TPTP Problem File: ANA143_1.008.032.p
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%------------------------------------------------------------------------------
% File : ANA143_1.008.032 : TPTP v9.0.0. Released v8.2.0.
% Domain : Number theory
% Problem : linear_limit_n8_m32__1
% Version : Especial.
% English : lim(f_1 x) = l_1
% ...
% lim(f_n x) = l_n
% =================
% lim(k_1 f_{i_1}(x) + ... + k_m f_{i_m}(x)) = k1 l_{i_1} ... k_m l_{i_m}
%
% with n = 8
% m = 32
% k_i in Q
% i_j in {1..n}
% Refs : [Sch22] Schoisswohl (2022), Email to G. Sutcliffe
% : [KK+23] Korovin et al. (2023), ALASCA: Reasoning in Quantified
% Source : [Sch22]
% Names : linear_limit_n8_m32__1.smt2 [Sch22]
% Status : Theorem
% Rating : 1.00 v8.2.0
% Syntax : Number of formulae : 26 ( 0 unt; 17 typ; 0 def)
% Number of atoms : 99 ( 9 equ)
% Maximal formula atoms : 11 ( 11 avg)
% Number of connectives : 117 ( 27 ~; 0 |; 36 &)
% ( 0 <=>; 54 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 11 avg)
% Maximal term depth : 37 ( 4 avg)
% Number arithmetic : 1693 ( 90 atm;1010 fun; 566 num; 27 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 0 usr; 0 prp; 2-2 aty)
% Number of functors : 71 ( 17 usr; 58 con; 0-2 aty)
% Number of variables : 27 ( 18 !; 9 ?; 27 :)
% SPC : TF0_THM_EQU_ARI
% Comments : Translated from SMT UFLRA by SMTtoTPTP.
%------------------------------------------------------------------------------
%% Declarations:
tff(l4,type,
l4: $real ).
tff(f5,type,
f5: $real > $real ).
tff(l5,type,
l5: $real ).
tff(f6,type,
f6: $real > $real ).
tff(f0,type,
f0: $real > $real ).
tff(l0,type,
l0: $real ).
tff(f4,type,
f4: $real > $real ).
tff(f2,type,
f2: $real > $real ).
tff(l2,type,
l2: $real ).
tff(a,type,
a: $real ).
tff(f7,type,
f7: $real > $real ).
tff(f1,type,
f1: $real > $real ).
tff(l1,type,
l1: $real ).
tff(l7,type,
l7: $real ).
tff(l3,type,
l3: $real ).
tff(f3,type,
f3: $real > $real ).
tff(l6,type,
l6: $real ).
%% Assertions:
%% ∀ epsilon:Real ((0.0 < epsilon) ⇒ ∃ delta:Real ((0.0 < delta) ∧ ∀ x:Real ((¬(x = a) ∧ ((if ((x - a) ≥ 0.0) (x - a) else -(x - a)) < delta)) ⇒ ((if ((f0(x) - l0) ≥ 0.0) (f0(x) - l0) else -(f0(x) - l0)) < epsilon))))
tff(formula_1,axiom,
! [Epsilon: $real] :
( $less(0.0,Epsilon)
=> ? [Delta: $real] :
( $less(0.0,Delta)
& ! [X: $real] :
( ( ( X != a )
& ( $greatereq($difference(X,a),0.0)
=> $less($difference(X,a),Delta) )
& ( ~ $greatereq($difference(X,a),0.0)
=> $less($uminus($difference(X,a)),Delta) ) )
=> ( ( $greatereq($difference(f0(X),l0),0.0)
=> $less($difference(f0(X),l0),Epsilon) )
& ( ~ $greatereq($difference(f0(X),l0),0.0)
=> $less($uminus($difference(f0(X),l0)),Epsilon) ) ) ) ) ) ).
%% ∀ epsilon:Real ((0.0 < epsilon) ⇒ ∃ delta:Real ((0.0 < delta) ∧ ∀ x:Real ((¬(x = a) ∧ ((if ((x - a) ≥ 0.0) (x - a) else -(x - a)) < delta)) ⇒ ((if ((f1(x) - l1) ≥ 0.0) (f1(x) - l1) else -(f1(x) - l1)) < epsilon))))
tff(formula_2,axiom,
! [Epsilon: $real] :
( $less(0.0,Epsilon)
=> ? [Delta: $real] :
( $less(0.0,Delta)
& ! [X: $real] :
( ( ( X != a )
& ( $greatereq($difference(X,a),0.0)
=> $less($difference(X,a),Delta) )
& ( ~ $greatereq($difference(X,a),0.0)
=> $less($uminus($difference(X,a)),Delta) ) )
=> ( ( $greatereq($difference(f1(X),l1),0.0)
=> $less($difference(f1(X),l1),Epsilon) )
& ( ~ $greatereq($difference(f1(X),l1),0.0)
=> $less($uminus($difference(f1(X),l1)),Epsilon) ) ) ) ) ) ).
