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trace2.txt
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trace2.txt
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mk_clause:
true
#1 after sort:
true
p: 3 x0^2 x1^2 x2^2 + x1^2 x2^2 - 6 x0 x1 x2^2 + 3 x2^2 - 6 x0 x1^2 x2 - 6 x0^2 x1 x2 + 4 x1 x2 + 6 x0 x2 + 3 x1^2 + 6 x0 x1 + 3 x0^2 + 1, uniq: 0x3e7c9a0
create: b1 3 x0^2 x1^2 x2^2 + x1^2 x2^2 - 6 x0 x1 x2^2 + 3 x2^2 - 6 x0 x1^2 x2 - 6 x0^2 x1 x2 + 4 x1 x2 + 6 x0 x2 + 3 x1^2 + 6 x0 x1 + 3 x0^2 + 1 > 0
inc: 1 0 3 x0^2 x1^2 x2^2 + x1^2 x2^2 - 6 x0 x1 x2^2 + 3 x2^2 - 6 x0 x1^2 x2 - 6 x0^2 x1 x2 + 4 x1 x2 + 6 x0 x2 + 3 x1^2 + 6 x0 x1 + 3 x0^2 + 1 > 0
mk_clause:
!(3 x0^2 x1^2 x2^2 + x1^2 x2^2 - 6 x0 x1 x2^2 + 3 x2^2 - 6 x0 x1^2 x2 - 6 x0^2 x1 x2 + 4 x1 x2 + 6 x0 x2 + 3 x1^2 + 6 x0 x1 + 3 x0^2 + 1 > 0)
#1 after sort:
!(3 x0^2 x1^2 x2^2 + x1^2 x2^2 - 6 x0 x1 x2^2 + 3 x2^2 - 6 x0 x1^2 x2 - 6 x0^2 x1 x2 + 4 x1 x2 + 6 x0 x2 + 3 x1^2 + 6 x0 x1 + 3 x0^2 + 1 > 0)
p: x0 x1 x2 - x2 - x1 - x0, uniq: 0x3e6d090
create: b2 x0 x1 x2 - x2 - x1 - x0 > 0
p: x2, uniq: 0x3e78e28
create: b3 x2 < 0
inc: 2 0 x0 x1 x2 - x2 - x1 - x0 > 0
inc: 3 0 x2 < 0
mk_clause:
x0 x1 x2 - x2 - x1 - x0 > 0 or !(x2 < 0)
#2 after sort:
x0 x1 x2 - x2 - x1 - x0 > 0 or !(x2 < 0)
p: x2, uniq: 0x3e78e28
mk_ineq_atom hash: 2544519863
x2 < 0
p: x0 x1 x2 - x1 x2 - x2 - x1 - x0 + 1, uniq: 0x3e733a0
create: b4 x0 x1 x2 - x1 x2 - x2 - x1 - x0 + 1 < 0
inc: 3 1 x2 < 0
inc: 4 0 x0 x1 x2 - x1 x2 - x2 - x1 - x0 + 1 < 0
mk_clause:
!(x2 < 0) or !(x0 x1 x2 - x1 x2 - x2 - x1 - x0 + 1 < 0)
#3 after sort:
!(x2 < 0) or !(x0 x1 x2 - x1 x2 - x2 - x1 - x0 + 1 < 0)
p: x2, uniq: 0x3e78e28
mk_ineq_atom hash: 2544519863
x2 < 0
p: x0 x1 x2 - x2 - x1 - x0, uniq: 0x3e6d090
mk_ineq_atom hash: 2498589943
x0 x1 x2 - x2 - x1 - x0 > 0
p: x1^3 x2^2 + 3 x1 x2^2 - x0 x1^3 x2 + 3 x1^2 x2 - 3 x0 x1 x2 + x1^3 + x0 x1^2 + 3 x0, uniq: 0x3e75300
create: b5 x1^3 x2^2 + 3 x1 x2^2 - x0 x1^3 x2 + 3 x1^2 x2 - 3 x0 x1 x2 + x1^3 + x0 x1^2 + 3 x0 > 0
inc: 3 2 x2 < 0
inc: 2 1 x0 x1 x2 - x2 - x1 - x0 > 0
inc: 5 0 x1^3 x2^2 + 3 x1 x2^2 - x0 x1^3 x2 + 3 x1^2 x2 - 3 x0 x1 x2 + x1^3 + x0 x1^2 + 3 x0 > 0
mk_clause:
x2 < 0 or !(x0 x1 x2 - x2 - x1 - x0 > 0) or !(x1^3 x2^2 + 3 x1 x2^2 - x0 x1^3 x2 + 3 x1^2 x2 - 3 x0 x1 x2 + x1^3 + x0 x1^2 + 3 x0 > 0)
#4 after sort:
!(x0 x1 x2 - x2 - x1 - x0 > 0) or x2 < 0 or !(x1^3 x2^2 + 3 x1 x2^2 - x0 x1^3 x2 + 3 x1^2 x2 - 3 x0 x1 x2 + x1^3 + x0 x1^2 + 3 x0 > 0)
p: x0, uniq: 0x3e78d48
create: b6 x0 > 0
inc: 6 0 x0 > 0
mk_clause:
x0 > 0
#5 after sort:
x0 > 0
p: x1 + 1, uniq: 0x3e66fe0
create: b7 x1 + 1 > 0
inc: 7 0 x1 + 1 > 0
mk_clause:
x1 + 1 > 0
#6 after sort:
x1 + 1 > 0
p: x2 - 1, uniq: 0x3e670d0
create: b8 x2 - 1 < 0
inc: 8 0 x2 - 1 < 0
mk_clause:
x2 - 1 < 0
#7 after sort:
x2 - 1 < 0
p: x2 - x1, uniq: 0x3e671c0
create: b9 x2 - x1 > 0
inc: 9 0 x2 - x1 > 0
mk_clause:
x2 - x1 > 0
#8 after sort:
x2 - x1 > 0
(declare-fun b0 () Bool)
(declare-fun x0 () Real)
(declare-fun x1 () Real)
(declare-fun x2 () Real)
(assert (and true
true
(not (> (+ (* 3 (* x0 x0 x1 x1 x2 x2)) (* (* x1 x1 x2 x2)) (* (- 6) (* x0 x1 x2 x2)) (* 3 (* x2 x2)) (* (- 6) (* x0 x1 x1 x2)) (* (- 6) (* x0 x0 x1 x2)) (* 4 (* x1 x2)) (* 6 (* x0 x2)) (* 3 (* x1 x1)) (* 6 (* x0 x1)) (* 3 (* x0 x0)) 1) 0))
(or (> (+ (* (* x0 x1 x2)) (* (- 1) x2) (* (- 1) x1) (* (- 1) x0)) 0) (not (< x2 0)))
(or (not (< x2 0)) (not (< (+ (* (* x0 x1 x2)) (* (- 1) (* x1 x2)) (* (- 1) x2) (* (- 1) x1) (* (- 1) x0) 1) 0)))
(or (not (> (+ (* (* x0 x1 x2)) (* (- 1) x2) (* (- 1) x1) (* (- 1) x0)) 0)) (< x2 0) (not (> (+ (* (* x1 x1 x1 x2 x2)) (* 3 (* x1 x2 x2)) (* (- 1) (* x0 x1 x1 x1 x2)) (* 3 (* x1 x1 x2)) (* (- 3) (* x0 x1 x2)) (* x1 x1 x1) (* (* x0 x1 x1)) (* 3 x0)) 0)))
(> x0 0)
(> (+ x1 1) 0)
(< (+ x2 (- 1)) 0)
(> (+ x2 (* (- 1) x1)) 0)
))
is_full_dimensional: 0
before:
!(3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0)
skoZ skoX skoY - skoY - skoX - skoZ > 0 or !(skoY < 0)
!(skoY < 0) or !(skoZ skoX skoY - skoX skoY - skoY - skoX - skoZ + 1 < 0)
!(skoZ skoX skoY - skoY - skoX - skoZ > 0) or skoY < 0 or !(skoX^3 skoY^2 + 3 skoX skoY^2 - skoZ skoX^3 skoY + 3 skoX^2 skoY - 3 skoZ skoX skoY + skoX^3 + skoZ skoX^2 + 3 skoZ > 0)
skoY - 1 < 0
skoY - skoX > 0
permutation: 1 2 4 5 0 3
after:
skoZ skoX skoY - skoY - skoX - skoZ > 0 or !(skoY < 0)
