(real,M),cart(real,N)),G0))) = s(fun(cart(real,M),cart(real,M)),i1) )
=> p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),G0)))) ) ).
fof(aLINEARu_BIJECTIVEu_LEFTu_RIGHTu_INVERSE,axiom,
! [M,N,F0] :
( ( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
& ! [X,Y] :
( s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),Y)))
=> s(cart(real,M),X) = s(cart(real,M),Y) )
& ! [Y] :
? [X] : s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),Y) )
=> ? [G0] :
( p(s(bool,i(s(fun(fun(cart(real,N),cart(real,M)),bool),linear),s(fun(cart(real,N),cart(real,M)),G0))))
& ! [X] : s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),G0),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))) = s(cart(real,M),X)
& ! [Y] : s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),G0),s(cart(real,N),Y))))) = s(cart(real,N),Y) ) ) ).
fof(aMATRIXu_LEFTu_RIGHTu_INVERSE,axiom,
! [N,A5,AI_] :
( s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),N),cart(cart(real,N),N)),i(s(fun(cart(cart(real,N),N),fun(cart(cart(real,N),N),cart(cart(real,N),N))),matrixu_mul),s(cart(cart(real,N),N),A5))),s(cart(cart(real,N),N),AI_))) = s(cart(cart(real,N),N),i(s(fun(num,cart(cart(real,N),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))
<=> s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),N),cart(cart(real,N),N)),i(s(fun(cart(cart(real,N),N),fun(cart(cart(real,N),N),cart(cart(real,N),N))),matrixu_mul),s(cart(cart(real,N),N),AI_))),s(cart(cart(real,N),N),A5))) = s(cart(cart(real,N),N),i(s(fun(num,cart(cart(real,N),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) ) ).
fof(aMATRIXu_LEFTu_INVERTIBLE,axiom,
! [N,M,F0] :
( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
=> ( ? [B0] : s(cart(cart(real,M),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,M),N),cart(cart(real,M),M))),matrixu_mul),s(cart(cart(real,N),M),B0))),s(cart(cart(real,M),N),i(s(fun(fun(cart(real,M),cart(real,N)),cart(cart(real,M),N)),matrix),s(fun(cart(real,M),cart(real,N)),F0))))) = s(cart(cart(real,M),M),i(s(fun(num,cart(cart(real,M),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))
<=> ? [G0] :
( p(s(bool,i(s(fun(fun(cart(real,N),cart(real,M)),bool),linear),s(fun(cart(real,N),cart(real,M)),G0))))
& s(fun(cart(real,M),cart(real,M)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),cart(real,M))),i(s(fun(fun(cart(real,N),cart(real,M)),fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),cart(real,M)))),o),s(fun(cart(real,N),cart(real,M)),G0))),s(fun(cart(real,M),cart(real,N)),F0))) = s(fun(cart(real,M),cart(real,M)),i1) ) ) ) ).
fof(aMATRIXu_RIGHTu_INVERTIBLE,axiom,
! [M,N,F0] :
( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
=> ( ? [B0] : s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),N)),i(s(fun(cart(cart(real,M),N),fun(cart(cart(real,N),M),cart(cart(real,N),N))),matrixu_mul),s(cart(cart(real,M),N),i(s(fun(fun(cart(real,M),cart(real,N)),cart(cart(real,M),N)),matrix),s(fun(cart(real,M),cart(real,N)),F0))))),s(cart(cart(real,N),M),B0))) = s(cart(cart(real,N),N),i(s(fun(num,cart(cart(real,N),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))
<=> ? [G0] :
( p(s(bool,i(s(fun(fun(cart(real,N),cart(real,M)),bool),linear),s(fun(cart(real,N),cart(real,M)),G0))))
& s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),cart(real,M)),fun(cart(real,N),cart(real,N))),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,N),cart(real,M)),fun(cart(real,N),cart(real,N)))),o),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,N),cart(real,M)),G0))) = s(fun(cart(real,N),cart(real,N)),i1) ) ) ) ).
fof(aINVERTIBLEu_LEFTu_INVERSE,axiom,
! [N,A5] :
( p(s(bool,i(s(fun(cart(cart(real,N),N),bool),invertible),s(cart(cart(real,N),N),A5))))
<=> ? [B0] : s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),N),cart(cart(real,N),N)),i(s(fun(cart(cart(real,N),N),fun(cart(cart(real,N),N),cart(cart(real,N),N))),matrixu_mul),s(cart(cart(real,N),N),B0))),s(cart(cart(real,N),N),A5))) = s(cart(cart(real,N),N),i(s(fun(num,cart(cart(real,N),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) ) ).