%% ∀ epsilon:Real ((0.0 < epsilon) ⇒ ∃ delta:Real ((0.0 < delta) ∧ ∀ x:Real ((¬(x = a) ∧ ((if ((x - a) ≥ 0.0) (x - a) else -(x - a)) < delta)) ⇒ ((if ((f2(x) - l2) ≥ 0.0) (f2(x) - l2) else -(f2(x) - l2)) < epsilon))))
tff(formula_3,axiom,
! [Epsilon: $real] :
( $less(0.0,Epsilon)
=> ? [Delta: $real] :
( $less(0.0,Delta)
& ! [X: $real] :
( ( ( X != a )
& ( $greatereq($difference(X,a),0.0)
=> $less($difference(X,a),Delta) )
& ( ~ $greatereq($difference(X,a),0.0)
=> $less($uminus($difference(X,a)),Delta) ) )
=> ( ( $greatereq($difference(f2(X),l2),0.0)
=> $less($difference(f2(X),l2),Epsilon) )
& ( ~ $greatereq($difference(f2(X),l2),0.0)
=> $less($uminus($difference(f2(X),l2)),Epsilon) ) ) ) ) ) ).
%% ∀ epsilon:Real ((0.0 < epsilon) ⇒ ∃ delta:Real ((0.0 < delta) ∧ ∀ x:Real ((¬(x = a) ∧ ((if ((x - a) ≥ 0.0) (x - a) else -(x - a)) < delta)) ⇒ ((if ((f3(x) - l3) ≥ 0.0) (f3(x) - l3) else -(f3(x) - l3)) < epsilon))))
tff(formula_4,axiom,
! [Epsilon: $real] :
( $less(0.0,Epsilon)
=> ? [Delta: $real] :
( $less(0.0,Delta)
& ! [X: $real] :
( ( ( X != a )
& ( $greatereq($difference(X,a),0.0)
=> $less($difference(X,a),Delta) )
& ( ~ $greatereq($difference(X,a),0.0)
=> $less($uminus($difference(X,a)),Delta) ) )
=> ( ( $greatereq($difference(f3(X),l3),0.0)
=> $less($difference(f3(X),l3),Epsilon) )
& ( ~ $greatereq($difference(f3(X),l3),0.0)
=> $less($uminus($difference(f3(X),l3)),Epsilon) ) ) ) ) ) ).
%% ∀ epsilon:Real ((0.0 < epsilon) ⇒ ∃ delta:Real ((0.0 < delta) ∧ ∀ x:Real ((¬(x = a) ∧ ((if ((x - a) ≥ 0.0) (x - a) else -(x - a)) < delta)) ⇒ ((if ((f4(x) - l4) ≥ 0.0) (f4(x) - l4) else -(f4(x) - l4)) < epsilon))))
tff(formula_5,axiom,
! [Epsilon: $real] :
( $less(0.0,Epsilon)
=> ? [Delta: $real] :
( $less(0.0,Delta)
& ! [X: $real] :
( ( ( X != a )
& ( $greatereq($difference(X,a),0.0)
=> $less($difference(X,a),Delta) )
& ( ~ $greatereq($difference(X,a),0.0)
=> $less($uminus($difference(X,a)),Delta) ) )
=> ( ( $greatereq($difference(f4(X),l4),0.0)
=> $less($difference(f4(X),l4),Epsilon) )
& ( ~ $greatereq($difference(f4(X),l4),0.0)
=> $less($uminus($difference(f4(X),l4)),Epsilon) ) ) ) ) ) ).
%% ∀ epsilon:Real ((0.0 < epsilon) ⇒ ∃ delta:Real ((0.0 < delta) ∧ ∀ x:Real ((¬(x = a) ∧ ((if ((x - a) ≥ 0.0) (x - a) else -(x - a)) < delta)) ⇒ ((if ((f5(x) - l5) ≥ 0.0) (f5(x) - l5) else -(f5(x) - l5)) < epsilon))))
tff(formula_6,axiom,
! [Epsilon: $real] :
( $less(0.0,Epsilon)
=> ? [Delta: $real] :
( $less(0.0,Delta)
& ! [X: $real] :
( ( ( X != a )
& ( $greatereq($difference(X,a),0.0)
=> $less($difference(X,a),Delta) )
& ( ~ $greatereq($difference(X,a),0.0)
=> $less($uminus($difference(X,a)),Delta) ) )
=> ( ( $greatereq($difference(f5(X),l5),0.0)
=> $less($difference(f5(X),l5),Epsilon) )
& ( ~ $greatereq($difference(f5(X),l5),0.0)
=> $less($uminus($difference(f5(X),l5)),Epsilon) ) ) ) ) ) ).