!(skoY < 0) or !(skoZ skoX skoY - skoX skoY - skoY - skoX - skoZ + 1 < 0)
skoY - 1 < 0
skoY - skoX > 0
!(3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0)
!(skoZ skoX skoY - skoY - skoX - skoZ > 0) or skoY < 0 or !(skoX^3 skoY^2 + 3 skoX skoY^2 - skoZ skoX^3 skoY + 3 skoX^2 skoY - 3 skoZ skoX skoY + skoX^3 + skoZ skoX^2 + 3 skoZ > 0)
starting search...
true
!(3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0)
skoZ skoX skoY - skoY - skoX - skoZ > 0 or !(skoY < 0)
!(skoY < 0) or !(skoZ skoX skoY - skoX skoY - skoY - skoX - skoZ + 1 < 0)
!(skoZ skoX skoY - skoY - skoX - skoZ > 0) or skoY < 0 or !(skoX^3 skoY^2 + 3 skoX skoY^2 - skoZ skoX^3 skoY + 3 skoX^2 skoY - 3 skoZ skoX skoY + skoX^3 + skoZ skoX^2 + 3 skoZ > 0)
skoZ > 0
skoX + 1 > 0
skoY - 1 < 0
skoY - skoX > 0
assignment:
b0 -> l_undef
b1 -> l_undef 3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0
b2 -> l_undef skoZ skoX skoY - skoY - skoX - skoZ > 0
b3 -> l_undef skoY < 0
b4 -> l_undef skoZ skoX skoY - skoX skoY - skoY - skoX - skoZ + 1 < 0
b5 -> l_undef skoX^3 skoY^2 + 3 skoX skoY^2 - skoZ skoX^3 skoY + 3 skoX^2 skoY - 3 skoZ skoX skoY + skoX^3 + skoZ skoX^2 + 3 skoZ > 0
b6 -> l_undef skoZ > 0
b7 -> l_undef skoX + 1 > 0
b8 -> l_undef skoY - 1 < 0
b9 -> l_undef skoY - skoX > 0
---
var order:
0 -> skoZ
1 -> skoX
2 -> skoY
ASSERTED
true
!(3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0)
skoZ skoX skoY - skoY - skoX - skoZ > 0 or !(skoY < 0)
!(skoY < 0) or !(skoZ skoX skoY - skoX skoY - skoY - skoX - skoZ + 1 < 0)
!(skoZ skoX skoY - skoY - skoX - skoZ > 0) or skoY < 0 or !(skoX^3 skoY^2 + 3 skoX skoY^2 - skoZ skoX^3 skoY + 3 skoX^2 skoY - 3 skoZ skoX skoY + skoX^3 + skoZ skoX^2 + 3 skoZ > 0)
skoZ > 0
skoX + 1 > 0
skoY - 1 < 0
skoY - skoX > 0
assignment:
b0 -> l_undef
b1 -> l_undef 3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0
b2 -> l_undef skoZ skoX skoY - skoY - skoX - skoZ > 0
b3 -> l_undef skoY < 0
b4 -> l_undef skoZ skoX skoY - skoX skoY - skoY - skoX - skoZ + 1 < 0
b5 -> l_undef skoX^3 skoY^2 + 3 skoX skoY^2 - skoZ skoX^3 skoY + 3 skoX^2 skoY - 3 skoZ skoX skoY + skoX^3 + skoZ skoX^2 + 3 skoZ > 0
b6 -> l_undef skoZ > 0
b7 -> l_undef skoX + 1 > 0
b8 -> l_undef skoY - 1 < 0
b9 -> l_undef skoY - skoX > 0
---
ASSERTED
b0
!b1
b2 or !b3
!b3 or !b4
!b2 or b3 or !b5
b6
b7
b8
b9
{
((0 < 1)),
(!(3*x0^2*x1^2*x2^2 + x1^2*x2^2 - 6*x0*x1*x2^2 + 3*x2^2 - 6*x0*x1^2*x2 - 6*x0^2*x1*x2 + 4*x1*x2 + 6*x0*x2 + 3*x1^2 + 6*x0*x1 + 3*x0^2 + 1 > 0)),
(x0*x1*x2 - x2 - x1 - x0 > 0 || !(x2 < 0)),
(!(x2 < 0) || !(x0*x1*x2 - x1*x2 - x2 - x1 - x0 + 1 < 0)),
(!(x0*x1*x2 - x2 - x1 - x0 > 0) || x2 < 0 || !(x1^3*x2^2 + 3*x1*x2^2 - x0*x1^3*x2 + 3*x1^2*x2 - 3*x0*x1*x2 + x1^3 + x0*x1^2 + 3*x0 > 0)),
(x0 > 0),
(x1 + 1 > 0),
(x2 - 1 < 0),
(x2 - x1 > 0)}
(declare-fun b0 () Bool)
(declare-fun x0 () Real)
(declare-fun x1 () Real)
(declare-fun x2 () Real)
(assert (and true
true
(not (> (+ (* 3 (* x0 x0 x1 x1 x2 x2)) (* (* x1 x1 x2 x2)) (* (- 6) (* x0 x1 x2 x2)) (* 3 (* x2 x2)) (* (- 6) (* x0 x1 x1 x2)) (* (- 6) (* x0 x0 x1 x2)) (* 4 (* x1 x2)) (* 6 (* x0 x2)) (* 3 (* x1 x1)) (* 6 (* x0 x1)) (* 3 (* x0 x0)) 1) 0))
(or (> (+ (* (* x0 x1 x2)) (* (- 1) x2) (* (- 1) x1) (* (- 1) x0)) 0) (not (< x2 0)))
(or (not (< x2 0)) (not (< (+ (* (* x0 x1 x2)) (* (- 1) (* x1 x2)) (* (- 1) x2) (* (- 1) x1) (* (- 1) x0) 1) 0)))
(or (not (> (+ (* (* x0 x1 x2)) (* (- 1) x2) (* (- 1) x1) (* (- 1) x0)) 0)) (< x2 0) (not (> (+ (* (* x1 x1 x1 x2 x2)) (* 3 (* x1 x2 x2)) (* (- 1) (* x0 x1 x1 x1 x2)) (* 3 (* x1 x1 x2)) (* (- 3) (* x0 x1 x2)) (* x1 x1 x1) (* (* x0 x1 x1)) (* 3 x0)) 0)))
(> x0 0)
(> (+ x1 1) 0)
(< (+ x2 (- 1)) 0)
(> (+ x2 (* (- 1) x1)) 0)
))
xk: x4294967295 bk: b0
processing variable 1 boolean b0
no atom for true
no atom for true
assigning literal: true <- true
b0 -> l_true
xk: x0 bk: b2147483647
processing variable skoZ 1
maximal variable not assigned skoZ > 0
maximal variable not assigned skoZ > 0
maximal variable not assigned skoZ > 0
maximal variable not assigned skoZ > 0
infeasible set for literal: skoZ > 0
{(-oo, p6, 0]}
skoZ > 0
num_undef: 1
assigning literal: skoZ > 0 <- skoZ > 0
b6 -> l_true
updating infeasible set
{}
{(-oo, p6, 0]}
new infeasible set:
{(-oo, p6, 0]}
infeasible intervals: {(-oo, p6, 0]}
assigning skoZ(x0) -> 1
value as root object: (# - 1, 1)
xk: x1 bk: b2147483647