fof(aINVERTIBLEu_RIGHTu_INVERSE,axiom,
! [N,A5] :
( p(s(bool,i(s(fun(cart(cart(real,N),N),bool),invertible),s(cart(cart(real,N),N),A5))))
<=> ? [B0] : s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),N),cart(cart(real,N),N)),i(s(fun(cart(cart(real,N),N),fun(cart(cart(real,N),N),cart(cart(real,N),N))),matrixu_mul),s(cart(cart(real,N),N),A5))),s(cart(cart(real,N),N),B0))) = s(cart(cart(real,N),N),i(s(fun(num,cart(cart(real,N),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) ) ).
fof(aMATRIXu_INVERTIBLE,axiom,
! [N,F0] :
( p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),F0))))
=> ( p(s(bool,i(s(fun(cart(cart(real,N),N),bool),invertible),s(cart(cart(real,N),N),i(s(fun(fun(cart(real,N),cart(real,N)),cart(cart(real,N),N)),matrix),s(fun(cart(real,N),cart(real,N)),F0))))))
<=> ? [G0] :
( p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),G0))))
& s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),cart(real,N)),fun(cart(real,N),cart(real,N))),i(s(fun(fun(cart(real,N),cart(real,N)),fun(fun(cart(real,N),cart(real,N)),fun(cart(real,N),cart(real,N)))),o),s(fun(cart(real,N),cart(real,N)),F0))),s(fun(cart(real,N),cart(real,N)),G0))) = s(fun(cart(real,N),cart(real,N)),i1)
& s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),cart(real,N)),fun(cart(real,N),cart(real,N))),i(s(fun(fun(cart(real,N),cart(real,N)),fun(fun(cart(real,N),cart(real,N)),fun(cart(real,N),cart(real,N)))),o),s(fun(cart(real,N),cart(real,N)),G0))),s(fun(cart(real,N),cart(real,N)),F0))) = s(fun(cart(real,N),cart(real,N)),i1) ) ) ) ).
fof(aLINEARu_INVERTIBLEu_BOUNDEDu_BELOWu_POS,axiom,
! [N,M,F0,G0] :
( ( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
& p(s(bool,i(s(fun(fun(cart(real,N),cart(real,M)),bool),linear),s(fun(cart(real,N),cart(real,M)),G0))))
& s(fun(cart(real,M),cart(real,M)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),cart(real,M))),i(s(fun(fun(cart(real,N),cart(real,M)),fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),cart(real,M)))),o),s(fun(cart(real,N),cart(real,M)),G0))),s(fun(cart(real,M),cart(real,N)),F0))) = s(fun(cart(real,M),cart(real,M)),i1) )
=> ? [B0] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,B0))))
& ! [X] : p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,B0))),s(real,i(s(fun(cart(real,M),real),vectoru_norm),s(cart(real,M),X))))))),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X)))))))) ) ) ).
fof(aLINEARu_INVERTIBLEu_BOUNDEDu_BELOW,axiom,
! [N,M,F0,G0] :
( ( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
& p(s(bool,i(s(fun(fun(cart(real,N),cart(real,M)),bool),linear),s(fun(cart(real,N),cart(real,M)),G0))))
& s(fun(cart(real,M),cart(real,M)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),cart(real,M))),i(s(fun(fun(cart(real,N),cart(real,M)),fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),cart(real,M)))),o),s(fun(cart(real,N),cart(real,M)),G0))),s(fun(cart(real,M),cart(real,N)),F0))) = s(fun(cart(real,M),cart(real,M)),i1) )
=> ? [B0] :
! [X] : p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,B0))),s(real,i(s(fun(cart(real,M),real),vectoru_norm),s(cart(real,M),X))))))),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X)))))))) ) ).
fof(aLINEARu_INJECTIVEu_BOUNDEDu_BELOWu_POS,axiom,
! [N,M,F0] :
( ( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
& ! [X,Y] :
( s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),Y)))
=> s(cart(real,M),X) = s(cart(real,M),Y) ) )
=> ? [B0] :
( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,B0))))
& ! [X] : p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(cart(real,M),real),vectoru_norm),s(cart(real,M),X))))),s(real,B0))))),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X)))))))) ) ) ).