%% ∀ epsilon:Real ((0.0 < epsilon) ⇒ ∃ delta:Real ((0.0 < delta) ∧ ∀ x:Real ((¬(x = a) ∧ ((if ((x - a) ≥ 0.0) (x - a) else -(x - a)) < delta)) ⇒ ((if ((f6(x) - l6) ≥ 0.0) (f6(x) - l6) else -(f6(x) - l6)) < epsilon))))
tff(formula_7,axiom,
! [Epsilon: $real] :
( $less(0.0,Epsilon)
=> ? [Delta: $real] :
( $less(0.0,Delta)
& ! [X: $real] :
( ( ( X != a )
& ( $greatereq($difference(X,a),0.0)
=> $less($difference(X,a),Delta) )
& ( ~ $greatereq($difference(X,a),0.0)
=> $less($uminus($difference(X,a)),Delta) ) )
=> ( ( $greatereq($difference(f6(X),l6),0.0)
=> $less($difference(f6(X),l6),Epsilon) )
& ( ~ $greatereq($difference(f6(X),l6),0.0)
=> $less($uminus($difference(f6(X),l6)),Epsilon) ) ) ) ) ) ).
%% ∀ epsilon:Real ((0.0 < epsilon) ⇒ ∃ delta:Real ((0.0 < delta) ∧ ∀ x:Real ((¬(x = a) ∧ ((if ((x - a) ≥ 0.0) (x - a) else -(x - a)) < delta)) ⇒ ((if ((f7(x) - l7) ≥ 0.0) (f7(x) - l7) else -(f7(x) - l7)) < epsilon))))
tff(formula_8,axiom,
! [Epsilon: $real] :
( $less(0.0,Epsilon)
=> ? [Delta: $real] :
( $less(0.0,Delta)
& ! [X: $real] :
( ( ( X != a )
& ( $greatereq($difference(X,a),0.0)
=> $less($difference(X,a),Delta) )
& ( ~ $greatereq($difference(X,a),0.0)
=> $less($uminus($difference(X,a)),Delta) ) )
=> ( ( $greatereq($difference(f7(X),l7),0.0)
=> $less($difference(f7(X),l7),Epsilon) )
& ( ~ $greatereq($difference(f7(X),l7),0.0)
=> $less($uminus($difference(f7(X),l7)),Epsilon) ) ) ) ) ) ).
%% ∀ epsilon:Real ((0.0 < epsilon) ⇒ ∃ delta:Real ((0.0 < delta) ∧ ∀ x:Real ((¬(x = a) ∧ ((if ((x - a) ≥ 0.0) (x - a) else -(x - a)) < delta)) ⇒ ((if (((((52.0 / 80.0) * f6(x)) + (-(20.0 / 53.0) * f0(x)) + ((14.0 / 81.0) * f2(x)) + ((61.0 / 5.0) * f2(x)) + (-(96.0 / 63.0) * f0(x)) + (-(19.0 / 27.0) * f2(x)) + (-(30.0 / 40.0) * f6(x)) + (-(12.0 / 84.0) * f7(x)) + (-(83.0 / 100.0) * f1(x)) + ((67.0 / 99.0) * f0(x)) + ((83.0 / 23.0) * f5(x)) + (-(45.0 / 32.0) * f5(x)) + (-(83.0 / 100.0) * f5(x)) + ((43.0 / 26.0) * f5(x)) + ((33.0 / 30.0) * f6(x)) + (-(67.0 / 74.0) * f6(x)) + ((95.0 / 60.0) * f6(x)) + (-(79.0 / 46.0) * f1(x)) + ((76.0 / 75.0) * f3(x)) + (-(82.0 / 18.0) * f7(x)) + (-(14.0 / 6.0) * f0(x)) + (-(100.0 / 57.0) * f2(x)) + ((89.0 / 58.0) * f0(x)) + (-(32.0 / 28.0) * f6(x)) + (-(23.0 / 38.0) * f3(x)) + ((61.0 / 76.0) * f3(x)) + (-(97.0 / 25.0) * f7(x)) + (-(52.0 / 85.0) * f7(x)) + ((61.0 / 58.0) * f4(x)) + (-(41.0 / 99.0) * f0(x)) + (-(100.0 / 8.0) * f3(x)) + (-(71.0 / 13.0) * f3(x))) - (((52.0 / 80.0) * l6) + (-(20.0 / 53.0) * l0) + ((14.0 / 81.0) * l2) + ((61.0 / 5.0) * l2) + (-(96.0 / 63.0) * l0) + (-(19.0 / 27.0) * l2) + (-(30.0 / 40.0) * l6) + (-(12.0 / 84.0) * l7) + (-(83.0 / 100.0) * l1) + ((67.0 / 99.0) * l0) + ((83.0 / 23.0) * l5) + (-(45.0 / 32.0) * l5) + (-(83.0 / 100.0) * l5) + ((43.0 / 26.0) * l5) + ((33.0 / 30.0) * l6) + (-(67.0 / 74.0) * l6) + ((95.0 / 60.0) * l6) + (-(79.0 / 46.0) * l1) + ((76.0 / 75.0) * l3) + (-(82.0 / 18.0) * l7) + (-(14.0 / 6.0) * l0) + (-(100.0 / 57.0) * l2) + ((89.0 / 58.0) * l0) + (-(32.0 / 28.0) * l6) + (-(23.0 / 38.0) * l3) + ((61.0 / 76.0) * l3) + (-(97.0 / 25.0) * l7) + (-(52.0 / 85.0) * l7) + ((61.0 / 58.0) * l4) + (-(41.0 / 99.0) * l0) + (-(100.0 / 8.0) * l3) + (-(71.0 / 