processing variable skoX 1
maximal variable not assigned skoX + 1 > 0
maximal variable not assigned skoX + 1 > 0
maximal variable not assigned skoX + 1 > 0
maximal variable not assigned skoX + 1 > 0
infeasible set for literal: skoX + 1 > 0
{(-oo, p7, -1]}
skoX + 1 > 0
num_undef: 1
assigning literal: skoX + 1 > 0 <- skoX + 1 > 0
b7 -> l_true
updating infeasible set
{}
{(-oo, p7, -1]}
new infeasible set:
{(-oo, p7, -1]}
infeasible intervals: {(-oo, p7, -1]}
assigning skoX(x1) -> 0
value as root object: (#, 1)
xk: x2 bk: b2147483647
processing variable skoY 6
maximal variable not assigned skoZ skoX skoY - skoY - skoX - skoZ > 0
maximal variable not assigned !(skoY < 0)
maximal variable not assigned skoZ skoX skoY - skoY - skoX - skoZ > 0
maximal variable not assigned skoZ skoX skoY - skoY - skoX - skoZ > 0
maximal variable not assigned skoZ skoX skoY - skoY - skoX - skoZ > 0
infeasible set for literal: skoZ skoX skoY - skoY - skoX - skoZ > 0
{[-1, p2, oo)}
skoZ skoX skoY - skoY - skoX - skoZ > 0 or !(skoY < 0)
maximal variable not assigned !(skoY < 0)
maximal variable not assigned !(skoY < 0)
maximal variable not assigned !(skoY < 0)
infeasible set for literal: !(skoY < 0)
{(-oo, ~p3, 0)}
skoZ skoX skoY - skoY - skoX - skoZ > 0 or !(skoY < 0)
num_undef: 2
assigning literal: skoZ skoX skoY - skoY - skoX - skoZ > 0 <- decision
b2 -> l_true
updating infeasible set
{}
{[-1, p2, oo)}
new infeasible set:
{[-1, p2, oo)}
maximal variable not assigned !(skoY < 0)
maximal variable not assigned !(skoZ skoX skoY - skoX skoY - skoY - skoX - skoZ + 1 < 0)
maximal variable not assigned !(skoY < 0)
maximal variable not assigned !(skoY < 0)
maximal variable not assigned !(skoY < 0)
infeasible set for literal: !(skoY < 0)
{(-oo, ~p3, 0)}
!(skoY < 0) or !(skoZ skoX skoY - skoX skoY - skoY - skoX - skoZ + 1 < 0)
infeasible set + current set = R, skip literal
!(skoY < 0) or !(skoZ skoX skoY - skoX skoY - skoY - skoX - skoZ + 1 < 0)
assigning literal: skoY < 0 <- skoY < 0 or !(skoZ skoX skoY - skoY - skoX - skoZ > 0)
b3 -> l_true
maximal variable not assigned !(skoZ skoX skoY - skoX skoY - skoY - skoX - skoZ + 1 < 0)
maximal variable not assigned !(skoZ skoX skoY - skoX skoY - skoY - skoX - skoZ + 1 < 0)
maximal variable not assigned !(skoZ skoX skoY - skoX skoY - skoY - skoX - skoZ + 1 < 0)
infeasible set for literal: !(skoZ skoX skoY - skoX skoY - skoY - skoX - skoZ + 1 < 0)
{(0, ~p4, oo)}
!(skoY < 0) or !(skoZ skoX skoY - skoX skoY - skoY - skoX - skoZ + 1 < 0)
infeasible set is a subset of current set, found literal
assigning literal: !(skoZ skoX skoY - skoX skoY - skoY - skoX - skoZ + 1 < 0) <- !(skoZ skoX skoY - skoY - skoX - skoZ > 0) or !(skoZ skoX skoY - skoX skoY - skoY - skoX - skoZ + 1 < 0)
skoZ skoX skoY - skoY - skoX - skoZ > 0 or !(skoY < 0)
b4 -> l_false
maximal variable not assigned skoY - 1 < 0
maximal variable not assigned skoY - 1 < 0
maximal variable not assigned skoY - 1 < 0
maximal variable not assigned skoY - 1 < 0
infeasible set for literal: skoY - 1 < 0
{[1, p8, oo)}
skoY - 1 < 0
infeasible set is a subset of current set, found literal
assigning literal: skoY - 1 < 0 <- !(skoZ skoX skoY - skoY - skoX - skoZ > 0) or skoY - 1 < 0
skoZ skoX skoY - skoY - skoX - skoZ > 0 or !(skoY < 0)
b8 -> l_true
maximal variable not assigned skoY - skoX > 0
maximal variable not assigned skoY - skoX > 0
maximal variable not assigned skoY - skoX > 0
maximal variable not assigned skoY - skoX > 0
infeasible set for literal: skoY - skoX > 0
{(-oo, p9, 0]}
skoY - skoX > 0
infeasible set + current set = R, skip literal
skoY - skoX > 0
assigning literal: !(skoY - skoX > 0) <- !(skoY - skoX > 0) or !(skoZ skoX skoY - skoY - skoX - skoZ > 0)
b9 -> l_false
num_undef: 0
STARTING RESOLUTION
STARTING RESOLUTION
resolve, conflicting clause:
skoY - skoX > 0
xk: skoY
scope_lvl: 1
current assignment
b0 -> true
b2 skoZ skoX skoY - skoY - skoX - skoZ > 0 -> true
b3 skoY < 0 -> true
b4 skoZ skoX skoY - skoX skoY - skoY - skoX - skoZ + 1 < 0 -> false
b6 skoZ > 0 -> true
b7 skoX + 1 > 0 -> true
b8 skoY - 1 < 0 -> true
b9 skoY - skoX > 0 -> false
b0 -> l_true
b1 -> l_undef 3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0
b2 -> l_true skoZ skoX skoY - skoY - skoX - skoZ > 0
b3 -> l_true skoY < 0
b4 -> l_false skoZ skoX skoY - skoX skoY - skoY - skoX - skoZ + 1 < 0