fof(aDIMu_INJECTIVEu_LINEARu_IMAGE,axiom,
! [N,M,F0,S0] :
( ( p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))))
& ! [X,Y] :
( s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),Y)))
=> s(cart(real,M),X) = s(cart(real,M),Y) ) )
=> s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,M),bool),S0))))) = s(num,i(s(fun(fun(cart(real,M),bool),num),dim),s(fun(cart(real,M),bool),S0))) ) ).
fof(arowvector,axiom,
! [N,U_1] :
( ! [V,J0] : s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),U_1),s(cart(real,N),V))),s(num,J0))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),V))),s(num,J0)))
=> ! [U_0] :
( ! [V,I0] : s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(real,N),fun(num,cart(real,N))),U_0),s(cart(real,N),V))),s(num,I0))) = s(cart(real,N),i(s(fun(fun(num,real),cart(real,N)),lambda),s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),U_1),s(cart(real,N),V)))))
=> ! [V] : s(cart(cart(real,N),n10),i(s(fun(cart(real,N),cart(cart(real,N),n10)),rowvector),s(cart(real,N),V))) = s(cart(cart(real,N),n10),i(s(fun(fun(num,cart(real,N)),cart(cart(real,N),n10)),lambda),s(fun(num,cart(real,N)),i(s(fun(cart(real,N),fun(num,cart(real,N))),U_0),s(cart(real,N),V))))) ) ) ).
fof(acolumnvector,axiom,
! [N,U_1] :
( ! [V,I0,J0] : s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(real,N),fun(num,fun(num,real))),U_1),s(cart(real,N),V))),s(num,I0))),s(num,J0))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),V))),s(num,I0)))
=> ! [U_0] :
( ! [V,I0] : s(cart(real,n10),i(s(fun(num,cart(real,n10)),i(s(fun(cart(real,N),fun(num,cart(real,n10))),U_0),s(cart(real,N),V))),s(num,I0))) = s(cart(real,n10),i(s(fun(fun(num,real),cart(real,n10)),lambda),s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(real,N),fun(num,fun(num,real))),U_1),s(cart(real,N),V))),s(num,I0)))))
=> ! [V] : s(cart(cart(real,n10),N),i(s(fun(cart(real,N),cart(cart(real,n10),N)),columnvector),s(cart(real,N),V))) = s(cart(cart(real,n10),N),i(s(fun(fun(num,cart(real,n10)),cart(cart(real,n10),N)),lambda),s(fun(num,cart(real,n10)),i(s(fun(cart(real,N),fun(num,cart(real,n10))),U_0),s(cart(real,N),V))))) ) ) ).
fof(aTRANSPu_COLUMNVECTOR,axiom,
! [Q131708,V] : s(cart(cart(real,Q131708),n10),i(s(fun(cart(cart(real,n10),Q131708),cart(cart(real,Q131708),n10)),transp),s(cart(cart(real,n10),Q131708),i(s(fun(cart(real,Q131708),cart(cart(real,n10),Q131708)),columnvector),s(cart(real,Q131708),V))))) = s(cart(cart(real,Q131708),n10),i(s(fun(cart(real,Q131708),cart(cart(real,Q131708),n10)),rowvector),s(cart(real,Q131708),V))) ).
fof(aTRANSPu_ROWVECTOR,axiom,
! [Q131723,V] : s(cart(cart(real,n10),Q131723),i(s(fun(cart(cart(real,Q131723),n10),cart(cart(real,n10),Q131723)),transp),s(cart(cart(real,Q131723),n10),i(s(fun(cart(real,Q131723),cart(cart(real,Q131723),n10)),rowvector),s(cart(real,Q131723),V))))) = s(cart(cart(real,n10),Q131723),i(s(fun(cart(real,Q131723),cart(cart(real,n10),Q131723)),columnvector),s(cart(real,Q131723),V))) ).
fof(aDOTu_ROWVECTORu_COLUMNVECTOR,axiom,
! [M,N,A5,V] : s(cart(cart(real,n10),M),i(s(fun(cart(real,M),cart(cart(real,n10),M)),columnvector),s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),A5))),s(cart(real,N),V))))) = s(cart(cart(real,n10),M),i(s(fun(cart(cart(real,n10),N),cart(cart(real,n10),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,n10),N),cart(cart(real,n10),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,n10),N),i(s(fun(cart(real,N),cart(cart(real,n10),N)),columnvector),s(cart(real,N),V))))) ).