13.0) * l3))) ≥ 0.0) ((((52.0 / 80.0) * f6(x)) + (-(20.0 / 53.0) * f0(x)) + ((14.0 / 81.0) * f2(x)) + ((61.0 / 5.0) * f2(x)) + (-(96.0 / 63.0) * f0(x)) + (-(19.0 / 27.0) * f2(x)) + (-(30.0 / 40.0) * f6(x)) + (-(12.0 / 84.0) * f7(x)) + (-(83.0 / 100.0) * f1(x)) + ((67.0 / 99.0) * f0(x)) + ((83.0 / 23.0) * f5(x)) + (-(45.0 / 32.0) * f5(x)) + (-(83.0 / 100.0) * f5(x)) + ((43.0 / 26.0) * f5(x)) + ((33.0 / 30.0) * f6(x)) + (-(67.0 / 74.0) * f6(x)) + ((95.0 / 60.0) * f6(x)) + (-(79.0 / 46.0) * f1(x)) + ((76.0 / 75.0) * f3(x)) + (-(82.0 / 18.0) * f7(x)) + (-(14.0 / 6.0) * f0(x)) + (-(100.0 / 57.0) * f2(x)) + ((89.0 / 58.0) * f0(x)) + (-(32.0 / 28.0) * f6(x)) + (-(23.0 / 38.0) * f3(x)) + ((61.0 / 76.0) * f3(x)) + (-(97.0 / 25.0) * f7(x)) + (-(52.0 / 85.0) * f7(x)) + ((61.0 / 58.0) * f4(x)) + (-(41.0 / 99.0) * f0(x)) + (-(100.0 / 8.0) * f3(x)) + (-(71.0 / 13.0) * f3(x))) - (((52.0 / 80.0) * l6) + (-(20.0 / 53.0) * l0) + ((14.0 / 81.0) * l2) + ((61.0 / 5.0) * l2) + (-(96.0 / 63.0) * l0) + (-(19.0 / 27.0) * l2) + (-(30.0 / 40.0) * l6) + (-(12.0 / 84.0) * l7) + (-(83.0 / 100.0) * l1) + ((67.0 / 99.0) * l0) + ((83.0 / 23.0) * l5) + (-(45.0 / 32.0) * l5) + (-(83.0 / 100.0) * l5) + ((43.0 / 26.0) * l5) + ((33.0 / 30.0) * l6) + (-(67.0 / 74.0) * l6) + ((95.0 / 60.0) * l6) + (-(79.0 / 46.0) * l1) + ((76.0 / 75.0) * l3) + (-(82.0 / 18.0) * l7) + (-(14.0 / 6.0) * l0) + (-(100.0 / 57.0) * l2) + ((89.0 / 58.0) * l0) + (-(32.0 / 28.0) * l6) + (-(23.0 / 38.0) * l3) + ((61.0 / 76.0) * l3) + (-(97.0 / 25.0) * l7) + (-(52.0 / 85.0) * l7) + ((61.0 / 58.0) * l4) + (-(41.0 / 99.0) * l0) + (-(100.0 / 8.0) * l3) + (-(71.0 / 13.0) * l3))) else -((((52.0 / 80.0) * f6(x)) + (-(20.0 / 53.0) * f0(x)) + ((14.0 / 81.0) * f2(x)) + ((61.0 / 5.0) * f2(x)) + (-(96.0 / 63.0) * f0(x)) + (-(19.0 / 27.0) * f2(x)) + (-(30.0 / 40.0) * f6(x)) + (-(12.0 / 84.0) * f7(x)) + (-(83.0 / 100.0) * f1(x)) + ((67.0 / 99.0) * f0(x)) + ((83.0 / 23.0) * f5(x)) + (-(45.0 / 32.0) * f5(x)) + (-(83.0 / 100.0) * f5(x)) + ((43.0 / 26.0) * f5(x)) + ((33.0 / 30.0) * f6(x)) + (-(67.0 / 74.0) * f6(x)) + ((95.0 / 60.0) * f6(x)) + (-(79.0 / 46.0) * f1(x)) + ((76.0 / 75.0) * f3(x)) + (-(82.0 / 18.0) * f7(x)) + (-(14.0 / 6.0) * f0(x)) + (-(100.0 / 57.0) * f2(x)) + ((89.0 / 58.0) * f0(x)) + (-(32.0 / 28.0) * f6(x)) + (-(23.0 / 38.0) * f3(x)) + ((61.0 / 76.0) * f3(x)) + (-(97.0 / 25.0) * f7(x)) + (-(52.0 / 85.0) * f7(x)) + ((61.0 / 58.0) * f4(x)) + (-(41.0 / 99.0) * f0(x)) + (-(100.0 / 8.0) * f3(x)) + (-(71.0 / 13.0) * f3(x))) - (((52.0 / 80.0) * l6) + (-(20.0 / 53.0) * l0) + ((14.0 / 81.0) * l2) + ((61.0 / 5.0) * l2) + (-(96.0 / 63.0) * l0) + (-(19.0 / 27.0) * l2) + (-(30.0 / 40.0) * l6) + (-(12.0 / 84.0) * l7) + (-(83.0 / 100.0) * l1) + ((67.0 / 99.0) * l0) + ((83.0 / 23.0) * l5) + (-(45.0 / 32.0) * l5) + (-(83.0 / 100.0) * l5) + ((43.0 / 26.0) * l5) + ((33.0 / 30.0) * l6) + (-(67.0 / 74.0) * l6) + ((95.0 / 60.0) * l6) + (-(79.0 / 46.0) * l1) + ((76.0 / 75.0) * l3) + (-(82.0 / 18.0) * l7) + (-(14.0 / 6.0) * l0) + (-(100.0 / 57.0) * l2) + ((89.0 / 58.0) * l0) + (-(32.0 / 28.0) * l6) + (-(23.0 / 38.0) * l3) + ((61.0 / 76.0) * l3) + (-(97.0 / 25.0) * l7) + (-(52.0 / 85.0) * l7) + ((61.0 / 58.0) * l4) + (-(41.0 / 99.0) * l0) + (-(100.0 / 8.0) * l3) + (-(71.0 / 13.0) * l3)))) < epsilon))))