b5 -> l_undef skoX^3 skoY^2 + 3 skoX skoY^2 - skoZ skoX^3 skoY + 3 skoX^2 skoY - 3 skoZ skoX skoY + skoX^3 + skoZ skoX^2 + 3 skoZ > 0
b6 -> l_true skoZ > 0
b7 -> l_true skoX + 1 > 0
b8 -> l_true skoY - 1 < 0
b9 -> l_false skoY - skoX > 0
skoZ -> 1
skoX -> 0
resolving clause for b: 2147483647
skoY - skoX > 0
resolving skoY - skoX > 0
resolving
b9
resolving antecedent: skoY - skoX > 0
b_lvl: 1, is_marked(b): 0, m_num_marks: 0
literal is in the same level and stage, increasing marks
found marked: b9
skoY - skoX > 0
resolving lazy_justification for b9
assignment lemma
Resolve[ForAll[{x0, x1, x2}, !(x0 == 1 && x1 == 0) || !(x2 - x1 > 0) || !(x0*x1*x2 - x2 - x1 - x0 > 0)], Reals]
enter explain: skoY - skoX > 0 or skoZ skoX skoY - skoY - skoX - skoZ > 0
inc: 9 1 skoY - skoX > 0
inc: 2 2 skoZ skoX skoY - skoY - skoX - skoZ > 0
inc: 9 2 skoY - skoX > 0
dec: 9 2 skoY - skoX > 0
inc: 2 3 skoZ skoX skoY - skoY - skoX - skoZ > 0
dec: 2 3 skoZ skoX skoY - skoY - skoX - skoZ > 0
p: 4 x0^2 + 4, uniq: 0x3e67120
create: b10 4 skoZ^2 + 4 > 0
inc: 10 0 4 skoZ^2 + 4 > 0
p: x0, uniq: 0x3e78d48
mk_ineq_atom hash: 2099698683
skoZ > 0
inc: 6 1 skoZ > 0
p: x0 x1 - 1, uniq: 0x3e67080
create: b11 skoZ skoX - 1 < 0
inc: 11 0 skoZ skoX - 1 < 0
p: x0 x1^2 - 2 x1 - x0, uniq: 0x3e690c0
create: b12 skoZ skoX^2 - 2 skoX - skoZ < 0
inc: 12 0 skoZ skoX^2 - 2 skoX - skoZ < 0
1 x0 x1 - 1 x0 x1 - 1
inc: 13 0 skoX < root[1](skoZ skoX - 1)
p: x0, uniq: 0x3e78d48
mk_ineq_atom hash: 2099698683
skoZ > 0
dec: 9 1 skoY - skoX > 0
dec: 2 2 skoZ skoX skoY - skoY - skoX - skoZ > 0
inc: 9 1 skoY - skoX > 0
inc: 2 2 skoZ skoX skoY - skoY - skoX - skoZ > 0
Resolve[ForAll[{x0, x1, x2}, !(4*x0^2 + 4 > 0) || !(x0 > 0) || !(x0*x1 - 1 < 0) || !(x0*x1^2 - 2*x1 - x0 < 0) || !(x1 < Root[x0*#1 - 1 &, 1]) || !(x2 - x1 > 0) || !(x0*x1*x2 - x2 - x1 - x0 > 0)], Reals]
theory lemma
!b10 or !b6 or !b11 or !b12 or !b13 or !b9 or !b2
m_xk: 2, skoY
new valid clause:
!(4 skoZ^2 + 4 > 0) or !(skoZ > 0) or !(skoZ skoX - 1 < 0) or !(skoZ skoX^2 - 2 skoX - skoZ < 0) or !(skoX < root[1](skoZ skoX - 1)) or !(skoY - skoX > 0) or !(skoZ skoX skoY - skoY - skoX - skoZ > 0)
resolving skoY - skoX > 0
!(4 skoZ^2 + 4 > 0) or !(skoZ > 0) or !(skoZ skoX - 1 < 0) or !(skoZ skoX^2 - 2 skoX - skoZ < 0) or !(skoX < root[1](skoZ skoX - 1)) or !(skoY - skoX > 0) or !(skoZ skoX skoY - skoY - skoX - skoZ > 0)
resolving b9
!b10 or !b6 or !b11 or !b12 or !b13 or !b9 or !b2
resolving antecedent: !(4 skoZ^2 + 4 > 0)
literal is unassigned, but it is false in arithmetic interpretation, adding it to lemma
inc: 10 1 4 skoZ^2 + 4 > 0
resolving antecedent: !(skoZ > 0)
b_lvl: 0, is_marked(b): 0, m_num_marks: 0
previous level or stage, adding literal to lemma
max_var(b): 0, m_xk: 2, lvl: 0, scope_lvl: 1
inc: 6 2 skoZ > 0
resolving antecedent: !(skoZ skoX - 1 < 0)
literal is unassigned, but it is false in arithmetic interpretation, adding it to lemma
inc: 11 1 skoZ skoX - 1 < 0
resolving antecedent: !(skoZ skoX^2 - 2 skoX - skoZ < 0)
literal is unassigned, but it is false in arithmetic interpretation, adding it to lemma
inc: 12 1 skoZ skoX^2 - 2 skoX - skoZ < 0
resolving antecedent: !(skoX < root[1](skoZ skoX - 1))
literal is unassigned, but it is false in arithmetic interpretation, adding it to lemma
inc: 13 1 skoX < root[1](skoZ skoX - 1)
resolving antecedent: !(skoZ skoX skoY - skoY - skoX - skoZ > 0)
b_lvl: 1, is_marked(b): 0, m_num_marks: 0
literal is in the same level and stage, increasing marks
found marked: b2
skoZ skoX skoY - skoY - skoX - skoZ > 0
found decision
inc: 2 3 skoZ skoX skoY - skoY - skoX - skoZ > 0
New lemma
!(4 skoZ^2 + 4 > 0) or !(skoZ > 0) or !(skoZ skoX - 1 < 0) or !(skoZ skoX^2 - 2 skoX - skoZ < 0) or !(skoX < root[1](skoZ skoX - 1)) or !(skoZ skoX skoY - skoY - skoX - skoZ > 0)
=========================
New lemma
!b10 or !b6 or !b11 or !b12 or !b13 or !b2
=========================
new lemma:
!(4 skoZ^2 + 4 > 0) or !(skoZ > 0) or !(skoZ skoX - 1 < 0) or !(skoZ skoX^2 - 2 skoX - skoZ < 0) or !(skoX < root[1](skoZ skoX - 1)) or !(skoZ skoX skoY - skoY - skoX - skoZ > 0)
found_decision: 1
fail to find new lvl, using previous one
backtracking to new level: 0, curr: 1
inc: 10 2 4 skoZ^2 + 4 > 0
inc: 6 3 skoZ > 0
inc: 11 2 skoZ skoX - 1 < 0
inc: 12 2 skoZ skoX^2 - 2 skoX - skoZ < 0