fof(aDOTu_MATRIXu_PRODUCT,axiom,
! [N,X,Y] : s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),X))),s(cart(real,N),Y))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,n10),fun(num,real)),d_),s(cart(real,n10),i(s(fun(num,cart(real,n10)),i(s(fun(cart(cart(real,n10),n10),fun(num,cart(real,n10))),d_),s(cart(cart(real,n10),n10),i(s(fun(cart(cart(real,n10),N),cart(cart(real,n10),n10)),i(s(fun(cart(cart(real,N),n10),fun(cart(cart(real,n10),N),cart(cart(real,n10),n10))),matrixu_mul),s(cart(cart(real,N),n10),i(s(fun(cart(real,N),cart(cart(real,N),n10)),rowvector),s(cart(real,N),X))))),s(cart(cart(real,n10),N),i(s(fun(cart(real,N),cart(cart(real,n10),N)),columnvector),s(cart(real,N),Y))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) ).
fof(aDOTu_MATRIXu_VECTORu_MUL,axiom,
! [N,A5,B0,X,Y] : s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(cart(real,N),N),fun(cart(real,N),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,N),N),A5))),s(cart(real,N),X))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(cart(real,N),N),fun(cart(real,N),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,N),N),B0))),s(cart(real,N),Y))))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,n10),fun(num,real)),d_),s(cart(real,n10),i(s(fun(num,cart(real,n10)),i(s(fun(cart(cart(real,n10),n10),fun(num,cart(real,n10))),d_),s(cart(cart(real,n10),n10),i(s(fun(cart(cart(real,n10),N),cart(cart(real,n10),n10)),i(s(fun(cart(cart(real,N),n10),fun(cart(cart(real,n10),N),cart(cart(real,n10),n10))),matrixu_mul),s(cart(cart(real,N),n10),i(s(fun(cart(real,N),cart(cart(real,N),n10)),rowvector),s(cart(real,N),X))))),s(cart(cart(real,n10),N),i(s(fun(cart(cart(real,n10),N),cart(cart(real,n10),N)),i(s(fun(cart(cart(real,N),N),fun(cart(cart(real,n10),N),cart(cart(real,n10),N))),matrixu_mul),s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),N),cart(cart(real,N),N)),i(s(fun(cart(cart(real,N),N),fun(cart(cart(real,N),N),cart(cart(real,N),N))),matrixu_mul),s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),N),cart(cart(real,N),N)),transp),s(cart(cart(real,N),N),A5))))),s(cart(cart(real,N),N),B0))))),s(cart(cart(real,n10),N),i(s(fun(cart(real,N),cart(cart(real,n10),N)),columnvector),s(cart(real,N),Y))))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) ).
fof(aMATRIXu_VECTORu_MULu_INu_COLUMNSPACE,axiom,
! [M,N,A5,X] : p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),X))))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(cart(cart(real,M),N),fun(cart(real,N),bool)),columns),s(cart(cart(real,M),N),A5)))))))) ).
fof(aSUBSPACEu_ORTHOGONALu_TOu_VECTOR,axiom,
! [Q131992,U_0] :
( ! [X,GENR_PVARR_327] :
( p(s(bool,i(s(fun(cart(real,Q131992),bool),i(s(fun(cart(real,Q131992),fun(cart(real,Q131992),bool)),U_0),s(cart(real,Q131992),X))),s(cart(real,Q131992),GENR_PVARR_327))))
<=> ? [Y] : p(s(bool,i(s(fun(cart(real,Q131992),bool),i(s(fun(bool,fun(cart(real,Q131992),bool)),i(s(fun(cart(real,Q131992),fun(bool,fun(cart(real,Q131992),bool))),setspec),s(cart(real,Q131992),GENR_PVARR_327))),s(bool,i(s(fun(cart(real,Q131992),bool),i(s(fun(cart(real,Q131992),fun(cart(real,Q131992),bool)),orthogonal),s(cart(real,Q131992),X))),s(cart(real,Q131992),Y))))),s(cart(real,Q131992),Y)))) )
=> ! [X] : p(s(bool,i(s(fun(fun(cart(real,Q131992),bool),bool),subspace),s(fun(cart(real,Q131992),bool),i(s(fun(fun(cart(real,Q131992),bool),fun(cart(real,Q131992),bool)),gspec),s(fun(cart(real,Q131992),bool),i(s(fun(cart(real,Q131992),fun(cart(real,Q131992),bool)),U_0),s(cart(real,Q131992),X)))))))) ) ).