tff(formula_9,conjecture,
! [Epsilon: $real] :
( $less(0.0,Epsilon)
=> ? [Delta: $real] :
( $less(0.0,Delta)
& ! [X: $real] :
( ( ( X != a )
& ( $greatereq($difference(X,a),0.0)
=> $less($difference(X,a),Delta) )
& ( ~ $greatereq($difference(X,a),0.0)
=> $less($uminus($difference(X,a)),Delta) ) )
=> ( ( $greatereq($difference($sum($product($quotient(52.0,80.0),f6(X)),$sum($product($uminus($quotient(20.0,53.0)),f0(X)),$sum($product($quotient(14.0,81.0),f2(X)),$sum($product($quotient(61.0,5.0),f2(X)),$sum($product($uminus($quotient(96.0,63.0)),f0(X)),$sum($product($uminus($quotient(19.0,27.0)),f2(X)),$sum($product($uminus($quotient(30.0,40.0)),f6(X)),$sum($product($uminus($quotient(12.0,84.0)),f7(X)),$sum($product($uminus($quotient(83.0,100.0)),f1(X)),$sum($product($quotient(67.0,99.0),f0(X)),$sum($product($quotient(83.0,23.0),f5(X)),$sum($product($uminus($quotient(45.0,32.0)),f5(X)),$sum($product($uminus($quotient(83.0,100.0)),f5(X)),$sum($product($quotient(43.0,26.0),f5(X)),$sum($product($quotient(33.0,30.0),f6(X)),$sum($product($uminus($quotient(67.0,74.0)),f6(X)),$sum($product($quotient(95.0,60.0),f6(X)),$sum($product($uminus($quotient(79.0,46.0)),f1(X)),$sum($product($quotient(76.0,75.0),f3(X)),$sum($product($uminus($quotient(82.0,18.0)),f7(X)),$sum($product($uminus($quotient(14.0,6.0)),f0(X)),$sum($product($uminus($quotient(100.0,57.0)),f2(X)),$sum($product($quotient(89.0,58.0),f0(X)),$sum($product($uminus($quotient(32.0,28.0)),f6(X)),$sum($product($uminus($quotient(23.0,38.0)),f3(X)),$sum($product($quotient(61.0,76.0),f3(X)),$sum($product($uminus($quotient(97.0,25.0)),f7(X)),$sum($product($uminus($quotient(52.0,85.0)),f7(X)),$sum($product($quotient(61.0,58.0),f4(X)),$sum($product($uminus($quotient(41.0,99.0)),f0(X)),$sum($product($uminus($quotient(100.0,8.0)),f3(X)),$product($uminus($quotient(71.0,13.0)),f3(X))))))))))))))))))))))))))))))))),$sum($product($quotient(52.0,80.0),l6),$sum($product($uminus($quotient(20.0,53.0)),l0),$sum($product($quotient(14.0,81.0),l2),$sum($product($quotient(61.0,5.0),l2),$sum($product($uminus($quotient(96.0,63.0)),l0),$sum($product($uminus($quotient(19.0,27.0)),l2),$sum($product($uminus($quotient(30.0,40.0)),l6),$sum($product($uminus($quotient(12.0,84.0)),l7),$sum($product($uminus($quotient(83.0,100.0)),l1),$sum($product($quotient(67.0,99.0),l0),$sum($product($quotient(83.0,23.0),l5),$sum($product($uminus($quotient(45.0,32.0)),l5),$sum($product($uminus($quotient(83.0,100.0)),l5),$sum($product($quotient(43.0,26.0),l5),$sum($product($quotient(33.0,30.0),l6),$sum($product($uminus($quotient(67.0,74.0)),l6),$sum($product($quotient(95.0,60.0),l6),$sum($product($uminus($quotient(79.0,46.0)),l1),$sum($product($quotient(76.0,75.0),l3),$sum($product($uminus($quotient(82.0,18.0)),l7),$sum($product($uminus($quotient(14.0,6.0)),l0),$sum($product($uminus($quotient(100.0,57.0)),l2),$sum($product($quotient(89.0,58.0),l0),$sum($product($uminus($quotient(32.0,28.0)),l6),$sum($product($uminus($quotient(23.0,38.0)),l3),$sum($product($quotient(61.0,76.0),l3),$sum($product($uminus($quotient(97.0,25.0)),l7),$sum($product($uminus($quotient(52.0,85.0)),l7),$sum($product($quotient(61.0,58.0),l4),$sum($product($uminus($quotient(41.0,99.0)),l0),$sum($product($uminus($quotient(100.0,8.0)),l3),$product($uminus($quotient(71.0,13.0)),l3))))))))))))))))))))))))))))))))),0.0)