inc: 13 2 skoX < root[1](skoZ skoX - 1)
inc: 2 4 skoZ skoX skoY - skoY - skoX - skoZ > 0
mk_clause:
!(4 skoZ^2 + 4 > 0) or !(skoZ > 0) or !(skoZ skoX - 1 < 0) or !(skoZ skoX^2 - 2 skoX - skoZ < 0) or !(skoX < root[1](skoZ skoX - 1)) or !(skoZ skoX skoY - skoY - skoX - skoZ > 0)
#9 after sort:
!(skoZ > 0) or !(4 skoZ^2 + 4 > 0) or !(skoZ skoX - 1 < 0) or !(skoX < root[1](skoZ skoX - 1)) or !(skoZ skoX^2 - 2 skoX - skoZ < 0) or !(skoZ skoX skoY - skoY - skoX - skoZ > 0)
assigned value l_false for !(skoZ > 0)
evaluated value l_false for !(4 skoZ^2 + 4 > 0)
value of: !(4 skoZ^2 + 4 > 0) := l_false
xk: 2, a->max_var(): 0
b0 -> true
b6 skoZ > 0 -> true
b7 skoX + 1 > 0 -> true
b0 -> l_true
b1 -> l_undef 3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0
b2 -> l_undef skoZ skoX skoY - skoY - skoX - skoZ > 0
b3 -> l_undef skoY < 0
b4 -> l_undef skoZ skoX skoY - skoX skoY - skoY - skoX - skoZ + 1 < 0
b5 -> l_undef skoX^3 skoY^2 + 3 skoX skoY^2 - skoZ skoX^3 skoY + 3 skoX^2 skoY - 3 skoZ skoX skoY + skoX^3 + skoZ skoX^2 + 3 skoZ > 0
b6 -> l_true skoZ > 0
b7 -> l_true skoX + 1 > 0
b8 -> l_undef skoY - 1 < 0
b9 -> l_undef skoY - skoX > 0
b10 -> l_undef 4 skoZ^2 + 4 > 0
b11 -> l_undef skoZ skoX - 1 < 0
b12 -> l_undef skoZ skoX^2 - 2 skoX - skoZ < 0
b13 -> l_undef skoX < root[1](skoZ skoX - 1)
skoZ -> 1
skoX -> 0
evaluated value l_false for !(skoZ skoX - 1 < 0)
value of: !(skoZ skoX - 1 < 0) := l_false
xk: 2, a->max_var(): 1
b0 -> true
b6 skoZ > 0 -> true
b7 skoX + 1 > 0 -> true
b0 -> l_true
b1 -> l_undef 3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0
b2 -> l_undef skoZ skoX skoY - skoY - skoX - skoZ > 0
b3 -> l_undef skoY < 0
b4 -> l_undef skoZ skoX skoY - skoX skoY - skoY - skoX - skoZ + 1 < 0
b5 -> l_undef skoX^3 skoY^2 + 3 skoX skoY^2 - skoZ skoX^3 skoY + 3 skoX^2 skoY - 3 skoZ skoX skoY + skoX^3 + skoZ skoX^2 + 3 skoZ > 0
b6 -> l_true skoZ > 0
b7 -> l_true skoX + 1 > 0
b8 -> l_undef skoY - 1 < 0
b9 -> l_undef skoY - skoX > 0
b10 -> l_undef 4 skoZ^2 + 4 > 0
b11 -> l_undef skoZ skoX - 1 < 0
b12 -> l_undef skoZ skoX^2 - 2 skoX - skoZ < 0
b13 -> l_undef skoX < root[1](skoZ skoX - 1)
skoZ -> 1
skoX -> 0
evaluated value l_false for !(skoX < root[1](skoZ skoX - 1))
value of: !(skoX < root[1](skoZ skoX - 1)) := l_false
xk: 2, a->max_var(): 1
b0 -> true
b6 skoZ > 0 -> true
b7 skoX + 1 > 0 -> true
b0 -> l_true
b1 -> l_undef 3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0
b2 -> l_undef skoZ skoX skoY - skoY - skoX - skoZ > 0
b3 -> l_undef skoY < 0
b4 -> l_undef skoZ skoX skoY - skoX skoY - skoY - skoX - skoZ + 1 < 0
b5 -> l_undef skoX^3 skoY^2 + 3 skoX skoY^2 - skoZ skoX^3 skoY + 3 skoX^2 skoY - 3 skoZ skoX skoY + skoX^3 + skoZ skoX^2 + 3 skoZ > 0
b6 -> l_true skoZ > 0
b7 -> l_true skoX + 1 > 0
b8 -> l_undef skoY - 1 < 0
b9 -> l_undef skoY - skoX > 0
b10 -> l_undef 4 skoZ^2 + 4 > 0
b11 -> l_undef skoZ skoX - 1 < 0
b12 -> l_undef skoZ skoX^2 - 2 skoX - skoZ < 0
b13 -> l_undef skoX < root[1](skoZ skoX - 1)
skoZ -> 1
skoX -> 0
evaluated value l_false for !(skoZ skoX^2 - 2 skoX - skoZ < 0)
value of: !(skoZ skoX^2 - 2 skoX - skoZ < 0) := l_false
xk: 2, a->max_var(): 1
b0 -> true
b6 skoZ > 0 -> true
b7 skoX + 1 > 0 -> true
b0 -> l_true
b1 -> l_undef 3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0
b2 -> l_undef skoZ skoX skoY - skoY - skoX - skoZ > 0
b3 -> l_undef skoY < 0
b4 -> l_undef skoZ skoX skoY - skoX skoY - skoY - skoX - skoZ + 1 < 0
b5 -> l_undef skoX^3 skoY^2 + 3 skoX skoY^2 - skoZ skoX^3 skoY + 3 skoX^2 skoY - 3 skoZ skoX skoY + skoX^3 + skoZ skoX^2 + 3 skoZ > 0
b6 -> l_true skoZ > 0
b7 -> l_true skoX + 1 > 0
b8 -> l_undef skoY - 1 < 0
b9 -> l_undef skoY - skoX > 0
b10 -> l_undef 4 skoZ^2 + 4 > 0
b11 -> l_undef skoZ skoX - 1 < 0
b12 -> l_undef skoZ skoX^2 - 2 skoX - skoZ < 0
b13 -> l_undef skoX < root[1](skoZ skoX - 1)
skoZ -> 1
skoX -> 0
maximal variable not assigned !(skoZ skoX skoY - skoY - skoX - skoZ > 0)
assigned value l_false for !(skoZ > 0)
evaluated value l_false for !(4 skoZ^2 + 4 > 0)
value of: !(4 skoZ^2 + 4 > 0) := l_false
xk: 2, a->max_var(): 0
b0 -> true
b6 skoZ > 0 -> true
b7 skoX + 1 > 0 -> true
b0 -> l_true
b1 -> l_undef 3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0
b2 -> l_undef skoZ skoX skoY - skoY - skoX - skoZ > 0
b3 -> l_undef skoY < 0
b4 -> l_undef skoZ skoX skoY - skoX skoY - skoY - skoX - skoZ + 1 < 0