fof(aSUBSPACEu_ORTHOGONALu_TOu_VECTORS,axiom,
! [Q132023,U_0] :
( ! [S0,GENR_PVARR_328] :
( p(s(bool,i(s(fun(cart(real,Q132023),bool),i(s(fun(fun(cart(real,Q132023),bool),fun(cart(real,Q132023),bool)),U_0),s(fun(cart(real,Q132023),bool),S0))),s(cart(real,Q132023),GENR_PVARR_328))))
<=> ? [Y,V] :
( ( p(s(bool,V))
<=> ! [X] :
( p(s(bool,i(s(fun(fun(cart(real,Q132023),bool),bool),i(s(fun(cart(real,Q132023),fun(fun(cart(real,Q132023),bool),bool)),in),s(cart(real,Q132023),X))),s(fun(cart(real,Q132023),bool),S0))))
=> p(s(bool,i(s(fun(cart(real,Q132023),bool),i(s(fun(cart(real,Q132023),fun(cart(real,Q132023),bool)),orthogonal),s(cart(real,Q132023),X))),s(cart(real,Q132023),Y)))) ) )
& p(s(bool,i(s(fun(cart(real,Q132023),bool),i(s(fun(bool,fun(cart(real,Q132023),bool)),i(s(fun(cart(real,Q132023),fun(bool,fun(cart(real,Q132023),bool))),setspec),s(cart(real,Q132023),GENR_PVARR_328))),s(bool,V))),s(cart(real,Q132023),Y)))) ) )
=> ! [S0] : p(s(bool,i(s(fun(fun(cart(real,Q132023),bool),bool),subspace),s(fun(cart(real,Q132023),bool),i(s(fun(fun(cart(real,Q132023),bool),fun(cart(real,Q132023),bool)),gspec),s(fun(cart(real,Q132023),bool),i(s(fun(fun(cart(real,Q132023),bool),fun(cart(real,Q132023),bool)),U_0),s(fun(cart(real,Q132023),bool),S0)))))))) ) ).
fof(aORTHOGONALu_TOu_SPAN,axiom,
! [Q132081,S0,X] :
( ! [Y] :
( p(s(bool,i(s(fun(fun(cart(real,Q132081),bool),bool),i(s(fun(cart(real,Q132081),fun(fun(cart(real,Q132081),bool),bool)),in),s(cart(real,Q132081),Y))),s(fun(cart(real,Q132081),bool),S0))))
=> p(s(bool,i(s(fun(cart(real,Q132081),bool),i(s(fun(cart(real,Q132081),fun(cart(real,Q132081),bool)),orthogonal),s(cart(real,Q132081),X))),s(cart(real,Q132081),Y)))) )
=> ! [Y] :
( p(s(bool,i(s(fun(fun(cart(real,Q132081),bool),bool),i(s(fun(cart(real,Q132081),fun(fun(cart(real,Q132081),bool),bool)),in),s(cart(real,Q132081),Y))),s(fun(cart(real,Q132081),bool),i(s(fun(fun(cart(real,Q132081),bool),fun(cart(real,Q132081),bool)),span),s(fun(cart(real,Q132081),bool),S0))))))
=> p(s(bool,i(s(fun(cart(real,Q132081),bool),i(s(fun(cart(real,Q132081),fun(cart(real,Q132081),bool)),orthogonal),s(cart(real,Q132081),X))),s(cart(real,Q132081),Y)))) ) ) ).