=> $less($difference($sum($product($quotient(52.0,80.0),f6(X)),$sum($product($uminus($quotient(20.0,53.0)),f0(X)),$sum($product($quotient(14.0,81.0),f2(X)),$sum($product($quotient(61.0,5.0),f2(X)),$sum($product($uminus($quotient(96.0,63.0)),f0(X)),$sum($product($uminus($quotient(19.0,27.0)),f2(X)),$sum($product($uminus($quotient(30.0,40.0)),f6(X)),$sum($product($uminus($quotient(12.0,84.0)),f7(X)),$sum($product($uminus($quotient(83.0,100.0)),f1(X)),$sum($product($quotient(67.0,99.0),f0(X)),$sum($product($quotient(83.0,23.0),f5(X)),$sum($product($uminus($quotient(45.0,32.0)),f5(X)),$sum($product($uminus($quotient(83.0,100.0)),f5(X)),$sum($product($quotient(43.0,26.0),f5(X)),$sum($product($quotient(33.0,30.0),f6(X)),$sum($product($uminus($quotient(67.0,74.0)),f6(X)),$sum($product($quotient(95.0,60.0),f6(X)),$sum($product($uminus($quotient(79.0,46.0)),f1(X)),$sum($product($quotient(76.0,75.0),f3(X)),$sum($product($uminus($quotient(82.0,18.0)),f7(X)),$sum($product($uminus($quotient(14.0,6.0)),f0(X)),$sum($product($uminus($quotient(100.0,57.0)),f2(X)),$sum($product($quotient(89.0,58.0),f0(X)),$sum($product($uminus($quotient(32.0,28.0)),f6(X)),$sum($product($uminus($quotient(23.0,38.0)),f3(X)),$sum($product($quotient(61.0,76.0),f3(X)),$sum($product($uminus($quotient(97.0,25.0)),f7(X)),$sum($product($uminus($quotient(52.0,85.0)),f7(X)),$sum($product($quotient(61.0,58.0),f4(X)),$sum($product($uminus($quotient(41.0,99.0)),f0(X)),$sum($product($uminus($quotient(100.0,8.0)),f3(X)),$product($uminus($quotient(71.0,13.0)),f3(X))))))))))))))))))))))))))))))))),$sum($product($quotient(52.0,80.0),l6),$sum($product($uminus($quotient(20.0,53.0)),l0),$sum($product($quotient(14.0,81.0),l2),$sum($product($quotient(61.0,5.0),l2),$sum($product($uminus($quotient(96.0,63.0)),l0),$sum($product($uminus($quotient(19.0,27.0)),l2),$sum($product($uminus($quotient(30.0,40.0)),l6),$sum($product($uminus($quotient(12.0,84.0)),l7),$sum($product($uminus($quotient(83.0,100.0)),l1),$sum($product($quotient(67.0,99.0),l0),$sum($product($quotient(83.0,23.0),l5),$sum($product($uminus($quotient(45.0,32.0)),l5),$sum($product($uminus($quotient(83.0,100.0)),l5),$sum($product($quotient(43.0,26.0),l5),$sum($product($quotient(33.0,30.0),l6),$sum($product($uminus($quotient(67.0,74.0)),l6),$sum($product($quotient(95.0,60.0),l6),$sum($product($uminus($quotient(79.0,46.0)),l1),$sum($product($quotient(76.0,75.0),l3),$sum($product($uminus($quotient(82.0,18.0)),l7),$sum($product($uminus($quotient(14.0,6.0)),l0),$sum($product($uminus($quotient(100.0,57.0)),l2),$sum($product($quotient(89.0,58.0),l0),$sum($product($uminus($quotient(32.0,28.0)),l6),$sum($product($uminus($quotient(23.0,38.0)),l3),$sum($product($quotient(61.0,76.0),l3),$sum($product($uminus($quotient(97.0,25.0)),l7),$sum($product($uminus($quotient(52.0,85.0)),l7),$sum($product($quotient(61.0,58.0),l4),$sum($product($uminus($quotient(41.0,99.0)),l0),$sum($product($uminus($quotient(100.0,8.0)),l3),$product($uminus($quotient(71.0,13.0)),l3))))))))))))))))))))))))))))))))),Epsilon) )