b5 -> l_undef skoX^3 skoY^2 + 3 skoX skoY^2 - skoZ skoX^3 skoY + 3 skoX^2 skoY - 3 skoZ skoX skoY + skoX^3 + skoZ skoX^2 + 3 skoZ > 0
b6 -> l_true skoZ > 0
b7 -> l_true skoX + 1 > 0
b8 -> l_undef skoY - 1 < 0
b9 -> l_undef skoY - skoX > 0
b10 -> l_undef 4 skoZ^2 + 4 > 0
b11 -> l_undef skoZ skoX - 1 < 0
b12 -> l_undef skoZ skoX^2 - 2 skoX - skoZ < 0
b13 -> l_undef skoX < root[1](skoZ skoX - 1)
skoZ -> 1
skoX -> 0
evaluated value l_false for !(skoZ skoX - 1 < 0)
value of: !(skoZ skoX - 1 < 0) := l_false
xk: 2, a->max_var(): 1
b0 -> true
b6 skoZ > 0 -> true
b7 skoX + 1 > 0 -> true
b0 -> l_true
b1 -> l_undef 3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0
b2 -> l_undef skoZ skoX skoY - skoY - skoX - skoZ > 0
b3 -> l_undef skoY < 0
b4 -> l_undef skoZ skoX skoY - skoX skoY - skoY - skoX - skoZ + 1 < 0
b5 -> l_undef skoX^3 skoY^2 + 3 skoX skoY^2 - skoZ skoX^3 skoY + 3 skoX^2 skoY - 3 skoZ skoX skoY + skoX^3 + skoZ skoX^2 + 3 skoZ > 0
b6 -> l_true skoZ > 0
b7 -> l_true skoX + 1 > 0
b8 -> l_undef skoY - 1 < 0
b9 -> l_undef skoY - skoX > 0
b10 -> l_undef 4 skoZ^2 + 4 > 0
b11 -> l_undef skoZ skoX - 1 < 0
b12 -> l_undef skoZ skoX^2 - 2 skoX - skoZ < 0
b13 -> l_undef skoX < root[1](skoZ skoX - 1)
skoZ -> 1
skoX -> 0
evaluated value l_false for !(skoX < root[1](skoZ skoX - 1))
value of: !(skoX < root[1](skoZ skoX - 1)) := l_false
xk: 2, a->max_var(): 1
b0 -> true
b6 skoZ > 0 -> true
b7 skoX + 1 > 0 -> true
b0 -> l_true
b1 -> l_undef 3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0
b2 -> l_undef skoZ skoX skoY - skoY - skoX - skoZ > 0
b3 -> l_undef skoY < 0
b4 -> l_undef skoZ skoX skoY - skoX skoY - skoY - skoX - skoZ + 1 < 0
b5 -> l_undef skoX^3 skoY^2 + 3 skoX skoY^2 - skoZ skoX^3 skoY + 3 skoX^2 skoY - 3 skoZ skoX skoY + skoX^3 + skoZ skoX^2 + 3 skoZ > 0
b6 -> l_true skoZ > 0
b7 -> l_true skoX + 1 > 0
b8 -> l_undef skoY - 1 < 0
b9 -> l_undef skoY - skoX > 0
b10 -> l_undef 4 skoZ^2 + 4 > 0
b11 -> l_undef skoZ skoX - 1 < 0
b12 -> l_undef skoZ skoX^2 - 2 skoX - skoZ < 0
b13 -> l_undef skoX < root[1](skoZ skoX - 1)
skoZ -> 1
skoX -> 0
evaluated value l_false for !(skoZ skoX^2 - 2 skoX - skoZ < 0)
value of: !(skoZ skoX^2 - 2 skoX - skoZ < 0) := l_false
xk: 2, a->max_var(): 1
b0 -> true
b6 skoZ > 0 -> true
b7 skoX + 1 > 0 -> true
b0 -> l_true
b1 -> l_undef 3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0
b2 -> l_undef skoZ skoX skoY - skoY - skoX - skoZ > 0
b3 -> l_undef skoY < 0
b4 -> l_undef skoZ skoX skoY - skoX skoY - skoY - skoX - skoZ + 1 < 0
b5 -> l_undef skoX^3 skoY^2 + 3 skoX skoY^2 - skoZ skoX^3 skoY + 3 skoX^2 skoY - 3 skoZ skoX skoY + skoX^3 + skoZ skoX^2 + 3 skoZ > 0
b6 -> l_true skoZ > 0
b7 -> l_true skoX + 1 > 0
b8 -> l_undef skoY - 1 < 0
b9 -> l_undef skoY - skoX > 0
b10 -> l_undef 4 skoZ^2 + 4 > 0
b11 -> l_undef skoZ skoX - 1 < 0
b12 -> l_undef skoZ skoX^2 - 2 skoX - skoZ < 0
b13 -> l_undef skoX < root[1](skoZ skoX - 1)
skoZ -> 1
skoX -> 0
maximal variable not assigned !(skoZ skoX skoY - skoY - skoX - skoZ > 0)
maximal variable not assigned !(skoZ skoX skoY - skoY - skoX - skoZ > 0)
maximal variable not assigned !(skoZ skoX skoY - skoY - skoX - skoZ > 0)
infeasible set for literal: !(skoZ skoX skoY - skoY - skoX - skoZ > 0)
{(-oo, ~p2, -1)}
!(skoZ > 0) or !(4 skoZ^2 + 4 > 0) or !(skoZ skoX - 1 < 0) or !(skoX < root[1](skoZ skoX - 1)) or !(skoZ skoX^2 - 2 skoX - skoZ < 0) or !(skoZ skoX skoY - skoY - skoX - skoZ > 0)
num_undef: 1
assigning literal: !(skoZ skoX skoY - skoY - skoX - skoZ > 0) <- !(skoZ > 0) or !(4 skoZ^2 + 4 > 0) or !(skoZ skoX - 1 < 0) or !(skoX < root[1](skoZ skoX - 1)) or !(skoZ skoX^2 - 2 skoX - skoZ < 0) or !(skoZ skoX skoY - skoY - skoX - skoZ > 0)
b2 -> l_false
updating infeasible set
{}
{(-oo, ~p2, -1)}
new infeasible set:
{(-oo, ~p2, -1)}
new lemma processed done
b0 -> true
b2 skoZ skoX skoY - skoY - skoX - skoZ > 0 -> false
b6 skoZ > 0 -> true
b7 skoX + 1 > 0 -> true
b0 -> l_true
b1 -> l_undef 3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0
b2 -> l_false skoZ skoX skoY - skoY - skoX - skoZ > 0
b3 -> l_undef skoY < 0
b4 -> l_undef skoZ skoX skoY - skoX skoY - skoY - skoX - skoZ + 1 < 0
b5 -> l_undef skoX^3 skoY^2 + 3 skoX skoY^2 - skoZ skoX^3 skoY + 3 skoX^2 skoY - 3 skoZ skoX skoY + skoX^3 + skoZ skoX^2 + 3 skoZ > 0
b6 -> l_true skoZ > 0