fof(aORTHOGONALu_TOu_SPANu_EQ,axiom,
! [Q132106,S0,X] :
( ! [Y] :
( p(s(bool,i(s(fun(fun(cart(real,Q132106),bool),bool),i(s(fun(cart(real,Q132106),fun(fun(cart(real,Q132106),bool),bool)),in),s(cart(real,Q132106),Y))),s(fun(cart(real,Q132106),bool),i(s(fun(fun(cart(real,Q132106),bool),fun(cart(real,Q132106),bool)),span),s(fun(cart(real,Q132106),bool),S0))))))
=> p(s(bool,i(s(fun(cart(real,Q132106),bool),i(s(fun(cart(real,Q132106),fun(cart(real,Q132106),bool)),orthogonal),s(cart(real,Q132106),X))),s(cart(real,Q132106),Y)))) )
<=> ! [Y] :
( p(s(bool,i(s(fun(fun(cart(real,Q132106),bool),bool),i(s(fun(cart(real,Q132106),fun(fun(cart(real,Q132106),bool),bool)),in),s(cart(real,Q132106),Y))),s(fun(cart(real,Q132106),bool),S0))))
=> p(s(bool,i(s(fun(cart(real,Q132106),bool),i(s(fun(cart(real,Q132106),fun(cart(real,Q132106),bool)),orthogonal),s(cart(real,Q132106),X))),s(cart(real,Q132106),Y)))) ) ) ).
fof(aORTHOGONALu_TOu_SPANSu_EQ,axiom,
! [Q132154,S0,T0] :
( ! [X,Y] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q132154),bool),bool),i(s(fun(cart(real,Q132154),fun(fun(cart(real,Q132154),bool),bool)),in),s(cart(real,Q132154),X))),s(fun(cart(real,Q132154),bool),i(s(fun(fun(cart(real,Q132154),bool),fun(cart(real,Q132154),bool)),span),s(fun(cart(real,Q132154),bool),S0))))))
& p(s(bool,i(s(fun(fun(cart(real,Q132154),bool),bool),i(s(fun(cart(real,Q132154),fun(fun(cart(real,Q132154),bool),bool)),in),s(cart(real,Q132154),Y))),s(fun(cart(real,Q132154),bool),i(s(fun(fun(cart(real,Q132154),bool),fun(cart(real,Q132154),bool)),span),s(fun(cart(real,Q132154),bool),T0)))))) )
=> p(s(bool,i(s(fun(cart(real,Q132154),bool),i(s(fun(cart(real,Q132154),fun(cart(real,Q132154),bool)),orthogonal),s(cart(real,Q132154),X))),s(cart(real,Q132154),Y)))) )
<=> ! [X,Y] :
( ( p(s(bool,i(s(fun(fun(cart(real,Q132154),bool),bool),i(s(fun(cart(real,Q132154),fun(fun(cart(real,Q132154),bool),bool)),in),s(cart(real,Q132154),X))),s(fun(cart(real,Q132154),bool),S0))))
& p(s(bool,i(s(fun(fun(cart(real,Q132154),bool),bool),i(s(fun(cart(real,Q132154),fun(fun(cart(real,Q132154),bool),bool)),in),s(cart(real,Q132154),Y))),s(fun(cart(real,Q132154),bool),T0)))) )
=> p(s(bool,i(s(fun(cart(real,Q132154),bool),i(s(fun(cart(real,Q132154),fun(cart(real,Q132154),bool)),orthogonal),s(cart(real,Q132154),X))),s(cart(real,Q132154),Y)))) ) ) ).
fof(aORTHOGONALu_NULLSPACEu_ROWSPACE,axiom,
! [N,M,A5,X,Y] :
( ( s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
& p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),Y))),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),span),s(fun(cart(real,M),bool),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),bool)),rows),s(cart(cart(real,M),N),A5)))))))) )
=> p(s(bool,i(s(fun(cart(real,M),bool),i(s(fun(cart(real,M),fun(cart(real,M),bool)),orthogonal),s(cart(real,M),X))),s(cart(real,M),Y)))) ) ).
fof(aNULLSPACEu_INTERu_ROWSPACE,axiom,
! [N,M,A5,X] :
( ( s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
& p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),span),s(fun(cart(real,M),bool),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),bool)),rows),s(cart(cart(real,M),N),A5)))))))) )
<=> s(cart(real,M),X) = s(cart(real,M),i(s(fun(num,cart(real,M)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ).
fof(aMATRIXu_VECTORu_MULu_INJECTIVEu_ONu_ROWSPACE,axiom,
! [N,M,A5,X,Y] :
( ( p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),span),s(fun(cart(real,M),bool),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),bool)),rows),s(cart(cart(real,M),N),A5))))))))
& p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),Y))),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),span),s(fun(cart(real,M),bool),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),bool)),rows),s(cart(cart(real,M),N),A5))))))))
& s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),Y))) )
=> s(cart(real,M),X) = s(cart(real,M),Y) ) ).