& ( ~ $greatereq($difference($sum($product($quotient(52.0,80.0),f6(X)),$sum($product($uminus($quotient(20.0,53.0)),f0(X)),$sum($product($quotient(14.0,81.0),f2(X)),$sum($product($quotient(61.0,5.0),f2(X)),$sum($product($uminus($quotient(96.0,63.0)),f0(X)),$sum($product($uminus($quotient(19.0,27.0)),f2(X)),$sum($product($uminus($quotient(30.0,40.0)),f6(X)),$sum($product($uminus($quotient(12.0,84.0)),f7(X)),$sum($product($uminus($quotient(83.0,100.0)),f1(X)),$sum($product($quotient(67.0,99.0),f0(X)),$sum($product($quotient(83.0,23.0),f5(X)),$sum($product($uminus($quotient(45.0,32.0)),f5(X)),$sum($product($uminus($quotient(83.0,100.0)),f5(X)),$sum($product($quotient(43.0,26.0),f5(X)),$sum($product($quotient(33.0,30.0),f6(X)),$sum($product($uminus($quotient(67.0,74.0)),f6(X)),$sum($product($quotient(95.0,60.0),f6(X)),$sum($product($uminus($quotient(79.0,46.0)),f1(X)),$sum($product($quotient(76.0,75.0),f3(X)),$sum($product($uminus($quotient(82.0,18.0)),f7(X)),$sum($product($uminus($quotient(14.0,6.0)),f0(X)),$sum($product($uminus($quotient(100.0,57.0)),f2(X)),$sum($product($quotient(89.0,58.0),f0(X)),$sum($product($uminus($quotient(32.0,28.0)),f6(X)),$sum($product($uminus($quotient(23.0,38.0)),f3(X)),$sum($product($quotient(61.0,76.0),f3(X)),$sum($product($uminus($quotient(97.0,25.0)),f7(X)),$sum($product($uminus($quotient(52.0,85.0)),f7(X)),$sum($product($quotient(61.0,58.0),f4(X)),$sum($product($uminus($quotient(41.0,99.0)),f0(X)),$sum($product($uminus($quotient(100.0,8.0)),f3(X)),$product($uminus($quotient(71.0,13.0)),f3(X))))))))))))))))))))))))))))))))),$sum($product($quotient(52.0,80.0),l6),$sum($product($uminus($quotient(20.0,53.0)),l0),$sum($product($quotient(14.0,81.0),l2),$sum($product($quotient(61.0,5.0),l2),$sum($product($uminus($quotient(96.0,63.0)),l0),$sum($product($uminus($quotient(19.0,27.0)),l2),$sum($product($uminus($quotient(30.0,40.0)),l6),$sum($product($uminus($quotient(12.0,84.0)),l7),$sum($product($uminus($quotient(83.0,100.0)),l1),$sum($product($quotient(67.0,99.0),l0),$sum($product($quotient(83.0,23.0),l5),$sum($product($uminus($quotient(45.0,32.0)),l5),$sum($product($uminus($quotient(83.0,100.0)),l5),$sum($product($quotient(43.0,26.0),l5),$sum($product($quotient(33.0,30.0),l6),$sum($product($uminus($quotient(67.0,74.0)),l6),$sum($product($quotient(95.0,60.0),l6),$sum($product($uminus($quotient(79.0,46.0)),l1),$sum($product($quotient(76.0,75.0),l3),$sum($product($uminus($quotient(82.0,18.0)),l7),$sum($product($uminus($quotient(14.0,6.0)),l0),$sum($product($uminus($quotient(100.0,57.0)),l2),$sum($product($quotient(89.0,58.0),l0),$sum($product($uminus($quotient(32.0,28.0)),l6),$sum($product($uminus($quotient(23.0,38.0)),l3),$sum($product($quotient(61.0,76.0),l3),$sum($product($uminus($quotient(97.0,25.0)),l7),$sum($product($uminus($quotient(52.0,85.0)),l7),$sum($product($quotient(61.0,58.0),l4),$sum($product($uminus($quotient(41.0,99.0)),l0),$sum($product($uminus($quotient(100.0,8.0)),l3),$product($uminus($quotient(71.0,13.0)),l3))))))))))))))))))))))))))))))))),0.0)