b7 -> l_true skoX + 1 > 0
b8 -> l_undef skoY - 1 < 0
b9 -> l_undef skoY - skoX > 0
b10 -> l_undef 4 skoZ^2 + 4 > 0
b11 -> l_undef skoZ skoX - 1 < 0
b12 -> l_undef skoZ skoX^2 - 2 skoX - skoZ < 0
b13 -> l_undef skoX < root[1](skoZ skoX - 1)
skoZ -> 1
skoX -> 0
processing variable skoY 7
assigned value l_false for skoZ skoX skoY - skoY - skoX - skoZ > 0
maximal variable not assigned !(skoY < 0)
assigned value l_false for skoZ skoX skoY - skoY - skoX - skoZ > 0
maximal variable not assigned !(skoY < 0)
maximal variable not assigned !(skoY < 0)
maximal variable not assigned !(skoY < 0)
infeasible set for literal: !(skoY < 0)
{(-oo, ~p3, 0)}
skoZ skoX skoY - skoY - skoX - skoZ > 0 or !(skoY < 0)
num_undef: 1
assigning literal: !(skoY < 0) <- skoZ skoX skoY - skoY - skoX - skoZ > 0 or !(skoY < 0)
b3 -> l_false
updating infeasible set
{(-oo, ~p2, -1)}
{(-oo, ~p3, 0)}
new infeasible set:
{(-oo, ~p3, 0)}
assigned value l_true for !(skoY < 0)
-3 := true
maximal variable not assigned skoY - 1 < 0
maximal variable not assigned skoY - 1 < 0
maximal variable not assigned skoY - 1 < 0
maximal variable not assigned skoY - 1 < 0
infeasible set for literal: skoY - 1 < 0
{[1, p8, oo)}
skoY - 1 < 0
num_undef: 1
assigning literal: skoY - 1 < 0 <- skoY - 1 < 0
b8 -> l_true
updating infeasible set
{(-oo, ~p3, 0)}
{[1, p8, oo)}
new infeasible set:
{(-oo, ~p3, 0), [1, p8, oo)}
maximal variable not assigned skoY - skoX > 0
maximal variable not assigned skoY - skoX > 0
maximal variable not assigned skoY - skoX > 0
maximal variable not assigned skoY - skoX > 0
infeasible set for literal: skoY - skoX > 0
{(-oo, p9, 0]}
skoY - skoX > 0
num_undef: 1
assigning literal: skoY - skoX > 0 <- skoY - skoX > 0
b9 -> l_true
updating infeasible set
{(-oo, ~p3, 0), [1, p8, oo)}
{(-oo, p9, 0]}
new infeasible set:
{(-oo, p9, 0], [1, p8, oo)}
maximal variable not assigned !(3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0)
maximal variable not assigned !(3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0)
maximal variable not assigned !(3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0)
maximal variable not assigned !(3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0)
infeasible set for literal: !(3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0)
{(-oo, ~p1, oo)}*
!(3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0)
infeasible set is R, skip literal
assigning literal: 3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0 <- 3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0
b1 -> l_true
num_undef: 0
STARTING RESOLUTION
STARTING RESOLUTION
resolve, conflicting clause:
!(3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0)
xk: skoY
scope_lvl: 0
current assignment
b0 -> true
b1 3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0 -> true
b2 skoZ skoX skoY - skoY - skoX - skoZ > 0 -> false
b3 skoY < 0 -> false
b6 skoZ > 0 -> true
b7 skoX + 1 > 0 -> true
b8 skoY - 1 < 0 -> true
b9 skoY - skoX > 0 -> true
b0 -> l_true
b1 -> l_true 3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0
b2 -> l_false skoZ skoX skoY - skoY - skoX - skoZ > 0
b3 -> l_false skoY < 0
b4 -> l_undef skoZ skoX skoY - skoX skoY - skoY - skoX - skoZ + 1 < 0
b5 -> l_undef skoX^3 skoY^2 + 3 skoX skoY^2 - skoZ skoX^3 skoY + 3 skoX^2 skoY - 3 skoZ skoX skoY + skoX^3 + skoZ skoX^2 + 3 skoZ > 0
b6 -> l_true skoZ > 0
b7 -> l_true skoX + 1 > 0
b8 -> l_true skoY - 1 < 0
b9 -> l_true skoY - skoX > 0
b10 -> l_undef 4 skoZ^2 + 4 > 0
b11 -> l_undef skoZ skoX - 1 < 0
b12 -> l_undef skoZ skoX^2 - 2 skoX - skoZ < 0
b13 -> l_undef skoX < root[1](skoZ skoX - 1)
skoZ -> 1
skoX -> 0
dec: 10 2 4 skoZ^2 + 4 > 0
dec: 6 3 skoZ > 0
dec: 11 2 skoZ skoX - 1 < 0
dec: 12 2 skoZ skoX^2 - 2 skoX - skoZ < 0
dec: 13 2 skoX < root[1](skoZ skoX - 1)
dec: 2 4 skoZ skoX skoY - skoY - skoX - skoZ > 0
resolving clause for b: 2147483647
!(3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0)
resolving !(3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0)
resolving
!b1
resolving antecedent: !(3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0)
b_lvl: 0, is_marked(b): 0, m_num_marks: 0
literal is in the same level and stage, increasing marks
found marked: b1
3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0
resolving lazy_justification for b1
assignment lemma