fof(aDIMu_ROWSu_LEu_DIMu_COLUMNS,axiom,
! [M,N,A5] : p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(cart(real,M),bool),num),dim),s(fun(cart(real,M),bool),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),bool)),rows),s(cart(cart(real,M),N),A5))))))),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),i(s(fun(cart(cart(real,M),N),fun(cart(real,N),bool)),columns),s(cart(cart(real,M),N),A5)))))))) ).
fof(arank,axiom,
! [M,N,A5] : s(num,i(s(fun(cart(cart(real,M),N),num),rank),s(cart(cart(real,M),N),A5))) = s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),i(s(fun(cart(cart(real,M),N),fun(cart(real,N),bool)),columns),s(cart(cart(real,M),N),A5))))) ).
fof(aRANKu_ROW,axiom,
! [M,N,A5] : s(num,i(s(fun(cart(cart(real,M),N),num),rank),s(cart(cart(real,M),N),A5))) = s(num,i(s(fun(fun(cart(real,M),bool),num),dim),s(fun(cart(real,M),bool),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),bool)),rows),s(cart(cart(real,M),N),A5))))) ).
fof(aRANKu_TRANSP,axiom,
! [M,N,A5] : s(num,i(s(fun(cart(cart(real,N),M),num),rank),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,N),M)),transp),s(cart(cart(real,M),N),A5))))) = s(num,i(s(fun(cart(cart(real,M),N),num),rank),s(cart(cart(real,M),N),A5))) ).
fof(aMATRIXu_VECTORu_MULu_BASIS,axiom,
! [M,N,A5,K0] :
( ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,K0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,K0))),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ)))))) )
=> s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),i(s(fun(num,cart(real,M)),basis),s(num,K0))))) = s(cart(real,N),i(s(fun(cart(cart(real,M),N),cart(real,N)),i(s(fun(num,fun(cart(cart(real,M),N),cart(real,N))),column),s(num,K0))),s(cart(cart(real,M),N),A5))) ) ).
fof(aCOLUMNSu_IMAGEu_BASIS,axiom,
! [N,M,U_1] :
( ! [GENR_PVARR_331] :
( p(s(bool,i(s(fun(cart(real,M),bool),U_1),s(cart(real,M),GENR_PVARR_331))))
<=> ? [I0,V] :
( ( p(s(bool,V))
<=> ( p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ)))))) ) )
& p(s(bool,i(s(fun(cart(real,M),bool),i(s(fun(bool,fun(cart(real,M),bool)),i(s(fun(cart(real,M),fun(bool,fun(cart(real,M),bool))),setspec),s(cart(real,M),GENR_PVARR_331))),s(bool,V))),s(cart(real,M),i(s(fun(num,cart(real,M)),basis),s(num,I0)))))) ) )
=> ! [U_0] :
( ! [A5,X] : s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),U_0),s(cart(cart(real,M),N),A5))),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),X)))
=> ! [A5] : s(fun(cart(real,N),bool),i(s(fun(cart(cart(real,M),N),fun(cart(real,N),bool)),columns),s(cart(cart(real,M),N),A5))) = s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),U_0),s(cart(cart(real,M),N),A5))))),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),gspec),s(fun(cart(real,M),bool),U_1))))) ) ) ).
fof(aRANKu_DIMu_IM,axiom,
! [N,M,U_0] :
( ! [A5,X] : s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),U_0),s(cart(cart(real,M),N),A5))),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),X)))
=> ! [A5] : s(num,i(s(fun(cart(cart(real,M),N),num),rank),s(cart(cart(real,M),N),A5))) = s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),U_0),s(cart(cart(real,M),N),A5))))),s(fun(cart(real,M),bool),univ))))) ) ).
fof(aDIMu_EQu_SPAN,axiom,
! [N,S0,T0] :
( ( p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),T0))))
& p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),T0))))),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0)))))) )
=> s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0))) = s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),T0))) ) ).
fof(aDIMu_EQu_FULL,conjecture,
! [N,S0] :
( s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0))) = s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))
<=> s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0))) = s(fun(cart(real,N),bool),univ) ) ).
%------------------------------------------------------------------------------