=> $less($uminus($difference($sum($product($quotient(52.0,80.0),f6(X)),$sum($product($uminus($quotient(20.0,53.0)),f0(X)),$sum($product($quotient(14.0,81.0),f2(X)),$sum($product($quotient(61.0,5.0),f2(X)),$sum($product($uminus($quotient(96.0,63.0)),f0(X)),$sum($product($uminus($quotient(19.0,27.0)),f2(X)),$sum($product($uminus($quotient(30.0,40.0)),f6(X)),$sum($product($uminus($quotient(12.0,84.0)),f7(X)),$sum($product($uminus($quotient(83.0,100.0)),f1(X)),$sum($product($quotient(67.0,99.0),f0(X)),$sum($product($quotient(83.0,23.0),f5(X)),$sum($product($uminus($quotient(45.0,32.0)),f5(X)),$sum($product($uminus($quotient(83.0,100.0)),f5(X)),$sum($product($quotient(43.0,26.0),f5(X)),$sum($product($quotient(33.0,30.0),f6(X)),$sum($product($uminus($quotient(67.0,74.0)),f6(X)),$sum($product($quotient(95.0,60.0),f6(X)),$sum($product($uminus($quotient(79.0,46.0)),f1(X)),$sum($product($quotient(76.0,75.0),f3(X)),$sum($product($uminus($quotient(82.0,18.0)),f7(X)),$sum($product($uminus($quotient(14.0,6.0)),f0(X)),$sum($product($uminus($quotient(100.0,57.0)),f2(X)),$sum($product($quotient(89.0,58.0),f0(X)),$sum($product($uminus($quotient(32.0,28.0)),f6(X)),$sum($product($uminus($quotient(23.0,38.0)),f3(X)),$sum($product($quotient(61.0,76.0),f3(X)),$sum($product($uminus($quotient(97.0,25.0)),f7(X)),$sum($product($uminus($quotient(52.0,85.0)),f7(X)),$sum($product($quotient(61.0,58.0),f4(X)),$sum($product($uminus($quotient(41.0,99.0)),f0(X)),$sum($product($uminus($quotient(100.0,8.0)),f3(X)),$product($uminus($quotient(71.0,13.0)),f3(X))))))))))))))))))))))))))))))))),$sum($product($quotient(52.0,80.0),l6),$sum($product($uminus($quotient(20.0,53.0)),l0),$sum($product($quotient(14.0,81.0),l2),$sum($product($quotient(61.0,5.0),l2),$sum($product($uminus($quotient(96.0,63.0)),l0),$sum($product($uminus($quotient(19.0,27.0)),l2),$sum($product($uminus($quotient(30.0,40.0)),l6),$sum($product($uminus($quotient(12.0,84.0)),l7),$sum($product($uminus($quotient(83.0,100.0)),l1),$sum($product($quotient(67.0,99.0),l0),$sum($product($quotient(83.0,23.0),l5),$sum($product($uminus($quotient(45.0,32.0)),l5),$sum($product($uminus($quotient(83.0,100.0)),l5),$sum($product($quotient(43.0,26.0),l5),$sum($product($quotient(33.0,30.0),l6),$sum($product($uminus($quotient(67.0,74.0)),l6),$sum($product($quotient(95.0,60.0),l6),$sum($product($uminus($quotient(79.0,46.0)),l1),$sum($product($quotient(76.0,75.0),l3),$sum($product($uminus($quotient(82.0,18.0)),l7),$sum($product($uminus($quotient(14.0,6.0)),l0),$sum($product($uminus($quotient(100.0,57.0)),l2),$sum($product($quotient(89.0,58.0),l0),$sum($product($uminus($quotient(32.0,28.0)),l6),$sum($product($uminus($quotient(23.0,38.0)),l3),$sum($product($quotient(61.0,76.0),l3),$sum($product($uminus($quotient(97.0,25.0)),l7),$sum($product($uminus($quotient(52.0,85.0)),l7),$sum($product($quotient(61.0,58.0),l4),$sum($product($uminus($quotient(41.0,99.0)),l0),$sum($product($uminus($quotient(100.0,8.0)),l3),$product($uminus($quotient(71.0,13.0)),l3)))))))))))))))))))))))))))))))))),Epsilon) ) ) ) ) ) ).
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