Resolve[ForAll[{x0, x1, x2}, !(x0 == 1 && x1 == 0) || 3*x0^2*x1^2*x2^2 + x1^2*x2^2 - 6*x0*x1*x2^2 + 3*x2^2 - 6*x0*x1^2*x2 - 6*x0^2*x1*x2 + 4*x1*x2 + 6*x0*x2 + 3*x1^2 + 6*x0*x1 + 3*x0^2 + 1 > 0], Reals]
dec: 10 1 4 skoZ^2 + 4 > 0
dec: 6 2 skoZ > 0
dec: 11 1 skoZ skoX - 1 < 0
dec: 12 1 skoZ skoX^2 - 2 skoX - skoZ < 0
dec: 13 1 skoX < root[1](skoZ skoX - 1)
dec: 9 1 skoY - skoX > 0
dec: 2 3 skoZ skoX skoY - skoY - skoX - skoZ > 0
enter explain: !(3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0)
inc: 1 1 3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0
inc: 1 2 3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0
dec: 1 2 3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0
dec: 1 1 3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0
inc: 1 1 3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0
Resolve[ForAll[{x0, x1, x2}, 3*x0^2*x1^2*x2^2 + x1^2*x2^2 - 6*x0*x1*x2^2 + 3*x2^2 - 6*x0*x1^2*x2 - 6*x0^2*x1*x2 + 4*x1*x2 + 6*x0*x2 + 3*x1^2 + 6*x0*x1 + 3*x0^2 + 1 > 0], Reals]
theory lemma
b1
m_xk: 2, skoY
new valid clause:
3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0
resolving 3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0
3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0
resolving b1
b1
New lemma
=========================
New lemma
=========================
empty clause generated
true
!(3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0)
skoZ skoX skoY - skoY - skoX - skoZ > 0 or !(skoY < 0)
!(skoY < 0) or !(skoZ skoX skoY - skoX skoY - skoY - skoX - skoZ + 1 < 0)
!(skoZ skoX skoY - skoY - skoX - skoZ > 0) or skoY < 0 or !(skoX^3 skoY^2 + 3 skoX skoY^2 - skoZ skoX^3 skoY + 3 skoX^2 skoY - 3 skoZ skoX skoY + skoX^3 + skoZ skoX^2 + 3 skoZ > 0)
skoZ > 0
skoX + 1 > 0
skoY - 1 < 0
skoY - skoX > 0
Lemmas:
!(skoZ > 0) or !(4 skoZ^2 + 4 > 0) or !(skoZ skoX - 1 < 0) or !(skoX < root[1](skoZ skoX - 1)) or !(skoZ skoX^2 - 2 skoX - skoZ < 0) or !(skoZ skoX skoY - skoY - skoX - skoZ > 0)
assignment:
b0 -> true
b1 3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0 -> true
b2 skoZ skoX skoY - skoY - skoX - skoZ > 0 -> false
b3 skoY < 0 -> false
b6 skoZ > 0 -> true
b7 skoX + 1 > 0 -> true
b8 skoY - 1 < 0 -> true
b9 skoY - skoX > 0 -> true
b0 -> l_true
b1 -> l_true 3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0
b2 -> l_false skoZ skoX skoY - skoY - skoX - skoZ > 0
b3 -> l_false skoY < 0
b4 -> l_undef skoZ skoX skoY - skoX skoY - skoY - skoX - skoZ + 1 < 0
b5 -> l_undef skoX^3 skoY^2 + 3 skoX skoY^2 - skoZ skoX^3 skoY + 3 skoX^2 skoY - 3 skoZ skoX skoY + skoX^3 + skoZ skoX^2 + 3 skoZ > 0
b6 -> l_true skoZ > 0
b7 -> l_true skoX + 1 > 0
b8 -> l_true skoY - 1 < 0
b9 -> l_true skoY - skoX > 0
b10 -> l_undef 4 skoZ^2 + 4 > 0
b11 -> l_undef skoZ skoX - 1 < 0
b12 -> l_undef skoZ skoX^2 - 2 skoX - skoZ < 0
b13 -> l_undef skoX < root[1](skoZ skoX - 1)
skoZ -> 1
skoX -> 0
---
dec: 1 1 3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0
dec: 1 0 3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0
del: b1 0 3 skoZ^2 skoX^2 skoY^2 + skoX^2 skoY^2 - 6 skoZ skoX skoY^2 + 3 skoY^2 - 6 skoZ skoX^2 skoY - 6 skoZ^2 skoX skoY + 4 skoX skoY + 6 skoZ skoY + 3 skoX^2 + 6 skoZ skoX + 3 skoZ^2 + 1 > 0
dec: 2 2 skoZ skoX skoY - skoY - skoX - skoZ > 0
dec: 3 2 skoY < 0
dec: 3 1 skoY < 0
dec: 4 0 skoZ skoX skoY - skoX skoY - skoY - skoX - skoZ + 1 < 0
del: b4 0 skoZ skoX skoY - skoX skoY - skoY - skoX - skoZ + 1 < 0
dec: 2 1 skoZ skoX skoY - skoY - skoX - skoZ > 0
dec: 3 0 skoY < 0
del: b3 0 skoY < 0
dec: 5 0 skoX^3 skoY^2 + 3 skoX skoY^2 - skoZ skoX^3 skoY + 3 skoX^2 skoY - 3 skoZ skoX skoY + skoX^3 + skoZ skoX^2 + 3 skoZ > 0
del: b5 0 skoX^3 skoY^2 + 3 skoX skoY^2 - skoZ skoX^3 skoY + 3 skoX^2 skoY - 3 skoZ skoX skoY + skoX^3 + skoZ skoX^2 + 3 skoZ > 0
dec: 6 1 skoZ > 0
dec: 7 0 skoX + 1 > 0
del: b7 0 skoX + 1 > 0
dec: 8 0 skoY - 1 < 0
del: b8 0 skoY - 1 < 0
dec: 9 0 skoY - skoX > 0
del: b9 0 skoY - skoX > 0
dec: 6 0 skoZ > 0
del: b6 0 skoZ > 0
dec: 10 0 4 skoZ^2 + 4 > 0
del: b10 0 4 skoZ^2 + 4 > 0
dec: 11 0 skoZ skoX - 1 < 0
del: b11 0 skoZ skoX - 1 < 0
dec: 13 0 skoX < root[1](skoZ skoX - 1)
del: b13 0 skoX < root[1](skoZ skoX - 1)
dec: 12 0 skoZ skoX^2 - 2 skoX - skoZ < 0
del: b12 0 skoZ skoX^2 - 2 skoX - skoZ < 0
dec: 2 0 skoZ skoX skoY - skoY - skoX - skoZ > 0
del: b2 0 skoZ skoX skoY - skoY - skoX - skoZ > 0
unsat